numeracy activities that promote problem solving skills

Problem Solving Activities: 7 Strategies

• Critical Thinking

Problem solving can be a daunting aspect of effective mathematics teaching, but it does not have to be! In this post, I share seven strategic ways to integrate problem solving into your everyday math program.

In the middle of our problem solving lesson, my district math coordinator stopped by for a surprise walkthrough. 

I was so excited!

We were in the middle of what I thought was the most brilliant math lesson– teaching my students how to solve problem solving tasks using specific problem solving strategies. 

It was a proud moment for me!

Each week, I presented a new problem solving strategy and the students completed problems that emphasized the strategy. 

Genius right? 

After observing my class, my district coordinator pulled me aside to chat. I was excited to talk to her about my brilliant plan, but she told me I should provide the tasks and let my students come up with ways to solve the problems. Then, as students shared their work, I could revoice the student’s strategies and give them an official name. 

What a crushing blow! Just when I thought I did something special, I find out I did it all wrong. 

I took some time to consider her advice. Once I acknowledged she was right, I was able to make BIG changes to the way I taught problem solving in the classroom. 

When I Finally Saw the Light

To give my students an opportunity to engage in more authentic problem solving which would lead them to use a larger variety of problem solving strategies, I decided to vary the activities and the way I approached problem solving with my students. 

Problem Solving Activities

Here are seven ways to strategically reinforce problem solving skills in your classroom. 

Seasonal Problem Solving

Many teachers use word problems as problem solving tasks. Instead, try engaging your students with non-routine tasks that look like word problems but require more than the use of addition, subtraction, multiplication, and division to complete. Seasonal problem solving tasks and daily challenges are a perfect way to celebrate the season and have a little fun too!

Cooperative Problem Solving Tasks

Go cooperative! If you’ve got a few extra minutes, have students work on problem solving tasks in small groups. After working through the task, students create a poster to help explain their solution process and then post their poster around the classroom. Students then complete a gallery walk of the posters in the classroom and provide feedback via sticky notes or during a math talk session.

Notice and Wonder

Before beginning a problem solving task, such as a seasonal problem solving task, conduct a Notice and Wonder session. To do this, ask students what they notice about the problem. Then, ask them what they wonder about the problem. This will give students an opportunity to highlight the unique characteristics and conditions of the problem as they try to make sense of it. 

Want a better experience? Remove the stimulus, or question, and allow students to wonder about the problem. Try it! You’ll gain some great insight into how your students think about a problem.

Math Starters

Start your math block with a math starter, critical thinking activities designed to get your students thinking about math and provide opportunities to “sneak” in grade-level content and skills in a fun and engaging way. These tasks are quick, designed to take no more than five minutes, and provide a great way to turn-on your students’ brains. Read more about math starters here ! 

Create your own puzzle box! The puzzle box is a set of puzzles and math challenges I use as fast finisher tasks for my students when they finish an assignment or need an extra challenge. The box can be a file box, file crate, or even a wall chart. It includes a variety of activities so all students can find a challenge that suits their interests and ability level.

Calculators

Use calculators! For some reason, this tool is not one many students get to use frequently; however, it’s important students have a chance to practice using it in the classroom. After all, almost everyone has access to a calculator on their cell phones. There are also some standardized tests that allow students to use them, so it’s important for us to practice using calculators in the classroom. Plus, calculators can be fun learning tools all by themselves!

Three-Act Math Tasks

Use a three-act math task to engage students with a content-focused, real-world problem! These math tasks were created with math modeling in mind– students are presented with a scenario and then given clues and hints to help them solve the problem. There are several sites where you can find these awesome math tasks, including Dan Meyer’s Three-Act Math Tasks and Graham Fletcher’s 3-Acts Lessons . 

Getting the Most from Each of the Problem Solving Activities

When students participate in problem solving activities, it is important to ask guiding, not leading, questions. This provides students with the support necessary to move forward in their thinking and it provides teachers with a more in-depth understanding of student thinking. Selecting an initial question and then analyzing a student’s response tells teachers where to go next. 

Ready to jump in? Grab a free set of problem solving challenges like the ones pictured using the form below. 

Which of the problem solving activities will you try first? Respond in the comments below.

Shametria Routt Banks

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2 Responses

This is a very cool site. I hope it takes off and is well received by teachers. I work in mathematical problem solving and help prepare pre-service teachers in mathematics.

Thank you, Scott! Best wishes to you and your pre-service teachers this year!

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Numeracy focuses on the core skills of applying numerical concepts. It is the ability of understanding fundamental mathematical operations such as multiplication, division, addition and subtraction. These activities are created for all ages and all cognitive levels.

Activities should be adapted based on the learner's cognitive ability.

Numeracy activities are important for learners to develop logical thinking and strategies in everyday life. Learners also need numeracy to make sense of numbers, solve problems, play sports, cook and understand instructions.

Ask the learner to write a math story or word problem and have someone else draw it out and solve it!

This activity ensures that learners understand the real world applications of mathematics and encourages them to use math to solve these problems

Ask the learner to think about a very short story for their word problem. Think of questions such as:

- Who is the character in the story?

- Where is the story happening?

- What is his or her problem?

- What question are you looking to answer?

Once the learner has the story, think about the math involved:

- How many steps will be needed to solve the problem?

- Which operation/s will be needed? (addition, subtraction, multiplication, and division)

- How large will the numbers be?

Finally, tell the learner to write the problem and ask someone else to solve it by drawing a picture and writing a number sentence to go with it!

Emily made 10 cookies at home for her family and herself. Her brother ate 4 cookies, how many are left for the rest of the family?

Choose a number and then show different ways to split a number into two whole numbers.

This activity ensures that learners understand how to create connections between numbers using addition.

Ask the learner to create a list with numbers and pick one number from the list, or ask the learner to think of a number in their head and say it out loud. Alternatively the learner can roll one or two dice to decide the number.

Next, ask the learner how many ways they can split the number into whole numbers. For example, if their number is 10, they can come up with:

- 10 can be added using the numbers 5, 5

- 10 can be added using the numbers 8, 2

- 10 can be added using the numbers 7, 3

- 10 can be added using the numbers 6, 4

Finally, tell the learner to see how many ways they can think of to reach their chosen number.

Ask the learner to play this with a partner or in a group, and whoever has the most ways of reaching the number, wins.

Ask the learner to try to split the number with different mathematical operations such as subtraction, division and multiplication.

Ask the learner to set a goal for themselves: “I will think of 5 different ways to make this number.”

Roll two or more dice and create math equations to solve for.

This activity ensures that learners know their math facts automatically.

Ask the learner to decide what operation they wish to do (addition, subtraction, multiplication or division)

Next, get two dice and roll them.

Finally, solve the problem.

For example: if they chose addition and rolled 2 on one dice and 3 on another dice, do 2 + 3 and solve this equation.

Assist the learner in creating their own dice like the picture!

If the learner wants to work with bigger numbers, then change the numbers on the dice.

The learner can play this with a partner or in a group, and whoever has the most correct answers, wins.

Set a timer for the learner and keep rolling the dice and solving the equations. Start the timer again and then tell the learner to try to beat their previous score.

For a longer project where the learner can create their own math games, please refer to Math Cards here: Link

Two or more people pick a card each. The person with the higher number will move their car one step ahead. Whoever reaches the finish line first, wins.

To ensure the learners are able to compare number values.

Help the learner create about 20-30 number cards. (cut an A4 piece of paper in 8 or 12 cards)

Next, ask the learner to get two toy cars and create a race track on some chart paper like the one in the picture.

Then, place the cars on the starting position and each person pick up a number card. The person with the higher number moves one step forward.

Finally, the person who reaches the finish line first, wins.

Use numbers in the tens, hundreds or thousands or even larger to make it more challenging. The number cards can also be decimals, fractions or integers if the learner knows them.

Two or more people take turns putting a playing card one on top of another. The person who calculates the decided number first says snap and collects the cards. Keep going until one person loses all their cards.

This activity ensures the learners are able to compute their basic math facts automatically.

Deal all the number cards equally among the players.

Next, ask the learner to decide which operation they wish to work with and what the total must be. For example: They decide they want to work with addition and the total number must be 10.

Then, hand out the cards to each player, facing down. Each player takes a turn picking up a card from their own pile and placing it face up in the center, one on top of each other.

Keep calculating the top 2 cards (e.g., 3+4, 2+8), and when the numbers equal the predetermined total (e.g., 10), a player calls “Snap” while slapping their hand onto the top of the pile of cards. The first player to do this wins the pile and adds these cards to the bottom of their pile.

The player that runs out of cards is out of the game and the player with the most cards wins.

If the learner wants to include the other cards (e.g., WILD, Jacks etc.), then assign each of them a number value.

Ask the learner to make their own number cards. About 30-40, with any number they wish to have.

Two or more people take turns picking up two cards at a time and adding them. The person who gets the higher total collects the cards. Keep going till one person loses all their cards.

Deal all the number cards from a playing cards deck equally among all players. If the learner wants to include the other cards (e.g., WILD, Jacks etc.), then assign each of them a number value.

Then, hand out the cards to each player, facing down. Each player takes turn placing two cards, facing up, in front of them.

Next, add the numbers on the cards (e.g.: if they get 3 and 2, then their answer is 5). Tell everyone the answer. The player with the highest answer adds everyone’s cards to the bottom of their pile.

If the player gets the same number in both cards, they can DOUBLE their answer! (e.g.: if they get 3 and 3, add them and get 6 and then double this to get 12 as the final answer!)

Play this game with subtraction or multiplication too!

Two or more people take turns subtracting. The person who gets the lower total collects the cards. Keep going until one person loses all their cards.

This activity ensures the learners are able to do basic operations mentally.

Deal the number cards (1-9) from a playing cards deck to all the players.

Next, the players look at their cards and make a 2 digit number using two cards (e.g.: if I have 3, 6, 7 and 9, I can make numbers such as 36 and 97, etc.)

Then, each player subtracts the smallest number from their largest number and tells the answer (e.g.: 97-36= 51). This should be done mentally, if possible.

The player with the highest number for the answer keeps their cards, but the other players return their cards to the bottom of the middle pile.

Keep going until the cards are all done. The person with the most cards wins.

This game can be played with addition, multiplication or division too!

Use only 1 digit numbers, using 1 card, and subtracting the smallest number from the largest number.

Using a deck of cards, shuffle the cards and then lay 5 cards out on the table and all other cards face down in a pile on the side.

Next, the first player picks one card from the deck of the cards and lays it face up beside the pile.

Then, the players attempt to create an equation using any of the 5 cards to make the number they have turned over.

For example: if they have placed 5 cards - 3, 6, 2, 5 and 10 on the table, and 7 is the number they chose, then they can make the equations 5 + 2, or 10 – 3, or 5x2 - 3 and so on that all equal 7.

The first player to think of an equation says “Made My Number” and says the equation. If they are correct, they keep those number cards and the number card chosen, all of which are then replaced in the next round.

If the players are unable to make the number, just place the chosen card at the bottom of the pile and pick a new one. Keep going until the cards are all done. The person with the most cards wins.

This game can be played by using a timer and challenging players to come up with as many equations within the time limit as possible!

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Maths problem-solving – Activities for Early Years settings

• Written By: Judith Dancer
• Subject: Maths

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Critical thinking doesn’t have to be a daunting prospect. There are simple, effective and exciting ways to encourage children’s maths problem-solving skills, says Judith Dancer…

Maths is a subject many adults lack confidence in. Having struggled with it at school they often avoid it, wherever possible, when grown up.

But if maths seems scary for some people, then maths problem-solving can cause even more anxiety. There is no ‘safety net’ of knowing the ‘correct answer’ beforehand. This is because maths problem-solving lends itself to investigation and exploration with lots of possible tangents.

Understandably this is often the area of maths where many practitioners feel least confident. However, young children, who are not restrained by right answers, feel the most enthused and animated.

The non-statutory  Development Matters Guidance , as part of ‘creating and thinking critically’ in the Characteristics of Effective Learning, identifies that practitioners need to observe how a child is learning, noting how a child is:

• thinking of ideas;
• finding ways to solve problems;
• finding new ways to do things;
• making links and noticing patterns in their experience;
• making predictions;
• testing their ideas;
• developing ideas of grouping, sequences, cause and effect;
• planning, making decisions about how to approach a task, solve a problem and reach a goal;
• checking how well their activities are going;
• changing strategy as needed;
• reviewing how well the approach worked.

All of these elements are, at one time or another, part of the problem-identifying and solving process – although not at the same time and in the same problem.

Role of the adult

Maths problem-solving for young children involves them understanding and using two kinds of maths:

• Maths knowledge – learning and applying an aspect of maths such as counting, calculating or measuring.
• Maths thinking skills – reasoning, predicting, talking the problem through, making connections, generalising, identifying patterns and finding solutions.

The best maths problems for children are the ones that they identify themselves. They will be enthused, fascinated and more engaged in these ‘real’, meaningful problems.

Children need opportunities to problem-solve together. As they play, they will often find their own mathematical problems.

One of the key roles of practitioners is to provide time, space and support for children. We need to develop situations and provide opportunities in which children can refine their maths problem-solving skills and apply their mathematical knowledge.

Supporting maths problem-solving

You can effectively support children’s developing maths problem-solving strategies through:

• Modelling maths talk and discussion – language is part of maths learning because talking problems through is vital. Children need to hear specific mathematical vocabulary in context. You can promote discussion through the use of comments, enabling statements and open-ended questions.
• Providing hands-on maths problem-solving activities across all areas of the setting. Children learn maths through all their experiences and need frequent opportunities to take part in creative and engaging experiences. Maths doesn’t just happen in the maths learning zone!
• Identifying potential maths learning indoors and outdoors. Provide rich and diverse open-ended resources that children can use in a number of different ways to support their own learning. It is important to include natural and everyday objects and items that have captured children’s imaginations, including popular culture.

Maths problem-solving possibilities

Spell it out.

This experience gives children lots of opportunities to explore calculating, mark making, categorising and decisions about how to approach a task.

What you need to provide:

• Assorted containers filled with natural materials. This includes leaves, pebbles, gravel, conkers, twigs, shells, fir cones, mud and sand. Include some ‘treasure’ – sequins, gold nuggets, jewels and glitter.
• Bottles and jugs of water, large mixing bowls, cups, a ‘cauldron’, small bottles, spoons and ladles.
• Cloaks and wizard hats.
• Laminated ‘spells’ – e.g. “To make a disappearing spell, mix 2 smooth pebbles, 2 gold nuggets, 4 fir cones, a pinch of sparkle dust, 3 cups of water”.
• Writing frameworks for children’s own spell recipes and a shiny ‘Spell Book’ to stick these in.
• Temporary mark-making opportunities such as chalk on slate.

The important thing with open-ended maths problem-solving experiences like this is to observe, wait and listen. Then, if appropriate, join in as a co-player with children, following their play themes.

So if children are mixing potions, note how children sort or categorise the objects. What strategies do they use to solve problems? What happens if they want eight pebbles and they run out? Observe what they do next.

When supporting children’s maths problem-solving, you need to develop a wide range of strategies and ‘dip into’ these appropriately. Rather than asking questions, it is often more effective to make comments about what you can see. For example, say, “Wow, it looks as though there is too much potion for that bottle”.

Acting as a co-player offers lots of opportunities to model mathematical behaviours. This might include reading recipes for potions and spells out loud, focusing on the numbers – one feather, three shells…

Going, going, gone

We all know that children will engage more fully when involved in experiences that fascinate them. If a particular group has a real passion for cars and trucks , consider introducing maths problem-solving opportunities that extend this interest.

This activity offers opportunities for classifying, sorting, counting, adding and subtracting, among many other things.

• Some unfamiliar trucks and cars and some old favourites. Ensure these include metal, plastic and wooden vehicles that can be sorted in different ways.
• Masking tape and scissors.
• Sticky labels and markers.

Mark out some parking lots on a smooth floor, or huge piece of paper using masking tape. Lining paper is great for this. Line the vehicles up around the edge of the floor area.

Encourage one child to select two vehicles that have something the same about them. Ask the child, “What is the same about them?”.

When the children have agreed on what is the same – e.g. size, materials, colour, lorries or racing cars – the child selects a ‘parking lot’ to put the vehicles in. So this first parking lot could be for ‘red vehicles’.

Another child chooses two more vehicles that have something the same. Do they belong in the same ‘parking lot’, or a different parking lot? E.g. these vehicles could both be racing cars.

What happens when a specific vehicle could belong in both lots? E.g. it could belong in the set of red vehicles and also belongs in the set of racing cars.

Support the children as they discuss the vehicle. Make new ‘parking lots’ with masking tape and create labels for the groups, if you choose.

Observe children’s strategies

It’s really important to observe the strategies the children use. Where appropriate, ask the children to explain what they are doing and why.

If necessary, introduce and model the use of the vocabulary ‘the same as’ and ‘different from’. Follow children’s discussions and interests. If they start talking about registration plates, consider making car number plates for all the wheeled toys outdoors.

Do the children know the format of registration plates? Can you take photos of cars you can see in the local environment?

Camping out

Constructing camps and dens outdoors is a good way to give children the opportunity to be involved in lots of maths problem-solving experiences and construction skills learning. This experience offers opportunities for using the language of position, shape and space, and finding solutions to practical problems.

• Materials to construct a tent or den such as sheets, curtains, poles, clips and string.
• Rucksacks, water bottles, compasses and maps.
• Oven shelf and bricks to build a campfire or barbecue.
• Buckets and bowls and water for washing up.

Encourage the children to explore the resources and decide which materials they need to build the camp. Suggest they source extra resources as they are needed.

Talk with the children about the best place to make a den or erect a tent and barbecue. During the discussion, model the use of positional words and phrases.

Follow children’s play themes. This could include going on a scavenger hunt collecting stones, twigs and leaves and going back to the campsite to sort them out.

Encourage children to try different solutions to the practical problems they identify. Use a running commentary on what is happening without providing the solution to the problem.

Look for opportunities to develop children’s mathematical reasoning skills by making comments such as, “I wonder why Rafit chose that box to go on the top of his den.”

If the children are familiar with traditional tales, you could extend this activity by laying a crumb trail round the outdoor area for children to follow. Make sure that there is something exciting at the end of the trail. It could be a large dinosaur sitting in a puddle, or a bear in a ‘cave’.

Children rarely have opportunities to investigate objects that are really heavy. Sometimes they have two objects and are asked the question, “Which one is heavy?” when both objects are actually light.

This experience gives children the chance to explore really heavy things and measures (weight). They also need to cooperate and find new ways to do things.

• A ‘building site’ in the outdoor area. Include hard hats, builders’ buckets, small buckets, shovels, spades, water, sand, pebbles, gravel, guttering, building blocks, huge cardboard boxes and fabric (this could be on a tarpaulin).
• Some distance away, builders’ buckets filled with damp sand and large gravel.
• Bucket balances and bathroom scales.

With an open-ended activity such as this, it is even more important to observe, wait and listen as the children explore the building site and the buckets full of sand and gravel.

Listen to the discussions the children have about moving the sand and the gravel to the building site. What language do they use?

Note the strategies they use when they can’t lift the large buckets. Who empties some of the sand into smaller buckets? Who works together collaboratively to move the full bucket? Does anyone introduce another strategy, for example, finding a wheelbarrow or pull-along truck?

Where and when appropriate, join in the children’s play as a co-player. You could act in role as a customer or new builder. Ask, “How can I get all this sand into my car?”. “How much sand and gravel do we need to make the cement for the foundations?”.

Extend children’s learning by modelling the language of weight:

• heavy/heavier than/heaviest
• light/lighter than/lightest
• about the same weight as/as heavy as
• balance/weigh

Judith Dancer is an author, consultant and trainer specialising in communication and language and mathematics. She is co-author, with Carole Skinner, of  Foundations of Mathematics – An active approach to number, shape and measures in the Early Years .

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Maths Problem Solving: Engaging Your Students And Strengthening Their Mathematical Skills

Meriel Willatt

Maths problem solving can be challenging for pupils. There’s no ‘one size fits all’ approach or strategy and questions often combine different topic areas. Pupils often don’t know where to start. It’s no surprise that problem solving is a common topic teachers struggle to teach effectively to their pupils.

In this blog, we consider the importance of problem solving and share with you some ideas and resources for you to tackle problem solving in your maths classroom, from KS2 up to GCSE.

What is maths problem solving?

Maths problem solving is when a mathematical task challenges pupils to apply their knowledge, logic and reasoning in unfamiliar contexts. Problem solving questions often combine several elements of maths.

We know from talking to the hundreds of school leaders and maths teachers that we work with as one to one online maths tutoring providers that this is one of their biggest challenges: equipping pupils with the skills and confidence necessary to approach problem solving questions.

The Ultimate Guide to Problem Solving Techniques

Download these 9 ready-to-go problem solving techniques that every pupil should know

Why is maths problem solving so difficult?

The challenge with problem solving in maths is that there is no generic problem solving skill that can be taught in an isolated maths lesson. It’s a skill that teachers must explicitly teach to pupils, embed into their learning and revisit often.

When pupils are first introduced to a topic, they cannot start problem solving straight away using it. Problem solving relies on deep knowledge of concepts. Pupils need to become familiar with it and practice using it in different contexts before they can make connections, reason and problem solve with it. In fact, some researchers suggest that it could take up to two years to do this (Burkhardt, 2017). 

At Third Space Learning, we specialise in online one to one maths tutoring for schools, from KS1 all the way up to GCSE. Our lessons are designed by maths teachers and pedagogy experts to break down complex problems into their constituent parts. Our specialist tutors then carefully scaffold learning to build students’ confidence in key skills before combining them to tackle problem solving questions.

How to develop problem solving skills in maths

In order to develop problem solving skills in maths, pupils need lots of different contexts and word problems in which to practise them and the opportunity to engage in mathematical talk that draws on their metacognitive skills. 

The EEF suggests that to develop problem solving skills in maths, teachers need to teach pupils:

• To use different approaches to problem solving
• Use worked examples
• To use metacognition to plan, monitor and reflect on their approaches to problem solving

Below, we take a closer look at problem solving at each stage, from primary school all the way to GCSEs. We’ve also included links to maths resources and CPD to support you and your team’s classroom teaching.

Maths problem solving KS2

At lower KS2, the National Curriculum states that pupils should develop their ability to solve a range of problems. However, these will involve simple calculations as pupils develop their numeracy skills. As pupils progress to upper KS2, the demand for problem solving skills increases. 

“At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems.” National curriculum in England: mathematics programmes of study (Upper key stage 2 – years 5 and 6)

KS2 problem solving can often fall into the trap of relying on acronyms, such as RICE, RIDE or even QUACK. The most popular is RUCSAC (Read, Underline, Calculate, Solve, Answer, Check). While these do aim to simplify the process for young minds, it encourages a superficial, formulaic approach to problem solving, rather than deep mathematical thinking. Also, consider how much is wrapped up within the word ‘solve’ – is this helpful?

We teach thousands of pupils KS2 maths problem solving skills every week through our one to one online tutoring programme for maths. In our interventions, we encourage deep mathematical thinking by using a simplified version of George Polya’s four stages of problem solving. Here are the four stages:

Understand the problem

• Devise a strategy for solving it
• Carry out the problem solving strategy
• Check the result

We use UCR as a simplified model: Understand, Communicate & Reflect. You may choose to adapt this depending on the age and ability of your class.

For example:

Maisy, Heidi and Freddie are children in the same family. The product of their ages is a score. How old might they be?

There are three people.

There are three numbers that multiply together to make twenty (a score is equal to 20). There will be lots of answers, but no ‘right’ answer.

Communicate

To solve the word problem we need to find the numbers that will go into 20 without a remainder (the factors).

The factors of 20 are 1, 2, 4, 5, 10 and 20.

Combinations of numbers that could work are: 1, 1, 20 1, 2, 10 1, 4, 5 2, 2, 5.

The question says children, which means ‘under 18 years’, so that would mean we could remove 1, 1, 20 from our list of possibilities. 

In our sessions, we create a nurturing learning environment where pupils feel safe to make mistakes. This is so important in the context of problem solving as the best problem solvers will be resilient and able to overcome challenges in the ‘Reflect’ stage. Read more: What is a growth mindset

Looking for more support teaching KS2 problem solving? We’ve developed a powerpoint on problem solving, reasoning and planning for depth that is designed to be used as CPD by primary school teachers, maths leads and SLT. 

The resource reflects on how metacognition can enhance reasoning and problem solving abilities, the ‘curse’ of real life maths (think ‘Carl buys 60 watermelons…) and how teachers can practically implement and teach strategies in the classroom.

You may also be interested in: 

• Developing Thinking Skills At KS2
• KS2 Maths Investigations
• Word problems for Year 6

Maths problem solving KS3

At KS3, the importance of seeing mathematical concepts as interconnected with other skills, including problem solving, is foregrounded. The National Curriculum also stresses the importance of a strong foundation in maths before moving on to complex problem solving.

“Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programme of study for key stage 3 is organised into apparently distinct domains, but pupils should build on key stage 2 and connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems” National curriculum in England: mathematics programmes of study (Key stage 3)

“Decisions about progression should be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content in preparation for key stage 4.” National curriculum in England: mathematics programmes of study (Key stage 3)

For many students, the transition from primary to secondary school can be a huge challenge.

Especially in the aftermath of the Covid-19 pandemic and the resultant school closures, students may arrive into Year 7 with various learning gaps and misconceptions that will hold them. Some students may need focused support to plug these gaps and grow in confidence.

You can give pupils a smoother transition from KS2 to KS3 with personalised one to one online tuition with specialist tutors with Third Space Learning. Our lessons cover content from Years 5-7 and build a solid foundation for pupils to develop their problem solving skills. Pupils are supported towards independent practice through worked examples, questioning and support slides.

The challenge for KS3 maths problem solving activities is that learners may struggle to get invested unless you start with a convincing hook. Engage your young mathematicians on topics you know well or you know they’ll be invested in and try your hand at designing your own mathematical problems. Alternatively, get some inspiration from our crossover ability and fun maths problems .

Maths problem solving GCSE

Since the new GCSE specification began in 2015, there has been an increased focus on non-routine problem solving questions. These questions demand students to make sense of lots of new information at once before they even move on to selecting the strategies they’ll use to find the correct answer. This is where many learners get stuck.

In recent years, teachers and researchers in pedagogy (including Ofsted) have recognised that open ended problem solving tasks do not in fact lead to improved student understanding. While they may be enjoyable and engage learners, they may not lead to improved results.

SSDD problems (Same Surface Different Depth) can offer a solution that develops students’ critical thinking skills, while ensuring they engage fully with the information they’re provided. The idea behind them is to provide a set of questions that look the same and use the same mathematical hook but each question requires a different mathematical process to be solved.

Read more about SSDD problems , tips on writing your own questions and download free printable examples. There are also plenty of more examples on the NRICH website.

Worked examples, careful questioning and constructing visual representations can help students to convert the information embedded in a maths challenge into mathematical notations. Read our blog on problem solving maths questions for Foundation, Crossover & Higher examples, worked solutions and strategies.

Remember that students can only move on to mathematics problem solving once they have secure knowledge in a topic. If you know there are areas your students need extra support, check our Secondary Maths Resources library for revision guides, teaching resources and worksheets for KS3 and GCSE topics.

DO YOU HAVE STUDENTS WHO NEED MORE SUPPORT IN MATHS?

Every week Third Space Learning’s specialist online maths tutors support thousands of students across hundreds of schools with weekly online 1 to 1 maths lessons designed to plug gaps and boost progress.

Since 2013 these personalised one to 1 lessons have helped over 150,000 primary and secondary students become more confident, able mathematicians.

Learn how the programmes are aligned to maths mastery teaching or request a personalised quote for your school to speak to us about your school’s needs and how we can help.

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3 Problem-Solving Math Activities

Scottie Altland · September 5, 2018 · 1 Comment

A problem is simply a “problem” because there is no immediate, known solution. Problem solving activities in mathematics extend well beyond traditional word problems .

You can provide your student with activities that promote application of math skills while “busting boredom” at the same time! Puzzles and riddles, patterns, and logic problems can all be valuable exercises for students at all levels of mathematics. By engaging in short, fun activities like these, you can help your student become a more skillful, resilient, and successful problem-solver.

When practicing problem-solving skills, be certain to give your student time to explore a problem on her own to see how they might get started. Then discuss their approach together. It is important to provide support during the problem-solving process by showing that you value their ideas and helping them to see that mistakes can be useful. You can do this by asking open-ended questions to help your student gain a starting point, focus on a particular strategy, or help see a pattern or relationship. Questions such as, “What have you done before like this?”, “What can be made from …?” or “What might happen if you change…?” may serve as prompts when they needs inspiration.

Try the activities below to boost your student’s problem-solving skills.

Download the activities here .

1) Toothpick Puzzles

Toothpick puzzles (also referred to as matchstick puzzles) provide students a visualization challenge by applying their knowledge of basic geometric shapes and orientations. The only supplies you need are a box of toothpicks, a workspace, and a puzzle to solve. The goal is for students to transform given geometric figures into others by adding, moving, or removing toothpicks. These puzzles range in complexity and can be found online or in math puzzle books. As an extension, challenge your student to create their own puzzle for someone else to solve.

Sample toothpick puzzles of varying difficulty:

Download solutions to this activity here.

2) Fencing Numbers

The goal of this activity is to create a border or “fence” around each numeral by connecting dots horizontally and vertically so that each digit is bordered by the correct number of line segments.

Print a sheet of dot paper .

Use pencils and scissors to cut the size grid you want to use.

This game can be modified for abilities by adjusting the size of the grid and amount of numerals written. For example, a beginning student might begin with a grid that is 5 x 5 dots with a total of four numerals, while a more advanced student might increase the grid to 7 x 7 dots with six to eight numerals.

Begin by writing the digits 0, 1, 2, and 3 spread repeatedly in between “squares” on the dot paper. Each digit represents the number of line segments that will surround that square. For instance, a square that contains a 3 would have line segments on three sides, and a square that contains a 2 would have line segments on two sides, and so on. See the example boards and solutions for a 5 x 5 grid below.

Beware; there may be multiple solutions for the same problem! Thus, encourage your student to replicate the same problem grid multiple times and look for different solutions. A more advanced student can be challenged to create their own problem. Can they make a grid with only one solution? Is it possible to make a problem with four or more possible solutions?

3) It’s Knot a Problem!

Exercise lateral thinking skills– solving a problem through an indirect and creative approach that is not immediately obvious. You need two people, two pieces of string (or yarn) about one meter long each (or long enough so the person who will wear it can easily step over it), and some empty space to move around. If possible, use two different colored pieces of string. Each person needs a piece of string with a loop tied in both ends so it can be worn like “handcuffs”. Before tying off the loop on the second wrist, the participants loop the string around each other so they are hooked together. The figure below illustrates how the strings should appear when completed.

The goal is to unhook the strings while following these guidelines:

1) The string must remain tied and may not be removed from either participant’s wrists. 2) The string cannot be broken, cut, or damaged in any way.

Caution! This activity not only tests problem-solving skills, but it also promotes positive communication, teamwork, and persistence.

Problem-solving skills are not always taught directly but often learned indirectly through experience and practice. When incorporating problem solving activities aim to make them open-ended and playful to keep your student engaged. Incorporating fun activities like these from time to time foster creative and flexible thinking and can help your student transfer problem solving skills to other subject areas. By providing guidance and helping your student to see a problem from different perspectives, you will help foster a positive disposition towards problem-solving. As your student continues to learn how to effectively solve problems, they increase their understanding of the world around them and develop the tools they need to make decisions about the way they approach a problem.

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February 25, 2020 at 11:13 am

The ideas are very brilliant it encourages critical thinking and also help student think for a solution. Awesome!😍

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Unlocking the Power of Math Learning: Strategies and Tools for Success

posted on September 20, 2023

Mathematics, the foundation of all sciences and technology, plays a fundamental role in our everyday lives. Yet many students find the subject challenging, causing them to shy away from it altogether. This reluctance is often due to a lack of confidence, a misunderstanding of unclear concepts, a move ahead to more advanced skills before they are ready, and ineffective learning methods. However, with the right approach, math learning can be both rewarding and empowering. This post will explore different approaches to learning math, strategies for success, and cutting-edge tools to help you achieve your goals.

Math Learning

Math learning can take many forms, including traditional classroom instruction, online courses, and self-directed learning. A multifaceted approach to math learning can improve understanding, engage students, and promote subject mastery. A 2014 study by the National Council of Teachers of Mathematics found that the use of multiple representations, such as visual aids, graphs, and real-world examples, supports the development of mathematical connections, reasoning, and problem-solving skills.

Moreover, the importance of math learning goes beyond solving equations and formulas. Advanced math skills are essential for success in many fields, including science, engineering, finance, health care, and technology. In fact, a report by Burning Glass Technologies found that 71% of high-salary, entry-level positions require advanced math skills.

Benefits of Math Learning

In today’s 21st-century world, having a broad knowledge base and strong reading and math skills is essential. Mathematical literacy plays a crucial role in this success. It empowers individuals to comprehend the world around them and make well-informed decisions based on data-driven understanding. More than just earning good grades in math, mathematical literacy is a vital life skill that can open doors to economic opportunities, improve financial management, and foster critical thinking. We’re not the only ones who say so:

• Math learning enhances problem-solving skills, critical thinking, and logical reasoning abilities. (Source: National Council of Teachers of Mathematics )
• It improves analytical skills that can be applied in various real-life situations, such as budgeting or analyzing data. (Source: Southern New Hampshire University )
• Math learning promotes creativity and innovation by fostering a deep understanding of patterns and relationships. (Source: Purdue University )
• It provides a strong foundation for careers in fields such as engineering, finance, computer science, and more. These careers generally correlate to high wages. (Source: U.S. Bureau of Labor Statistics )
• Math skills are transferable and can be applied across different academic disciplines. (Source: Sydney School of Education and Social Work )

How to Know What Math You Need to Learn

Often students will find gaps in their math knowledge; this can occur at any age or skill level. As math learning is generally iterative, a solid foundation and understanding of the math skills that preceded current learning are key to success. The solution to these gaps is called mastery learning, the philosophy that underpins Khan Academy’s approach to education .

Mastery learning is an educational philosophy that emphasizes the importance of a student fully understanding a concept before moving on to the next one. Rather than rushing students through a curriculum, mastery learning asks educators to ensure that learners have “mastered” a topic or skill, showing a high level of proficiency and understanding, before progressing. This approach is rooted in the belief that all students can learn given the appropriate learning conditions and enough time, making it a markedly student-centered method. It promotes thoroughness over speed and encourages individualized learning paths, thus catering to the unique learning needs of each student.

Students will encounter mastery learning passively as they go through Khan Academy coursework, as our platform identifies gaps and systematically adjusts to support student learning outcomes. More details can be found in our Educators Hub . 

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How to learn math.

Learning at School

One of the most common methods of math instruction is classroom learning. In-class instruction provides students with real-time feedback, practical application, and a peer-learning environment. Teachers can personalize instruction by assessing students’ strengths and weaknesses, providing remediation when necessary, and offering advanced instruction to students who need it.

Learning at Home

Supplemental learning at home can complement traditional classroom instruction. For example, using online resources that provide additional practice opportunities, interactive games, and demonstrations, can help students consolidate learning outside of class. E-learning has become increasingly popular, with a wealth of online resources available to learners of all ages. The benefits of online learning include flexibility, customization, and the ability to work at one’s own pace. One excellent online learning platform is Khan Academy, which offers free video tutorials, interactive practice exercises, and a wealth of resources across a range of mathematical topics.

Moreover, parents can encourage and monitor progress, answer questions, and demonstrate practical applications of math in everyday life. For example, when at the grocery store, parents can ask their children to help calculate the price per ounce of two items to discover which one is the better deal. Cooking and baking with your children also provides a lot of opportunities to use math skills, like dividing a recipe in half or doubling the ingredients. 

Learning Math with the Help of Artificial Intelligence (AI) 

AI-powered tools are changing the way students learn math. Personalized feedback and adaptive practice help target individual needs. Virtual tutors offer real-time help with math concepts while AI algorithms identify areas for improvement. Custom math problems provide tailored practice, and natural language processing allows for instant question-and-answer sessions. 

Using Khan Academy’s AI Tutor, Khanmigo

Transform your child’s grasp of mathematics with Khanmigo , the 24/7 AI-powered tutor that specializes in tailored, one-on-one math instruction. Available at any time, Khanmigo provides personalized support that goes beyond mere answers to nurture genuine mathematical understanding and critical thinking. Khanmigo can track progress, identify strengths and weaknesses, and offer real-time feedback to help students stay on the right track. Within a secure and ethical AI framework, your child can tackle everything from basic arithmetic to complex calculus, all while you maintain oversight using robust parental controls.

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You can learn anything .

Math learning is essential for success in the modern world, and with the right approach, it can also be enjoyable and rewarding. Learning math requires curiosity, diligence, and the ability to connect abstract concepts with real-world applications. Strategies for effective math learning include a multifaceted approach, including classroom instruction, online courses, homework, tutoring, and personalized AI support. 

So, don’t let math anxiety hold you back; take advantage of available resources and technology to enhance your knowledge base and enjoy the benefits of math learning.

National Council of Teachers of Mathematics, “Principles to Actions: Ensuring Mathematical Success for All” , April 2014

Project Lead The Way Research Report, “The Power of Transportable Skills: Assessing the Demand and Value of the Skills of the Future” , 2020

Page. M, “Why Develop Quantitative and Qualitative Data Analysis Skills?” , 2016

Mann. EL, Creativity: The Essence of Mathematics, Journal for the Education of the Gifted. Vol. 30, No. 2, 2006, pp. 236–260, http://www.prufrock.com ’

Nakakoji Y, Wilson R.” Interdisciplinary Learning in Mathematics and Science: Transfer of Learning for 21st Century Problem Solving at University ”. J Intell. 2020 Sep 1;8(3):32. doi: 10.3390/jintelligence8030032. PMID: 32882908; PMCID: PMC7555771.

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How to build your child's numeracy skills from birth to Grade 2

​​​​​This page includes tips on how to build your child's skills in maths and numeracy through everyday situations.

On this page

General tips, talking about maths, counting every day, hunting for numbers, using playing cards, playing shop, playing games, playing with shapes, making patterns, moving with maths, measuring things, asking questions to investigate, animations to watch together.

A child’s first years are a time of rapid learning. Research tells us that babies have an innate capacity to understand numbers. As your child’s first teacher, you play a key role in developing their numeracy skills from an early age.

Developing numeracy skills early gives children an important foundation for their learning and development. It helps prepare them for daily life, including general problem-solving and handling money. Maths includes noticing numbers, shapes, patterns, size, time and measurement. Incorporating maths into everyday experiences is easy and fun. Maths is everywhere – in the playground, at the shops and home. Children need lots of experiences in making, counting, drawing and talking about numbers. This section will help you to build these skills in the children in your care. You may feel the maths your child is doing at their early childhood centre, kindergarten or school is different from how you were taught, but you can still support your child in many ways. Make connections for your child by explaining how numbers and counting are a part of everyday life.

Doing maths together at home

It is important for children to develop specific language skills related to maths. Visits to the playground, or helping at home, provide rich and meaningful contexts to develop these skills. it might take time for your child to use these terms and language effectively, but exposure to this mathematical talk is strong support for future learning.

• Use specific terms when asking for items. For example, ask your child to get the ‘one-litre’ milk bottle from the fridge, or the ‘one-kilo’ bag of flour from the cupboard.
• When cooking, talk about different measurements used, such as teaspoons, millilitres, litres, and cups. Discuss ideas about empty and full.
• As you walk, talk and play together describe your child’s movements as they climb ‘over’ the fence, slide ‘between’ the poles, and swing ‘under’ the monkey bars. This helps your child understand language related to spatial awareness.
• Sorting activities support your child to understand concepts such as ‘same’ and ‘different’. Use recycling as an opportunity to sort items to place in the rubbish. For example, paper, plastic, food waste and general waste.

Counting is one of the first experiences of maths for young children.

Learning to say numbers often begins with a favourite song or rhyme and the repetition of the number names. Children will often say the numbers before they recognise and identify individual numbers.

Here are some activities and tips to engage your child with counting:

• Listen for the counting sequence in these songs and rhymes, which can all be found on youtube.com : - Five Little Ducks - Ten in the Bed - 1, 2, 3, 4, 5, Once I Caught a Fish Alive - Ten Green Bottles - Five Little Monkeys - 1, 2, Buckle My Shoe
• Children will begin by counting all objects in a group, for example, fingers and toes, the buttons on their clothes, steps to the house, or their toys.
• As children move on to counting a set of objects, they begin to link each object with one number. In the beginning, encourage your child to touch each object as they say the matching number.
• When beginning to count a group of objects, children may need to arrange the objects in a line to help them count. Later they will be able to start counting from any object without arranging the objects.
• Once your child is confident, use different numbers as the starting point for practising counting. For example, start counting from 6 or 10. Ask your child to count forwards and backwards. Ask what number comes before, or what number comes after, a given number.

You can incorporate counting into everyday activities such as:

• Cut fruit into six pieces and ask your child to count the pieces.
• Count the pieces of toast you cooked for breakfast.
• Add the total number of cutlery items at the table.
• Count the number of people travelling in the car or on the bus.
• Count the number of houses as you walk along the street.
• Count how many steps it takes to walk from the kitchen to the bathroom.
• Practice counting when grocery shopping with your child (for example, counting the number of apples you put into the bag).
• Encourage your child to talk about the number of things in the pictures they draw.

Number hunts are a fun and engaging activity for your child. Ask your child to find numbers around you. Look at and say the numbers on car number plates, signs, calendars, newspapers, shopping catalogues, speed signs, and houses.

Playing with cards is always a fun activity, particularly on a rainy day or on holidays. You can:

• Play matching number games like ‘Snap’ with playing cards.
• Order the numbers on the cards from smallest to largest, or largest to smallest.

Playing shop helps ground your child’s maths learning in the real world while also developing their social skills. One way to play shop is to create a mini-shop at home. Here are a few tips and activities:

• Collect food and grocery items and label them with prices written on sticky notes, or prices cut out of shopping catalogues.
• Talk about how we pay for items using coins, notes and cards.
• Make paper money or use play money to buy and sell goods from the mini-shop.
• Collect old receipts or price tags and use them in the mini-shop.
• Notice the features of different coins, including their shapes and the animals and people shown. Discuss the differences. Create coin rubbings with pencils and paper.
• Make a play credit card with a string of numbers on it. Make a paper keypad to press numbers that match those on the card.
• Encourage your child to order food items by height (tallest to the shortest) or by cost (least expensive to most expensive).
• Introduce kitchen scales to the mini-shop to weigh foods, such as a box of tea bags or a bag of rice, and order items by weight.

Making maths fun and interactive by playing games will help engage your child. Here are some ideas:

• Play ‘I Spy’ or other games to help your child identify shapes, numbers and patterns.
• Board games are a fun way to involve the whole family with maths. Help your child when rolling dice to count, move, and stop after moving the number shown on the dice.
• When using dice your child may count all the dots on the die face to determine the total number. Over time they will begin to recognise automatically the value on the die face without counting.
• Play number games online with your child. Here is a short list of good websites to help begin your online search for resources: - FUSE (select Early Childhood or Primary Students tabs) - Count Us In - ABC Education - ABC Education - ictgames

Playing with shapes helps develop your child’s awareness of different shapes. It also improves their hand-eye coordination. Here are some tips and activities:

• Jigsaw puzzles, tangrams or shape-sorting toys help teach your child problem-solving skills and spatial awareness.
• Name and notice the similarities and differences between shapes. For example, shapes with curves, corners or edges.
• Help your child draw shapes, cut them out and sort them into groups. Ask your child to explain why they have sorted the shapes this way.
• Use cookie cutters to explore different shapes using playdough. Encourage your child to identify shapes in their everyday life, such as a round ball, square window or hexagonal ‘STOP’ sign.
• Making paper planes together combines many mathematical concepts, including angles, shapes, halving and symmetry. Once complete, you can compare which plane flew the furthest and have fun measuring too.
• Use building blocks to create a tower. Using the same number of blocks, ask your child to build another tower that’s different to the first tower.

Recognising and making patterns are important maths skills for exploring numbers, shapes and symmetry. Activities include:

• Identify and explain visual patterns on clothing, wrapping paper, buildings, crockery, cards and furniture. Create a scrapbook to refer back to for ideas during arts and crafts.
• Use coloured pegs, blocks, beads or cutlery to begin a pattern for your child to continue. Once confident, ask them to copy or create a pattern of their own.
• Try to incorporate some patterns in rhythm. Create a clapping pattern and ask your child to copy and then create their own pattern.
• Encourage your child to draw, create and describe their own patterns. Use them for borders on greeting cards.

These ideas use the movement of the body to experience counting:

• Count each toss of the ball as you play a game.
• Estimate how many jumps it will take to get to… Then count how many jumps it takes to get to…
• Count with your child as you climb steps or walk from the park bench to the slide.
• Ask your child to find ways to balance their weight with a friend on the see-saw.
• Sing rhymes and songs that involve counting while skipping.

Understanding measurement and scale are crucial to your child’s understanding of maths. Here are some tips and activities:

• Use a wall measuring chart to measure the height of people in your family.
• Talk to your child about objects around them and help them judge which is bigger or smaller, taller or shorter.
• Cut a piece of string for your child – any length will do. Use the string to measure the objects in your house to find out what is longer or shorter than your ‘string measuring tape’. Ask your child to identify anything that is the same length.
• Explore other ways of measuring, such as using a cup, jug, teaspoon, icy pole sticks, footprints or hand lengths.
• Help your child to build a tower of blocks that is taller than a favourite toy. Ask your child to count the total blocks to measure the height of the tower.
• Estimate and measure who can jump the furthest, stand on one foot for a longer period, or how many buttons might fill a jar.
• Explore the size of different containers by pouring and filling them. Estimate, then check to see which holds more or less.
• Notice changes in the weather and the time of day. Use an old bottle and create a ‘rain gauge’ to measure and monitor how much it rains.

Ask your child questions like these to encourage them to investigate maths:

• What shapes can you see?
• How could we measure the...?
• How will we find half?
• What is the best way to share the...?
• How do I get from … to …?
• Which is closer: the sandpit or the swing?
• How tall can you build a tower before it falls?

The Everyday Maths Animations encourage families to explore maths together as they walk, talk and play in everyday situations. The set of three animations support families to bring mathematics and numeracy into conversations in the home, the supermarket and outdoors.

The Mathscots animation series has been developed to support families engage in numeracy and to build home-school connections around mathematics learning. Following the introductory episode, there are 9 stand-alone episodes (each between one and two minutes long). Longer play versions have in-built pauses along with prompts and questions to encourage families to talk about the maths presented. There are also suggested activities that families may like to explore after watching the episodes.

Updated 25 January 2023

• ParentPowered, formerly Ready4K, is going to high school! Explore the new curriculum

• Families Count! Nurturing Early Numeracy Skills for Kindergarten Readiness

by ParentPowered contributing author Curran Mahowald, M.A. Cognitive Science in Education

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You may also like, answering common parent questions about early math, when should my child start learning math, why are early numeracy skills important, how do children develop early numeracy skills, what strategies can i use to support my child’s early numeracy and math at home, education equity and early numeracy skills, shareable math messages for families.

When I was in kindergarten, the 100th day of school was special. Each child was asked to bring in one hundred of something. I first looked at some of my favorite objects — beanie babies and roly polies—but soon realized I didn’t have (or couldn’t wrangle, in the case of the live bugs) one hundred of those. I settled on one hundred pieces of my favorite cereal, and my parents helped me pack the right amount into a plastic bag. The next day I was proudly counting each item one by one along with my classmates and their collections of paper clips, pennies, and popsicle sticks.

Most of what I remember from that day, which feels like it happened a century ago, is eating cereal (in addition to my one hundred pieces, there was an activity for the whole class in which we strung one hundred fruit loops onto a necklace). But I was also learning important mathematical concepts and numerical abilities through the counting, estimating, and number talk that was going on that day. From an educational perspective, that day was about early numeracy skills.

Early numeracy development has become better appreciated in education because developmental psychology research is revealing that preschool-aged children’s numerical skills in the early years actually lay the foundation for learning math concepts once they get to school. Children’s early experiences with caregivers and early childhood educators play a big role in building this foundational mathematical knowledge.

This means there’s a lot parents can do to invest in their child’s future mathematical abilities—if only they knew what and how! Parents often have questions about when their children should begin learning math, how they can support their children’s math learning at home, and what they can do to help a child struggling in math.

In this article, we’ll answer some of these common questions from families. We’ll explain what early numeracy skills are, why they matter, how they can be developed, and how early childhood teachers and families can partner to improve learning outcomes for all children through family math activities .

Educators play a key role in supporting parents in their efforts to promote early numeracy. Having answers ready to some common parent questions is a great way to foster understanding and equity around math readiness and achievement. Being a trusted source of helpful information about their child’s learning process can also go a long way in building meaningful relationships with families.

Although students don’t typically multiply or divide before third grade, they do learn important mathematical skills and concepts well before kindergarten. Also known as number sense, early numeracy skills are the foundations of mathematical reasoning that children acquire in early childhood. For example, by about four years of age, children can recognize and complete simple patterns, identify the number of objects in a small set, and compare physical attributes such as height. These are all examples of early numeracy skills! You can check out the “Cognition” domain of the Head Start Early Learning Outcomes Framework to see more specific math-related skills and concepts that children should learn before kindergarten.

Just as early reading skills and literacy development refers to the basic building blocks of language and reading (the alphabet, the sounds letters make, phonological awareness, common word meanings, and an understanding of how stories work), early numeracy refers to the basic building blocks of mathematics ability—counting with numerals, comparing size, matching and sorting, combining and separating quantities, parts of a whole, and recognizing the use of numbers in everyday life (e.g. prices, addresses, shoe sizes).

Early numeracy skills are the ways of thinking that support future mathematical skills, and they can be organized into three main categories:

Numbers and operations

The basic understanding and manipulation of numbers. This category of mathematical skills includes several numerical abilities such as:

• Number recognition : The ability to identify and name numbers when they are seen or heard.
• Counting : The numerical ability to recite numbers in the correct order and understand that each number represents a quantity.
• One-to-one correspondence : The understanding that each object in a set can be counted once and only once.
• Quantity comparisons : The ability to understand the concepts of more, less, greater than, and less than.
• Basic arithmetic : The understanding of addition, subtraction, multiplication, and division, initially with small numbers.

Geometry and spatial awareness

Identifying shapes, reasoning about spatial relationships, and mentally manipulating objects in space. Key components of this category include:

• Shapes : Children learn to identify and name different shapes, such as circles, squares, triangles, and rectangles. They also understand the characteristics and properties of these shapes.
• Spatial Relationships : This skill involves understanding and describing the relative positions of objects in space, such as above, below, next to, behind, and in front of.
• Directional Concepts : Children develop an understanding of directional terms like left, right, up, and down. They learn to follow and give directions based on this conceptual knowledge.
• Visualization : Spatial awareness includes the ability to mentally manipulate objects or visualize shapes and patterns in different orientations.

Patterns and measurement

Recognizing and understanding patterns, as well as developing the mathematical concept of measurement. Key skills include:

• Pattern Recognition : Children learn to recognize and create patterns using various attributes, such as color, shape, size, or number sequences.
• Pattern Extension : This skill involves continuing or completing a given pattern by identifying the missing elements based on the pattern’s rules.
• Measurement : Early measurement skills include understanding and comparing attributes like length, height, weight, capacity, and time. Children learn to use non-standard units (e.g., using blocks to measure length) before progressing to standard units (e.g., inches, pounds).
• Estimation : Children develop the ability to estimate or make educated guesses about quantities and measurements based on their understanding of number and measurement concepts.

By developing proficiency in these three categories, children build a strong foundation in early numeracy skills, which is crucial for their mathematical development as they progress through school.

1. Early numeracy skills help children make sense of their world.

The same conceptual knowledge that prepares children for developing formal math skills also helps children process what they perceive in their environment by observing and organizing it in meaningful ways. Numeracy development involves thinking logically, reasoning about the physical and imagined world, and connecting related ideas. Even outside the realm of mathematical performance per se, mathematical learning also supports science, social studies, art, and music. 

2. A focus on the early years can improve mathematics outcomes later.

The research is in—math success begins before school. This is because formal math skills rely on basic conceptual knowledge that children develop early in life. For example, before children can learn to manipulate fractions, they must understand the concept of parts of a whole.

Longitudinal studies that have followed children from early childhood to adolescence have shown a strong association between early numeracy skills and mathematics ability later on. For example, Siegler et al., 2012 found that children’s ability with fractions and division in elementary school predicts their knowledge in algebra and overall academic achievement in high school.

3. Formal math skills have prerequisites. 

Like many domains of academic achievement, math builds on itself, even beginning with very fundamental concepts. Some of these concepts are so basic that adults forget we ever had to develop or learn them. But as babies, we did not come pre-programmed with the knowledge that numbers represent quantity or even that quantity is conserved despite changing shape . We had to learn it through interacting with the world. We all had to develop the ability to perceive multiple dimensions, like width and height, and take them into account when estimating volume.

Children also have to learn that the last number used to count a group of objects represents how many are in the group (the cardinality principle). This is why a child may count to 10 while touching each item once, but when asked how many are in the set, he has to start from 1 again.

This important cognitive development happens over the course of children’s early experiences in the physical world. It’s important that children have opportunities to actively play and explore with adult support and enrichment so they can develop these concepts. It’s also important for children to acquire the mathematical language for these concepts, which they pick up from adults using words in context.

Children develop early numeracy skills through a combination of innate abilities, environmental variables, intergenerational variables, and intentional instruction. Here are some key factors that contribute to the development of these skills:

Natural curiosity and exploration

Young children have an innate curiosity about their environment, including numbers and quantities. They naturally engage in activities that involve counting, sorting objects, and making comparisons. Early childhood teachers and caregivers can help by encouraging this exploration, which provides a foundation for developing early numeracy skills.

Everyday experiences

Daily experiences offer numerous opportunities for children to encounter and engage with numbers and math concepts. For example, they may count toys, identify numbers on street signs, measure ingredients while cooking, or compare the sizes of objects during play. These real-life experiences help children form a strong association between the concepts of math and the real world.

Language and communication

Language abilities play a crucial role in developing early numeracy skills. Through conversations, songs, and stories, children learn number words, counting rhymes, and mathematical vocabulary. Adults and caregivers can facilitate math abilities by engaging children in math-related conversations and providing mathematical language to describe their experiences.

Play-based learning

Play is an essential vehicle for the development of mathematical abilities. Playful activities, such as building with blocks, puzzles, board games, and pretend play with numbers and shapes, allow children to explore mathematical concepts in a hands-on and meaningful way. These activities promote problem-solving, reasoning, and spatial awareness.

Explicit instruction

While natural exploration and play are important, deliberate instruction also plays a role in laying the foundations for mathematical achievement. Teachers and caregivers can provide intentional instruction by introducing concepts like counting, number recognition, basic operations, and shape identification. They can use concrete materials, visual aids, and manipulatives to make learning more tangible and engaging.

Progression and building on concepts

Early numeracy skills develop in a sequential manner. Children start with basic concepts like counting and number recognition and gradually build upon them. Teachers and caregivers should scaffold instruction, providing support and gradually increasing the complexity of tasks to help children progress in their understanding of numbers, operations, patterns, and measurement.

Individual differences and readiness

It’s important to recognize that children develop at their own pace and have different strengths, interests, and needs. Some children may grasp certain concepts quickly, while others may require more time and practice. Creating a supportive and inclusive learning environment that accommodates individual differences is essential for promoting mathematical achievement.

Many adults hesitate before getting involved in their child’s math learning because of the anxiety they feel about their own math abilities . But it turns out that promoting math skills in preschool children as well as older children isn’t as difficult as many parents fear. Here are some insights to help families feel more confident about supporting their children’s mathematical development.

Good questions help more than right answers.

To help a child with math, you don’t need to have good answers—you just need to have good questions. In a previous blog post, we shared some examples of the types of questions that help children overcome difficulties in mathematics . 

Growth mindset improves mathematical achievement.

“I’m not a numbers person.”

Many people think that math skills are something you either have or you don’t. And adults who think this way can inadvertently pass along a misguided belief to their children. Because the truth is, anyone can learn and excel at math with the right instruction, practice, and persistence. Math is not a talent that some people are born with and others aren’t. This is a much more positive disposition that encourages sustained effort, which is known to play a major role in mathematical achievement. Parents and early childhood teachers can model this effort-based philosophy for their children.

In an earlier blog post, we shared ways to reframe common statements about math using a positive disposition and growth mindset. It’s amazing how the way we talk about mathematical development affects academic achievement.

Mistakes help your brain grow.

When most people think of math, they think of a world of right and wrong. And it never feels good to be wrong. Except when you realize that making a mistake is one of the best things that can happen to your brain for learning!

When you make mistakes, it signals your brain that there is something new to figure out. Your brain gets challenged to find different ways to solve problems or correct the errors. As you work through these mistakes, your brain forms new connections and pathways, strengthening your understanding of math concepts.

We don’t need to be afraid of mistakes in math—they’re a natural part of learning and growing!

Mistakes provide valuable learning opportunities, and they promote resilience, a deeper understanding of mathematical concepts, and problem-solving skills in preschool children. 

Math is all around us!

Everyday activities are full of opportunities to gain mathematical knowledge. For example, molding clay, cutting and folding paper to make different shapes, and playing with blocks can help young children build conceptual knowledge related to spatial reasoning and geometry. For older children, sorting laundry by color or pattern, guessing how much time something will take, and pointing out numbers throughout daily routines around the house or while running errands are all ways to support math abilities in the realm of numbers and operations.

As we discussed above, children pick up some foundational knowledge about numbers and math even before they enter kindergarten. This is important because what they know about math when they start school can affect their learning for many years to come, all the way from elementary school to high school.

But there are disparities in mathematics achievement based on race and income. Children from low-income and minority backgrounds are at risk for poor math performance ( Hanushek & Rivkin, 2006 ). Preschool-aged children from low-income families are more likely to start school with less advanced mathematics ability than kids from middle-income families.

And as they go through school, this gap in math abilities between low-income and middle-income kids keeps getting bigger, ultimately leading to disparities in mathematical learning in high school and beyond.

The good news is that children’s early mathematical development can be promoted through education in school and parental support at home. Well-informed early childhood teachers can partner with families to increase all children’s school readiness and help close the achievement gap.

Here are some ideas for supporting early numeracy that early childhood educators can share with families. These are sets of text messages that are part of ParentPowered’s ParentPowered family engagement program.

FACT : Using words like more/less and bigger/smaller with your baby is a great way to introduce early math concepts. Math words help your baby’s growing brain.

TIP : As you feed your baby, try using math words. Say, “Look, the spoon is full. Now it’s empty. That was a big bite! You’re a hungry baby! Do you want more?”

GROWTH : Keep using math words. You’re building your baby’s brain. Now count items as you hand them to your baby during playtime: “One. Two. Three. Three bears!”

FACT : When we count things with kids, they have fun learning the names of numbers. It’s also key for helping kids learn that numbers have meaning.

TIP : Count in the tub! Scrub your child’s fingers and count each finger as you do: “1, 2, 3, 4, 5, 6, 7, 8, 9, 10. You have 10 fingers!” Try toes, too!

GROWTH : Keep counting. Now count your fingers and their fingers all together: 1, 2, 3…18, 19, 20! Gently wiggle each finger as you count it.

FACT : When you match colors, you help your toddler learn to make observations and classify things. These key early math skills will pay off down the road.

TIP : After a snack, name a color on your child’s shirt. Now hunt around the house for other things that are the same color: The pillow is blue like your shirt!

GROWTH : Keep matching colors. You’re helping your toddler grow! As you sort laundry, invite your toddler to make a pile of all the clothes that are white.

FACT : Patterns are hiding here, there, and everywhere! When children discover and talk about patterns, they are learning key math concepts.

TIP : When getting dressed, describe a pattern you see. Say, “I spy a pattern that goes red stripe, blue stripe, red stripe, blue stripe. Can you find it?”

GROWTH : Keep finding patterns for success in math. Now, as your child gets dressed, challenge them to share a pattern that they see around them.

Kindergarten

FACT : As kids learn to count higher and higher, they get stronger in math! You can build this skill with fun counting challenges throughout the day.

TIP : As you do dishes ask, “Do you think I can wash the plates before you count to 20? Ready, set, go!” Jump in and offer help if your child gets stuck.

GROWTH : Keep counting to build math skills! Now count to 30 as your child puts on their socks and shoes. When you get to 29 ask, “What number comes next”?

FACT : When you ask questions that involve addition and subtraction, your child gets better at solving word problems. Word problems are key to math.

TIP : Have fun asking addition questions at the table. Try questions like, “I have 3 beans and you have 2. How many beans do we have all together?”

GROWTH : Keep solving word problems! Now ask a subtraction question at the table. Say, “I have 5 carrots but I’m about to eat 1. How many will be left?”

About the author

Curran Mahowald is a former high school language teacher turned education research advocate. In addition to having worked at ParentPowered, she has also designed parent-facing informational materials at Oakland Unified School District and currently works on improving national research-to-practice infrastructure at the Annenberg Institute for School Reform at Brown University. Curran holds an M.A. in Cognitive Science in Education from Teachers College, Columbia University and B.A.s in Linguistics and French from the University of Southern California.

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Engaging Maths

Dr catherine attard, promoting creative and critical thinking in mathematics and numeracy.

• by cattard2017
• Posted on June 25, 2017

What is critical and creative thinking, and why is it so important in mathematics and numeracy education?

Numeracy is often defined as the ability to apply mathematics in the context of day to day life. However, the term ‘critical numeracy’ implies much more. One of the most basic reasons for learning mathematics is to be able to apply mathematical skills and knowledge to solve both simple and complex problems, and, more than just allowing us to navigate our lives through a mathematical lens, being numerate allows us to make our world a better place.

The mathematics curriculum in Australia provides teachers with the perfect opportunity to teach mathematics through critical and creative thinking. In fact, it’s mandated. Consider the core processes of the curriculum. The Australian Curriculum (ACARA, 2017), requires teachers to address four proficiencies : Problem Solving, Reasoning, Fluency, and Understanding. Problem solving and reasoning require critical and creative thinking (). This requirement is emphasised more heavily in New South wales, through the graphical representation of the mathematics syllabus content , which strategically places Working Mathematically (the proficiencies in NSW) and problem solving, at its core. Alongside the mathematics curriculum, we also have the General Capabilities , one of which is Critical and Creative Thinking – there’s no excuse!

Critical and creative thinking need to be embedded in every mathematics lesson . Why? When we embed critical and creative thinking, we transform learning from disjointed, memorisation of facts, to sense-making mathematics. Learning becomes more meaningful and purposeful for students.

How and when do we embed critical and creative thinking?

There are many tools and many methods of promoting thinking. Using a range of problem solving activities is a good place to start, but you might want to also use some shorter activities and some extended activities. Open-ended tasks are easy to implement, allow all learners the opportunity to achieve success, and allow for critical thinking and creativity. Tools such as Bloom’s Taxonomy and Thinkers Keys  are also very worthwhile tasks. For good mathematical problems go to the nrich website . For more extended mathematical investigations and a wonderful array of rich tasks, my favourite resource is Maths300   (this is subscription based, but well worth the money). All of the above activities can be used in class and/or for homework, as lesson starters or within the body of a lesson.

Will critical and creative thinking take time away from teaching basic concepts?

No, we need to teach mathematics in a way that has meaning and relevance, rather than through isolated topics. Therefore, teaching through problem-solving rather than for problem-solving. A classroom that promotes and critical and creative thinking provides opportunities for:

• higher-level thinking within authentic and meaningful contexts;
• complex problem solving;
• open-ended responses; and
• substantive dialogue and interaction.

Who should be engaging in critical and creative thinking?

Is it just for students? No! There are lots of reasons that teachers should be engaged with critical and creative thinking. First, it’s important that we model this type of thinking for our students. Often students see mathematics as black or white, right or wrong. They need to learn to question, to be critical, and to be creative. They need to feel they have permission to engage in exploration and investigation. They need to move from consumers to producers of mathematics.

Secondly, teachers need to think critically and creatively about their practice as teachers of mathematics. We need to be reflective practitioners who constantly evaluate our work, questioning curriculum and practice, including assessment, student grouping, the use of technology, and our beliefs of how children best learn mathematics.

Critical and creative thinking is something we cannot ignore if we want our students to be prepared for a workforce and world that is constantly changing. Not only does it equip then for the future, it promotes higher levels of student engagement, and makes mathematics more relevant and meaningful.

How will you and your students engage in critical and creative thinking?

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Number and algebra

• The Number System and Place Value
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• Fractions, Decimals, Percentages, Ratio and Proportion
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Geometry and measure

• Angles, Polygons, and Geometrical Proof
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Probability and statistics

• Handling, Processing and Representing Data
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Working mathematically

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For younger learners

• Early Years Foundation Stage

Advanced mathematics

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Published 2018

The Problem-solving Classroom

• Visualising
• Working backwards
• Reasoning logically
• Conjecturing
• Working systematically
• Looking for patterns
• Trial and improvement.

• stage of the lesson 
• level of thinking
• mathematical skill.
• The length of student response increases (300-700%)
• More responses are supported by logical argument.
• An increased number of speculative responses.
• The number of questions asked by students increases.
• Student - student exchanges increase (volleyball).
• Failures to respond decrease.
• 'Disciplinary moves' decrease.
• The variety of students participating increases.  As does the number of unsolicited, but appropriate contributions.
• Student confidence increases.
• conceptual understanding
• procedural fluency
• strategic competence
• adaptive reasoning
• productive disposition

• Aug 18, 2023

Making Math Fun in Kindergarten: Engaging Activities for Numeracy Development

Mathematics lays the foundation for logical thinking, problem-solving, and critical reasoning. It is crucial to foster a positive attitude towards math from an early age. By making math fun and engaging, we can ignite a love for numbers and build strong numeracy skills in kindergarten. In this blog post, we will explore a variety of creative and hands-on activities that will make math enjoyable for young learners while promoting their numeracy development.

Math Games and Puzzles:

Introduce math games and puzzles that incorporate counting, number recognition, and basic operations. Use manipulatives such as counters, dice, or number cards to make the activities interactive. Games like "Count and Seek," "Number Bingo," or "Shape Matching" not only reinforce mathematical concepts but also promote critical thinking and problem-solving skills.

Math Manipulatives:

Provide a range of math manipulatives such as blocks, pattern blocks, cubes, and linking chains. These hands-on materials allow kindergartners to explore mathematical concepts through tactile experiences. Children can use them to create patterns, build shapes, sort objects, or practice counting, developing a deeper understanding of mathematical concepts.

Math Storybooks:

Incorporate math-themed storybooks into your classroom library. Books like "The Doorbell Rang" by Pat Hutchins or "Ten Black Dots" by Donald Crews introduce mathematical concepts in an engaging narrative format. Read these stories aloud, and afterward, engage children in discussions and activities related to the math concepts presented in the book.

Math Centers:

Set up math centers with various activities that focus on different math skills. These centers can include pattern-making stations, measurement exploration, shape recognition puzzles, or number sense activities. Rotate the activities regularly to maintain children's interest and provide opportunities for independent exploration and discovery.

Math Songs and Rhymes:

Introduce catchy math songs and rhymes that reinforce math concepts and number sense. Songs like "Five Little Ducks," "Five Green and Speckled Frogs," or "Ten in the Bed" help children practice counting, subtraction, and number recognition. Singing and moving to math-related songs make learning memorable and enjoyable.

Real-Life Math Experiences:

Connect math to real-life experiences by engaging children in practical math activities. Involve them in measuring ingredients for cooking or baking, sorting and classifying objects in the classroom, or creating graphs based on favorite classroom activities. These experiences help children understand the relevance of math in everyday life and develop problem-solving skills in context.

Math Outdoor Exploration:

Take math learning outdoors by incorporating math activities into nature walks or playground time. Encourage children to count natural objects, observe shapes in the environment, or measure distances using non-standard units like footsteps. Outdoor exploration stimulates curiosity, critical thinking, and the application of math skills in a real-world setting.

Mathematics can be a joyful and exciting subject for kindergartners when approached with creativity and enthusiasm. By incorporating math games, manipulatives, storybooks, journals, centers, songs, real-life experiences, and outdoor exploration, educators can make math fun and engaging while promoting numeracy development. Remember to provide a supportive and encouraging environment that celebrates children's efforts and fosters a positive attitude towards math. Let us inspire a lifelong love for mathematics in our young learners, setting them on a path of mathematical success and enjoyment.

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• Shell Centre/
• National Numeracy Day - 22nd May 2024/

Numeracy Through Problem Solving

Numeracy Through Problem Solving is a sequence of five modules which develop students' ability to use mathematics together with other skills. In tackling problems of concern or situations of interest in everyday life - the original definition of numeracy, which was reinforced by the Cockcroft Report. The five modules have all been designed for pupils of all abilities to complement the GCSE Mathematics curriculum for 16 year olds in England and Wales. Each module is designed to take between 10 and 20 hours to complete. Each provides a theme within which the students take responsibility for planning, organising or designing. They are based around the everyday interests of most students. Students work both individually and in groups and are able to choose which areas of mathematics to deploy. They also implement the results of their own decisions - a vital educational experience! It has been developed with students of all abilities in the age range 13-16, and their teachers. Each module package provides comprehensive materials for both teaching and assessment, related to a practical context which has proved interesting and enjoyable to the students who have taken part in its development. It is accessible to those who normally find mathematics difficult, while at the same time it provides a challenge for the most able.

• Mathematics
• Activity sheet
• Include Physical Resources

Design a Board Game

In this Shell Centre module, groups carefully design and produce their own board games. These games are then played and evaluated by other class members.

This involves developing ideas from 2-dimensional shape-and-...

Be a Shrewd Chooser

In this Shell Centre activity, students research and provide expert consumer advice for clients in their class.

Students listen to a radio show on audiotape which contains a number of interviews with people who have...

Plan a Trip

In this Shell Centre module students plan and undertake a class trip using costings, scheduling, surveys and everyday arithmetic.

In a card game simulation, groups undertake and record imaginary trips, encounter problems and errors of judgement, then seek to correct them by better planning. Groups share...

Be a Paper Engineer

In this Shell Centre activity students design make and evaluate 3D paper products including gift boxes and pop-up greetings cards. They explore 3D shape-and-space, making generalisations using words and algebra.

In groups, students make a wide variety of pop-up cards, gift boxes and envelopes in order to...

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Problem-Solving Skills, Memory Power, and Early Childhood Mathematics: Understanding the Significance of the Early Childhood Mathematics in an Individual’s Life

• Published: 09 January 2024

Cite this article

• Wensheng Chen 1  

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Early childhood mathematics is the process of teaching mathematics and learning mathematics in a playful manner to the interests and questions of children. Early childhood mathematics includes counting and the application of counting, which includes mathematical activities such as sorting, matching, and pattern recognition. Deeper understanding of basic math concepts that include number sense, shapes and spatial awareness, measurement, patterns, and basic operations such as addition and subtraction. This study aims to investigate the relationship between children’s mathematical knowledge and skills developed in early stages and their later achievements in mathematics. Research data were collected from 53 children’s parents and 36 experts through telephonic interview questionnaire methods. The data collected was analyzed using SPSS software. The validity and reliability of the variables in the questionnaire have been tested. The results of this study reveal a significant positive correlation between children’s early mathematical knowledge and skills and later achievement in mathematics. Specifically, children who demonstrated higher levels of mathematical competencies during their early years exhibited greater success in later academic performance in mathematics. Additionally, the study identified several factors that influence this relationship, including parental involvement, socioeconomic status, and quality of early mathematics instruction. The novelty of this study is highlighting the importance of early math development; it leads to an understanding of educational practices that improve children’s math learning and promote future success in math. Based on the study findings, it is suggested that educators and policymakers emphasize the importance of early mathematical education and provide targeted interventions and support to enhance children’s mathematical knowledge and skills during their formative years.

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Chen, W. Problem-Solving Skills, Memory Power, and Early Childhood Mathematics: Understanding the Significance of the Early Childhood Mathematics in an Individual’s Life. J Knowl Econ (2024). https://doi.org/10.1007/s13132-023-01557-6

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Journal of Applied Research in Higher Education

ISSN : 2050-7003

Article publication date: 21 January 2019

Issue publication date: 18 June 2019

The purpose of this paper is to present an educational approach to elevating problem-solving and numeracy competencies of business undergraduates to meet workplace demand. The approach is grounded in the theory of constraints following the Decoding the Discipline model. The authors investigated a cognitive bottleneck involving problem modeling and an affective bottleneck concerning low self-efficacy of numeracy and designed specific interventions to address both bottlenecks simultaneously. The authors implemented the proposed approach in an introductory level analytics course in business operations.

Design/methodology/approach

The authors use an empirical study to evaluate the effectiveness of the proposed approach in addressing deficiency in numeracy and problem-solving skills. Cognitive and affective learning interventions were introduced in an undergraduate core course in analytics. The perceived effectiveness of the interventions was evaluated with the use of a survey at the end of the course. To further investigate the effectiveness of the proposed interventions beyond self-reporting, the impact of the interventions on actual learning was evaluated by comparing the exam scores between classes with and without the interventions.

Students who underwent the interventions successfully overcame both learning bottlenecks and indicated a positive change in attitude toward the analytics discipline as well as achieved higher exam scores in the analytics course.

Research limitations/implications

This study succeeds in strengthening the body of research in teaching and learning. The authors also offer a holistic treatment of cognitive and affective learning bottlenecks, and provide empirical evidence to support the effectiveness of the proposed approach in elevating numeracy and problem-solving competencies of business undergraduates.

Practical implications

The proposed approach is useful for business educators to improve business students’ quantitative modeling skill and attitude. Researchers can also extend the approach to other courses and settings to build up the body of research in learning and skill development. Educational policy makers may consider promoting promising approaches to improve students’ quantitative skill development. They can also set a high standard for higher education institutions to assess students’ numeracy and problem-solving competencies. Employers will find college graduates bring to their initial positions the high levels of numeracy and problem-solving skills demanded for knowledge work to sustain business growth and innovation.

Social implications

As students’ numeracy and problem-solving skills are raised, they will develop an aptitude for quantitative-oriented coursework that equips them with the set of quantitative information-processing skills needed to succeed in the twenty-first century society and global economy.

Originality/value

The proposed approach provides a goal-oriented three-step process to improve learning by overcoming learning bottlenecks as constraints of a learning process. The integral focus on identifying learning bottlenecks, creating learning interventions and assessing learning outcomes in the proposed approach is instrumental in introducing manageable interventions to address challenges in student learning thereby elevating students’ numeracy and problem-solving competencies.

• Problem solving
• Theory of constraints
• Decoding the Discipline
• Learning bottleneck
• Workplace skills
• Analytics education

Lee-Post, A. (2019), "Developing numeracy and problem-solving skills by overcoming learning bottlenecks", Journal of Applied Research in Higher Education , Vol. 11 No. 3, pp. 398-414. https://doi.org/10.1108/JARHE-03-2018-0049

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3 Simple Strategies to Improve Students’ Problem-Solving Skills

These strategies are designed to make sure students have a good understanding of problems before attempting to solve them.

Research provides a striking revelation about problem solvers. The best problem solvers approach problems much differently than novices. For instance, one meta-study showed that when experts evaluate graphs , they tend to spend less time on tasks and answer choices and more time on evaluating the axes’ labels and the relationships of variables within the graphs. In other words, they spend more time up front making sense of the data before moving to addressing the task.

While slower in solving problems, experts use this additional up-front time to more efficiently and effectively solve the problem. In one study, researchers found that experts were much better at “information extraction” or pulling the information they needed to solve the problem later in the problem than novices. This was due to the fact that they started a problem-solving process by evaluating specific assumptions within problems, asking predictive questions, and then comparing and contrasting their predictions with results. For example, expert problem solvers look at the problem context and ask a number of questions:

• What do we know about the context of the problem?
• What assumptions are underlying the problem? What’s the story here?
• What qualitative and quantitative information is pertinent?
• What might the problem context be telling us? What questions arise from the information we are reading or reviewing?
• What are important trends and patterns?

As such, expert problem solvers don’t jump to the presented problem or rush to solutions. They invest the time necessary to make sense of the problem.

Now, think about your own students: Do they immediately jump to the question, or do they take time to understand the problem context? Do they identify the relevant variables, look for patterns, and then focus on the specific tasks?

If your students are struggling to develop the habit of sense-making in a problem- solving context, this is a perfect time to incorporate a few short and sharp strategies to support them.

3 Ways to Improve Student Problem-Solving

1. Slow reveal graphs: The brilliant strategy crafted by K–8 math specialist Jenna Laib and her colleagues provides teachers with an opportunity to gradually display complex graphical information and build students’ questioning, sense-making, and evaluating predictions.

For instance, in one third-grade class, students are given a bar graph without any labels or identifying information except for bars emerging from a horizontal line on the bottom of the slide. Over time, students learn about the categories on the x -axis (types of animals) and the quantities specified on the y -axis (number of baby teeth).

The graphs and the topics range in complexity from studying the standard deviation of temperatures in Antarctica to the use of scatterplots to compare working hours across OECD (Organization for Economic Cooperation and Development) countries. The website offers a number of graphs on Google Slides and suggests questions that teachers may ask students. Furthermore, this site allows teachers to search by type of graph (e.g., scatterplot) or topic (e.g., social justice).

2. Three reads: The three-reads strategy tasks students with evaluating a word problem in three different ways . First, students encounter a problem without having access to the question—for instance, “There are 20 kangaroos on the grassland. Three hop away.” Students are expected to discuss the context of the problem without emphasizing the quantities. For instance, a student may say, “We know that there are a total amount of kangaroos, and the total shrinks because some kangaroos hop away.”

Next, students discuss the important quantities and what questions may be generated. Finally, students receive and address the actual problem. Here they can both evaluate how close their predicted questions were from the actual questions and solve the actual problem.

To get started, consider using the numberless word problems on educator Brian Bushart’s site . For those teaching high school, consider using your own textbook word problems for this activity. Simply create three slides to present to students that include context (e.g., on the first slide state, “A salesman sold twice as much pears in the afternoon as in the morning”). The second slide would include quantities (e.g., “He sold 360 kilograms of pears”), and the third slide would include the actual question (e.g., “How many kilograms did he sell in the morning and how many in the afternoon?”). One additional suggestion for teams to consider is to have students solve the questions they generated before revealing the actual question.

3. Three-Act Tasks: Originally created by Dan Meyer, three-act tasks follow the three acts of a story . The first act is typically called the “setup,” followed by the “confrontation” and then the “resolution.”

This storyline process can be used in mathematics in which students encounter a contextual problem (e.g., a pool is being filled with soda). Here students work to identify the important aspects of the problem. During the second act, students build knowledge and skill to solve the problem (e.g., they learn how to calculate the volume of particular spaces). Finally, students solve the problem and evaluate their answers (e.g., how close were their calculations to the actual specifications of the pool and the amount of liquid that filled it).

Often, teachers add a fourth act (i.e., “the sequel”), in which students encounter a similar problem but in a different context (e.g., they have to estimate the volume of a lava lamp). There are also a number of elementary examples that have been developed by math teachers including GFletchy , which offers pre-kindergarten to middle school activities including counting squares , peas in a pod , and shark bait .

Students need to learn how to slow down and think through a problem context. The aforementioned strategies are quick ways teachers can begin to support students in developing the habits needed to effectively and efficiently tackle complex problem-solving.

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Promoting Problem-solving Skills in Young Children

Roselia Ramirez : I'd like to welcome you to the Home Visiting webinar series. We are happy that you have joined us today. The topic for our session is focused on problem-solving and how home visitors can partner with parents to really support its development. Before we get started, we want to tell you a little bit about us and want to have you meet your hosts for today's session.

My name is Roselia Ramirez and I am a senior training and technical assistance specialist at the National Center on Early Childhood Development Teaching and Learning, or DTL for short. I'm happy to be joining you from my home state of Arizona, and I'm going to turn it over to my colleagues and have them introduce themselves. Hey Joyce.

Joyce Escorcia: I am Joyce Escorcia, and thanks everyone for choosing to spend your hour with us. I work alongside Roselia and Sarah at DTL as a senior T and T specialist. You may have seen me in the Coaching Corner webinars and some other places and spaces. Thanks for joining us. We're excited to dig into our topic today. Sarah, do you want to introduce yourself, and share a little bit about yourself?

Sarah Basler: I'm excited to join you all today; you might recognize me as one of the presenters of the Coaching Corner webinar series and my role and work tends to be around coaching and specifically using PBC to support practitioners and even supporting coaches in their PBC practice. I also have a background in pyramid model practices. I'm excited to be here today and talk with you all about problem-solving, which is one of my passions. Thanks so much for having me today.

Roselia: Thanks for joining us, Sarah. It's exciting to see you and to have you as our guest for today on this often-challenging topic for many home visitors as well as parents. Thank you again, and it's so nice to see you. We do probably have some new viewers joining us today. We were wondering if you could start by giving an overview of the Practice-Based Coaching model and then share with our viewers some of the benefits of coaching for a home visitor.

Sarah: Sure. A quick little recap for some of you, and an introduction for others, Practice-Based Coaching or PBC as we call it for short, is a coaching model that when used with fidelity can lead to positive outcomes for children and their families. PBC can be used with anyone, so you can, a coach can support teachers or support home visitors, family childcare providers, or even other coaches. We refer to those that are receiving the coaching as a coachee, to support them to use a set of effective practices. PBC is a content-ready model, which means that any set of practices can be the focus for the middle of the cycle, visual, and so whatever set of practices that you might want to be the focus of coaching can go in the middle there.

The coach and the coachee together identify some strengths and needs related to those effective practices that have been selected for coaching and together they write a goal and an action plan to support that coachee in their implementation of those goals. The coach and the coachee engage in focused observation. The coach will come in and observe the coachee using those effective practices selected in their action plan. Then they meet and reflect about what happened during the focused observation, and the coach will give some feedback, some supportive, and some constructive feedback.

All of these components of PBC fit within a collaborative partnership. PBC occurs in that context, and it's really about a coach and a coachee coming together to work together and support the implementation of those effective practices. When we think about what those benefits might be for a home visitor, a home visitor could share with their coach, challenges that they might be facing related to working with families and together, a coach and the home visitor could talk through maybe some possible solutions or strategies that the home visitor may want to try with the family or support the home visitor in learning a little bit more about a certain set of effective practices.

Sometimes it's really nice to have that support and a colleague to ask your questions and get some ideas. A coach can support a home visitor to grow their home visiting practices. A coach could support them not only around maybe effective practices to try with the, to support the family to use, but could support the home visitor in growing their home visiting practices themselves. Thinking about how to enhance those skills.

Roselia: Thanks, Sarah, I really like the whole notion. The first thing that kind of comes to my mind is this whole idea of having a thought partner. But before we go any further into this topic, and this discussion, if you're just joining the session, we would like to remind you to visit that teal color widget that's at the bottom of your screen. Here's where you can gain access to this participant's guide that you're seeing a little screenshot on your screen now. This resource is intended to be interactive and you're going to hear us reference it and then direct you there during the session for some opportunities for engagement as well as some reflection.

I also want to point out that on the first page of the participant's guide, you're going to find some icons and images that we have been using in our home webinar series, such as the focus on equity segment and this is represented by that little magnifying glass image. I also wanted to mention that not every one of our Home Visiting webinars will have each of the segments in each of the webinars, but just to give you an idea of what those are when you do see them. The other thing we want to do before we go any further is we want to review the learning objectives that we have established for this session.

We have identified and framed the session around two learning goals. First, by the end of the session, we anticipate that you'll be able to describe some essential components of problem-solving, and then second, that you will have some practical strategies and resources that are intended to not only strengthen but nurture problem-solving within that home environment. Now in your participant's guide, we have provided a space for you to reflect and to think about your own learning goals and what you would like to walk away with from this session. Think about that for a moment. What's something that maybe a question that you might have or a type of reflection, something that you would like to walk away with. Take a moment and then jot down your thoughts in your participant's guide.

Joyce: To frame the space that we're in today for our Home Visiting webinar series this year, we've been focusing in on topics that have an impact on social and emotional development. As many of you know, social-emotional development is one of the domains in the Head Start Early Learning and Outcomes Framework, or the ELOF . You can see we have it highlighted here on the slide. When we began the series this year in October, we focused in on the home environment, and then in December, we focused in on relationships. In our last webinar, we really focused in on emotional literacy.

If you missed these webinars, don't worry, you can catch it on Push Play, and you'll have information about that towards the end of our webinar today. For our time today, we're really excited; again, I'm super excited to have my cohost from the Coaching Corner webinar series. I'm excited to be here with Sarah to focus on problem-solving and the practical strategies that we're going to be talking about today. We're really going to be looking at how a home visitor can support and partner with families kind of introduce and nurture that skill within young children. That's really where we're going to be at today.

Again, we wanted to make that connection with the Pyramid Model. While we're not going to go deep into the pyramid, we do want to just make that connection today that the Pyramid Model is a framework of evidence-based practices for promoting young children's social-emotional development. The Pyramid Model builds upon a tiered public health approach by providing universal support to, universal supports for [inaudible]. Animations are going a little wonky on me today. Universal support to all children to promote wellness and then targeted services to those who need more support and then also intensive services for those that need them.

In this webinar, we're going to be focusing in on problem-solving, which is that tier two targeted kind of social-emotional support piece, which we know are essential and important to healthy social development. That's where we're going to be focusing in on today, with, we're thinking about the pyramid. If you want to know more about the pyramid, check out the National Center for Pyramid Model Innovations, or NCPMI . We have links to that within the resource, within your viewer's guide for today. Be sure and check that out as well. We are again super fortunate to have Sarah with us today. We just really want to draw on all of her experience that she's had out in the field and really sharing some of her insight on problem-solving. Sarah, I'm going to pass it over to you.

Sarah: Social competencies like self-regulation, empathy, perspective taking, and problem-solving skills are really foundational to that healthy social-emotional development, and this includes positive interactions like friendship and relationship skills between peers and siblings. Young children really need that support of adults in their lives to help them learn these skills so that they can develop healthy relationships among peers and find ways to really work through social conflicts. As home visitors, you can support this process by really supporting teaching and modeling with families how to help their children develop these skills earlier on.

It can start as young as infants and toddlers. Home visitors can support building these foundational problem-solving and relationship skills that most children can access with adult support and start to use independently as they start to, as they continue to develop these skills. Children, as they become more independent, they'll tend to run into situations in their environment that can lead to frustration or even some challenging behavior.

If parents are intentional and teach children these skills early on in their development, they can become pretty fluent in problem-solving. Then as they learn these skills, they can become more independent and successful with these skills. Their self-esteem will then, in turn, increase, and they will be likely to be able to cope with certain levels of frustration as a result and engage hopefully in less challenging behavior. When they feel confident in these social interactions and are able to problem solve successfully, then we're going to likely see less challenging behavior.

Roselia: Sarah, this is a good place to note that as you get to know your families, you may also discover that there might be some children who struggle, and they don't readily learn these skills through those foundational teaching strategies such as modeling or co-regulation. This might include children with disabilities or suspected delays. Establishing that strong relationship with the parent becomes even more important to get more familiar with and to be aware of the struggles so that you as a home visitor can then explore and use some of those more individualized practices to work on these skills when children need that extra support. We're going to talk some more about that throughout this webinar, but we just thought that would be really important to point that out.

Let's talk a bit more about why problem-solving is important in child development. We know that the earlier that children begin solving those problems, the more ready they are to deal with bigger challenges as they mature. We know that the home is a safe, it's a controlled environment, where parents can direct children as they develop and practice those problem-solving skills. By viewing problems as opportunities to grow, children begin to broaden their understanding while building that confidence that you were talking about.

We also know that when children feel overwhelmed or maybe hopeless, they often, they're not going to attempt to address a problem and that's where some of this challenging behavior for us adults may come up. When they have support, and then adults really support them with that clear formula and some steps for solving problems, they'll feel more confident in their ability to even give it a try. By introducing problem-solving skills at a young age, children learn to think in terms of manageable steps. Sarah, can you share with us how a home visitor might go about this process with families?

Sarah: There are some steps to problem-solving that home visitors can use and introduce to parents and there are some ways that you can support families to incorporate these steps as they encounter social conflict in the home or in socialization. The first is to support children in identifying the problem. This can be simply stating what the problem is out loud and it can make a big difference for children and that even includes infants and toddlers as well as preschool-age children who are feeling stuck. Parents can really think about how to do this in an age-appropriate way to support their child to state what the problem that they're encountering is, such as, your sister doesn't want to play with you, or I see you're having a hard time rolling over, or would you like a turn?

Once the problem has been identified, parents can help their child to think about what some solutions might be to solving their problems. Parents can help to brainstorm possible ways that they might solve that problem. As a home visitor, we can help parents understand that all solutions don't necessarily need to be a good idea, meaning that really just the idea of children coming up with these ideas or sharing some possible solutions. We want to support that process and allow children to share no matter how silly it may sound, and we can support them by offering suggestions to them. The goal is for parents to help their child explore options and the key is to help them do this with creativity and support them to find many different potential solutions because we know that there's not one right way to solve a problem and we want to support children to be able to think of multiple solutions.

Parents can even talk through and help their child identify what the pros and cons of each solution might be. Parents really play this critical role in helping their child identify potential positive and maybe negative consequences for each potential solution they've identified. Once the child has evaluated the possible pros and cons of each solution, the parent can encourage them to pick a solution and try it out and see what happens.

That's where even sometimes those silly solutions that they come up with, it's okay, let them try it out because if it doesn't work, you can support them to try out a different solution. And finally, the last step would be really analyzing or evaluating if it worked. Did this solution that you tried work? Was it, did it solve your problem? And if it doesn't work, you can always come up with a different solution and help them to brainstorm new ones.

Roselia: Thanks Sarah. I think that's a really great way to kind of break down that process and a great way for home visitors to support parents as they're kind of working through that. From your experience as a coach, and then just the various different learning settings that you had the opportunity to work in, why do you think problem-solving is so important?

Sarah: Problem-solving skills give children that independence that they really crave. It gives them agency in their own lives. Even though they may not be able to do this independently right away, when we give children the tools that they need to be able to do this successfully, they're able to navigate interactions with others and it helps to build social competence that they're going to carry with them for the rest of their lives. No matter what the learning environment is that you are in, social interactions are inevitable. They happen all the time. It's important that adults give children the tools that they need and support them to use those tools when they need them so that they become independent and confident in solving these problems when they arise.

Joyce: When Sarah was talking, I said I really love how you made that connection about the importance of parents supporting that, because I think it goes back to what we stated when we started. That about supporting children to become these confident, capable children really does kind of lead into being confident, capable adults who can kind of explore the world around them with all the skills that they need. I think that it just makes a case why this is so important. Because we know that solving problems really is about making choices. As young children develop their problem-solving skills, they build their confidence and we just know that you know, that having all of that, being able to solve problems, figuring things out, really makes them happier, more content, and just independent individuals. That's really what we want.We know when they tackle problems on their own or in a group, they become resilient and persistent. They learn how to look at challenges from a fresh perspective, and therefore, they're confident enough to take more calculated risks and problem-solving is so important in child development.

Again, because we know if we do it and we get it right when they're little, it really turns into this other thing when they become adults that they become confident and capable and are good with taking risk in all kinds of other different ways. Some of you may be wondering why you're here with us, wondering what skills do children need to be successful at problem solving? This is important, like I know it's important. What skills do they need in order to be able to do it well and in order for children to be successful at problem-solving and developing relationships there are a lot of prerequisite skills that are required and needed. 

We're going to talk a little bit about that, but we want to open up the Q and A for you guys to say okay, what skills do you think are important for children? What do you think that they might need in order to problem solve? We're going to ask you to pop that into the Q and A, right there, just click on the Q and A widget and put your responses there. We're going to share some of those out. While you guys are kind of thinking and popping ideas into the Q and A, we want to ask Sarah and bring her into the conversation of, Sarah, can you share with participants what some of those, what you think some of those prerequisites could be?

Sarah: For prerequisite skills, as you mentioned Joyce, problem-solving is really complex and it's going to require that a child be able to do many different things at the same time. When we think about children three and up, what they might need to be successful at problem-solving, then you really need to be able to initiate and respond to others. That could be a verbal or a nonverbal interaction or response, and it would vary, of course, based on the child's age or ability. This might look like if a child wants a toy that another child has, it could look like holding out their hand to ask or asking for a turn. A response might look like the other child saying no, I don't want to give you a turn, or pulling the item back to say, I don't want to give you the toy. Children really need to be able to initiate and respond to be successful at problem solving. 

Another thing that they need to be able to do is identify emotions in themselves and in others. The reason this is important is because have you ever tried to solve a problem when you're upset? It's really hard. You're not thinking clearly. It's just not going to work. Children need to be able to return themselves to that state of calm before they're able to come up with solutions to their problem, or even to recognize what their problem is. Another step is being able to calm themselves or having an adult support them to calm down. 

The next skill might seem obvious, but children really need to be able to identify what the problem is. That could look like a child identifying hey, I've got two apples but there are three siblings here. And what, my problem is I've got two apples, and we don't have enough. Once they've identified the problem, children really need to be able to then come up with possible solutions to solve their problem. That could be that child identifying hey, if I split this apple, we all have some. Or it might be, I don't like apples, so you can have mine. 

These skills that I just mentioned are really higher level for maybe preschool-age children, but a home visitor can also support families of infants and toddlers by setting the stage for problem solving. Making sure the environment really promotes interactions with others. Are there opportunities for that child or other children in the home to engage with one another? There usually are, even in routines that we don't think there are, you can build in possible opportunities. Pointing those out for the family, helping them think about what they might do or say and providing, helping support them to provide more opportunities throughout the day.

Another way that a family could support problem-solving in the environment is narrating or pointing out the intentions or what another child might be wanting or needing so that could sound like, “oh, I see Julia crawling towards you. It looks like she wants to play with your ball.” What this does is really builds awareness of the wants and needs and intentions of others. I think that's so important because often I know you've been around children, you know that sometimes it feels like a threat and when we can narrate what's going on, we can frame what's going on for the child so that then they approach it as in a different way. 

Of course, it's important to share that if a coach is working with a home visitor to support families to use these practices, a coach can help a home visitor identify what those prerequisite skills are that might need to be taught to the child first, the family or the child to be successful. It's important to note that a coach can be an extra set of eyes. And that, some of the things that I mentioned are coming in on the chat, I'm seeing, or in the Q and A, some people are saying kids need to be able to share, kids need to be able to ask for what they need, kids need to be able to identify the problem, and so it looks like you guys are right in line with what we were talking about. Really having friendship skills is important. Thank you so much for your responses.

Joyce: I feel like folks have a lot of ideas to share about what it takes to problem solve. And again, thank you for all your responses; keep them coming in. We just talked about, there are a lot of things needed for children to be successful at problem-solving and we still see a lot of the responses here we see coming in in the chat. We have Kate and Catrina that talk about regulating emotions. We have Tom that talked about think about possible solutions and then also as adults think about how can we help kind of set them up with possible solutions. Thank you for putting all of those things in there. As you can see, there's a list there added to the list that is coming in the Q and A. All of those things all in mind, problem-solving steps that we talked about and how a home visitor might support the development of this process.

Sarah, just to pop in with a quick question here, when you were talking and explaining the, when you were explaining kind of the why. Like why because it kind of helps to take away that threat aspect of it. As a coach we do that with our coachee or home visitor and do you think that there's some importance or connection then as a home visitor having that knowledge than to be able to have that parallel process of sharing that information with a print of like this is why it's important to narrate kind of that parallel top piece. Do you think that that could also be helpful for a home visitor?

Sarah: Yes, absolutely. I think as adult learners, and when you're working with parents, working with adult learners, it's really important for them to know the why. Why are you telling me to narrate? Pairing the narration is important because it helps children feel less threatened by the other child and you share the intentions. Then it helps make it more, gives the parents the why. Why would I do this? And then they know that the possible impact that using that practice might have. It's really a parallel process. What you would, your coach would use with you, you might also use some of those strategies with the families that you would work with.

Joyce: Yeah, thank you for sharing that. I said it was just when you said that, that light bulb went off, like wow, that's important information to kind of share on both sides, so thank you for that. 

Now we're going to just summarize some of those key ideas and practices for home visitors and how they can support some of those problem-solving skills. Again, a lot of things have been coming in through the Q and A. Number one is just to promote healthy relationships, that home visitors can support parents in how they engage with and offer opportunities for young children to work on relationship skills. Sharing and helping and cooperating and comforting and making suggestions about play, even celebrating each other, and creating developmentally appropriate opportunities for practicing those skills throughout the day. 

Home visitors can support parents in creating opportunities within the home as well as exploring options where children can practice turn-taking and sharing. Maybe through a socialization activity. Particularly when you're thinking about when there's just one child in the home, parents may have a concern about their child not having opportunities to engage with other children, so that could be a great time to just kind of pause and think about the value they place on peer relationships and how they might be able to provide some of those opportunities for their child. Thinking about some of those being intentional and some might be planning some outdoor activities, some field trips, some going to the park, visiting with their cousins or whatever that aspect. 

Just knowing that can also help with thinking about, like, 'Wow, every interaction could be a learning moment, an opportunity to kind of learn and grow these skills.' Thinking about teaching problem-solving steps that earlier we talked about - some steps that home visitors can work through with parents. When it comes to developing problem-solving skills, young children are learning to manage their emotions and behaviors through co-regulation. They're beginning to reason and understand simple consequences. Our role as a home visitor, we have that opportunity to work with parents and support the development of problem-solving.

Problem-solving development at this young age allows children to identify problems, brainstorm possible solutions, and then test those out, test out those appropriate solutions, and then analyze and think about, "Okay, so what kind of results did I get? Did I get what I wanted in the end?" Parents can support children to work through these steps and gain confidence in their ability to work through the problems that they encounter.

Another component would be teaching problem-solving in the moment. Problem-solving is hard work. It is hard work, but a 2-year-old solving problems is hard work for everyone involved sometimes. As home visitors, we have that unique opportunity of supporting this process. We want to build a parent's skill base and their confidence really to help their child use problem-solving steps in the moment. As home visitors can partner with parents to brainstorm ways they can anticipate those social conflicts before they happen. When a problem arises, the parent can anticipate or recognize problems before things can escalate and get out of hand and feel overwhelming or intervene as needed to work through those problem-solving steps that home visitors can support. 

How parents individualize strategies they use to provide support, all these skills, really based on the learning kind of style and needs of their child. We know that some children may need the amount of language used to be modified; some children may need visual cues or gestures kind of paired with verbal language; some children may need specific feedback about consequences to really help them learn about the effect of their behavior on the environment really based on the individual needs of that family and the children as well.

Roselia: Thanks for sharing all that, Joyce. That's a lot of great information, and as you were saying all these things that we're doing to support parents or children rather — I think someone mentioned this earlier — about even as adults, problem-solving is difficult for us sometimes. To imagine for children that don't have the words and they're struggling with all these different emotions and wanting to stake their independence, it can really be a tough process. 

As home visitors, we're in that unique position to really help support. Thanks for sharing all that. Throughout this webinar, we've really been discussing ways to foster problem-solving skills for all children. Today, in our focus on equity segment, we're going to use our equity lens to take a closer look and really lift up the value of equity in all learning environments as we work with diverse families in our communities.

As home visitors, it is safe to say that we are working with a diverse group of families, and we never want to make any assumptions. Let's reflect on this question: How can a home visitor be sure that they are being culturally responsive to a family's values related to relationships and problem-solving? Think about that because we know it's not a cookie-cutter approach and we know that there are cultures within cultures. It's important that we don't make any assumptions, and thinking about being culturally responsive, how can a home visitor ensure that that is happening?

We'd like for you to take some time and share some of your thoughts with us in the Q and A. While you're doing that, we do have a few suggestions that we would like for you to consider. First, we want to make sure that the skills that you're introducing are culturally relevant to the family that you're working with. It's important to really take the time and think back to the information that you've gathered as you've been developing a relationship with the family. You want to be sure that you're considering the values, beliefs, what's important to them, what's important that, the importance and the goals that they have for their children, and again, not making any assumptions and really asking these types of questions as you're moving through the process.

We also recommend that you take the time to gather input about social problems that the child may face at home or perhaps other settings that they're participating in. Then lastly, although we just mentioned this, we wanted to place an emphasis on the importance of gathering information about the family's values. As you're building those relationships, as you're observing the family, just really asking those questions, and not making assumptions from your perspective but from how the family states it. It's important to remember that problem-solving and how it is approached is not going to look the same for all families. Again, even if you have families that are from the same culture, what works for one family may not work for another. It's important for the suggestions and the strategies to be culturally responsive and respectful of a family's values. Sarah, folks are still entering their thoughts into the Q and A. Is there anything that you would like to add?

Sarah: Those suggestions you gave are great. Something that I think is important is you want to make sure that teaching problem-solving is relevant. You mentioned that, but we want to make sure that it's meeting the needs of the family, like what you're suggesting. Think about, when I think about it from a coach's perspective, this might be an opportunity to support the home visitor to come up with some ideas.

For example, if a home visitor asks the family what kind of social problems are popping up at home, or in their socialization settings with their child, it could be, “Oh, my child is taking toys, and they don't think sharing is important.” What you might do is offer different suggestions, but it might be tricky for a home visitor if they don't value sharing. What else could I offer? That could be where coming to your coach and trying to brainstorm and problem-solve or with your colleagues or your supervisor. 

If coaching isn't offered, to come up with some different ideas of what they might offer to that family, what they might suggest they teach their child instead. That could be asking for a turn or asking their sibling to give them a turn when they're finished, so there isn't just one right way to do things, and I think sometimes we forget that even as home visitors, our culture and what we value, we bring that into the environment and what we value isn't the only way. That's where getting the input and what the family values because ultimately, you're there to support them to support their child. Remembering that although your culture is relevant as well when you're there to support the family, you want to think about their values and really incorporate it that way.

Some of the responses that are coming in are pretty much in line with what we just talked about. It's looking very similar, getting input from the family, not making assumptions. I'm seeing finding out what they value, learning about their culture is something new that we didn't mention. Getting the parents' input can be really, really helpful. Thank you for those responses.

Joyce: Thank you, and Sarah, like you said, those responses just keep coming in and we encourage you just to keep sharing and keep thinking about, what we need to do to support families in a way that's culturally responsive. 

Now, we want to move into our next portion of our time together, and we want to turn our focus just a bit on looking at how home visitors can support families. We've been talking about this, and that's a great segue into this, so just want to explore that just a little bit more. We want to do that by highlighting the resource, and then you have the link to the resource in your viewer's guide for today.

One resource that was developed by the National Center on Quality Teaching and Learning is “Problem-solving in the Moment.” This is a 15-minute in-service suite developed for preschool classroom teachers to help children problem-solve as they arise or in the moment. We've included a link to those materials in the participant's guide.

The content here really talks about these five steps that support and guide children's behavior to encourage problem-solving in the moment. You'll see that the five steps are here: anticipate, be close, provide support, multiple solutions, and then celebrating the success. We're going to explore each of these steps and relate them to how home visitors can partner with parents to guide their child's behavior at home to problem-solve in the moment. Rosalia is going to help us dig into that a little bit more.

Roselia: Anticipate is the first and very important step of this process. As home visitors, we can really work with parents to try and stay one step ahead of problems by recognizing and being proactive. Home visitors can support parents in sensing some of those changes in a child's behavior, as well as their emotions, and then really starting to pay attention to some of those identifying triggers. Home visitors can also help parents be aware as well as to be ready to activate some of those problem-solving steps that we have been talking about.

Let's move on here and talk about the next step, which is to be close. We know that often parents can be very busy, and they're not always going to be physically close when a problem situation presents itself. What parents can do is to relocate themselves and be near the location when the problem is beginning to occur. That's where it becomes important to start to identify some of those triggers, some of the changes in behaviors that are starting to happen, and then start to relocate. 

We want to work with parents to recognize some signs that a problem is about to occur so that they can then move themselves closer to that situation at this stage, rather than when the problem is in full swing. We want parents to know that when they are close, it's an opportunity for them to be able to explore and to begin to provide some support for their child. As a home visitor, you can really support families in beginning to pay attention, starting to recognize, and when to offer some of that proactive or preemptive support and figuring out some of those patterns of the behavior.

Being close, time also provides for families an opportunity to model how to remain calm and then some of those gentle approaches to problem-solving so when the parents are close, they're better able to support and then talk through identifying the problem as well as some of those possible solutions that we've been talking about. They can also support their child in regulating their emotions before they get to that heightened level, and then it's going to be a lot harder for them to be able to calm down. Parents being close also provides that opportunity for them to be able to provide that comfort that might be needed before things just really become too escalated and get out of control. Joyce, tell us a little bit about what this support might look like.

Joyce: One of the things that home visitors can explore with their family when it comes to being close and providing support for their child is knowing what level of support to provide to really ensure there is a teachable moment taking place. Sometimes, that support means helping their child stay near and in proximity to where the problem happens so they can problem-solve effectively. Sometimes, that could mean prompting their child to walk through the problem-solving steps. 

It can also mean verbal prompting, like, “Do you remember what to do when baby sister doesn't want to take a turn?” or maybe the parent can involve an older sibling in it if they're available, saying, “Hey, let's ask brother what would you do?” Sometimes it's really when children don't have those verbal skills, support can mean to use like visual cues as well and to prompt, that prompts them perhaps, takes them into those problem-solving steps. It really depends; that level of support depends kind of on the specific needs of their child. Knowing it's okay to kind of try out different levels of support to figure out what's needed.

Now we want to talk about the next step, which is multiple solutions. Like we said, there's a whole bunch of different ways to be right about things, and so there can be situations in which one solution maybe a good solution but we know that it may not always work. As children become older, parents can support problem-solving skills by encouraging their child to generate multiple solutions. Maybe with younger children they're going to need parents to support to generate choices or solutions. 

This is going to allow children to begin to grow their own toolbox of solutions to draw from when they encounter problems. The solutions don't need to be complicated and can be as simple as maybe using a timer, waiting patiently, or maybe even flipping a coin. Home visitors can support parents by talking through and really helping parents to determine some solutions they can present and help their child when problem-solving, and when problems arise. Sarah, we just want to tag you in here and ask you, do you have any resources in your toolbox that may support families with identifying solutions at home?

Sarah: There's a great resource from the National Center on Pyramid Model Innovations, and it's called the “Solution Kit.” They have a home edition, and it includes some common solutions to everyday social problems and it comes in multiple languages, which is great. Visual supports can be super helpful for young children and this resource might be something that a home visitor can share with families. 

Another great resource for teaching problem-solving is this scripted story, we can be problem solvers at home. This scripted story can be used by the family to help children understand the steps for problem-solving and it includes some scenario cards that you can use with children to help them think about solutions to common social problems that they're going to face, either in the home or the community. Those are two of my favorite resources.

Roselia: I love those, Sarah. Those are actually some of my favorites as well and I really love that they're visual and that they really have been designed to help support in the home environment, because often we see that there is resources for center-based children, but I love that these are specifically designed for the home. We have included the information in your Participant's Guide Resource List, so we want to make sure that you take the time to explore those and think about ways that you can utilize those with families that you might be supporting. 

Continuing on and thinking about the five steps that we've been talking about, the last step that we want to talk about is just as important as anticipating a problem and that is celebrating success. Reinforcing a child's success in problem-solving really supports their development as effective problem solvers, and as home visitors, we want to be sure that you share this with parents. They can reinforce that celebrating success. It can be formal, or it can be informal. Some examples of that informal celebration might be things such as a high five, acknowledging that they did a really great job, you can give them a thumbs up, a wink, a verbal praise, or even just a hug. 

Just letting them know that you're really proud of how they worked through that particular problem. As home visitors, you can really brainstorm some different options and some of those informal gestures that are culturally appropriate and relevant for their family. Then you can also support them in coming up with some more formal ways to celebrate the success. The important thing here is that we want to make sure that parents are acknowledging when children are working through those problems and that they're becoming much more independent so that children feel accomplished and of course if you recognize it in that positive way, they're going to want to do it again. They're going to feel that appreciation. 

We're going to watch a video clip. In this video clip, you're going to notice that the setting is a preschool classroom and that there are two children that have encountered a problem. We want you to take note on how the teacher handles the situation to really engage the children in working through problem-solving. In your participant's guide, you have some space, and we want for you to take some notes and really pay attention to some of the strategies that the teacher is using. It is a classroom; however, think about how this scenario might play out, perhaps in a home between two siblings or even at a group socialization between two children. Let's take a look.

[Video begins]

Teacher 1: Janny, what's the problem? You're getting it to make the fort and it looks like Amy's holding it too. Thanks, Elena for moving so I could get up. So what are we going to do about it? You both want the same block? What are we going to do about it? How are we going to fix the problem? I'm going to hold the block for a minute while you guys help figure it out. What's your idea?

Child 1: [Inaudible] 

Teacher 1: You want to play with it over there. Shall we find out what Jammy's idea was? What was your idea, Janny?

Child 2: [Inaudible] 

Teacher 1:  Oh, and she thinks she needs it for that building. So, you both need this block for two different buildings. Do you want to look for an idea in the basket? Grab the book. See what you can come up with. There's another one over there, right. I think Amy's got the book. What are we going to do? She's looking, so let's play together, so that would be building the same building together. 

Take a break, so you just take a break from building. Wait until she's done. One more minute, so she would have it for a minute and then you would have it for a minute. You build with something else, maybe next time. Playing together. You would build it together. Do you want to build together, Janny? Look at Amy's talking to you. Sorry, I just said it and Amy was saying it. Sorry about that, Amy. Here. So Amy, you're going to help Janny build her tower.

Child 1: Let's do this one.

Teacher 1: Excellent. You guys are expert problem solvers.

[Video ends] 

Joyce: We see some of the strategies coming through in the Q and A, we'll ask you to keep putting those out there for us, and just want to check in with Rosalia and Sarah to say what did you guys notice anything there about some of those great problem-solving skills that we saw happening?

Sarah: My favorite part of that video is that she really supported those two children to solve their own problem. She gave them support by prompting them to find the materials to help them problem solve. She read through some of the problems with them, or solutions with them, but ultimately the teacher didn't solve the problem for them. And that was really great to see because I think sometimes as adults, we want to be the fixer and in this video the children were really the experts. They were the expert problem solvers here. I thought that was…

Roselia: I agree, Sarah. I really love that and just the anticipation from the teacher, but also having their little solution book that they can kind of, the visual to work through and see they had multiple choices to choose from. That was my favorite part.

Joyce: Yeah, definitely lots to see in that one. I like that one. I think watching the adult and also watching the kids and how they react to that. Sarah, we just want to give you some space as we're kind of wrapping up to hear a little bit more from your coaching experience and just maybe some more tips for supporting home visitors and partnering with families.

Sarah: Sure. It's really important to remember that parents are their children's' best teachers and most children already, most of what children know or what they know when you come into a relationship with that family, has been learned by their parents. As home visitors, when we partner with parents, we really want to set the stage to provide those intentional opportunities for learning within the home setting. 

These tips for child size problems that children can solve with the help of their parents or on their own. Here are some tips that you can share with families to set the stage for their child to become problem solvers. One would be to help the child to relax. When children are faced with a problem, they can become upset, frustrated, angry, they might get their feelings hurt or even cry. 

This is not the time to try to solve the problem. When the child becomes calm, we want to help them to work through their problem, but when they're at the height of these emotions, that's not the time. We want to regulate, use some calming strategies to get them to calm down. Then we can support them to problem solve. You can support families to understand that supporting children to calm down is a really important step of this process. 

We want to make sure that we're giving uninterrupted time. As home visitors you want to partner with parents to help them understand that developing problem-solving skills is complicated and it takes time. Giving them uninterrupted time that's not rushed to talk through and support them to thinking through problems. Also, we want parents to feel like they are a coach. When we're talking about being a coach, we're not talking about home visitors coaching parents but what we mean here is that children at a very young age are still developing these skills. 

We want you to work with parents on developing their ability to identify opportunities and support their children through asking questions and helping their children think and share through what maybe these problems and solutions might be. Active listening is a really important part of this process, as parents it can be hard sometimes, we want to throw out our ideas and suggestions but active listening for children is so important. 

Here are some strategies that a home visitor can share with families, and we want you to jot down some notes in your participant guide. Encourage parents to withhold from solving those problems for children, so support them to support children and not solve them for them. Support parents in developing questions that they might ask when problems arise. Help parents to identify when they are, their critical solutions to their child is proposing, so try not to judge the solution. Sometimes they may be silly; let them try it out. Provide that active listening. All those strategies, you can remember those that will support families.

Joyce: Definitely, and we've included all of these tips in a handout, and that's part of your participant's guide as well. You may think, "What's my role in supporting some of these practices?" Rosalia, if you want to give maybe one kind of tip to close us out, what do you think that one thing would be regarding the role of the home visitor?

Roselia: I think the important thing, and I think Sarah has kind of really touched on this throughout, is just really taking the time to listen to the family. Finding out what's important to them, and then just kind of being a facilitator if you will — just kind of really asking some of those haunting questions to get the parent to start thinking about some of those steps that we talked about, like anticipating that behavior, looking at problem-solving as an opportunity for learning, and just helping children to really put words to those emotions that sometimes even we as adults struggle with. 

I think really being that partner, that reflective partner with the parent, and then providing some of these strategies to help them work through that and again just really seeing it as an opportunity and not necessarily as a behavior that challenges us. Just kind of taking that time to explore with their child and just giving them the words for those emotions to kind of help them become more aware as they kind of go out into the world and face some of those social conflicts if you will. That would be my suggestion.

Joyce: I think that's a great one to leave us with today. Thank you, Sarah, so much for joining us. Thank you everyone here. If you have any questions or anything, drop them in the Q and A. Also, feel free to reach out to us, we have to keep this conversation going, and we will see you guys next time. Thank you.

How young children approach and solve problems is critical to their overall development. Problem-solving supports how young children understand the world around them. It can impact their ability to form relationships as well as the quality of those relationships. Supporting the development of problem-solving skills is not a one-size-fits-all approach. Explore strategies and resources home visitors can use to partner with parents to strengthen and nurture these skills and help children cope with challenges as they arise. 

Note: The evaluation, certificate, and engagement tools mentioned in the video were for the participants of the live webinar and are no longer available. For information about webinars that will be broadcast live soon, visit the Upcoming Events section.

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Resource Type: Video

National Centers: Early Childhood Development, Teaching and Learning

Age Group: Infants and Toddlers

Audience: Home Visitors

Series: Home Visiting Series

Last Updated: April 2, 2024

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IIT Guwahati, Samagra Shiksha Assam partner to host Mega Science, Maths Olympiad

The programme, under the auspices of the rashtriya avishkar abhiyan initiative, aimed at nurturing talent, fostering critical thinking, and cultivating problem-solving skills among students..

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With the aim of fostering scientific curiosity and mathematical proficiency among students in the state, Indian Institute of Technology Guwahati in collaboration with Samagra Shiksha Assam, organised a massive Science and Maths Olympiad, one of the largest in country. Over 1.14 lakh students from 3,828 schools across Assam participated in this mega-event, which aimed to nurture talent, promote critical thinking, and enhance problem-solving abilities among the students in STEM (Science, Technology, Engineering, and Mathematics) subjects. Through a series of rigorous competitions and engaging activities, the participants were encouraged to delve into the fascinating realms of STEM subjects, expanding their knowledge, creativity and understanding.

Speaking about successfully hosting the activities of Samagra Shiksha and the Olympiad, Professor Parameswar K. Iyer, Dean PRBR, IIT Guwahati, said, “IIT Guwahati has been working very closely with the education department of Assam in enhancing the STEM activities across the state and promoting it through lively activities such as Olympiads.”

Professor Rajeev Ahuja, Officiating Director, IIT Guwahati, in his congratulatory message to the winners of the Olympiads mentioned that, “IIT Guwahati is very happy to organise this Olympiad event and will do everything in its capacity to enhance the quality of STEM education in Assam and the northeast region and promote activities related to STEM education by engaging with all stakeholders of the education sector.”

• Cultivating a culture of scientific inquiry and mathematical reasoning among school students
• Identifying and nurturing talented individuals in the fields of STEM subjects
• Providing a competitive platform for students to demonstrate their skills and abilities
• Raising awareness about the significance of STEM (Science, Technology, Engineering, and Mathematics) education among students and educators
• Fostering innovation and critical thinking skills among students

The Olympiad comprised two phases: an OMR-based physical pen-paper test for secondary school students across Assam, designed to assess their understanding and application of scientific and mathematical concepts, followed by a state-level round. The district-level test was conducted on March 18, 2024.

The top 2 performers from each district were selected to participate in the final round of the Olympiad at IIT Guwahati. This round provided a platform for the finalists to interact with peers from across the state. Held on March 30, 2024, the final round saw 62 (with 32 female and 30 male) finalists from classes 9th and 10th competing, with 3 state winners emerging from the competition. These included:

·1 st Prize – Chandan Kaushik Saikia, Namdeuri HS, Jorhat

·2 nd Prize – Jnanarun Hazarika, Dhalasatra HS, Jorhat

MORE ACTIVITIES

• Mentoring schools across Assam
• Establishing Science and Maths Clubs in schools
• Setting up live labs in schools with hands-on experience
• Residential teacher’s training
• Curriculum enhancement
• School outreach activities and visits to IIT Guwahati campus
• Training for School Principals