a problem with problem solving teaching thinking without teaching knowledge

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ERIC EJ841561: A Problem with Problem Solving: Teaching Thinking without Teaching Knowledge

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The Mathematics Educator 2007, Vol. 17, No. 2, 7–14 A Problem With Problem Solving : Teaching Thinking Without Teaching Knowledge Jamin Carson

Problem solving theory and practice suggest that thinking is more important to solving problems than knowledge and that it is possible to teach thinking in situations where little or no knowledge of the problem is needed. Such an assumption has led problem solving advocates to champion content-less heuristics as the primary element of problem solving while relegating the knowledge base and the application of concepts or transfer to secondary status. In the following theoretical analysis, it will be argued that the knowledge base and transfer of knowledge—not the content-less heuristic —are the most essential elements of problem solving.

Problem solving theory and practice suggest that is to know the meaning of the term problem. This thinking is more important in solving problems than theoretical framework uses the definition of problem knowledge and that it is possible to teach thinking in presented by Stephen Krulik and Jesse Rudnick (1980) situations where little or no knowledge of the problem in Problem Solving: A Handbook for Teachers. A is needed. Such an assumption has led problem solving problem is “a situation, quantitative or otherwise, that advocates to champion content-less heuristics as the confronts an individual or group of individuals , that primary element of problem solving while relegating requires resolution, and for which the individual sees the knowledge base and the transfer or application of no apparent or obvious means or path to obtaining a conceptual knowledge to secondary status. Yet if one solution” (p. 3). analyzes the meaning of problem solving, the The Definition of Problem Solving knowledge base and the transfer of that knowledge are the most essential elements in solving problems. Krulik and Rudnick (1980) also define problem solving as Theoretical Framework the means by which an individual uses previously Problem solving is only one type of a larger acquired knowledge, skills, and understanding to category of thinking skills that teachers use to teach satisfy the demands of an unfamiliar situation. The students how to think. Other means of developing student must synthesize what he or she has learned, thinking skills are problem-based learning , critical and apply it to a new and different situation. (p. 4) thinking skills, creative thinking skills, decision This definition is similar to the definition of the making, conceptualizing, and information processing eighth element of problem solving, transfer: “[w]hen (Ellis, 2005). Although scholars and practitioners often learning in one situation facilitates learning or imply different meanings by each of these terms, most performance in another situation” (Ormrod, 1999, p. thinking skills programs share the same basic elements: 348). (1) the definition of a problem, (2) the definition of problem solving, (3) algorithms , (4) heuristics, (5) the Problem Solving is Not an Algorithm relationship between theory and practice, (6) teaching One of the primary elements of this framework is creativity , (7) a knowledge base, and (8) the transfer or that problem solving is not an algorithm. For example, the application of conceptual knowledge. Krulik and Rudnick (1980) say, The Definition of a Problem The existence of a problem implies that the The first element of the theory of problem solving individual is confronted by something he or she does not recognize, and to which he or she cannot merely apply a model. A problem will no longer be Dr. Jamin Carson is an assistant professor of curriculum and considered a problem once it can easily be solved instruction at East Carolina University. He teaches the theory and practice of instruction as well as classroom management and by algorithms that have been previously learned. discipline. His primary research interest is the epistemology of (p. 3) curriculum and instruction.

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Table 1 Types of Problem Solving

John Dewey (1933) George Polya (1988) Stephen Krulik and Jesse Rudnick (1980)

Confront Problem Understanding the Problem Read

Steps in Diagnose or Define Problem Devising a Plan Explore Problem Solving Inventory Several Solutions Carrying Out the Plan Select a Strategy

Conjecture Consequences of Looking Back Solve Solutions

Test Consequences Review and Extend

Additionally, advocates of problem solving imply one large long table. How many of these small that algorithms are inferior models of thinking because tables are needed to seat all 24 people? (Krulik & they do not require thought on a high level, nor do they Rudnick, 1987, pp. 29–31) require deep understanding of the concept or problem. The first step, Read, is when one identifies the Algorithms only require memory and routine problem. The problem solver does this by noting key application. Further, they are not useful for solving words, asking oneself what is being asked in the new problems (Krulik & Rudnick, 1980). problem, or restating the problem in language that he Problem Solving is a Heuristic or she can understand more easily. The key words of Advocates of problem solving argue that educators the problem are small square tables, twelve couples, need to teach a method of thought that does not pertain one large table, and 24 people. to specific or pre-solved problems or to any specific The second step, Explore, is when one looks for content or knowledge. A heuristic is this kind of patterns or attempts to determine the concept or method. It is a process or a set of guidelines that a principle at play within the problem. This is essentially person applies to various situations. Heuristics do not a higher form of step one in which the student guarantee success as an algorithm does (Krulik & identifies what the problem is and represents it in a Rudnick, 1980; Ormrod, 1999), but what is lost in way that is easier to understand. In this step, however, effectiveness is gained in utility. the student is really asking, “What is this problem Three examples of a problem solving heuristic are like?” He or she is connecting the new problem to prior presented in Table 1. The first belongs to John Dewey , knowledge. The student might draw a picture of what who explicated a method of problem solving in How the situation would look like for one table, two tables, We Think (1933). The second is George Polya’s, whose three tables, and so on. After drawing the tables, the method is mostly associated with problem solving in student would note patterns in a chart. (See below.) mathematics. The last is a more contemporary version The third step, Select a Strategy, is where one developed by Krulik and Rudnick, in which they draws a conclusion or makes a hypothesis about how to explicate what should occur in each stage of problem solve the problem based on the what he or she found in solving. I will explain the last one because it is the steps one and two. One experiments , looks for a more recently developed. However, the three are simpler problem, and then conjectures, guesses, forms fundamentally the same. a tentative hypothesis, and assumes a solution. The following is an example of how the heuristic is The fourth step is Solve the Problem. Once the applied to a problem. method has been selected the student applies it to the problem. In this instance, one could simply continue Problem: Twelve couples have been invited to a the chart in step three until one reached 24 guests. party. The couples will be seated at a series of small square tables, placed end to end so as to form

8 Problem Solving

Step 2: Explore. The final step, Review and Extend, is where the student verifies his or her answer and looks for Draw a diagram to represent the problem. variations in the method of solving the problem; e.g., n " 2 t = , where represents the number of tables. Or we 2 could ask for a formula to determine how many guests we can seat given the number of tables. For example, n = 2t + 2 or n = 2(t + 1). ! Problem Solving Connects Theory and Practice A perennial charge brought against education is that it fails to prepare students for the real world. It teaches theory but not practice. Problem solving connects theory and practice. In a sense this element is the same as the definitions of problem solving and transfer, only it specifically relates to applying abstract Make a chart, record the data, and look for patterns. school knowledge to concrete real world experiences (Krulik & Rudnick, 1980). Number of 1 2 3 4 . . . Problem Solving Teaches Creativity tables Real world situations require creativity. However, Number of it has often been claimed that traditional classrooms or 4 6 8 10 . . . guests teaching approaches do not focus on developing the creative faculty of students. Advocates of problem Pattern : As we add a table, the number of guests that solving, by contrast, claim that problem solving can be seated increases by 2. develops the students’ creative capacities (Frederiksen, 1984; Slavin, 1997). Successful Problem Solvers Have a Complete and Step 3: Select a Strategy. Organized Knowledge Base

A knowledge base consists of all of the specific Number of knowledge a student has that he or she can use to solve 1 2 3 4 5 6 7 tables a given problem. For example, in order to solve algebraic problems, one not only needs to know Number of 4 6 8 10 12 14 16 information about numbers and how to add, subtract, guests multiply, and divide, but one must also possess the knowledge that goes beyond basic arithmetic. A Form a tentative hypothesis. Since the pattern seems to knowledge base is what must accompany the teaching be holding true for 16 guests, we can continue to add 1 of a heuristic for successful problem solving to occur. table for every additional guest until we reach 24. Therefore, we add 4 additional tables for the additional Problem Solving Teaches Transfer or How to Apply guests (16 + 8 = 24). Hypothesis: It will take 11 tables Conceptual Knowledge to accommodate 24 guests. Transfer, or the application of conceptual knowledge, is the connecting of two or more real-life Step 4: Solve the Problem problems or situations together because they share the same concept or principle. Transfer or the application Number of conceptual knowledge helps students see similarities of 1 2 3 4 5 6 7 8 9 10 11 and patterns among seemingly different problems that tables are in fact the same, or similar, on the conceptual level. Some research about problem solving claim that it Number is more effective than traditional instruction (Lunyk- of 4 6 8 10 12 14 16 18 20 22 24 Child, et al., 2001; Stepien, Gallagher, & Workman, guests 1993), that it results in better long-term retention than

Jamin Carson 9

traditional instruction (Norman & Schmidt, 1992), and successful. Heuristic is a method of thought that does that it promotes the development of effective thinking not pertain to any specific problems or content. The skills (Gallagher, Stepien, & Rosenthal, 1994; Hmelo element is problematic because it contradicts three & Ferrari, 1997). other elements within the theory: the definition of On the other hand, in Research on Educational problem solving, successful problem solving requires a Innovations , Arthur Ellis (2005) notes that the research knowledge base, and problem solving enables learners base on problem solving lacks definition, possesses to transfer knowledge. Each of these three elements measurement validity problems and questionable implies that previously learned knowledge of the causality , and it fails to answer the claim that problem is necessary to solving the problem, whereas successful problem solvers must have a wealth of use of a heuristic assumes no knowledge is necessary. content-specific knowledge. Ellis further notes that I argue, like Peikoff (1985), that there is no way to there is “no generally agreed-on set of definitions of separate thinking or problem solving from knowledge. terms” (p. 109), that thinking skills are notoriously Just like instruction and curriculum, these concepts difficult to measure, and that given these first two imply one another and cannot be discussed separately problems, it is impossible to trace cause back to any for long. Likewise, to acquire knowledge, one must specific set of curricular instances. Ellis states, think. This is not to say that students cannot construct knowledge as they solve a given problem, only to say [t]he idea that thinking skills are content specific and cannot be taught generically must be seriously that often the problems they are presented only require entertained until it is discredited. We don’t think them to apply existing knowledge. From this that will happen. And if this is so, how does one perspective, it must be assumed that students do not construct content-free tests to measure thinking construct all of the knowledge in a given curriculum. skills? (pp. 109–110) Yet problem solving as a heuristic is the most The conclusions of Ellis and other research studies cherished aspect of problem solving because it is I will cite later state that it would be impossible to content-less. For example, in the preface to reinvent solutions to every problem that develops Mathematical Discovery, George Polya (1962), one of without recourse to past knowledge. This recourse to the foremost thinkers on problem solving says, past knowledge is evidence, in itself, that one must not I wish to call heuristic the study that the present completely construct reality . One must apply work attempts, the study of means and methods of knowledge that has already been formed by others and problem solving. The term heuristic, which was understand that knowledge, or else not solve the used by some philosophers in the past, is half- problem. It is this critique that I will invoke in the forgotten and half-discredited nowadays, but I am following treatment of problem solving. What I hope to not afraid to use it. show is that the heuristic for problem solving cannot be In fact, most of the time the present work successful if one holds strongly to the theoretical offers a down-to-earth practical aspect of heuristic. framework in which it is often situated. Rather, one (p. vi) must accept that already formed knowledge is essential Instructional textbooks sometimes play off this to problem solving. In fact, the meanings of problem process versus content dichotomy: a teacher can either solving found in articles and textbooks often convey teach students to be critical thinkers and problem this contradiction. On the one hand, it is argued that solvers or she can teach students more content problem solving is the antithesis of a content-centered knowledge. The authors of one textbook say, curriculum. On the other hand, a successful problem solver must possess a strong knowledge base of Too often children are taught in school as though the answers to all the important questions were in specific information, not merely a generalizeable textbooks. In reality, most of the problems faced by heuristic that can be applied across several different individuals have no easy answers. There are no situations. reference books in which one can find the solution The Problem With Problem Solving to life’s perplexing problems. (Gunter, Estes, & Schwab, 2003, pp. 128–129) The main problem with problem solving lies in the The dichotomy implies that thinking and knowledge fourth element listed above: problem solving is a are mutually exclusive, when in fact critical thinking heuristic. Recall that a heuristic is a guideline that may and problem solving require a great deal of specific or may not yield success but, unlike an algorithm, it content knowledge. does not depend on knowledge of the problem to be

10 Problem Solving

Problem solving and heuristics cannot be content- same as the old in principle. For example, the principle less and still be effective. Critical thinking, problem of addition a student would use to solve the problem 1 solving, and heuristics must include a knowledge base + 2 = 3 is essentially the same principle one would (Fredricksen, 1984; Ormrod, 1999). Including the apply to 1 + x = 3. The form may be different but knowledge base enables the principle cognitive ultimately the same principle is used to solve both function of problem solving—the application of problems. If this is the case, then a more proper conceptual knowledge, or transfer—to occur (Peikoff, element of problem solving would be number eight, the 1985). However, the degree to which Dewey and Polya transfer of knowledge or application of conceptual actually believed that a heuristic could be completely knowledge. content-less and still be effective is not clear. Further, The third and fourth elements algorithms and many instructional textbooks actually stress the heuristics are problematic. Krulik and Rudnick (1980) importance of content knowledge in solving problems distinguish between algorithms and heuristics. Unlike (Henson, 2004; Kauchak & Eggen, 2007; Lang & employing an algorithm, using a heuristic requires the Evans, 2006). problem solver to think on the highest level and fully understand the problem. Krulik and Rudnick also The Elements of Problem Solving Revised prefer heuristics to algorithms because the latter only Each of the above elements of problem solving applies to specific situations, whereas a heuristic will be reviewed again in light of the relationship applies to many as yet undiscovered problems. between thinking and knowledge and the research base However, an algorithm requires more than mere on problem solving. Element one, the definition of a memorization; it requires deep thinking too. First, in problem, implies that one must have some knowledge order to apply an algorithm, the student must have of the problem to solve it. How can one solve a sufficient information about the problem to know problem without first knowing what the problem is? In which algorithm to apply. This would only be possible fact, identification of the problem is what is called for if the student possessed a conceptual understanding of in the first two steps, Read and Explore, of the the subject matter . Further, even if a student could heuristic. In this step, the student first becomes aware somehow memorize when to apply certain algorithms, of the problem and then seeks to define what it is or it does not follow that he or she would also be able to what the problem requires for its solution. Awareness memorize how to apply it (Hu, 2006; Hundhausen & and definition comprise the knowledge that is essential Brown, 2008; Johanning, 2006; Rusch, 2005). to solving the problem. Consider the effectiveness of Second, algorithms and problem solving are students relative to their respective experiences with a related to one another. Algorithms are the product of given problem. The student more familiar with the successful problem solving and to be a successful problem will probably be better able to solve it. In problem solver one often must have knowledge of contrast, the student new to the problem, who has only algorithms (Hu, 2006; Hundhausen & Brown, 2008; studied the heuristic, would have to re-invent the Johanning, 2006; Rusch, 2005). Algorithms exist to solution to the problem. eliminate needless thought, and in this sense, they So the first two steps of the heuristic imply that actually are the end product of heuristics. The necessity one needs a great deal of knowledge about the problem to teach heuristics exists, but heuristics and algorithms to be an effective problem solver. In fact, if one wants should not be divided and set against one another. to solve the problem for the long term, one would want Rather, teachers should explain their relationship and to thoroughly study the problem until some kind of how both are used in solving problems. principles were developed with regard to it. The final A secondary problem that results from this flawed outcome of such an inquiry , ironically, would yield the dichotomy between algorithms and heuristics is that construction of an algorithm. advocates of problem solving prefer heuristics because The second element, the definition of problem algorithms only apply to specific situations, whereas solving, also implies a connection between thinking heuristics do not pertain to any specific knowledge. If and knowledge. It says that problem solving is one reflects upon the steps of problem solving listed essentially applying old knowledge to a new situation above one will see that they require one to know the (Krulik & Rudnick, 1987). However, if knowledge or a problem to be successful at solving it.. problem is genuinely new, then the old knowledge Consider the sample problem above to which the would not apply to it in any way. Ormrod (1999) heuristic was applied. If one knows the heuristic suggests that the so-called new situation is really the process and possesses no background knowledge of

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similar problems, one would not be able to solve the problem. The only ones who could solve it would be problem. For example, in the first step of the heuristic those who use an algorithm. Even if a teacher taught one is supposed to Read the problem, identify the the heuristic to students, he or she would essentially be problem, and list key facts of the problem. Without a teaching an algorithm. great deal of specific content knowledge how will the Advocates of problem solving are not solely to student know what the teacher means by “problem,” blame for the misconception between thinking and “key facts,” and so on? The teacher will probably have knowledge and between heuristics and algorithms. The to engage the student in several problems. Without misconception is likely due to teachers that have over- extensive knowledge of facts, how does the student used algorithms and never shown students how they know what mathematical facts are, and how they apply are formed, that they come from heuristics, and that to word problems, for example? one should have a conceptual understanding of when In the second step, Explore, the problem solver they should be used, not merely a memorized looks for a pattern or identifies the principle or understanding of them. concept. Again, how can one identify the pattern, The fundamentally flawed dichotomy within principle, or concept without already possessing problem solving probably stems from thinking in terms several stored patterns, principles, and concepts? of “either-ors.” One side defines appropriate education Indeed, to a student with very little mathematical as teaching algorithms by having students memorize knowledge, this problem would be extremely difficult when to use them but not why. The other side, by to solve. The heuristic would be of little help. contrast, emphasizes that thinking for understanding is The heuristic says to draw a diagram, presumably preferable to simply memorized knowledge. Perhaps to make the problem more concrete and therefore more what has happened in the shift from the former to the accessible to the student, but without already knowing latter practices is the instructional emphasis has shifted what the concept the problem exhibits this would very from content to thinking so much that the knowledge difficult, if not impossible. Using the chart with the base has been wiped out in the process. Ironically, data as an example, it would require previous eliminating knowledge from the equation also knowledge in mathematics to be able to construct it. It eliminates the effectiveness of problem solving. seems that the heuristic in this problem is in reality just The dichotomy between knowledge and thinking another algorithm that the teacher will have to teach as has also affected elements five and six. Number five directly and as repetitively until the students learn how states that problem solving connects theory and and when to apply it, which is the very opposite of practice. At the core of this element is yet another what advocates of problem solving want. The same is flawed dichotomy. Many educators hold that education also true of step five, Review and Extend. Presumably should prepare students for the real world by focusing if a student could represent this problem in algebraic less on theory and more on practice. However, dividing form, he or she should also be able to solve the same the two into separate cognitive domains that are problem without recourse to drawing diagrams, mutually exclusive is not possible. Thinking is actually recording data, etc. One could simply solve the the integration of theory and practice, the abstract and problem right after step one. the concrete, the conceptual and the particular. The sample problem illustrates what scientists have Theories are actually only general principles based on discovered about novices and experts . In studies that several practical instances. Likewise, abstract concepts examined expert and novice chess players, researchers are only general ideas based on several concrete found that their respective memories were no different particulars. Dividing the two is not possible because in relation to random arrangements of chess pieces. each implies the other (Lang & Evans, 2006). When the pieces were arranged in ways that would Effective instruction combines both theory and make sense in a chess game, the experts’ memories practice in specific ways. When effective teachers were much better. The theory is that an expert chess introduce a new concept, they first present a player is not a better problem solver, he or she just has perceptual, concrete example of it to the student. By a more extensive knowledge base than a novice player. presenting several concrete examples to the student, He or she is past the rudimentary hypothesis testing the concept is better understood because this is in fact stage of learning, past the problem solving heuristic the sequence of how humans form concepts (Bruner, stage and is now simply applying algorithms to Goodnow, & Austin, 1956; Cone 1969; Ormrod, 1999; already-solved problems (Ross, 2006). The same could Peikoff, 1993). They begin with two or more concrete be said for students applying a heuristic to the above particulars and abstract from them the essential

12 Problem Solving

defining characteristics into a concept. For example, example, changed the foundational assumptions of after experiencing several actual tables a human physics, but it was developed in concert with ideas that eventually abstracts the concept a piece of furniture already existed. There may be no such thing as pure with legs and a top (Lang & Evans, 2006). creativity, making something from nothing. What On the other hand, learning is not complete if one seems like creativity is more properly transfer or the can only match the concept with the particular example application of concepts, recognizing that what appears of it that the teacher has supplied. A successful student like two different things are really the same thing in is one who can match the concept to the as yet unseen principle. examples or present an example that the teacher has On the other hand, it is possible to provide an not presented. Using the table as an example, the environment that is conducive to creativity. Many student would be able to generate an example of a new problem-solving theorists have argued correctly for the table that the teacher has not exhibited or discussed. inclusion of such an atmosphere in classrooms (Christy This is an example of principle eight, the transfer of & Lima, 2007; Krulik & Rudnick, 1980; Slavin, 1997; knowledge or applying conceptual knowledge. Sriraman, 2001). I only object to the claim that The dichotomy between theory and practice also problem solving teaches creativity defined as creating seems to stem from the dichotomous relationship the new. It can, however, teach creativity defined as between the teaching for content-knowledge and the application of previously learned principles to new teaching for thinking. The former is typically situations. characterized as teaching concepts out of context, Element seven, problem solving requires a without a particular concrete example to experience knowledge base, although not problematic is only through the five senses . The latter, however, is often neglected within the theory of problem solving. This is characterized as being too concrete. Effective ironic given how important it is. Jeanne Ormrod (1999) instruction integrates both the concrete and abstract but says, “Successful (expert) problem solvers have a more in a specific sequence. First, new learning requires complete and better organized knowledge base for the specific real problems. Second, from these concrete problems they solve” (p. 370). She also relates how problems, the learner forms an abstract principle or one research inquiry that studied the practice of concept. Finally, the student then attempts to apply that problem solving in a high school physics class conceptual knowledge to a new, never before observed that the high achievers had “better organized experienced problem (Bruner, Goodnow, & Austin, information about concepts related to electricity” (p. 1956; Cone, 1969; Ormrod, 1999; Peikoff, 1993). 370). Not only was it better organized, the students The theory vs. practice debate is related to problem were also aware of “the particular relationships that solving because problem solving is often marketed as different concepts had with one another” (Cochran, the integration of theory and practice. I argue, 1988, p. 101). Norman (1980) also says, however, it leaves out too much theory in its effort to I do not believe we yet know enough to make be practical. That is, it leaves out the application of strong statements about what ought to be or ought conceptual knowledge and its requisite knowledge not to be included in a course on general problem base. solving methods. Although there are some general Element six, problem solving teaches creativity, is methods that could be of use…I suspect that in also problematic. To create is to generate the new, so most real situations it is…specific knowledge that one must ask how someone can teach another to is most important. (p. 101) generate something new. Are there specific processes Finally, element eight, problem solving is the within a human mind that lead to creative output that application of concepts or transfer, is also not can also be taught? The answer would depend at least problematic; it too is only neglected within the theory in part on the definition of create. When an artist of problem solving. Norman Frederiksen (1984) says, creates, he or she is actually re-creating reality for example, “the ability to formulate abstract concepts according to his or her philosophical viewpoint, but is an ability that underlies the acquisition of much, if not all, of what is included in the creation is knowledge. [Teaching how to conceptualize] accounts not a creation at all but an integration or an arranging for generality or transfer to new situations” (p. 379). of already existing things or ideas. So in one sense, no According to this passage, it is the application of one creates; one only integrates or applies previously conceptual knowledge and not the heuristic alone that learned knowledge. No idea is entirely new; it relates as Frederiksen says, “accounts for generality or to other ideas or things. The theory of relativity, for

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transfer,” (p. 379) which the advocates of problem Hundhausen, C. D., & Brown, J. L. (2008). Designing, visualizing, solving so desire. and discussing algorithms within a CS 1 studio experience: An empirical study. Computers & Education, 50, 301–326. Conclusion Johanning, D. (2006). Benchmarks and estimation: A critical element in supporting students as they develop fraction Problem solving would be more effective if the algorithms. In S. Alatorre, J. L. Cortina, M. Sáiz, & A. knowledge base and the application of that knowledge Méndez (Eds.), Proceedings of the 28th Annual Meeting of the were the primary principles of the theory and practice. North American Chapter of the International Group for the Currently, it seems that a content-less heuristic is the Psychology of Mathematics Education (pp. 384–386). Mérida, primary principle, which, as I have argued, is Mexico: Universidad Pedagógica Nacional. problematic because it dichotomizes thinking and Kauchak, D. P., & Eggen, P. D. 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Review of Educational Ross, P. E. (2006, August). The expert mind. Scientific American, Research, 54, 363–407. 64–71. Gallagher, S. A., Stepien, W. J., & Rosenthal, H. (1994). The Rusch, T. L. (2005). Step one for developing a great mathematics effects of problem-based learning on problem solving. Gifted lesson plan: Understand the mathematics. Ohio Journal of Child Quarterly, 36, 195–200. School Mathematics, 51, 25–34. Gunter, M. A., Estes, T. H., & Schwab, J. (2003). Instruction: A Slavin, R. E. (1997). Educational psychology : Theory and practice th models approach (4th ed.). Boston: Pearson Education, (5 ed.). Boston: Allyn and Bacon. Henson, K. T. (2004). Constructivist teaching strategies for diverse Sriraman, B. (2004). Understanding mathematical creativity: A middle-level classrooms. Boston: Pearson Education. framework for assessment in the high school classroom. In D. E. McDougall & J. A. Ross (Eds.), Proceedings of the 26th Hmelo, C. E., & Ferrari, M. (1997). The problem-based learning Annual Meeting of the North American Chapter of the tutorial: Cultivating higher order thinking skills. Journal for International Group for the Psychology of Mathematics the Education of the Gifted, 20, 401–422. Education (pp. 350–352). Toronto, Canada: OISE/UT. Hu, C. (2006). It’s mathematical after all—the nature of Stepien, W. J., Gallagher, S. A., & Workman, D. (1993). Problem- learning computer programming. Education & Information based learning for traditional and interdisciplinary classrooms. Technologies, 11, 83–92. Journal for the Education of the Gifted, 16, 338–357.

14 Problem Solving

Teaching problem solving: Let students get ‘stuck’ and ‘unstuck’

Subscribe to the center for universal education bulletin, kate mills and km kate mills literacy interventionist - red bank primary school helyn kim helyn kim former brookings expert @helyn_kim.

October 31, 2017

This is the second in a six-part  blog series  on  teaching 21st century skills , including  problem solving ,  metacognition , critical thinking , and collaboration , in classrooms.

In the real world, students encounter problems that are complex, not well defined, and lack a clear solution and approach. They need to be able to identify and apply different strategies to solve these problems. However, problem solving skills do not necessarily develop naturally; they need to be explicitly taught in a way that can be transferred across multiple settings and contexts.

Here’s what Kate Mills, who taught 4 th grade for 10 years at Knollwood School in New Jersey and is now a Literacy Interventionist at Red Bank Primary School, has to say about creating a classroom culture of problem solvers:

Helping my students grow to be people who will be successful outside of the classroom is equally as important as teaching the curriculum. From the first day of school, I intentionally choose language and activities that help to create a classroom culture of problem solvers. I want to produce students who are able to think about achieving a particular goal and manage their mental processes . This is known as metacognition , and research shows that metacognitive skills help students become better problem solvers.

I begin by “normalizing trouble” in the classroom. Peter H. Johnston teaches the importance of normalizing struggle , of naming it, acknowledging it, and calling it what it is: a sign that we’re growing. The goal is for the students to accept challenge and failure as a chance to grow and do better.

I look for every chance to share problems and highlight how the students— not the teachers— worked through those problems. There is, of course, coaching along the way. For example, a science class that is arguing over whose turn it is to build a vehicle will most likely need a teacher to help them find a way to the balance the work in an equitable way. Afterwards, I make it a point to turn it back to the class and say, “Do you see how you …” By naming what it is they did to solve the problem , students can be more independent and productive as they apply and adapt their thinking when engaging in future complex tasks.

After a few weeks, most of the class understands that the teachers aren’t there to solve problems for the students, but to support them in solving the problems themselves. With that important part of our classroom culture established, we can move to focusing on the strategies that students might need.

Here’s one way I do this in the classroom:

I show the broken escalator video to the class. Since my students are fourth graders, they think it’s hilarious and immediately start exclaiming, “Just get off! Walk!”

When the video is over, I say, “Many of us, probably all of us, are like the man in the video yelling for help when we get stuck. When we get stuck, we stop and immediately say ‘Help!’ instead of embracing the challenge and trying new ways to work through it.” I often introduce this lesson during math class, but it can apply to any area of our lives, and I can refer to the experience and conversation we had during any part of our day.

Research shows that just because students know the strategies does not mean they will engage in the appropriate strategies. Therefore, I try to provide opportunities where students can explicitly practice learning how, when, and why to use which strategies effectively  so that they can become self-directed learners.

For example, I give students a math problem that will make many of them feel “stuck”. I will say, “Your job is to get yourselves stuck—or to allow yourselves to get stuck on this problem—and then work through it, being mindful of how you’re getting yourselves unstuck.” As students work, I check-in to help them name their process: “How did you get yourself unstuck?” or “What was your first step? What are you doing now? What might you try next?” As students talk about their process, I’ll add to a list of strategies that students are using and, if they are struggling, help students name a specific process. For instance, if a student says he wrote the information from the math problem down and points to a chart, I will say: “Oh that’s interesting. You pulled the important information from the problem out and organized it into a chart.” In this way, I am giving him the language to match what he did, so that he now has a strategy he could use in other times of struggle.

The charts grow with us over time and are something that we refer to when students are stuck or struggling. They become a resource for students and a way for them to talk about their process when they are reflecting on and monitoring what did or did not work.

For me, as a teacher, it is important that I create a classroom environment in which students are problem solvers. This helps tie struggles to strategies so that the students will not only see value in working harder but in working smarter by trying new and different strategies and revising their process. In doing so, they will more successful the next time around.

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Teaching problem solving.

Print Version

Tips and Techniques

Expert vs. novice problem solvers, communicate.

• Have students  identify specific problems, difficulties, or confusions . Don’t waste time working through problems that students already understand.
• If students are unable to articulate their concerns, determine where they are having trouble by  asking them to identify the specific concepts or principles associated with the problem.
• In a one-on-one tutoring session, ask the student to  work his/her problem out loud . This slows down the thinking process, making it more accurate and allowing you to access understanding.
• When working with larger groups you can ask students to provide a written “two-column solution.” Have students write up their solution to a problem by putting all their calculations in one column and all of their reasoning (in complete sentences) in the other column. This helps them to think critically about their own problem solving and helps you to more easily identify where they may be having problems. Two-Column Solution (Math) Two-Column Solution (Physics)

Encourage Independence

• Model the problem solving process rather than just giving students the answer. As you work through the problem, consider how a novice might struggle with the concepts and make your thinking clear
• Have students work through problems on their own. Ask directing questions or give helpful suggestions, but  provide only minimal assistance and only when needed to overcome obstacles.
• Don’t fear  group work ! Students can frequently help each other, and talking about a problem helps them think more critically about the steps needed to solve the problem. Additionally, group work helps students realize that problems often have multiple solution strategies, some that might be more effective than others

Be sensitive

• Frequently, when working problems, students are unsure of themselves. This lack of confidence may hamper their learning. It is important to recognize this when students come to us for help, and to give each student some feeling of mastery. Do this by providing  positive reinforcement to let students know when they have mastered a new concept or skill.

Encourage Thoroughness and Patience

• Try to communicate that  the process is more important than the answer so that the student learns that it is OK to not have an instant solution. This is learned through your acceptance of his/her pace of doing things, through your refusal to let anxiety pressure you into giving the right answer, and through your example of problem solving through a step-by step process.

Experts (teachers) in a particular field are often so fluent in solving problems from that field that they can find it difficult to articulate the problem solving principles and strategies they use to novices (students) in their field because these principles and strategies are second nature to the expert. To teach students problem solving skills,  a teacher should be aware of principles and strategies of good problem solving in his or her discipline .

The mathematician George Polya captured the problem solving principles and strategies he used in his discipline in the book  How to Solve It: A New Aspect of Mathematical Method (Princeton University Press, 1957). The book includes  a summary of Polya’s problem solving heuristic as well as advice on the teaching of problem solving.

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• Published: 11 January 2023

The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature

• Enwei Xu   ORCID: orcid.org/0000-0001-6424-8169 1 ,
• Wei Wang 1 &
• Qingxia Wang 1  

Humanities and Social Sciences Communications volume  10 , Article number:  16 ( 2023 ) Cite this article

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Collaborative problem-solving has been widely embraced in the classroom instruction of critical thinking, which is regarded as the core of curriculum reform based on key competencies in the field of education as well as a key competence for learners in the 21st century. However, the effectiveness of collaborative problem-solving in promoting students’ critical thinking remains uncertain. This current research presents the major findings of a meta-analysis of 36 pieces of the literature revealed in worldwide educational periodicals during the 21st century to identify the effectiveness of collaborative problem-solving in promoting students’ critical thinking and to determine, based on evidence, whether and to what extent collaborative problem solving can result in a rise or decrease in critical thinking. The findings show that (1) collaborative problem solving is an effective teaching approach to foster students’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]); (2) in respect to the dimensions of critical thinking, collaborative problem solving can significantly and successfully enhance students’ attitudinal tendencies (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI[0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI[0.58, 0.82]); and (3) the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have an impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. On the basis of these results, recommendations are made for further study and instruction to better support students’ critical thinking in the context of collaborative problem-solving.

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Introduction.

Although critical thinking has a long history in research, the concept of critical thinking, which is regarded as an essential competence for learners in the 21st century, has recently attracted more attention from researchers and teaching practitioners (National Research Council, 2012 ). Critical thinking should be the core of curriculum reform based on key competencies in the field of education (Peng and Deng, 2017 ) because students with critical thinking can not only understand the meaning of knowledge but also effectively solve practical problems in real life even after knowledge is forgotten (Kek and Huijser, 2011 ). The definition of critical thinking is not universal (Ennis, 1989 ; Castle, 2009 ; Niu et al., 2013 ). In general, the definition of critical thinking is a self-aware and self-regulated thought process (Facione, 1990 ; Niu et al., 2013 ). It refers to the cognitive skills needed to interpret, analyze, synthesize, reason, and evaluate information as well as the attitudinal tendency to apply these abilities (Halpern, 2001 ). The view that critical thinking can be taught and learned through curriculum teaching has been widely supported by many researchers (e.g., Kuncel, 2011 ; Leng and Lu, 2020 ), leading to educators’ efforts to foster it among students. In the field of teaching practice, there are three types of courses for teaching critical thinking (Ennis, 1989 ). The first is an independent curriculum in which critical thinking is taught and cultivated without involving the knowledge of specific disciplines; the second is an integrated curriculum in which critical thinking is integrated into the teaching of other disciplines as a clear teaching goal; and the third is a mixed curriculum in which critical thinking is taught in parallel to the teaching of other disciplines for mixed teaching training. Furthermore, numerous measuring tools have been developed by researchers and educators to measure critical thinking in the context of teaching practice. These include standardized measurement tools, such as WGCTA, CCTST, CCTT, and CCTDI, which have been verified by repeated experiments and are considered effective and reliable by international scholars (Facione and Facione, 1992 ). In short, descriptions of critical thinking, including its two dimensions of attitudinal tendency and cognitive skills, different types of teaching courses, and standardized measurement tools provide a complex normative framework for understanding, teaching, and evaluating critical thinking.

Cultivating critical thinking in curriculum teaching can start with a problem, and one of the most popular critical thinking instructional approaches is problem-based learning (Liu et al., 2020 ). Duch et al. ( 2001 ) noted that problem-based learning in group collaboration is progressive active learning, which can improve students’ critical thinking and problem-solving skills. Collaborative problem-solving is the organic integration of collaborative learning and problem-based learning, which takes learners as the center of the learning process and uses problems with poor structure in real-world situations as the starting point for the learning process (Liang et al., 2017 ). Students learn the knowledge needed to solve problems in a collaborative group, reach a consensus on problems in the field, and form solutions through social cooperation methods, such as dialogue, interpretation, questioning, debate, negotiation, and reflection, thus promoting the development of learners’ domain knowledge and critical thinking (Cindy, 2004 ; Liang et al., 2017 ).

Collaborative problem-solving has been widely used in the teaching practice of critical thinking, and several studies have attempted to conduct a systematic review and meta-analysis of the empirical literature on critical thinking from various perspectives. However, little attention has been paid to the impact of collaborative problem-solving on critical thinking. Therefore, the best approach for developing and enhancing critical thinking throughout collaborative problem-solving is to examine how to implement critical thinking instruction; however, this issue is still unexplored, which means that many teachers are incapable of better instructing critical thinking (Leng and Lu, 2020 ; Niu et al., 2013 ). For example, Huber ( 2016 ) provided the meta-analysis findings of 71 publications on gaining critical thinking over various time frames in college with the aim of determining whether critical thinking was truly teachable. These authors found that learners significantly improve their critical thinking while in college and that critical thinking differs with factors such as teaching strategies, intervention duration, subject area, and teaching type. The usefulness of collaborative problem-solving in fostering students’ critical thinking, however, was not determined by this study, nor did it reveal whether there existed significant variations among the different elements. A meta-analysis of 31 pieces of educational literature was conducted by Liu et al. ( 2020 ) to assess the impact of problem-solving on college students’ critical thinking. These authors found that problem-solving could promote the development of critical thinking among college students and proposed establishing a reasonable group structure for problem-solving in a follow-up study to improve students’ critical thinking. Additionally, previous empirical studies have reached inconclusive and even contradictory conclusions about whether and to what extent collaborative problem-solving increases or decreases critical thinking levels. As an illustration, Yang et al. ( 2008 ) carried out an experiment on the integrated curriculum teaching of college students based on a web bulletin board with the goal of fostering participants’ critical thinking in the context of collaborative problem-solving. These authors’ research revealed that through sharing, debating, examining, and reflecting on various experiences and ideas, collaborative problem-solving can considerably enhance students’ critical thinking in real-life problem situations. In contrast, collaborative problem-solving had a positive impact on learners’ interaction and could improve learning interest and motivation but could not significantly improve students’ critical thinking when compared to traditional classroom teaching, according to research by Naber and Wyatt ( 2014 ) and Sendag and Odabasi ( 2009 ) on undergraduate and high school students, respectively.

The above studies show that there is inconsistency regarding the effectiveness of collaborative problem-solving in promoting students’ critical thinking. Therefore, it is essential to conduct a thorough and trustworthy review to detect and decide whether and to what degree collaborative problem-solving can result in a rise or decrease in critical thinking. Meta-analysis is a quantitative analysis approach that is utilized to examine quantitative data from various separate studies that are all focused on the same research topic. This approach characterizes the effectiveness of its impact by averaging the effect sizes of numerous qualitative studies in an effort to reduce the uncertainty brought on by independent research and produce more conclusive findings (Lipsey and Wilson, 2001 ).

This paper used a meta-analytic approach and carried out a meta-analysis to examine the effectiveness of collaborative problem-solving in promoting students’ critical thinking in order to make a contribution to both research and practice. The following research questions were addressed by this meta-analysis:

What is the overall effect size of collaborative problem-solving in promoting students’ critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills)?

How are the disparities between the study conclusions impacted by various moderating variables if the impacts of various experimental designs in the included studies are heterogeneous?

This research followed the strict procedures (e.g., database searching, identification, screening, eligibility, merging, duplicate removal, and analysis of included studies) of Cooper’s ( 2010 ) proposed meta-analysis approach for examining quantitative data from various separate studies that are all focused on the same research topic. The relevant empirical research that appeared in worldwide educational periodicals within the 21st century was subjected to this meta-analysis using Rev-Man 5.4. The consistency of the data extracted separately by two researchers was tested using Cohen’s kappa coefficient, and a publication bias test and a heterogeneity test were run on the sample data to ascertain the quality of this meta-analysis.

Data sources and search strategies

There were three stages to the data collection process for this meta-analysis, as shown in Fig. 1 , which shows the number of articles included and eliminated during the selection process based on the statement and study eligibility criteria.

This flowchart shows the number of records identified, included and excluded in the article.

First, the databases used to systematically search for relevant articles were the journal papers of the Web of Science Core Collection and the Chinese Core source journal, as well as the Chinese Social Science Citation Index (CSSCI) source journal papers included in CNKI. These databases were selected because they are credible platforms that are sources of scholarly and peer-reviewed information with advanced search tools and contain literature relevant to the subject of our topic from reliable researchers and experts. The search string with the Boolean operator used in the Web of Science was “TS = (((“critical thinking” or “ct” and “pretest” or “posttest”) or (“critical thinking” or “ct” and “control group” or “quasi experiment” or “experiment”)) and (“collaboration” or “collaborative learning” or “CSCL”) and (“problem solving” or “problem-based learning” or “PBL”))”. The research area was “Education Educational Research”, and the search period was “January 1, 2000, to December 30, 2021”. A total of 412 papers were obtained. The search string with the Boolean operator used in the CNKI was “SU = (‘critical thinking’*‘collaboration’ + ‘critical thinking’*‘collaborative learning’ + ‘critical thinking’*‘CSCL’ + ‘critical thinking’*‘problem solving’ + ‘critical thinking’*‘problem-based learning’ + ‘critical thinking’*‘PBL’ + ‘critical thinking’*‘problem oriented’) AND FT = (‘experiment’ + ‘quasi experiment’ + ‘pretest’ + ‘posttest’ + ‘empirical study’)” (translated into Chinese when searching). A total of 56 studies were found throughout the search period of “January 2000 to December 2021”. From the databases, all duplicates and retractions were eliminated before exporting the references into Endnote, a program for managing bibliographic references. In all, 466 studies were found.

Second, the studies that matched the inclusion and exclusion criteria for the meta-analysis were chosen by two researchers after they had reviewed the abstracts and titles of the gathered articles, yielding a total of 126 studies.

Third, two researchers thoroughly reviewed each included article’s whole text in accordance with the inclusion and exclusion criteria. Meanwhile, a snowball search was performed using the references and citations of the included articles to ensure complete coverage of the articles. Ultimately, 36 articles were kept.

Two researchers worked together to carry out this entire process, and a consensus rate of almost 94.7% was reached after discussion and negotiation to clarify any emerging differences.

Eligibility criteria

Since not all the retrieved studies matched the criteria for this meta-analysis, eligibility criteria for both inclusion and exclusion were developed as follows:

The publication language of the included studies was limited to English and Chinese, and the full text could be obtained. Articles that did not meet the publication language and articles not published between 2000 and 2021 were excluded.

The research design of the included studies must be empirical and quantitative studies that can assess the effect of collaborative problem-solving on the development of critical thinking. Articles that could not identify the causal mechanisms by which collaborative problem-solving affects critical thinking, such as review articles and theoretical articles, were excluded.

The research method of the included studies must feature a randomized control experiment or a quasi-experiment, or a natural experiment, which have a higher degree of internal validity with strong experimental designs and can all plausibly provide evidence that critical thinking and collaborative problem-solving are causally related. Articles with non-experimental research methods, such as purely correlational or observational studies, were excluded.

The participants of the included studies were only students in school, including K-12 students and college students. Articles in which the participants were non-school students, such as social workers or adult learners, were excluded.

The research results of the included studies must mention definite signs that may be utilized to gauge critical thinking’s impact (e.g., sample size, mean value, or standard deviation). Articles that lacked specific measurement indicators for critical thinking and could not calculate the effect size were excluded.

Data coding design

In order to perform a meta-analysis, it is necessary to collect the most important information from the articles, codify that information’s properties, and convert descriptive data into quantitative data. Therefore, this study designed a data coding template (see Table 1 ). Ultimately, 16 coding fields were retained.

The designed data-coding template consisted of three pieces of information. Basic information about the papers was included in the descriptive information: the publishing year, author, serial number, and title of the paper.

The variable information for the experimental design had three variables: the independent variable (instruction method), the dependent variable (critical thinking), and the moderating variable (learning stage, teaching type, intervention duration, learning scaffold, group size, measuring tool, and subject area). Depending on the topic of this study, the intervention strategy, as the independent variable, was coded into collaborative and non-collaborative problem-solving. The dependent variable, critical thinking, was coded as a cognitive skill and an attitudinal tendency. And seven moderating variables were created by grouping and combining the experimental design variables discovered within the 36 studies (see Table 1 ), where learning stages were encoded as higher education, high school, middle school, and primary school or lower; teaching types were encoded as mixed courses, integrated courses, and independent courses; intervention durations were encoded as 0–1 weeks, 1–4 weeks, 4–12 weeks, and more than 12 weeks; group sizes were encoded as 2–3 persons, 4–6 persons, 7–10 persons, and more than 10 persons; learning scaffolds were encoded as teacher-supported learning scaffold, technique-supported learning scaffold, and resource-supported learning scaffold; measuring tools were encoded as standardized measurement tools (e.g., WGCTA, CCTT, CCTST, and CCTDI) and self-adapting measurement tools (e.g., modified or made by researchers); and subject areas were encoded according to the specific subjects used in the 36 included studies.

The data information contained three metrics for measuring critical thinking: sample size, average value, and standard deviation. It is vital to remember that studies with various experimental designs frequently adopt various formulas to determine the effect size. And this paper used Morris’ proposed standardized mean difference (SMD) calculation formula ( 2008 , p. 369; see Supplementary Table S3 ).

Procedure for extracting and coding data

According to the data coding template (see Table 1 ), the 36 papers’ information was retrieved by two researchers, who then entered them into Excel (see Supplementary Table S1 ). The results of each study were extracted separately in the data extraction procedure if an article contained numerous studies on critical thinking, or if a study assessed different critical thinking dimensions. For instance, Tiwari et al. ( 2010 ) used four time points, which were viewed as numerous different studies, to examine the outcomes of critical thinking, and Chen ( 2013 ) included the two outcome variables of attitudinal tendency and cognitive skills, which were regarded as two studies. After discussion and negotiation during data extraction, the two researchers’ consistency test coefficients were roughly 93.27%. Supplementary Table S2 details the key characteristics of the 36 included articles with 79 effect quantities, including descriptive information (e.g., the publishing year, author, serial number, and title of the paper), variable information (e.g., independent variables, dependent variables, and moderating variables), and data information (e.g., mean values, standard deviations, and sample size). Following that, testing for publication bias and heterogeneity was done on the sample data using the Rev-Man 5.4 software, and then the test results were used to conduct a meta-analysis.

Publication bias test

When the sample of studies included in a meta-analysis does not accurately reflect the general status of research on the relevant subject, publication bias is said to be exhibited in this research. The reliability and accuracy of the meta-analysis may be impacted by publication bias. Due to this, the meta-analysis needs to check the sample data for publication bias (Stewart et al., 2006 ). A popular method to check for publication bias is the funnel plot; and it is unlikely that there will be publishing bias when the data are equally dispersed on either side of the average effect size and targeted within the higher region. The data are equally dispersed within the higher portion of the efficient zone, consistent with the funnel plot connected with this analysis (see Fig. 2 ), indicating that publication bias is unlikely in this situation.

This funnel plot shows the result of publication bias of 79 effect quantities across 36 studies.

Heterogeneity test

To select the appropriate effect models for the meta-analysis, one might use the results of a heterogeneity test on the data effect sizes. In a meta-analysis, it is common practice to gauge the degree of data heterogeneity using the I 2 value, and I 2  ≥ 50% is typically understood to denote medium-high heterogeneity, which calls for the adoption of a random effect model; if not, a fixed effect model ought to be applied (Lipsey and Wilson, 2001 ). The findings of the heterogeneity test in this paper (see Table 2 ) revealed that I 2 was 86% and displayed significant heterogeneity ( P  < 0.01). To ensure accuracy and reliability, the overall effect size ought to be calculated utilizing the random effect model.

The analysis of the overall effect size

This meta-analysis utilized a random effect model to examine 79 effect quantities from 36 studies after eliminating heterogeneity. In accordance with Cohen’s criterion (Cohen, 1992 ), it is abundantly clear from the analysis results, which are shown in the forest plot of the overall effect (see Fig. 3 ), that the cumulative impact size of cooperative problem-solving is 0.82, which is statistically significant ( z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]), and can encourage learners to practice critical thinking.

This forest plot shows the analysis result of the overall effect size across 36 studies.

In addition, this study examined two distinct dimensions of critical thinking to better understand the precise contributions that collaborative problem-solving makes to the growth of critical thinking. The findings (see Table 3 ) indicate that collaborative problem-solving improves cognitive skills (ES = 0.70) and attitudinal tendency (ES = 1.17), with significant intergroup differences (chi 2  = 7.95, P  < 0.01). Although collaborative problem-solving improves both dimensions of critical thinking, it is essential to point out that the improvements in students’ attitudinal tendency are much more pronounced and have a significant comprehensive effect (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]), whereas gains in learners’ cognitive skill are slightly improved and are just above average. (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

The analysis of moderator effect size

The whole forest plot’s 79 effect quantities underwent a two-tailed test, which revealed significant heterogeneity ( I 2  = 86%, z  = 12.78, P  < 0.01), indicating differences between various effect sizes that may have been influenced by moderating factors other than sampling error. Therefore, exploring possible moderating factors that might produce considerable heterogeneity was done using subgroup analysis, such as the learning stage, learning scaffold, teaching type, group size, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, in order to further explore the key factors that influence critical thinking. The findings (see Table 4 ) indicate that various moderating factors have advantageous effects on critical thinking. In this situation, the subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), learning scaffold (chi 2  = 9.03, P  < 0.01), and teaching type (chi 2  = 7.20, P  < 0.05) are all significant moderators that can be applied to support the cultivation of critical thinking. However, since the learning stage and the measuring tools did not significantly differ among intergroup (chi 2  = 3.15, P  = 0.21 > 0.05, and chi 2  = 0.08, P  = 0.78 > 0.05), we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving. These are the precise outcomes, as follows:

Various learning stages influenced critical thinking positively, without significant intergroup differences (chi 2  = 3.15, P  = 0.21 > 0.05). High school was first on the list of effect sizes (ES = 1.36, P  < 0.01), then higher education (ES = 0.78, P  < 0.01), and middle school (ES = 0.73, P  < 0.01). These results show that, despite the learning stage’s beneficial influence on cultivating learners’ critical thinking, we are unable to explain why it is essential for cultivating critical thinking in the context of collaborative problem-solving.

Different teaching types had varying degrees of positive impact on critical thinking, with significant intergroup differences (chi 2  = 7.20, P  < 0.05). The effect size was ranked as follows: mixed courses (ES = 1.34, P  < 0.01), integrated courses (ES = 0.81, P  < 0.01), and independent courses (ES = 0.27, P  < 0.01). These results indicate that the most effective approach to cultivate critical thinking utilizing collaborative problem solving is through the teaching type of mixed courses.

Various intervention durations significantly improved critical thinking, and there were significant intergroup differences (chi 2  = 12.18, P  < 0.01). The effect sizes related to this variable showed a tendency to increase with longer intervention durations. The improvement in critical thinking reached a significant level (ES = 0.85, P  < 0.01) after more than 12 weeks of training. These findings indicate that the intervention duration and critical thinking’s impact are positively correlated, with a longer intervention duration having a greater effect.

Different learning scaffolds influenced critical thinking positively, with significant intergroup differences (chi 2  = 9.03, P  < 0.01). The resource-supported learning scaffold (ES = 0.69, P  < 0.01) acquired a medium-to-higher level of impact, the technique-supported learning scaffold (ES = 0.63, P  < 0.01) also attained a medium-to-higher level of impact, and the teacher-supported learning scaffold (ES = 0.92, P  < 0.01) displayed a high level of significant impact. These results show that the learning scaffold with teacher support has the greatest impact on cultivating critical thinking.

Various group sizes influenced critical thinking positively, and the intergroup differences were statistically significant (chi 2  = 8.77, P  < 0.05). Critical thinking showed a general declining trend with increasing group size. The overall effect size of 2–3 people in this situation was the biggest (ES = 0.99, P  < 0.01), and when the group size was greater than 7 people, the improvement in critical thinking was at the lower-middle level (ES < 0.5, P  < 0.01). These results show that the impact on critical thinking is positively connected with group size, and as group size grows, so does the overall impact.

Various measuring tools influenced critical thinking positively, with significant intergroup differences (chi 2  = 0.08, P  = 0.78 > 0.05). In this situation, the self-adapting measurement tools obtained an upper-medium level of effect (ES = 0.78), whereas the complete effect size of the standardized measurement tools was the largest, achieving a significant level of effect (ES = 0.84, P  < 0.01). These results show that, despite the beneficial influence of the measuring tool on cultivating critical thinking, we are unable to explain why it is crucial in fostering the growth of critical thinking by utilizing the approach of collaborative problem-solving.

Different subject areas had a greater impact on critical thinking, and the intergroup differences were statistically significant (chi 2  = 13.36, P  < 0.05). Mathematics had the greatest overall impact, achieving a significant level of effect (ES = 1.68, P  < 0.01), followed by science (ES = 1.25, P  < 0.01) and medical science (ES = 0.87, P  < 0.01), both of which also achieved a significant level of effect. Programming technology was the least effective (ES = 0.39, P  < 0.01), only having a medium-low degree of effect compared to education (ES = 0.72, P  < 0.01) and other fields (such as language, art, and social sciences) (ES = 0.58, P  < 0.01). These results suggest that scientific fields (e.g., mathematics, science) may be the most effective subject areas for cultivating critical thinking utilizing the approach of collaborative problem-solving.

The effectiveness of collaborative problem solving with regard to teaching critical thinking

According to this meta-analysis, using collaborative problem-solving as an intervention strategy in critical thinking teaching has a considerable amount of impact on cultivating learners’ critical thinking as a whole and has a favorable promotional effect on the two dimensions of critical thinking. According to certain studies, collaborative problem solving, the most frequently used critical thinking teaching strategy in curriculum instruction can considerably enhance students’ critical thinking (e.g., Liang et al., 2017 ; Liu et al., 2020 ; Cindy, 2004 ). This meta-analysis provides convergent data support for the above research views. Thus, the findings of this meta-analysis not only effectively address the first research query regarding the overall effect of cultivating critical thinking and its impact on the two dimensions of critical thinking (i.e., attitudinal tendency and cognitive skills) utilizing the approach of collaborative problem-solving, but also enhance our confidence in cultivating critical thinking by using collaborative problem-solving intervention approach in the context of classroom teaching.

Furthermore, the associated improvements in attitudinal tendency are much stronger, but the corresponding improvements in cognitive skill are only marginally better. According to certain studies, cognitive skill differs from the attitudinal tendency in classroom instruction; the cultivation and development of the former as a key ability is a process of gradual accumulation, while the latter as an attitude is affected by the context of the teaching situation (e.g., a novel and exciting teaching approach, challenging and rewarding tasks) (Halpern, 2001 ; Wei and Hong, 2022 ). Collaborative problem-solving as a teaching approach is exciting and interesting, as well as rewarding and challenging; because it takes the learners as the focus and examines problems with poor structure in real situations, and it can inspire students to fully realize their potential for problem-solving, which will significantly improve their attitudinal tendency toward solving problems (Liu et al., 2020 ). Similar to how collaborative problem-solving influences attitudinal tendency, attitudinal tendency impacts cognitive skill when attempting to solve a problem (Liu et al., 2020 ; Zhang et al., 2022 ), and stronger attitudinal tendencies are associated with improved learning achievement and cognitive ability in students (Sison, 2008 ; Zhang et al., 2022 ). It can be seen that the two specific dimensions of critical thinking as well as critical thinking as a whole are affected by collaborative problem-solving, and this study illuminates the nuanced links between cognitive skills and attitudinal tendencies with regard to these two dimensions of critical thinking. To fully develop students’ capacity for critical thinking, future empirical research should pay closer attention to cognitive skills.

The moderating effects of collaborative problem solving with regard to teaching critical thinking

In order to further explore the key factors that influence critical thinking, exploring possible moderating effects that might produce considerable heterogeneity was done using subgroup analysis. The findings show that the moderating factors, such as the teaching type, learning stage, group size, learning scaffold, duration of the intervention, measuring tool, and the subject area included in the 36 experimental designs, could all support the cultivation of collaborative problem-solving in critical thinking. Among them, the effect size differences between the learning stage and measuring tool are not significant, which does not explain why these two factors are crucial in supporting the cultivation of critical thinking utilizing the approach of collaborative problem-solving.

In terms of the learning stage, various learning stages influenced critical thinking positively without significant intergroup differences, indicating that we are unable to explain why it is crucial in fostering the growth of critical thinking.

Although high education accounts for 70.89% of all empirical studies performed by researchers, high school may be the appropriate learning stage to foster students’ critical thinking by utilizing the approach of collaborative problem-solving since it has the largest overall effect size. This phenomenon may be related to student’s cognitive development, which needs to be further studied in follow-up research.

With regard to teaching type, mixed course teaching may be the best teaching method to cultivate students’ critical thinking. Relevant studies have shown that in the actual teaching process if students are trained in thinking methods alone, the methods they learn are isolated and divorced from subject knowledge, which is not conducive to their transfer of thinking methods; therefore, if students’ thinking is trained only in subject teaching without systematic method training, it is challenging to apply to real-world circumstances (Ruggiero, 2012 ; Hu and Liu, 2015 ). Teaching critical thinking as mixed course teaching in parallel to other subject teachings can achieve the best effect on learners’ critical thinking, and explicit critical thinking instruction is more effective than less explicit critical thinking instruction (Bensley and Spero, 2014 ).

In terms of the intervention duration, with longer intervention times, the overall effect size shows an upward tendency. Thus, the intervention duration and critical thinking’s impact are positively correlated. Critical thinking, as a key competency for students in the 21st century, is difficult to get a meaningful improvement in a brief intervention duration. Instead, it could be developed over a lengthy period of time through consistent teaching and the progressive accumulation of knowledge (Halpern, 2001 ; Hu and Liu, 2015 ). Therefore, future empirical studies ought to take these restrictions into account throughout a longer period of critical thinking instruction.

With regard to group size, a group size of 2–3 persons has the highest effect size, and the comprehensive effect size decreases with increasing group size in general. This outcome is in line with some research findings; as an example, a group composed of two to four members is most appropriate for collaborative learning (Schellens and Valcke, 2006 ). However, the meta-analysis results also indicate that once the group size exceeds 7 people, small groups cannot produce better interaction and performance than large groups. This may be because the learning scaffolds of technique support, resource support, and teacher support improve the frequency and effectiveness of interaction among group members, and a collaborative group with more members may increase the diversity of views, which is helpful to cultivate critical thinking utilizing the approach of collaborative problem-solving.

With regard to the learning scaffold, the three different kinds of learning scaffolds can all enhance critical thinking. Among them, the teacher-supported learning scaffold has the largest overall effect size, demonstrating the interdependence of effective learning scaffolds and collaborative problem-solving. This outcome is in line with some research findings; as an example, a successful strategy is to encourage learners to collaborate, come up with solutions, and develop critical thinking skills by using learning scaffolds (Reiser, 2004 ; Xu et al., 2022 ); learning scaffolds can lower task complexity and unpleasant feelings while also enticing students to engage in learning activities (Wood et al., 2006 ); learning scaffolds are designed to assist students in using learning approaches more successfully to adapt the collaborative problem-solving process, and the teacher-supported learning scaffolds have the greatest influence on critical thinking in this process because they are more targeted, informative, and timely (Xu et al., 2022 ).

With respect to the measuring tool, despite the fact that standardized measurement tools (such as the WGCTA, CCTT, and CCTST) have been acknowledged as trustworthy and effective by worldwide experts, only 54.43% of the research included in this meta-analysis adopted them for assessment, and the results indicated no intergroup differences. These results suggest that not all teaching circumstances are appropriate for measuring critical thinking using standardized measurement tools. “The measuring tools for measuring thinking ability have limits in assessing learners in educational situations and should be adapted appropriately to accurately assess the changes in learners’ critical thinking.”, according to Simpson and Courtney ( 2002 , p. 91). As a result, in order to more fully and precisely gauge how learners’ critical thinking has evolved, we must properly modify standardized measuring tools based on collaborative problem-solving learning contexts.

With regard to the subject area, the comprehensive effect size of science departments (e.g., mathematics, science, medical science) is larger than that of language arts and social sciences. Some recent international education reforms have noted that critical thinking is a basic part of scientific literacy. Students with scientific literacy can prove the rationality of their judgment according to accurate evidence and reasonable standards when they face challenges or poorly structured problems (Kyndt et al., 2013 ), which makes critical thinking crucial for developing scientific understanding and applying this understanding to practical problem solving for problems related to science, technology, and society (Yore et al., 2007 ).

Suggestions for critical thinking teaching

Other than those stated in the discussion above, the following suggestions are offered for critical thinking instruction utilizing the approach of collaborative problem-solving.

First, teachers should put a special emphasis on the two core elements, which are collaboration and problem-solving, to design real problems based on collaborative situations. This meta-analysis provides evidence to support the view that collaborative problem-solving has a strong synergistic effect on promoting students’ critical thinking. Asking questions about real situations and allowing learners to take part in critical discussions on real problems during class instruction are key ways to teach critical thinking rather than simply reading speculative articles without practice (Mulnix, 2012 ). Furthermore, the improvement of students’ critical thinking is realized through cognitive conflict with other learners in the problem situation (Yang et al., 2008 ). Consequently, it is essential for teachers to put a special emphasis on the two core elements, which are collaboration and problem-solving, and design real problems and encourage students to discuss, negotiate, and argue based on collaborative problem-solving situations.

Second, teachers should design and implement mixed courses to cultivate learners’ critical thinking, utilizing the approach of collaborative problem-solving. Critical thinking can be taught through curriculum instruction (Kuncel, 2011 ; Leng and Lu, 2020 ), with the goal of cultivating learners’ critical thinking for flexible transfer and application in real problem-solving situations. This meta-analysis shows that mixed course teaching has a highly substantial impact on the cultivation and promotion of learners’ critical thinking. Therefore, teachers should design and implement mixed course teaching with real collaborative problem-solving situations in combination with the knowledge content of specific disciplines in conventional teaching, teach methods and strategies of critical thinking based on poorly structured problems to help students master critical thinking, and provide practical activities in which students can interact with each other to develop knowledge construction and critical thinking utilizing the approach of collaborative problem-solving.

Third, teachers should be more trained in critical thinking, particularly preservice teachers, and they also should be conscious of the ways in which teachers’ support for learning scaffolds can promote critical thinking. The learning scaffold supported by teachers had the greatest impact on learners’ critical thinking, in addition to being more directive, targeted, and timely (Wood et al., 2006 ). Critical thinking can only be effectively taught when teachers recognize the significance of critical thinking for students’ growth and use the proper approaches while designing instructional activities (Forawi, 2016 ). Therefore, with the intention of enabling teachers to create learning scaffolds to cultivate learners’ critical thinking utilizing the approach of collaborative problem solving, it is essential to concentrate on the teacher-supported learning scaffolds and enhance the instruction for teaching critical thinking to teachers, especially preservice teachers.

Implications and limitations

There are certain limitations in this meta-analysis, but future research can correct them. First, the search languages were restricted to English and Chinese, so it is possible that pertinent studies that were written in other languages were overlooked, resulting in an inadequate number of articles for review. Second, these data provided by the included studies are partially missing, such as whether teachers were trained in the theory and practice of critical thinking, the average age and gender of learners, and the differences in critical thinking among learners of various ages and genders. Third, as is typical for review articles, more studies were released while this meta-analysis was being done; therefore, it had a time limit. With the development of relevant research, future studies focusing on these issues are highly relevant and needed.

Conclusions

The subject of the magnitude of collaborative problem-solving’s impact on fostering students’ critical thinking, which received scant attention from other studies, was successfully addressed by this study. The question of the effectiveness of collaborative problem-solving in promoting students’ critical thinking was addressed in this study, which addressed a topic that had gotten little attention in earlier research. The following conclusions can be made:

Regarding the results obtained, collaborative problem solving is an effective teaching approach to foster learners’ critical thinking, with a significant overall effect size (ES = 0.82, z  = 12.78, P  < 0.01, 95% CI [0.69, 0.95]). With respect to the dimensions of critical thinking, collaborative problem-solving can significantly and effectively improve students’ attitudinal tendency, and the comprehensive effect is significant (ES = 1.17, z  = 7.62, P  < 0.01, 95% CI [0.87, 1.47]); nevertheless, it falls short in terms of improving students’ cognitive skills, having only an upper-middle impact (ES = 0.70, z  = 11.55, P  < 0.01, 95% CI [0.58, 0.82]).

As demonstrated by both the results and the discussion, there are varying degrees of beneficial effects on students’ critical thinking from all seven moderating factors, which were found across 36 studies. In this context, the teaching type (chi 2  = 7.20, P  < 0.05), intervention duration (chi 2  = 12.18, P  < 0.01), subject area (chi 2  = 13.36, P  < 0.05), group size (chi 2  = 8.77, P  < 0.05), and learning scaffold (chi 2  = 9.03, P  < 0.01) all have a positive impact on critical thinking, and they can be viewed as important moderating factors that affect how critical thinking develops. Since the learning stage (chi 2  = 3.15, P  = 0.21 > 0.05) and measuring tools (chi 2  = 0.08, P  = 0.78 > 0.05) did not demonstrate any significant intergroup differences, we are unable to explain why these two factors are crucial in supporting the cultivation of critical thinking in the context of collaborative problem-solving.

Data availability

All data generated or analyzed during this study are included within the article and its supplementary information files, and the supplementary information files are available in the Dataverse repository: https://doi.org/10.7910/DVN/IPFJO6 .

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Acknowledgements

This research was supported by the graduate scientific research and innovation project of Xinjiang Uygur Autonomous Region named “Research on in-depth learning of high school information technology courses for the cultivation of computing thinking” (No. XJ2022G190) and the independent innovation fund project for doctoral students of the College of Educational Science of Xinjiang Normal University named “Research on project-based teaching of high school information technology courses from the perspective of discipline core literacy” (No. XJNUJKYA2003).

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Xu, E., Wang, W. & Wang, Q. The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature. Humanit Soc Sci Commun 10 , 16 (2023). https://doi.org/10.1057/s41599-023-01508-1

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The lack of upward mobility or opportunities for advancement in the teaching profession can also contribute to teachers’ desire to leave the field. I pursued national-board certification and then found a ceiling—there was nowhere to go in the school system. For professionals like me who desire continual career growth, this ceiling can drive us to look outside the teaching profession.

The professional journey of a teacher often lacks the lateral mobility enjoyed in other professions. For those working in other industries, professional boredom or unhappiness may mean moving to a new company or taking on a new role altogether. They have opportunities to build new skills and populate a robust resume.

In contrast, career-advancement opportunities for K-12 teachers are limited, primarily confined to administrative roles that do not appeal to many teachers. Furthermore, these positions require a different skill set than classroom teaching.

This lack of mobility within the profession, coupled with inadequate exposure to the culture of job-getting outside the education sector, can leave teachers at a disadvantage. When teachers are unfamiliar in the art of negotiating positions or adapting to new office politics, they lose out on these fundamental elements of professional growth.

The world of teaching alone also leaves many teachers feeling pigeonholed, their years of dedication to education paradoxically becoming their biggest barrier to exploration beyond it.

Teachers are often told that leading a classroom is the world’s most challenging and complex profession, but that sentiment doesn’t help them translate their teaching experience beyond the classroom. Many find the skills that define them as educators do not neatly translate into the resume language valued in the corporate world. Their expertise in people management, data analysis, and problem-solving, honed over years of managing classrooms and nurturing young minds, seems lost in translation when it comes to the corporate job market.

Instead, a teacher’s resume often reads as a static record of their employment history, devoid of the dynamic skills and achievements that could make them attractive candidates in other sectors.

For me, transitioning out of teaching required me to learn new skills. I took on volunteer and freelance work to broaden my skill set. Those experiences working outside the education space also gave me the opportunity to interact with a broader set of professionals in new spaces and apply the skills I had cultivated in the classroom beyond teaching.

Yet, hope is not lost. The pathway out of the classroom and into new professional realms requires a paradigm shift in how teachers and employers view teachers’ skills. The journey involves reimagining the resume not as a mere record but as a strategic tool that highlights the transferability of teaching skills to a wide array of sectors.

In my work developing a platform to support teachers’ career transitions, I help them understand how to translate their teaching skills into the language of various industries. It’s about recognizing the value in the competencies developed in the classroom—competencies that are desperately needed in the broader professional world.

I myself initially assumed that the skills I honed in the classroom were irrelevant outside it. This mindset kept me confined to education-focused roles for years before I realized the transferability of my teaching expertise and learned how to talk about the value I would bring to an organization.

We must also make systemic changes beyond what is in any one teacher’s control. First, districts need to create pathways for growth as teacher-leaders or other roles within schools that help them build a diverse skill set—and resume. No worker’s trajectory should flatten once they enter their chosen profession.

Secondly, schools of education could better support the professional growth of teachers by preparing education degree-seekers for an array of roles beyond the classroom. They should make students aware of the teacher-turnover rates, provide direct instruction around how to build skills valued in the workplace more generally, and advise on how to talk about their capabilities.

By offering courses that expressly focus on building transferable skills and building awareness of the array of career options for educators, these institutions can better equip graduates for the reality of their career trajectories. Teachers who end up choosing to transition out of education need to see how to translate what they’ve learned on the job.

Teacher-preparation programs can also support students by establishing partnerships between schools, businesses, and industry associations. These efforts—such as industry-sponsored projects, mentorship programs, or even guest lectures—would provide teacher-candidates with essential networking and skill-building opportunities.

Experiential learning opportunities, too, such as job-shadowing programs and internships can expose prospective teachers to the culture of job-getting in other industries. Such collaborative initiatives can bridge the gap between teaching roles and the broader landscape of available jobs for education professionals.

Teachers aren’t stuck, but they do face a Herculean task when they want to make a career pivot. It’s time we better support those who raise their hands to do the complex work of teaching and advocate a system that values their professional growth. We must recognize their potential not only in the classroom but in the wider world.

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difficulties encountered by the students in mathematical problems

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ABSTRACT Hafsah B. Mama and Johanisa M. Dibagulun. “Difficulties encountered in solving word problems in Mathematics”. An Undergraduate Thesis, Secondary and Elementary teaching Department, College of Education, Mindanao State University, Marawi City, June 2016. Thesis Adviser: Prof. Teodoro M. Drilon Word problems are consistently used as practice exercises and illustrations throughout Mathematics curriculum. However, problem solving is a difficult task as it involves a lot of steps. People have to hurdle the challenges in going from one step to another although the steps may not necessarily have to take in sequential manner. This study employed the mixed method design, a combination of quantitative and qualitative research methods. It aims to determine the difficulties encountered in solving word problems in Mathematics by the Grade six pupils in Amai Pakpak Central Elementary School. There were forty seven (47) pupils who participated in the study. Data were gathered through administering 10-item researchers’ made test regarding word problems. The test were administered right after it was statistically proven to be reliable using Richard-Kurson with value 0.84. Moreover, one-on-one interview with the respondents also took place. The interview questions were based on the three problems which most of the pupils answered incorrectly. Results showed that most (55.3%) of the respondents have satisfactory grades in English. Moreover, almost the same number of percentages (48.9% &46.8%) had passing and satisfactory grades in Mathematics. In addition, more than half of the respondents failed the test. It is also found that there is a significant relationship between English grade, Mathematics grade and performance in solving word problems. Findings revealed that pupils have difficulties in solving word problems in Mathematics. Some difficulties were lack of comprehension, lack of strategy, incorrect use of operations, inability to translate the problems in Mathematical equation, interchanging values and computational errors. After thorough analysis, it is suggested that students should enhance their skills in solving and vocabulary to understand the problem so that they could carry out the required solution. Furthermore, future researchers may consider the comprehension level of the pupils perhaps administering comprehension test simultaneously. Keywords: English Grade, Mathematics Grade, Difficulty, Solving, Word problem

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Creative thinking skills help children overcome real-life problems

A new study from The Ohio State University demonstrates that promoting creative thinking in children can prepare them to become more resilient to real-life problems.

The researchers trained third, fourth and fifth graders to use literary techniques such as perspective shifting, counterfactual (what if) thinking and causal (why) thinking to improve creativity in dealing with everyday challenges.

New ways to solve problems

Professor Angus Fletcher said the techniques helped kids come up with new, creative and practical ways to solve problems.

"There are concerns about the resiliency of American children in the wake of COVID-19 and this sense that many kids are having a hard time in school and in life," noted Professor Fletcher. "Creativity training can help kids come up with a second plan when things aren't working out for them."

Professor Fletcher said the program used in this study was similar to one he and his colleagues used successfully with the U.S. Army. That particular work earned Professor Fletcher the Public Service Commendation Medal, the fourth-highest public service decoration that the Army can grant a civilian.

How the study was conducted 

The research involved two separate studies focused on students attending a summer camp in a Columbus suburb. In the first study, students were split into two groups - a control group and a creative group.

The control group was asked to identify a special quality about themselves. They were told this was their special power that could help them solve any problem.

In the creative group, students were asked to think of a friend who did something special and think of them as their "creative friend" who could help them solve any problem. When children view a problem or challenge through the eyes of someone else, it is a creative process known as perspective-shifting.

"When you ask people to shift their perspective and imagine receiving advice from a friend, you get a lot more creative and effective solutions to problems than just trying to solve the problem yourself," explained Professor Fletcher. This is exactly what the study demonstrated.

Anticipating everyday challenges 

As part of the study, teachers identified a problem that may be challenging for their students, such as not being able to attend a friend's birthday party because they will be out of town. 

Students also thought about a challenging problem in their own lives, such as "my sister bullies me" or "my dad has to be away for two months."

What the researchers discovered 

The results of the study showed that without the perspective-shift training, less than half of the students were able to provide a solution to an age-typical problem, and almost none were able to provide a solution to their own problems.

On the other hand, 94 percent of students who were trained in perspective-shifting provided a solution to both types of problems. 

According to Professor Fletcher, these results showed how creativity training could boost children's sense of self-efficacy – the belief that they had some control and power over their own lives.

"Step back and say why does this matter? We often find that if you think more broadly about what you are trying to accomplish, and why it is so important, then you can see there are other ways of getting what you want."

Testing resilience 

After the training was completed, students were presented with age-typical problems and also examined one of their own problems. 

In an effort to test resilience, the researchers had an expected response when the children presented their proposed solutions. They told the students that their solution would not work. 

Every student in the creative thinking group was able to provide a second solution to both the age-typical and personal problems.

"With this training, the children were unfazed by being told their first solution didn't work. They came up with a second plan, which is a good test of resilience."

Helping children cope with problems 

Professor Fletcher said this study provides a hopeful message: There are things we can do to help children cope with their problems.

"We are at this moment in our society where our kids need help. We found that before this training, kids had this propensity to just give up when faced with problems. That could lead them to get angry, or embarrassed that they can't solve their problems, or look for adults to offer solutions."

"What narrative creativity training can do is teach children there are ways to approach real-life problems that don't have easy answers."

Teaching creative thinking through the arts

Professor Fletcher explained that kids can learn creative thinking through the arts, such as literature and theater, if they are presented in the right way. 

For example, rather than just asking students to analyze works of art, teachers could have students imagine themselves as different characters, explore new perspectives, and engage in why and what-if thinking.

"The ability to use this type of thinking can't be assessed via standardized tests. But it is still very important and can help children use and grow their creativity to solve real-world challenges."

Professor Fletcher conducted the research with Ohio State colleagues Professor Patricia Enciso and Mike Benveniste, also of Project Narrative.

The study is published in the Journal of Creativity .

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