define visual representation tok

IBDP Visual Arts

Website by Heather McReynolds & Shannon Brinkley

Updated 11 May 2024

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TOK: The 12 concepts

• Course Components
• Theory of Knowldege

You may not have noticed but TOK has changed it's framework... The main difference is that the new TOK curriculum is focused on "big ideas " through 12 concepts that that are transdisciplinary in nature and help us to understand why we are learning the content.

This page looks at these 12 concepts on which the TOK course is built. Some of the concepts link more directly to visual arts than others, but helping students to see how these concepts are relevant in art will help to support the transfer of their understandings and make TOK a more relevant and integrated part of their DP learning. For those concepts most relevant to our subject I have included links to activities and resources to explore in greater depth. Thanks to John Crane, author of the Psychology site, for the outline and the inspiration! 

Certainty           Culture            Evidence     Explanation          Interpretation    Justification

Objectivity        perspective      power          responsibility      truth                  values, how do these 12 concepts relate to art .

Unlike other areas of knowledge, certainty is certainly not what artists explore, but rather the opposite, uncertainty! I read somewhere that scientists are seeking answers, whereas artists are seeking more questions.

Related content -Viewer Exhibition Response  

TOK is interested in how culture affects our knowledge of the world around us. The sociocultural approach is one of the lenses through which we can analyze art works- so in this sense, we have a great link here to TOK. Cultural Significance (C) is one of the criterion for the Comparative Study and an integral part of the visual arts syllabus.

You will find many relevant pages and activities in the Culture and Context section, such as

Your Cultural Influences

Cultural and Geographic Focus  

Defining Culture  

The Role of Culture  

Artists Looking at Culture  

Cultural Assumptions  

Interpretive Frameworks  

Evidence is an important part of any kind of research, perhaps not the most relevant to art, but students do need to use research and find evidence to support their analysis in the CS and to investigate artists in the PP, and both require empirical evidence, documentation and citation.

Related content:

Research and Practice  

Referencing and Citing Sources  

Secondary Sources  

Explanation

Art tends to infer rather than explain, we are not looking for explanations but rather to be invited into an unknown territory, otherwise why make art? Documentary photography bears witness, journalism explains,, but art? Explanation however can be our attempt to understand why an art work is made in a certain way, how it is made, and what it communicates. Students offer a sort of explanation ( more of a justification-see below ) of their exhibition in the Curatorial Rationale

related pages:????

Critiques  

Feedback  

Interpretation

The way we interpret art and meaning is essential to our understanding of art. Interpretation is highly subjective in the arts.

Interpretation is influenced by culture- Cultural Assumptions  

Interpretation is influenced by knowledge- Art and Knowledge

Interpretation is influenced by the value we assign to art- Art and Values  

Interpretation is even influenced by how we title our work- Titling Work  

Try this fun activity for looking at how we view and understand art from different  Interpretive Frameworks

The resource   4 Ways of Looking at Art is useful for guided looking

Justification

Art making involves complex decision making, in the choice of materials, of subject matter, of scale, you name it, everything is a decision that impacts the art that evolves from it. Curatorial practice is decision making, where and how to display work, how meaning is impacted, and all of these considerations must be justified by the student in their final exhibition, giving reasons for their choices and decisions in their Curatorial Rationale  

Objectivity

Does objectivity in art exist? Is there not fundamentally a personal response? There are of course certain guidelines the examiner must follow when assessing work. Technical skill, for example, is supposedly an objective quality that we can quantify and agree upon....hmmm.

Under objectivity we might also explore our personal biases, our preferences, our aesthetic inclinations, and how this influences our response to a given art work.

Who decides what is good art? - Art and Values  

Try this look and respond slideshow Intuitive Response

Perspective

Perspective is related to objectivity, or rather, the opposite of it, and of course to interpretation and from what viewpoint we approach an art work.

We can consider point of view in visual art in a literal way: every composition has a viewpoint, creating the illusion of space requires understanding of linear perspective, and we can explore Perspective and Drawing Aides to achieve this.

We can also consider perspective as a cultural lens through which we view art and make art.

Your Cultural Influences  

Historical Context  

In TOK the idea of power is how knowledge can be power.   We can think about this concept in terms of how art can challenge society to change and develop in positive ways, for example Art that Challenges and Confronts , but also how Art and Money get mixed up and the power that is assigned to Celebrity Artists  

Responsibility

 What are the ethical responsibilities of artists? This is a tricky one, with very different parameters for students (see Ethical Expression  ) and those professional artists who seem to have no concern for ethics, or maybe wish to challenge us. 

Responsibility is a rich topic to explore in visual arts, try these questions:

• What moral responsibilities does the artist have or not have? Are they different from any other knower?

• To what extent does the artist have a moral obligation to avoid or confront issues that might shock or be contrary to most people?

• Do you think controversy is important for an artwork to have a strong impact? Why do artists often rely on the shock factor?

• What do we expect from art? Truth? Seduction? Provocation? Beauty

Relevant pages

Art and Values  

Art that Challenges and Confronts  

Veiled Content  

The function and purpose of art is not necessarily to tell the truth, although art may address truths about human nature in a way other disciplines cannot. Aristotle wrote that poetry is more true than history because it presents universal truths whereas history gives only particular truths and that poetry shows how a person might behave (or think, or feel).

Truth (even truth to human nature) is not a prerequisite in works of art, entire genres of art, such as music, and much visual art exist without it. Thus, the view that the purpose or function of art is to provide truth does not hold; perhaps the person who wants absolute truths had better turn to science or philosophy rather than to the arts. [1]

“We all know that Art is not truth. Art is a lie that makes us realize truth at least the truth that is given us to understand. The artist must know the manner whereby to convince others of the truthfulness of his lies.”- Pablo Picasso

Curiosity Cabinets  

How do we assign value to art?

What are the standards for judging whether art is good or bad?

Do we need education or knowledge in order to enjoy a work of art?

Is an art form legitimate if it can be enjoyed only by those trained in its appreciation?

Can a critical assessment of an art form be made by someone with no relevant education or cultural familiarity?

Does art need to be justified outside of its' own cultural context?

Do we apply these same rules (or exceptions to the rules) to science?

Art has power to change how people think, does this mean it should be controlled? Isn't art the ultimate freedom of expression? Should art serve a higher cause, a greater good or should it just be an expression of the individual?

Try the quiz in Interpretive Frameworks  

Explore Vasari's Five Criteria and come up with your own

• ^ https://www.britannica.om/topic/philosophy-of-art/Art-as-a-means-to-truth-or-knowledge

Visual Representations: 2023 TOK Essay Title 5 TOK Talk

Today I enjoyed tea and Talked some TOK with Kevin Hoye (IB English Literature and TOK Teacher) about 2023 TOK Essay Title 5: Are visual representations always helpful in the communication of knowledge? Discuss with reference to the human sciences and mathematics. We talked a lot about different ways into understanding this question.. Links to several examples discussed can be found on www.TOKTalk.org Thank you to the random street Shanghai musician, once again for the music bringing us in and out of this track. Guest: Kevin Hoye

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Visual Representation

What is visual representation.

Visual Representation refers to the principles by which markings on a surface are made and interpreted. Designers use representations like typography and illustrations to communicate information, emotions and concepts. Color, imagery, typography and layout are crucial in this communication.

Alan Blackwell, cognition scientist and professor, gives a brief introduction to visual representation:

• Transcript loading…

We can see visual representation throughout human history, from cave drawings to data visualization :

Art uses visual representation to express emotions and abstract ideas.

Financial forecasting graphs condense data and research into a more straightforward format.

Icons on user interfaces (UI) represent different actions users can take.

The color of a notification indicates its nature and meaning.

Van Gogh's "The Starry Night" uses visuals to evoke deep emotions, representing an abstract, dreamy night sky. It exemplifies how art can communicate complex feelings and ideas.

© Public domain

Importance of Visual Representation in Design

Designers use visual representation for internal and external use throughout the design process . For example:

Storyboards are illustrations that outline users’ actions and where they perform them.

Sitemaps are diagrams that show the hierarchy and navigation structure of a website.

Wireframes are sketches that bring together elements of a user interface's structure.

Usability reports use graphs and charts to communicate data gathered from usability testing.

User interfaces visually represent information contained in applications and computerized devices.

This usability report is straightforward to understand. Yet, the data behind the visualizations could come from thousands of answered surveys.

© Interaction Design Foundation, CC BY-SA 4.0

Visual representation simplifies complex ideas and data and makes them easy to understand. Without these visual aids, designers would struggle to communicate their ideas, findings and products . For example, it would be easier to create a mockup of an e-commerce website interface than to describe it with words.

Visual representation simplifies the communication of designs. Without mockups, it would be difficult for developers to reproduce designs using words alone.

Types of Visual Representation

Below are some of the most common forms of visual representation designers use.

Text and Typography

Text represents language and ideas through written characters and symbols. Readers visually perceive and interpret these characters. Typography turns text into a visual form, influencing its perception and interpretation.

We have developed the conventions of typography over centuries , for example, in documents, newspapers and magazines. These conventions include:

Text arranged on a grid brings clarity and structure. Gridded text makes complex information easier to navigate and understand. Tables, columns and other formats help organize content logically and enhance readability.

Contrasting text sizes create a visual hierarchy and draw attention to critical areas. For example, headings use larger text while body copy uses smaller text. This contrast helps readers distinguish between primary and secondary information.

Adequate spacing and paragraphing improve the readability and appearance of the text. These conventions prevent the content from appearing cluttered. Spacing and paragraphing make it easier for the eye to follow and for the brain to process the information.

Balanced image-to-text ratios create engaging layouts. Images break the monotony of text, provide visual relief and illustrate or emphasize points made in the text. A well-planned ratio ensures neither text nor images overwhelm each other. Effective ratios make designs more effective and appealing.

Designers use these conventions because people are familiar with them and better understand text presented in this manner.

This table of funerals from the plague in London in 1665 uses typographic conventions still used today. For example, the author arranged the information in a table and used contrasting text styling to highlight information in the header.

Illustrations and Drawings

Designers use illustrations and drawings independently or alongside text. An example of illustration used to communicate information is the assembly instructions created by furniture retailer IKEA. If IKEA used text instead of illustrations in their instructions, people would find it harder to assemble the furniture.

IKEA assembly instructions use illustrations to inform customers how to build their furniture. The only text used is numeric to denote step and part numbers. IKEA communicates this information visually to: 1. Enable simple communication, 2. Ensure their instructions are easy to follow, regardless of the customer’s language.

© IKEA, Fair use

Illustrations and drawings can often convey the core message of a visual representation more effectively than a photograph. They focus on the core message , while a photograph might distract a viewer with additional details (such as who this person is, where they are from, etc.)

For example, in IKEA’s case, photographing a person building a piece of furniture might be complicated. Further, photographs may not be easy to understand in a black-and-white print, leading to higher printing costs. To be useful, the pictures would also need to be larger and would occupy more space on a printed manual, further adding to the costs.

But imagine a girl winking—this is something we can easily photograph. 

Ivan Sutherland, creator of the first graphical user interface, used his computer program Sketchpad to draw a winking girl. While not realistic, Sutherland's representation effectively portrays a winking girl. The drawing's abstract, generic elements contrast with the distinct winking eye. The graphical conventions of lines and shapes represent the eyes and mouth. The simplicity of the drawing does not draw attention away from the winking.

A photo might distract from the focused message compared to Sutherland's representation. In the photo, the other aspects of the image (i.e., the particular person) distract the viewer from this message.

© Ivan Sutherland, CC BY-SA 3.0 and Amina Filkins, Pexels License

Information and Data Visualization

Designers and other stakeholders use data and information visualization across many industries.

Data visualization uses charts and graphs to show raw data in a graphic form. Information visualization goes further, including more context and complex data sets. Information visualization often uses interactive elements to share a deeper understanding.

For example, most computerized devices have a battery level indicator. This is a type of data visualization. IV takes this further by allowing you to click on the battery indicator for further insights. These insights may include the apps that use the most battery and the last time you charged your device.

macOS displays a battery icon in the menu bar that visualizes your device’s battery level. This is an example of data visualization. Meanwhile, macOS’s settings tell you battery level over time, screen-on-usage and when you last charged your device. These insights are actionable; users may notice their battery drains at a specific time. This is an example of information visualization.

© Low Battery by Jemis Mali, CC BY-NC-ND 4.0, and Apple, Fair use

Information visualization is not exclusive to numeric data. It encompasses representations like diagrams and maps. For example, Google Maps collates various types of data and information into one interface:

Data Representation: Google Maps transforms complex geographical data into an easily understandable and navigable visual map.

Interactivity: Users can interactively customize views that show traffic, satellite imagery and more in real-time.

Layered Information: Google Maps layers multiple data types (e.g., traffic, weather) over geographical maps for comprehensive visualization.

User-Centered Design : The interface is intuitive and user-friendly, with symbols and colors for straightforward data interpretation.

The volume of data contained in one screenshot of Google Maps is massive. However, this information is presented clearly to the user. Google Maps highlights different terrains with colors and local places and businesses with icons and colors. The panel on the left lists the selected location’s profile, which includes an image, rating and contact information.

© Google, Fair use

Symbolic Correspondence

Symbolic correspondence uses universally recognized symbols and signs to convey specific meanings . This method employs widely recognized visual cues for immediate understanding. Symbolic correspondence removes the need for textual explanation.

For instance, a magnifying glass icon in UI design signifies the search function. Similarly, in environmental design, symbols for restrooms, parking and amenities guide visitors effectively.

The Interaction Design Foundation (IxDF) website uses the universal magnifying glass symbol to signify the search function. Similarly, the play icon draws attention to a link to watch a video.

How Designers Create Visual Representations

Visual language.

Designers use elements like color , shape and texture to create a communicative visual experience. Designers use these 8 principles:

Size – Larger elements tend to capture users' attention readily.

Color – Users are typically drawn to bright colors over muted shades.

Contrast – Colors with stark contrasts catch the eye more effectively.

Alignment – Unaligned elements are more noticeable than those aligned ones.

Repetition – Similar styles repeated imply a relationship in content.

Proximity – Elements placed near each other appear to be connected.

Whitespace – Elements surrounded by ample space attract the eye.

Texture and Style – Users often notice richer textures before flat designs.

The 8 visual design principles.

In web design , visual hierarchy uses color and repetition to direct the user's attention. Color choice is crucial as it creates contrast between different elements. Repetition helps to organize the design—it uses recurring elements to establish consistency and familiarity.

In this video, Alan Dix, Professor and Expert in Human-Computer Interaction, explains how visual alignment affects how we read and absorb information:

Correspondence Techniques

Designers use correspondence techniques to align visual elements with their conceptual meanings. These techniques include color coding, spatial arrangement and specific imagery. In information visualization, different colors can represent various data sets. This correspondence aids users in quickly identifying trends and relationships .

Color coding enables the stakeholder to see the relationship and trend between the two pie charts easily.

In user interface design, correspondence techniques link elements with meaning. An example is color-coding notifications to state their nature. For instance, red for warnings and green for confirmation. These techniques are informative and intuitive and enhance the user experience.

The IxDF website uses blue for call-to-actions (CTAs) and red for warnings. These colors inform the user of the nature of the action of buttons and other interactive elements.

Perception and Interpretation

If visual language is how designers create representations, then visual perception and interpretation are how users receive those representations. Consider a painting—the viewer’s eyes take in colors, shapes and lines, and the brain perceives these visual elements as a painting.

In this video, Alan Dix explains how the interplay of sensation, perception and culture is crucial to understanding visual experiences in design:

Copyright holder: Michael Murphy _ Appearance time: 07:19 - 07:37 _ Link: https://www.youtube.com/watch?v=C67JuZnBBDc

Visual perception principles are essential for creating compelling, engaging visual representations. For example, Gestalt principles explain how we perceive visual information. These rules describe how we group similar items, spot patterns and simplify complex images. Designers apply Gestalt principles to arrange content on websites and other interfaces. This application creates visually appealing and easily understood designs.

In this video, design expert and teacher Mia Cinelli discusses the significance of Gestalt principles in visual design . She introduces fundamental principles, like figure/ground relationships, similarity and proximity.

Interpretation

Everyone's experiences, culture and physical abilities dictate how they interpret visual representations. For this reason, designers carefully consider how users interpret their visual representations. They employ user research and testing to ensure their designs are attractive and functional.

Leonardo da Vinci's "Mona Lisa", is one of the most famous paintings in the world. The piece is renowned for its subject's enigmatic expression. Some interpret her smile as content and serene, while others see it as sad or mischievous. Not everyone interprets this visual representation in the same way.

Color is an excellent example of how one person, compared to another, may interpret a visual element. Take the color red:

In Chinese culture, red symbolizes luck, while in some parts of Africa, it can mean death or illness.

A personal experience may mean a user has a negative or positive connotation with red.

People with protanopia and deuteranopia color blindness cannot distinguish between red and green.

In this video, Joann and Arielle Eckstut, leading color consultants and authors, explain how many factors influence how we perceive and interpret color:

Learn More about Visual Representation

Read Alan Blackwell’s chapter on visual representation from The Encyclopedia of Human-Computer Interaction.

Learn about the F-Shaped Pattern For Reading Web Content from Jakob Nielsen.

Read Smashing Magazine’s article, Visual Design Language: The Building Blocks Of Design .

Take the IxDF’s course, Perception and Memory in HCI and UX .

Questions related to Visual Representation

Some highly cited research on visual representation and related topics includes:

Roland, P. E., & Gulyás, B. (1994). Visual imagery and visual representation. Trends in Neurosciences, 17(7), 281-287. Roland and Gulyás' study explores how the brain creates visual imagination. They look at whether imagining things like objects and scenes uses the same parts of the brain as seeing them does. Their research shows the brain uses certain areas specifically for imagination. These areas are different from the areas used for seeing. This research is essential for understanding how our brain works with vision.

Lurie, N. H., & Mason, C. H. (2007). Visual Representation: Implications for Decision Making. Journal of Marketing, 71(1), 160-177.

This article looks at how visualization tools help in understanding complicated marketing data. It discusses how these tools affect decision-making in marketing. The article gives a detailed method to assess the impact of visuals on the study and combination of vast quantities of marketing data. It explores the benefits and possible biases visuals can bring to marketing choices. These factors make the article an essential resource for researchers and marketing experts. The article suggests using visual tools and detailed analysis together for the best results.

Lohse, G. L., Biolsi, K., Walker, N., & Rueter, H. H. (1994, December). A classification of visual representations. Communications of the ACM, 37(12), 36+.

This publication looks at how visuals help communicate and make information easier to understand. It divides these visuals into six types: graphs, tables, maps, diagrams, networks and icons. The article also looks at different ways these visuals share information effectively.

​​If you’d like to cite content from the IxDF website , click the ‘cite this article’ button near the top of your screen.

Some recommended books on visual representation and related topics include:

Chaplin, E. (1994). Sociology and Visual Representation (1st ed.) . Routledge.

Chaplin's book describes how visual art analysis has changed from ancient times to today. It shows how photography, post-modernism and feminism have changed how we see art. The book combines words and images in its analysis and looks into real-life social sciences studies.

Mitchell, W. J. T. (1994). Picture Theory. The University of Chicago Press.

Mitchell's book explores the important role and meaning of pictures in the late twentieth century. It discusses the change from focusing on language to focusing on images in cultural studies. The book deeply examines the interaction between images and text in different cultural forms like literature, art and media. This detailed study of how we see and read visual representations has become an essential reference for scholars and professionals.

Koffka, K. (1935). Principles of Gestalt Psychology. Harcourt, Brace & World.

"Principles of Gestalt Psychology" by Koffka, released in 1935, is a critical book in its field. It's known as a foundational work in Gestalt psychology, laying out the basic ideas of the theory and how they apply to how we see and think. Koffka's thorough study of Gestalt psychology's principles has profoundly influenced how we understand human perception. This book has been a significant reference in later research and writings.

A visual representation, like an infographic or chart, uses visual elements to show information or data. These types of visuals make complicated information easier to understand and more user-friendly.

Designers harness visual representations in design and communication. Infographics and charts, for instance, distill data for easier audience comprehension and retention.

For an introduction to designing basic information visualizations, take our course, Information Visualization .

Text is a crucial design and communication element, transforming language visually. Designers use font style, size, color and layout to convey emotions and messages effectively.

Designers utilize text for both literal communication and aesthetic enhancement. Their typography choices significantly impact design aesthetics, user experience and readability.

Designers should always consider text's visual impact in their designs. This consideration includes font choice, placement, color and interaction with other design elements.

In this video, design expert and teacher Mia Cinelli teaches how Gestalt principles apply to typography:

Designers use visual elements in projects to convey information, ideas, and messages. Designers use images, colors, shapes and typography for impactful designs.

In UI/UX design, visual representation is vital. Icons, buttons and colors provide contrast for intuitive, user-friendly website and app interfaces.

Graphic design leverages visual representation to create attention-grabbing marketing materials. Careful color, imagery and layout choices create an emotional connection.

Product design relies on visual representation for prototyping and idea presentation. Designers and stakeholders use visual representations to envision functional, aesthetically pleasing products.

Our brains process visuals 60,000 times faster than text. This fact highlights the crucial role of visual representation in design.

Our course, Visual Design: The Ultimate Guide , teaches you how to use visual design elements and principles in your work effectively.

Visual representation, crucial in UX, facilitates interaction, comprehension and emotion. It combines elements like images and typography for better interfaces.

Effective visuals guide users, highlight features and improve navigation. Icons and color schemes communicate functions and set interaction tones.

UX design research shows visual elements significantly impact emotions. 90% of brain-transmitted information is visual.

To create functional, accessible visuals, designers use color contrast and consistent iconography. These elements improve readability and inclusivity.

An excellent example of visual representation in UX is Apple's iOS interface. iOS combines a clean, minimalist design with intuitive navigation. As a result, the operating system is both visually appealing and user-friendly.

Michal Malewicz, Creative Director and CEO at Hype4, explains why visual skills are important in design:

Learn more about UI design from Michal in our Master Class, Beyond Interfaces: The UI Design Skills You Need to Know .

The fundamental principles of effective visual representation are:

Clarity : Designers convey messages clearly, avoiding clutter.

Simplicity : Embrace simple designs for ease and recall.

Emphasis : Designers highlight key elements distinctively.

Balance : Balance ensures design stability and structure.

Alignment : Designers enhance coherence through alignment.

Contrast : Use contrast for dynamic, distinct designs.

Repetition : Repeating elements unify and guide designs.

Designers practice these principles in their projects. They also analyze successful designs and seek feedback to improve their skills.

Read our topic description of Gestalt principles to learn more about creating effective visual designs. The Gestalt principles explain how humans group elements, recognize patterns and simplify object perception.

Color theory is vital in design, helping designers craft visually appealing and compelling works. Designers understand color interactions, psychological impacts and symbolism. These elements help designers enhance communication and guide attention.

Designers use complementary , analogous and triadic colors for contrast, harmony and balance. Understanding color temperature also plays a crucial role in design perception.

Color symbolism is crucial, as different colors can represent specific emotions and messages. For instance, blue can symbolize trust and calmness, while red can indicate energy and urgency.

Cultural variations significantly influence color perception and symbolism. Designers consider these differences to ensure their designs resonate with diverse audiences.

For actionable insights, designers should:

Experiment with color schemes for effective messaging. 

Assess colors' psychological impact on the audience. 

Use color contrast to highlight critical elements. 

Ensure color choices are accessible to all.

In this video, Joann and Arielle Eckstut, leading color consultants and authors, give their six tips for choosing color:

Learn more about color from Joann and Arielle in our Master Class, How To Use Color Theory To Enhance Your Designs .

Typography and font choice are crucial in design, impacting readability and mood. Designers utilize them for effective communication and expression.

Designers' perception of information varies with font type. Serif fonts can imply formality, while sans-serifs can give a more modern look.

Typography choices by designers influence readability and user experience. Well-spaced, distinct fonts enhance readability, whereas decorative fonts may hinder it.

Designers use typography to evoke emotions and set a design's tone. Choices in font size, style and color affect the emotional impact and message clarity.

Designers use typography to direct attention, create hierarchy and establish rhythm. These benefits help with brand recognition and consistency across mediums.

Read our article to learn how web fonts are critical to the online user experience .

Designers create a balance between simplicity and complexity in their work. They focus on the main messages and highlight important parts. Designers use the principles of visual hierarchy, like size, color and spacing. They also use empty space to make their designs clear and understandable.

The Gestalt law of Prägnanz suggests people naturally simplify complex images. This principle aids in making even intricate information accessible and engaging.

Through iteration and feedback, designers refine visuals. They remove extraneous elements and highlight vital information. Testing with the target audience ensures the design resonates and is comprehensible.

Michal Malewicz explains how to master hierarchy in UI design using the Gestalt rule of proximity:

Literature on Visual Representation

Here’s the entire UX literature on Visual Representation by the Interaction Design Foundation, collated in one place:

Learn more about Visual Representation

Take a deep dive into Visual Representation with our course Perception and Memory in HCI and UX .

How does all of this fit with interaction design and user experience? The simple answer is that most of our understanding of human experience comes from our own experiences and just being ourselves. That might extend to people like us, but it gives us no real grasp of the whole range of human experience and abilities. By considering more closely how humans perceive and interact with our world, we can gain real insights into what designs will work for a broader audience: those younger or older than us, more or less capable, more or less skilled and so on.

“You can design for all the people some of the time, and some of the people all the time, but you cannot design for all the people all the time.“ – William Hudson (with apologies to Abraham Lincoln)

While “design for all of the people all of the time” is an impossible goal, understanding how the human machine operates is essential to getting ever closer. And of course, building solutions for people with a wide range of abilities, including those with accessibility issues, involves knowing how and why some human faculties fail. As our course tutor, Professor Alan Dix, points out, this is not only a moral duty but, in most countries, also a legal obligation.

Portfolio Project

In the “ Build Your Portfolio: Perception and Memory Project ”, you’ll find a series of practical exercises that will give you first-hand experience in applying what we’ll cover. If you want to complete these optional exercises, you’ll create a series of case studies for your portfolio which you can show your future employer or freelance customers.

This in-depth, video-based course is created with the amazing Alan Dix , the co-author of the internationally best-selling textbook  Human-Computer Interaction and a superstar in the field of Human-Computer Interaction . Alan is currently a professor and Director of the Computational Foundry at Swansea University.

Gain an Industry-Recognized UX Course Certificate

Use your industry-recognized Course Certificate on your resume , CV , LinkedIn profile or your website.

All open-source articles on Visual Representation

Data visualization for human perception.

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• 5 years ago

Open Access—Link to us!

We believe in Open Access and the  democratization of knowledge . Unfortunately, world-class educational materials such as this page are normally hidden behind paywalls or in expensive textbooks.

If you want this to change , cite this page , link to us, or join us to help us democratize design knowledge !

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Visual Representation

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Graphical representation

The concept of “representation” captures the signs that stand in for and take the place of something else [ 5 ]. Visual representation, in particular, refers to the special case when these signs are visual (as opposed to textual, mathematical, etc.). On the other hand, there is no limit on what may be (visually) represented, which may range from abstract concepts to concrete objects in the real world or data items.

In addition to the above, however, the term “representation” is often overloaded and used to imply the actual process of connecting the two worlds of the original items and of their representatives. Typically, the context determines quite clearly which of the two meanings is intended in each case, hence, the term is used for both without further explanation.

Underneath any visual representation lies a mapping between the set of items that are being represented and the set of visual elements that are used to represent them, i.e., to...

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Recommended Reading

Card S.K., Mackinlay J.D., and Shneiderman B. Information visualization. In Readings in Information Visualization: Using Vision to Think, 1999, pp. 1–34.

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Haber E.M., Ioannidis Y., and Livny M. Foundations of visual metaphors for schema display. J. Intell. Inf. Syst., 3(3/4):263–298, 1994.

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Tufte E.R. Envisioning Information. Graphics Press, Cheshire, CO, 1990.

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Yannis Ioannidis

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Ioannidis, Y. (2009). Visual Representation. In: LIU, L., ÖZSU, M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_449

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Initial Thoughts

Perspectives & resources, what is high-quality mathematics instruction and why is it important.

• Page 1: The Importance of High-Quality Mathematics Instruction
• Page 2: A Standards-Based Mathematics Curriculum
• Page 3: Evidence-Based Mathematics Practices

What evidence-based mathematics practices can teachers employ?

• Page 4: Explicit, Systematic Instruction

Page 5: Visual Representations

• Page 6: Schema Instruction
• Page 7: Metacognitive Strategies
• Page 8: Effective Classroom Practices
• Page 9: References & Additional Resources
• Page 10: Credits

Research Shows

• Students who use accurate visual representations are six times more likely to correctly solve mathematics problems than are students who do not use them. However, students who use inaccurate visual representations are less likely to correctly solve mathematics problems than those who do not use visual representations at all. (Boonen, van Wesel, Jolles, & van der Schoot, 2014)
• Students with a learning disability (LD) often do not create accurate visual representations or use them strategically to solve problems. Teaching students to systematically use a visual representation to solve word problems has led to substantial improvements in math achievement for students with learning disabilities. (van Garderen, Scheuermann, & Jackson, 2012; van Garderen, Scheuermann, & Poch, 2014)
• Students who use visual representations to solve word problems are more likely to solve the problems accurately. This was equally true for students who had LD, were low-achieving, or were average-achieving. (Krawec, 2014)

Visual representations are flexible; they can be used across grade levels and types of math problems. They can be used by teachers to teach mathematics facts and by students to learn mathematics content. Visual representations can take a number of forms. Click on the links below to view some of the visual representations most commonly used by teachers and students.

How does this practice align?

High-leverage practice (hlp).

• HLP15 : Provide scaffolded supports

CCSSM: Standards for Mathematical Practice

• MP1 : Make sense of problems and persevere in solving them.

Number Lines

Definition : A straight line that shows the order of and the relation between numbers.

Common Uses : addition, subtraction, counting

Strip Diagrams

Definition : A bar divided into rectangles that accurately represent quantities noted in the problem.

Common Uses : addition, fractions, proportions, ratios

Definition : Simple drawings of concrete or real items (e.g., marbles, trucks).

Common Uses : counting, addition, subtraction, multiplication, division

Graphs/Charts

Definition : Drawings that depict information using lines, shapes, and colors.

Common Uses : comparing numbers, statistics, ratios, algebra

Graphic Organizers

Definition : Visual that assists students in remembering and organizing information, as well as depicting the relationships between ideas (e.g., word webs, tables, Venn diagrams).

Common Uses : algebra, geometry

Before they can solve problems, however, students must first know what type of visual representation to create and use for a given mathematics problem. Some students—specifically, high-achieving students, gifted students—do this automatically, whereas others need to be explicitly taught how. This is especially the case for students who struggle with mathematics and those with mathematics learning disabilities. Without explicit, systematic instruction on how to create and use visual representations, these students often create visual representations that are disorganized or contain incorrect or partial information. Consider the examples below.

Elementary Example

Mrs. Aldridge ask her first-grade students to add 2 + 4 by drawing dots.

Notice that Talia gets the correct answer. However, because Colby draws his dots in haphazard fashion, he fails to count all of them and consequently arrives at the wrong solution.

High School Example

Mr. Huang asks his students to solve the following word problem:

The flagpole needs to be replaced. The school would like to replace it with the same size pole. When Juan stands 11 feet from the base of the pole, the angle of elevation from Juan’s feet to the top of the pole is 70 degrees. How tall is the pole?

Compare the drawings below created by Brody and Zoe to represent this problem. Notice that Brody drew an accurate representation and applied the correct strategy. In contrast, Zoe drew a picture with partially correct information. The 11 is in the correct place, but the 70° is not. As a result of her inaccurate representation, Zoe is unable to move forward and solve the problem. However, given an accurate representation developed by someone else, Zoe is more likely to solve the problem correctly.

Manipulatives

Some students will not be able to grasp mathematics skills and concepts using only the types of visual representations noted in the table above. Very young children and students who struggle with mathematics often require different types of visual representations known as manipulatives. These concrete, hands-on materials and objects—for example, an abacus or coins—help students to represent the mathematical idea they are trying to learn or the problem they are attempting to solve. Manipulatives can help students develop a conceptual understanding of mathematical topics. (For the purpose of this module, the term concrete objects refers to manipulatives and the term visual representations refers to schematic diagrams.)

It is important that the teacher make explicit the connection between the concrete object and the abstract concept being taught. The goal is for the student to eventually understand the concepts and procedures without the use of manipulatives. For secondary students who struggle with mathematics, teachers should show the abstract along with the concrete or visual representation and explicitly make the connection between them.

A move from concrete objects or visual representations to using abstract equations can be difficult for some students. One strategy teachers can use to help students systematically transition among concrete objects, visual representations, and abstract equations is the Concrete-Representational-Abstract (CRA) framework.

If you would like to learn more about this framework, click here.

Concrete-Representational-Abstract Framework

• Concrete —Students interact and manipulate three-dimensional objects, for example algebra tiles or other algebra manipulatives with representations of variables and units.
• Representational — Students use two-dimensional drawings to represent problems. These pictures may be presented to them by the teacher, or through the curriculum used in the class, or students may draw their own representation of the problem.
• Abstract — Students solve problems with numbers, symbols, and words without any concrete or representational assistance.

CRA is effective across all age levels and can assist students in learning concepts, procedures, and applications. When implementing each component, teachers should use explicit, systematic instruction and continually monitor student work to assess their understanding, asking them questions about their thinking and providing clarification as needed. Concrete and representational activities must reflect the actual process of solving the problem so that students are able to generalize the process to solve an abstract equation. The illustration below highlights each of these components.

For Your Information

One promising practice for moving secondary students with mathematics difficulties or disabilities from the use of manipulatives and visual representations to the abstract equation quickly is the CRA-I strategy . In this modified version of CRA, the teacher simultaneously presents the content using concrete objects, visual representations of the concrete objects, and the abstract equation. Studies have shown that this framework is effective for teaching algebra to this population of students (Strickland & Maccini, 2012; Strickland & Maccini, 2013; Strickland, 2017).

Kim Paulsen discusses the benefits of manipulatives and a number of things to keep in mind when using them (time: 2:35).

Kim Paulsen, EdD Associate Professor, Special Education Vanderbilt University

View Transcript

Transcript: Kim Paulsen, EdD

Manipulatives are a great way of helping kids understand conceptually. The use of manipulatives really helps students see that conceptually, and it clicks a little more with them. Some of the things, though, that we need to remember when we’re using manipulatives is that it is important to give students a little bit of free time when you’re using a new manipulative so that they can just explore with them. We need to have specific rules for how to use manipulatives, that they aren’t toys, that they really are learning materials, and how students pick them up, how they put them away, the right time to use them, and making sure that they’re not distracters while we’re actually doing the presentation part of the lesson. One of the important things is that we don’t want students to memorize the algorithm or the procedures while they’re using the manipulatives. It really is just to help them understand conceptually. That doesn’t mean that kids are automatically going to understand conceptually or be able to make that bridge between using the concrete manipulatives into them being able to solve the problems. For some kids, it is difficult to use the manipulatives. That’s not how they learn, and so we don’t want to force kids to have to use manipulatives if it’s not something that is helpful for them. So we have to remember that manipulatives are one way to think about teaching math.

I think part of the reason that some teachers don’t use them is because it takes a lot of time, it takes a lot of organization, and they also feel that students get too reliant on using manipulatives. One way to think about using manipulatives is that you do it a couple of lessons when you’re teaching a new concept, and then take those away so that students are able to do just the computation part of it. It is true we can’t walk around life with manipulatives in our hands. And I think one of the other reasons that a lot of schools or teachers don’t use manipulatives is because they’re very expensive. And so it’s very helpful if all of the teachers in the school can pool resources and have a manipulative room where teachers can go check out manipulatives so that it’s not so expensive. Teachers have to know how to use them, and that takes a lot of practice.

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Visual Representation in Mathematics

Print Resource

by Ian Matheson and Nancy Hutchinson 

Mathematics is a subject that deals with abstract ideas in order to solve problems. Information can be represented with numbers, words, and other types of symbols. Representing information with symbols can be a difficult practice for students with learning disabilities (LDs) to understand, and eventually begin to use themselves.

Information is often represented visually in mathematics as a method of organizing, extending, or replacing other methods of presentation. Visual representation in mathematics involves creating and forming models that reflect mathematical information (van Garderen & Montague, 2003).

LDs and Problem-Solving

Although there are a number of problem solving strategies that students use in mathematics, good problem solvers usually construct a representation of the problem to help them comprehend it (van Garderen & Montague, 2003). Students with LDs can have an especially challenging experience solving problems in math, and research suggests that their use of visual representation strategies differs from their typically-achieving peers in:

• frequency of use (Montague, 1997),
• type of visual representations used (van Garderen & Montague, 2003), and
• quality of visual representations (van Garderen, Scheuermann, & Jackson, 2012b).

Creating a visual representation to solve a problem in mathematics is a process that involves:

• processing the information in the problem,
• selecting important information, and
• identifying the goal of the problem.

Students with LDs struggle with visual representation in mathematics because they typically have difficulties processing information (Swanson, Lussier, & Orosco, 2013).

Visual representation is an important skill because higher-level math and science courses increasingly draw on visualization and spatial reasoning skills to solve problems (Zhang, Ding, Stegall, & Mo, 2012). Additionally, it is simply another strategy that students can use when they are thinking of the best way to answer a problem in mathematics.

The Importance of Explicit Instruction

Perhaps the most consistent message in the literature about visual representation in mathematics is that it needs to be explicitly taught to students. Representing information visually is not a skill that comes naturally to students, and so it must be taught and practiced.

When first introducing a new skill to students, it is important to model the skill in order for them to see how it is used followed by opportunity for students to try it themselves.

Click here to access the article  Explicit Instruction: A Teaching Strategy in Reading, Writing, and Mathematics for Students with Learning Disabilities .

The concrete-representational-abstract (CRA) approach to instructing students is a method of explicit instruction that is supported by research as being effective for students with LDs (Doabler, Fien, Nelson-Walker, & Baker, 2012; Mancl, Miller, & Kennedy, 2012). The concrete level involves the use of objects to represent mathematical information (e.g., counters, cubes); the representational level involves the drawing of pictures to represent the objects that were used in the previous level; and the abstract level replaces pictures of objects with mathematical symbols and numbers.

Click here to access the article Concrete-Representational-Abstract: And Instructional Strategy for Math .

Scaffolding is another approach to teaching visual representation to students with LDs that is supported by research (van Garderen, Scheuermann, & Jackson, 2012a). Scaffolding involves the use of temporary supports during the learning process as needed by the student. Providing a student with an incomplete diagram and having them finish it and then use it to solve a problem is an example of a scaffolding technique.

Types of Visual Representation

When you are talking about visual representation in mathematics, you may be talking about representing information on a page with a diagram or chart , or representing information in your head with an image . Fortunately, researchers have focussed on helping students improve their visual representation both externally (e.g., van Garderen, 2007) and internally (e.g., Zhang et al., 2012). Developing both external and internal visual representation strategies is important for students as both help support student learning in mathematics for different types of problems.

In addition to the distinction between internal and external visual representations, researchers have also outlined differences in visual imagery based on the purpose. Pictorial imagery is used for representing the visual appearance of objects or information. Schematic imagery is used for representing the spatial relationships between objects or information. While both can be used to help students learn and solve problems in mathematics, schematic imagery is more effective as a method for supporting problem solving. Students with LDs are more likely to use pictorial imagery when solving problems in math (van Garderen & Montague, 2003).

External Visual Representation

Diagrams and graphic organizers are two types of external visual representations that are used in mathematics, and both are supported by research for use with students with LDs. This is a type of visual representation that can be modelled to students as it is something that can be seen on a page or on the board at the front of the class.

Diagrams are visual displays that use the important information in mathematical problems. They are typically used to demonstrate how the important information is related , and can be used to organize information as well as to compute the answer to a problem. A common type of diagram might be a drawing that a student creates to represent the objects within a word problem.

Individuals with LDs may have a poorer understanding of what a diagram is, as well as when and how to use it (van Garderen et al., 2012b). Diagrams are effective for students with LDs as they can help highlight essential information and leave out information that is not necessary for solving a problem. This can simplify the problem-solving process (Kolloffel et al., 2009).

Distinctions can be made between pictorial diagrams and schematic diagrams . An example of a pictorial diagram would be a drawing of the important objects within a word problem, while a schematic diagram would be a drawing that includes the spatial relationships between the objects. As mentioned earlier, schematic diagrams are more useful for students and typically result in more success with problem solving (van Garderen & Montague, 2003).

Tree Diagrams

A tree diagram is a method of representing independent events or conditions related to an action, and it is often used to teach students probability theory.

This type of diagram might be used to teach students about probability through coin flipping or through drawing from a deck of cards. It is considered a powerful method of teaching probability in math, and is a great example of a visual representation that is a diagram (Kolloffel, Eysink, de Jong, & Wilhelm, 2009).

Number Lines

A number line is another type of diagram that is being used increasingly by mathematicians (Gersten et al., 2009). A number line consists of a straight line that has equally spaced numbers along it on points, and can be easily drawn by students for use when solving problems.

Number lines are often used for the teaching of integers , as well as for simple addition and subtraction problems, as they provide students with a visual that they can touch to keep track of their place .

Graphic Organizers

A graphic organizer is another type of external visual representation that is often used in mathematics. There are many types of graphic organizers and each have situations that they are best used for. While graphic organizers are often thought of simply as organizational tools , they can be used to make rapid inferences to solve different types of problems.

Research supports the idea that students with language disorders may benefit from learning and instruction using nonverbal information such as a graphic organizer (Ives, 2007).  Additionally, the use of graphic organizers to support learning has been found to improve the comprehension of facts and text for students with LDs at all ages (Dexter & Hughes, 2011), as well as enhancing conceptual understanding in mathematics (Ives, 2007).

Graphic organizers may be a great support for students with LDs because they take some of the organizational pressure off these individuals who may have difficulty sorting through information and seeing the relationships between different mathematical objects or concepts (Ives, 2007).

Four main types of graphic organizers can be used in mathematics:

1. Semantic Maps

A semantic map is one type of graphic organizer that can be used to support learning in mathematics. This type of graphic organizer is mainly used to relate conceptual information , and could be used to support conceptual learning in mathematics.

One example might be to use a semantic map to help young students who are learning to classify shapes into different categories. While shapes might be the main heading, students might organize shapes into further sub-heading such as round, symmetrical, right-angle, etc.

2. Semantic Feature Analysis

A semantic feature analysis is another type of graphic organizer. This graphic organizer is characterized by a matrix format , where features or characteristics of objects or concepts are displayed. A semantic feature analysis might be used to compare shapes in geometry, where comparisons could be made between number of sides, vertices, types of angles, etc.

3. Syntactic/Semantic Feature Analysis

A syntactic/semantic feature analysis is similar to the semantic feature analysis, but sentences are added in to help students identify specific features about each object.

An example sentence that might follow the matrix is “ A ________ has the most sides of all of the shapes we have looked at. ”

4. Visual Displays

Selecting the Appropriate Graphic Organizer

Though each type of graphic organizer can be used for learning mathematics by individuals with LDs, the differences in their design suggest that they may be best used in specific situations.

• Semantic maps and Semantic feature analyses are considered to be better for recalling facts though they are more difficult to understand and to learn how to use (Dexter & Hughes, 2011).
• Syntactic/semantic feature analyses and visual displays are considered to be more efficient for making computations to solve problems, and for recalling the information within these types of graphic organizers (Dexter & Hughes, 2011).

The advantages to each type of graphic organizer suggest that initial instruction of a mathematical concept may be best with more complicated graphic organizers, and that independent review and studying could be done with less complicated graphic organizers to improve recall of information for students with LDs (Dexter & Hughes, 2011).

Explicit Instruction of External Visual Representation

It is important to remember that explicit instruction is necessary for both diagrams and graphic organizers. This instruction should highlight the purpose of each type of external visual representation, as well as when and how to use them .  Both types of external visual representations can be easily modelled for students as educators can physically construct them and explain their thinking as they do so in front of students.

In a study conducted by van Garderen (2007), the researcher examined the effectiveness of a three-phase instructional strategy for teaching students with LDs to use diagrams in mathematics:

• The first phase involved explicit instruction about what diagrams are, as well as how and when they are used.
• The second phase connected the use of diagrams to one-step word problems , where students created diagrams that represented the information that they knew and the information that they did not know.
• The third phase was focused on two-step word problems which have more than one unknown piece of information, and students used diagrams to determine the ultimate goal of the problem, as well as the secondary pieces of information that they would need to find in order to compute the ultimate goal.

Teaching students with LDs to use diagrams with this sequence of explicit instruction resulted in improved performance , satisfaction of the students, and students were also more likely to use diagrams with other types of problems.

Internal Visual Representation

While external visual representation can be easy to model and teach explicitly to students, internal visual representation is not as easy to show students as it is a mental exercise. A visual schematic representation involves the creation or recall of visual imagery to represent information.

Students are often asked to visualize the problem in order to better understand it and solve it. This can be a difficult task for students and it should not be assumed that this is a skill that all students already possess .

To create a mental picture when solving a word problem in math, students must combine information from the problem with their prior knowledge of the topic. While students cannot see the mental images that their teachers create, it is still possible to walk students through the process of creating the mental image as a verbal model , or even to draw images of what they are seeing in their head to make it more explicit.

Click here to access the article Verbalization in Math Problem-Solving .

A group of researchers (Krawec, Huang, Montague, Kressler, Melia de Alba, 2012) developed an intervention to support students with LDs as they solve problems in mathematics. The intervention was aimed at explicitly instructing students about the cognitive processes that proficient problem solvers use in math, including visualization . The intervention was delivered by teachers who were trained to follow a sequence of instruction that included teaching visualizing to the students. The intervention involved the teachers “ thinking aloud ” as they progressed through the stages of the problem solving process. Students who were a part of the intervention reported using more strategies when solving problems in math, including the strategy of visualizing the problem (Krawec et al., 2012).

Visual-Chunking

One strategy that teachers can use to support their students with LDs in creating internal visual representations is known as visual-chunking representation .  Chunking is the practice of combining bits of information that are related in some way in order to reduce the overall amount of information for easier processing.  For students with LDs, a reduction in the amount of information to be processed can make exercises such as math problem solving much easier.

A group of researchers examined one method of visual-chunking for students with difficulties in math, where students were working with geometric shapes and transformations (Zhang et al., 2012). One group received series of nets of geometric shapes, while another group received the same nets, though sections had been shaded or “chunked” in an effort to see if it made a difference in their transformations. The group that received the visual-chunking support performed better than the other group, and found the exercise to be easier when provided with the visual-chunking support (Zhang et al., 2012).

Visual Schematic Representations

Visual schematic representations have been shown to be effective for individuals with specific difficulties in math, which can include LDs (Swanson et al., 2013). Instructing students about how to create internal visual representations can be difficult as it does not easily lend itself to explicit instructional techniques . Despite this challenge, teachers can still support the development of this skill by creating diagrams of their mental images as well as by thinking aloud as they are visualizing while problem solving.

The use of visual representation during instruction and learning tends to be an effective practice across a number of subjects , including mathematics (Gersten et al., 2009). While using visual representation alone as a teaching method does produce significant learning improvements for students in mathematics, these improvements are even greater when other teaching methods are used as well (Gersten et al., 2009).

Having students represent mathematical information verbally and in written form along with visual representation is encouraged. For students with LD, both receiving instruction and solving problems in a number of ways will help support their deeper understanding of concepts and operations in mathematics (Suh & Moyer, 2007).

The importance of using explicit instruction to teach students how to make visual representations cannot be overstated. The CRA method is an example of an effective sequence of explicitly instructing students with LD to use visual representation as a step towards the use of mathematical symbols exclusively (Mancl et al., 2012).

There are many types of diagrams (Kolloffel et al., 2009) and graphic organizers (Dexter & Hughes, 2011) that can be effectively used support students with LD in mathematics. While internal visual representation can be difficult to model, strategies do exist that can support students with LD as they develop this skill (Zhang et al., 2012).  Educators are encouraged to use a combination of external and internal visual representation strategies in their instruction to students in the interest of helping students develop both types of skills.

Related Resources on the LD@school Website

Click here to access the article Mind Maps .

Click here to access the article LDs in Mathematics: Evidence-Based Interventions, Strategies, and Resources .

Dexter, D. D., & Hughes, C. A. (2011). Graphic organizers and students with learning disabilities: A meta-analysis. Learning Disability Quarterly, 34 , 51-72.

Doabler, C. T., Fien, H., Nelson-Walker, N. J., & Baker, S. K. (2012). Evaluating three elementary mathematics programs for presence of eight research-based instructional design principles. Learning Disability Quarterly, 35 , 200-211.

Gersten, R., Chard, D. J., Jayanthi, M., Baker, S. K., Morphy, P., & Flojo, J. (2009). Mathematics instruction for students with learning disabilities: A meta-analysis of instructional components. Review of Educational Research, 79 , 1202-1242.

Ives, B. (2007). Graphics organizers applied to secondary algebra instruction for students with learning disorders. Learning Disabilities Research & Practice, 22 , 110-118.

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Krawec, J., Huang, J., Montague, M., Kressler, B., Melia de Alba, A. (2012). The effects of cognitive strategy instruction on knowledge of math problem-solving processes of middle school students with learning disabilities. Learning Disabilities Quarterly, 36 , 80-92.

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Suh, J., & Moyer, P. S. (2007). Developing students’ representational fluency using virtual and physical algebra balances. Journal of Computers in Mathematics and Science Teaching, 26 , 155-173.

Swanson, H. L., Lussier, C., & Orosco, M. (2013). Effects of cognitive strategy interventions and cognitive moderators on word problem solving in children at risk for problem solving difficulties. Learning Disabilities Research & Practice, 28 , 170-183.

van Garderen, D. (2007). Teaching students with LD to use diagrams to solve mathematical word problems. Journal of Learning Disabilities, 40 , 540-553.

van Garderen, D., & Montague, M. (2003). Visual-spatial representation, mathematical problem solving, and students of varying abilities. Learning Disabilities Research & Practice, 18 , 246-254.

van Garderen, D., Scheuermann, A., & Jackson, C. (2012a). Developing representational ability in mathematics for students with learning disabilities: A content analysis of grades 6 and 7 textbooks. Learning Disability Quarterly, 35 , 24-38.

van Garderen, D., Scheuermann, A., & Jackson, C. (2012b). Examining how students with diverse abilities use diagrams to solve mathematics word problems. Learning Disabilities Quarterly, 36 , 145-160.

Zhang, D., Ding, Y., Stegall, J., & Mo, L. (2012). The effect of visual-chunking-representation accommodation on geometry testing for students with math disabilities. Learning Disabilities Research & Practice, 27 , 167-177.

Searches were conducted of the literature for content appropriate for this topic that was published in scientific journals and other academic sources. The search included online database searches (ERIC, PsycINFO, Queen’s Summons, and Google Scholar). The gathered materials were checked for relevance by analysing data in this hierarchical order: (a) titles; (b) abstracts; (c) method; and (d) entire text.

Relevant journals’ archives were also hand-searched between issues from 2010 and the most recent issues. These journals included Learning Disability Quarterly, Journal of Learning Disabilities, and Learning Disabilities Research & Practice.

Nancy L. Hutchinson is a professor of Cognitive Studies in the Faculty of Education at Queen’s University. Her research has focused on teaching students with learning disabilities (e.g., math and career development) and on enhancing workplace learning and co-operative education for students with disabilities and those at risk of dropping out of school. In the past five years, in addition to her research on transition out of school, Nancy has worked with a collaborative research group involving researchers from Ontario, Quebec, and Nova Scotia on transition into school of children with severe disabilities. She teaches courses on inclusive education in the preservice teacher education program as well as doctoral seminars on social cognition and master’s courses on topics including learning disabilities, inclusion, and qualitative research. She has published six editions of a textbook on teaching students with disabilities in the regular classroom and two editions of a companion casebook.

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