– all angles 60°
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.
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.
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.
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.
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.
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 Representations in Science
DOI link for Visual Representations in Science
Visual representations (photographs, diagrams, etc.) play crucial roles in scientific processes. They help, for example, to communicate research results and hypotheses to scientific peers as well as to the lay audience. In genuine research activities they are used as evidence or as surrogates for research objects which are otherwise cognitively inaccessible. Despite their important functional roles in scientific practices, philosophers of science have more or less neglected visual representations in their analyses of epistemic methods and tools of reasoning in science. This book is meant to fill this gap. It presents a detailed investigation into central conceptual issues and into the epistemology of visual representations in science.
Chapter 4 of this book is freely available as a downloadable Open Access PDF at https://www.taylorfrancis.com under a Creative Commons Attribution (CC-BY) 4.0 license.
Chapter 1 | 9 pages, introduction, chapter 2 | 124 pages, what are scientific visualisations, chapter 3 | 75 pages, functional roles, appearances and the problem of diversity, chapter 4 | 124 pages, the epistemic status of scientific visualisations, chapter 5 | 9 pages.
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Student Support, ToK Essay. The video guide to ToK Essay #5 May 23: Visual Representations has been posted on YouTube today (and is linked below). This essay was a real challenge for me to summarise in a short video. When I wrote the Essay Guide Notes (linked) I found it to be a very wide ranging subject, and the notes ran to over 6,300 words !
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. W e talked a lot about different ways into understanding this question, beginning ...
Three Connections to my Educational Experiences with International Mindedness 1. My involvement with the Roosevelt Asian Student Association 2. Taking a second language as an elective (Spanish) IB Theory of Knowledge Visual Representation of TOK 3. My engagement in my History
This is an overview guide for IB Theory of Knowledge Essay #5 May 23, the essay about visual representations.If you want more information about the points ra...
Discuss with reference to the human sciences and mathematics" at the beginning of the work, ensuring clarity for the TOK examiner. Throughout the essay, the focus remains on the helpfulness of visual representations in knowledge communication, with relevant examples and arguments from both the human sciences and mathematics.
Visual representations, such as graphs, diagrams, and maps, are commonly used in the human sciences to present data, illustrate concepts, and document the daily life of people and groups. In this essay, I will provide examples of visual representation in various subfields of human science, including psychology, sociology, anthropology ...
The video guide to ToK Essay #5 May 23: Visual Representations has been posted on YouTube today (and is linked below). This essay was a real challenge for me to summarise in a short video. When I wrote the Essay Guide Notes (linked) I found it to be a very wide ranging subject, and the notes ran t
TOK Talk. Education. 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 ...
The arts: a quick overview. The arts constitutes a diverse and multifaceted area of knowledge, encompassing various forms of creative expression such as visual arts, literature, music, dance, and theatre. At its essence, the arts serve as a medium for human communication and self-expression, transcending linguistic and cultural barriers.
The Arts include a range of disciplines including visual arts, theatre, dance, music, film and literature. The ways in which meaning is encoded, evoked and played out in these various forms of representation do not always overlap and may have no exact counterpart elsewhere. The arts, from the sublime to the mediocre (and even the banal) can ...
TOK Essay Title #5. Are visual representations always helpful in the communication of knowledge? Discuss with reference to the human sciences and mathematics. Here is the evidence from my video: The role of visual representations in scientific practices: from conceptual understanding and knowledge generation to 'seeing' how science works.
TOK ESSAY AND PRESENTATION OVERVIEW. There are only two IB assessments in TOK: the externally assessed essay and the internally assessed presentation. They are both focused on the in-depth investigation of Knowledge Questions. In practice though they are very different. Note: This writeup is aimed at students in the last cohort of the soon to ...
TOK. Essay. May 2023. A (Breakdown) Examiner's summary. Criterion A [9/10]:The student effectively communicates the chosen title "Are visual representations always helpful in the communication of knowledge? Discuss with reference to the human sciences and mathematics" at the beginning of the work, ensuring clarity for the TOK examiner. ...
Infogram. Data Visualization. Infographics. Charts. Blog. May 31, 2024. How to create and deliver a winning team presentation. May 24, 2024. What are AI writing tools and how can they help with making presentations?
Art forms can also be used to defend political views. The arts have persuasive power, as they can tap into people's emotions. This can happen, amongst others, through language or sensory images. Propaganda art and national anthems, for example, can be used to strengthen political powers as well as dominant discourse.
The use of visual representations (i.e., photographs, diagrams, models) has been part of science, and their use makes it possible for scientists to interact with and represent complex phenomena, not observable in other ways. Despite a wealth of research in science education on visual representations, the emphasis of such research has mainly been on the conceptual understanding when using ...
Page 5: Visual Representations. Yet another evidence-based strategy to help students learn abstract mathematics concepts and solve problems is the use of visual representations. More than simply a picture or detailed illustration, a visual representation—often referred to as a schematic representation or schematic diagram— is an accurate ...
The two meanings of 'visualization' are discussed as is the key role played by fluency in them in the attainment of expert status in the processes of science. The nature and origins of students' problems in attaining this 'metavisual competence' are derived from a review of the literature. Good practice in the teaching of the ...
A spatial depiction in 2D, 3D, or 4D. Visual representation is mainly the direct or symbolic reflection of something in the format of photos, the images, memes, graphics to represent people, things, a place, or a situation. Visual representation s are representation or demonstration of concepts accompanied by images or texts.
Despite the notable number of publications on the benefits of using visual representations in a variety of fields (Meyer, Höllerer, Jancsary, & Van Leeuwen, 2013), few studies have systematically investigated the possible pitfalls that exist when creating or interpreting visual representations.Some information visualization researchers, however, have raised the issue and called to action ...
ABSTRACT. Visual representations (photographs, diagrams, etc.) play crucial roles in scientific processes. They help, for example, to communicate research results and hypotheses to scientific peers as well as to the lay audience. In genuine research activities they are used as evidence or as surrogates for research objects which are otherwise ...
definition. visual representation. A visual representation (computer generated or hand-drawn rendering) of the artwork showing detailed and overall views; and a maquette, model, photograph and/or map showing the artwork in context. • Budget: Detailed budget listing all costs associated with the gift and identification of sources for funding.