{"id":914,"date":"2025-02-17T17:16:25","date_gmt":"2025-02-17T17:16:25","guid":{"rendered":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/?p=914"},"modified":"2025-02-18T10:34:39","modified_gmt":"2025-02-18T10:34:39","slug":"making-graphs-accessible-prize-winning-student-work-with-a-visually-impaired-learner","status":"publish","type":"post","link":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/2025\/02\/17\/making-graphs-accessible-prize-winning-student-work-with-a-visually-impaired-learner\/","title":{"rendered":"Making Graphs accessible: prize-winning student work with a visually-impaired learner."},"content":{"rendered":"

This post is written by Ben Leslie, winner of the Stanley Collings prize in 2024.<\/em><\/p>\n

The Stanley Collings prize is awarded annually by the School of Mathematics and Statistics. The prize is awarded to the student who best combines innovation in devising materials suitable for learners and insightful analysis of their learning. The post is a rewritten version of his final assignment in Learning and Doing Algebra (ME322).<\/em><\/p>\n

Congratulations Ben!<\/em><\/p>\n

While studying the module Learning and Doing Algebra, I worked with an adult learner, who I call Ina, and who is completely blind.\u00a0 Mathematics is generally taught as a visual subject so my objective was to make the tasks accessible but also to introduce concepts such as graphical illustrations that are common in the workplace. \u00a0I chose the following task from the module to introduce graphs and explain how to use them.<\/p>\n

Task 11 What’s the story?<\/span><\/strong><\/h4>\n
The following graphs provide information on two cars (car A and car B):<\/h5>\n
\"This

Comparing cars A and B<\/p><\/div>\n

(a) Are the following statements true or false?<\/span><\/span><\/h5>\n
(i) car A is more expensive than car B.<\/span><\/h5>\n
(ii) <\/span>car B is faster than car A.<\/span><\/h5>\n
(iii)\u00a0<\/span>car A costs less to insure than car B.<\/span><\/h5>\n
(iv) <\/span>the older car costs more in road tax. <\/span><\/h5>\n
(v) <\/span>the faster car costs more to insure.<\/span><\/h5>\n
(b) Write a short description for car A and car B.<\/span><\/h5>\n
(c) Use these axes to mark crosses to represent car A and car B.<\/span><\/h5>\n
\"This

Axes for comparing cars A and B<\/p><\/div>\n

I printed Braille graphs and selected dots or distinctly shaped beads to represent the cars. I wanted Ina to develop the algebraic reasoning to understand how the distance from the origin on each axis represented the value of the axis title.<\/p>\n

I printed a line of Braille dots for each axis and read aloud each task instruction and question.\"\" I mentioned that she need not give exact values, only its relation to the other car, for example, \u2018Car A is older than B.\u2019 She used this language when reasoning her responses to the statements. For statement (a)(i), she answered \u2018False, car B is more expensive because it is younger.\u2019 I re-phrased the question to, \u2018Ignoring age, which car is more expensive?\u2019 (I will elaborate why later, but I wanted her to practise using the y<\/em>-axis.) \u00a0She finished the remaining statements without much difficulty and gave good descriptions of the cars that I recorded.<\/p>\n

\"Handwritten

Ina’s answers<\/p><\/div>\n

In part (c) Ina’s difficulty using the y<\/em>-axis resurfaced when she tried to represent both variables on the x<\/em>-axis. For example, she correctly placed car A on the x<\/em>-axis for value before moving it along the same axis to identify the cost of insurance.<\/p>\n

\"The

Using the horizontal axis for both variables<\/p><\/div>\n

With a simple prompt she recognised and corrected it.<\/p>\n

The last part of the question was to imagine a third car, C, describe it and add Car C to all the graphs. Ina described car C using extreme terms: “super- valuable, super old – its a vintage; very slow, massive engine, free road tax, expensive insurance”.<\/p>\n

\"This<\/p>\n

I influenced her choice to give car C free road tax. It would be eligible for free road tax as it was\u00a0vintage, but\u00a0also, it would give her a zero value to work with which I wanted to see her represent in the graph, especially because road tax was the y<\/em>-axis which she found difficult. She managed this successfully.<\/p>\n

When analysing my learner\u2019s work, I identified three module ideas which are related to her key moments and decisions. They are relations, covariation and Invariance and change (all Open University, 2023).<\/p>\n

Relations<\/span><\/p>\n

I described letting my learner know that she did not have to assign values to each variable. Although there was nothing wrong with doing this, I felt it was important for her to be able to compare the cars without necessarily doing arithmetic. Inequalities can be used in algebraic expressions and being more confident with using the terminology \u2018greater than\u2019 and \u2018less than\u2019 will enable her to progress future mathematical study.\u00a0 This was also an important skill to have for the true or false statements, which were expressed as inequalities.<\/p>\n

Covariation<\/span><\/h4>\n

When my learner said car B was more expensive because it was younger.\u2019 I re-phrased the question to, \u2018Ignoring age, which car is more expensive?\u2019 Although an onlooker may have recognised that she had given the correct answer and possibly even jumped ahead to identifying covariance, I wanted to double check that she had used the y<\/em>-axis and was not just making the general assumption that new cars are more expensive than used cars. I was glad I checked, as it turned out that she had not used the y<\/em>-axis. This also revealed that she had more difficulty reading the y<\/em>-axis than the x<\/em>-axis which is something we then worked on throughout the task.\u00a0 After ensuring she was reading the graphs correctly, I revisited her first answer and explored covariance. I congratulated her for pointing out there is often a relationship between the age and value of items and explained that covariance does not imply causation. I encouraged her then, throughout the rest of the tasks, to identify if the covariations between different aspects of the cars make sense, for example, if the engine is larger,\u00a0 would the max speed be expected to change? It was interesting to watch which covariances she carried through in car C. For example, she continued with age and speed varying together, but age and value varying separately as she accounted for it being vintage.<\/p>\n

Invariance and Change<\/span><\/h4>\n

This task was set out well and allowed for my learner to not only explore different covariations, but also to change which relationships are explored. In part (c) two empty graphs were given. The change here was that the cost to insure, which was on the x<\/em>-axis in the previous graph, became the y<\/em>-axis in the new graph. Additionally, the value of the cars, which was previously a y<\/em>-axis became an x<\/em>-axis. This helped my learner ground her understanding of the y<\/em>-axis as she converted the approximate distance of y<\/em>-variable from the origin, into an x<\/em>-variable and vice versa with the cost to insure variable.<\/p>\n

Reflection<\/h3>\n

When choosing and preparing the tasks throughout this module, I had focused on improving my abilities to make them accessible and meaningful to my blind learner. On reflection, my preparations have improved dramatically from her first tasks, where I used random objects at hand as representations of numbers or symbols, to now where in this example I have carefully thought out how to write the task in an accessible format with clear meaning. This allowed me to follow Bruner\u2019s modes of representation (Open University, 2023) to help use tangibility to lay the foundation for concepts which can later be simplified into Braille symbols or even calculated mentally.<\/p>\n

I often had to apply the module concept of using variation in teaching to ensure that my learner grasped the concepts intended in the session (Open University, 2023). This would range from me needed to rephrase questions, like I did in this task, or writing new problems that would stretch my learner\u2019s thinking. This is related to the module idea of freedom and constraint (Open University, 2023), and I would often try to introduce or remove a constraint in her tasks to\u00a0 enhance the learning experience, in this task I did that more subtly by encouraging her to use free road tax for car C.<\/p>\n

Another module concept that I focused on was conjecturing and convincing (Open University, 2023). I liked the idea of allowing my learner to create her own conjectures based on the evidence in front of her, and then by testing that, was able to convince herself she was right. I really felt this was something important I wanted my learner to experience as I didn\u2019t want her to have my educational experience \u2013 knowing what the right answer was, without knowing \u00a0it was the right answer or \u00a0it came from.<\/p>\n

Overall, I have been struck by how the module ideas, when combined, demonstrate a very explorative and exciting way to teach and learn algebra. Before starting the module, I was anticipating there would be one or two clear-cut, tried and tested methods of drilling algebraic concepts into student\u2019s heads. But I have enjoyed how the learning experience has been more focused on enabling the learner to learn and discover for themselves and share that excitement with their teacher, who can also learn or observe something new in every lesson.<\/p>\n

References<\/h3>\n

The Open University (2023) ME322: Learning and doing algebra<\/em>. <\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

This post is written by Ben Leslie, winner of the Stanley Collings prize in 2024. The Stanley Collings prize is awarded annually by the School of Mathematics and Statistics. The prize is awarded to the student who best combines innovation … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-914","post","type-post","status-publish","format-standard","hentry","category-uncategorised"],"_links":{"self":[{"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/posts\/914","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/comments?post=914"}],"version-history":[{"count":11,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/posts\/914\/revisions"}],"predecessor-version":[{"id":934,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/posts\/914\/revisions\/934"}],"wp:attachment":[{"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/media?parent=914"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/categories?post=914"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.open.ac.uk\/blogs\/MathEd\/index.php\/wp-json\/wp\/v2\/tags?post=914"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}