{"id":5022,"date":"2018-05-07T12:30:30","date_gmt":"2018-05-07T16:30:30","guid":{"rendered":"https:\/\/blogs.swarthmore.edu\/its\/?p=5022"},"modified":"2018-05-07T14:51:15","modified_gmt":"2018-05-07T18:51:15","slug":"math-sounds","status":"publish","type":"post","link":"https:\/\/blogs.swarthmore.edu\/its\/2018\/05\/07\/math-sounds\/","title":{"rendered":"Math Sounds"},"content":{"rendered":"<h1>Math, visual impairment and linearity<\/h1>\n<h2>Confessions<\/h2>\n<p>Let me say right off the bat, I am not a \u2018math person\u2019. \u00a0I find it interesting, particularly in the context of math as language, but I really don\u2019t \u201cget\u201d it.\u00a0 Nor do I have a great understanding of how our brains work.<\/p>\n<h2>The Problem<\/h2>\n<p>Apparently there is a linearity problem for students of math who are also visually impaired, especially those who might be dependent on screen readers to interact with formulas. \u00a0The way it was explained to me is you can take a formula which is a symbolic expression of an equation and it has to be linearized to be consumed by screen reader technology. Below is a simple example of a formula followed by its linearization.<\/p>\n<p>Equation:<\/p>\n<figure id=\"attachment_5027\" aria-describedby=\"caption-attachment-5027\" style=\"width: 253px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-5027\" src=\"https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/mathFormulaOnly.png\" alt=\"\" width=\"253\" height=\"141\" srcset=\"https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/mathFormulaOnly.png 253w, https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/mathFormulaOnly-108x60.png 108w\" sizes=\"auto, (max-width: 253px) 100vw, 253px\" \/><figcaption id=\"caption-attachment-5027\" class=\"wp-caption-text\">Math as an equation<\/figcaption><\/figure>\n<p style=\"text-align: left;\">Linearized equation:<\/p>\n<p style=\"text-align: center;\"><em><strong>a = sqrt(((x super 2) &#8211; y) \/ z)<\/strong><\/em><\/p>\n<p>The longer the equation the more linearization is needed and the more human memory is required.<\/p>\n<p>I read somewhere that our brains, without training, can naturally and accurately remember between 5 and 7 things at a time. \u00a0A more complex equation could span at least a couple of paragraphs when put into a linear format. That is a lot to remember! \u00a0Imagine if you lost track of a parenthesis&#8230;<\/p>\n<p>(aside: <a href=\"http:\/\/www.ams.org\/notices\/200210\/comm-morin.pdf\">Visually impaired mathematicians in history[pdf]<\/a>)<\/p>\n<h2>Possible Solutions<\/h2>\n<p>Chloe Rose, TVI and Yue-Ting Siu, TVI, Ph.D recently gave a talk at the <a href=\"http:\/\/www.csun.edu\/cod\/conference\/2018\/sessions\/index.php\/\">2018 CSUN Assistive Technology Conference<\/a> explaining why many students with visual impairments struggle with math and suggested that engaging other senses like touch or sound might help these, and other, students better succeed in this area.<\/p>\n<p>What follows is some of the technology that is currently available or may soon be available:<\/p>\n<h3>Tactile Representations<\/h3>\n<h4>Refreshable Braille Displays<\/h4>\n<div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"An affordable, refreshable Braille tablet that relies on microfluidics\" width=\"720\" height=\"405\" src=\"https:\/\/www.youtube.com\/embed\/0fIg4rI4cDw?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/div>\n<h4>Tactile paper<\/h4>\n<figure id=\"attachment_5023\" aria-describedby=\"caption-attachment-5023\" style=\"width: 527px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-5023\" src=\"https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/MathTactileEquation.png\" alt=\"\" width=\"527\" height=\"254\" srcset=\"https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/MathTactileEquation.png 527w, https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/MathTactileEquation-300x145.png 300w, https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/MathTactileEquation-124x60.png 124w\" sizes=\"auto, (max-width: 527px) 100vw, 527px\" \/><figcaption id=\"caption-attachment-5023\" class=\"wp-caption-text\">Quadratic Equation in DotsPlus Braille Code<\/figcaption><\/figure>\n<figure id=\"attachment_5024\" aria-describedby=\"caption-attachment-5024\" style=\"width: 593px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-5024\" src=\"https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/mathAngles.png\" alt=\"\" width=\"593\" height=\"314\" srcset=\"https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/mathAngles.png 593w, https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/mathAngles-300x159.png 300w, https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/mathAngles-113x60.png 113w\" sizes=\"auto, (max-width: 593px) 100vw, 593px\" \/><figcaption id=\"caption-attachment-5024\" class=\"wp-caption-text\">Graphical Image in Printed Braille<\/figcaption><\/figure>\n<p><a href=\"http:\/\/atwiki.assistivetech.net\/index.php\/Math_notation\">http:\/\/atwiki.assistivetech.net\/index.php\/Math_notation<\/a><\/p>\n<h4>Refreshable Surface graphs<\/h4>\n<div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Amazing Technology Invented By MIT - Tangible Media\" width=\"720\" height=\"405\" src=\"https:\/\/www.youtube.com\/embed\/lvtfD_rJ2hE?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/div>\n<h4>Haptics<\/h4>\n<div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Rendering Volumetric Haptic Shapes in Mid-Air using Ultrasound\" width=\"720\" height=\"405\" src=\"https:\/\/www.youtube.com\/embed\/kaoO5cY1aHk?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/div>\n<h3>Integrated System Devices<\/h3>\n<h4>Graphati<\/h4>\n<div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Graphiti: A Revolution in Accessible Graphics\" width=\"720\" height=\"405\" src=\"https:\/\/www.youtube.com\/embed\/3fkDbk9rSqM?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/div>\n<h3>Tonal representations<\/h3>\n<h4>Desmos<\/h4>\n<div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"Accessibility Features in the Desmos Graphing Calculator\" width=\"720\" height=\"540\" src=\"https:\/\/www.youtube.com\/embed\/EqqiqTkThi8?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/div>\n<h4>SAS Accelerator<\/h4>\n<div class=\"jetpack-video-wrapper\"><iframe loading=\"lazy\" title=\"SAS Graphics Accelerator: Getting Started\" width=\"720\" height=\"405\" src=\"https:\/\/www.youtube.com\/embed\/yzqtOZvx7Sk?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" referrerpolicy=\"strict-origin-when-cross-origin\" allowfullscreen><\/iframe><\/div>\n<h2>Invitation<\/h2>\n<p>If you are interested in exploring more about this, let us know.<\/p>\n<p>You are also welcome to join us and attend next year\u2019s conference &#8211; just get in touch with accessibility at swarthmore.edu<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Math, visual impairment and linearity Confessions Let me say right off the bat, I am not a \u2018math person\u2019. \u00a0I find it interesting, particularly in the context of math as language, but I really don\u2019t \u201cget\u201d it.\u00a0 Nor do I &hellip; <a href=\"https:\/\/blogs.swarthmore.edu\/its\/2018\/05\/07\/math-sounds\/\" class=\"more-link\">Continue reading <span class=\"screen-reader-text\">Math Sounds<\/span><\/a><\/p>\n","protected":false},"author":57,"featured_media":5034,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[2,71,207,76,219],"tags":[90],"class_list":{"0":"post-5022","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","6":"hentry","7":"category-academic-technology","8":"category-accessibility","9":"category-active-learning","10":"category-digitaltools","11":"category-universal-design-for-learning","12":"tag-featured","14":"fallback-thumbnail"},"jetpack_featured_media_url":"https:\/\/blogs.swarthmore.edu\/its\/wp-content\/uploads\/2018\/05\/mathmusic1.jpg","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/ph2nPL-1j0","_links":{"self":[{"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/posts\/5022","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/users\/57"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/comments?post=5022"}],"version-history":[{"count":11,"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/posts\/5022\/revisions"}],"predecessor-version":[{"id":5043,"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/posts\/5022\/revisions\/5043"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/media\/5034"}],"wp:attachment":[{"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/media?parent=5022"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/categories?post=5022"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.swarthmore.edu\/its\/wp-json\/wp\/v2\/tags?post=5022"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}