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Math Accessibility

Math accessibility with numbers swirling toward human head

Why Accessible Math?

STEM Equity

Significant barriers exist in education and employment for disabled people in science and engineering, with 65% of STEM workers with disabilities holding less than a bachelor’s degree education (NCSES, 2023). While 11% of doctoral degrees awarded in 2021 went to people with disabilities, social sciences had the highest rate (13%) and engineering had the lowest rate (8%) (NCSES, 2023). Scientists and engineers with disabilities have a higher unemployment rate than both peers without disabilities and the general U.S. populations (Bernard, 2021).

In spite of significant research and our own lived experience demonstrating the strengths and creativity that disabled people bring the STEM fields, multiple barriers exist to disability inclusion. Faculty mentors who identify as disabled are important as role models, but all faculty can be instrumental in supporting students with disabilities, the science and engineering fields, and ultimately society as a whole.

Information Conveyed by Equations

We know that mathematics is an integral part of engineering content, but have you ever considered the information conveyed in an equation? Glancing at an equation or formula conveys visual information such as the length, hierarchy, complexity, use of parentheses, fractions, exponents, and often the context of the equation. Without the visual representation for support, the cognitive load of forming that same mental picture is much higher. Consider the following versions of this simple equation and the information gained from the spoken and visual representations.

Auditory Version of Equation (click to reveal)

Audio Reading of Equation (Microsoft, 2022)

Transcript of Equation (click to reveal)

Heading level 1 Math equation example 1. Heading level 2 solve for x colon.

Equation two plus three over four, times x, equals x minus, three over four.

Left side constant and term. 2 plus, three over four, times x

Left side constant. 2

Left side term. Plus, three over four, times x

Middle comparison. Equals

Right side term and constant. x minus, three over four.

Right side term. X

Right side constant. minus three over four

Visual of the Equation (click to reveal)

LaTeX: 2 + \frac{3}{4}x = x - \frac{3}{4}

LaTeX input into Canvas Equation Editor: 2 + \frac{3}{4}x = x – \frac{3}{4}

Video Demonstration of Alt Text and Screen Reader (click to reveal)

This YouTube video was a keynote address from mathematician Zach Lattin, who shares his passion for mathematics and accessibility in STEM (Lattin, 2022).

  • Beginning at timestamp 21:30, Zach provides sample alt text for an image and unintentionally illustrates the difficulty of creating a mental picture while unable to see the image.
  • Zach shares compelling reasons to create accessible math content so that blind mathematicians like him can share the pain of wrestling with complex equations like their sighted colleagues.
  • He shares the text and symbolic versions of a definition to illustrate the differences between representations favored by various audiences.
  • He demonstrates the use of a screen reader to navigate through the hyperbolic tangent definition using an equation built with MathType using MathML.
  • Finally, in his closing thoughts, Zach share how accessibility efforts in STEM fields can be compared to the limit definition of a derivative.

Accessible Math Language and Tools

  • What is Math ML?
  • Math Rendering Tools
  • Accessible Math Webinar

What is Math ML?

MathML (Mathematical Markup Language) is an international open standard for encoding math content. While similar, HTML does not have a standard way to mark up mathematical expressions. MathML uses a Extensible Markup Language (XML) tags to mark up both the presentation and mathematical semantics of equations, which provides access to both the visual representation and meaning of equations for assistive technology. MathML has a number of benefits such as changing font size, translation into native languages and allowing allow users of screen readers to take a deeper dive into the structure of equations using aural (audio) navigation.

MathML provides the highest level of accessibility to math in a digital format, While images with alternative text are considered an acceptable alternative for simple math content that can be accurately described using alternative text (alt text). For more complex equations, however, images with alt text do not provide true comparable access to the information found in equations built with MathML (DO-IT, 2023; Lattin, 2022).

Math Rendering Tools

MathType

  • MathType is a plugin for creating accessible MathML equations
  • MathType is a convenient authoring tool with its menu of mathematical symbols and templates, keyboard shortcuts, and LaTeX input capabilities
  • You can also enter LaTeX directly into Word documents and use MathType to render equations
  • MathPlayer, from the same company as MathType, is an plugin needed to visually render formulas and equations and to convey the structure and content to screen readers for audible rendering.

EquatIO

  • EquatIO includes several ways to create math content including typing the equations, using voice dictations, writing equations by hand, and taking screenshots of existing equations.
  • Output from EquatIO can be an image of the equations or formulas with alt text that would be read aloud by assistive technology such as a screen reader.
  • Output can also be MathML or LaTeX code that can be used to edit the equation or paste into other applications such as Canvas equation editor.

Canvas

The Canvas Equation Editor can be used to create equations using a simple menu or for more complex equations. You can also create or import LaTeX code to create accessible equations directly on a Canvas page.

LaTex code:

\frac{d\left(\frac fg\right)}{dx}(x)=\frac{g(x)\frac{df}{dx}(x)-f(x)\frac{dg}{dx}(x)}{g^2(x)} 

Results from Canvas Equation Editor:

LaTeX: \frac{d\left(\frac fg\right)}{dx}(x)=\frac{g(x)\frac{df}{dx}(x)-f(x)\frac{dg}{dx}(x)}{g^2(x)} 

Microsoft OneNote and Immersive Reader

  • Microsoft OneNote and Word feature an immersive reader to read aloud math expressions.
  • In OneNote, you can use the drawing feature to handwrite math expressions, select the drawing using the marquee tool, and convert the handwriting to text using the Math button. You can see the steps involved to solve the equation, and insert both the equation and solution steps into OneNote.
  • Solving Math Equations with Math Assistant in OneNote

MathML and Browser Compatibility

  • Mozilla Firefox directly supports the use of MathML
  • Microsoft Internet Explorer requires the MathPlayer plugin

EquatIO Resources:

  • Text Help UserGuide
  • Additional User Resources
  • Speech Input Commands

MathType Resources:

  • Accessible Math Equations with NVDA and MathPlayer Demonstration (YouTube Video)

Accessible Math Webinar

This video hosted by blind mathematician Stacy Scott dives into the complex subject of accessible math. A panel of accessible math content creators demonstrates a possible workflow beginning with an inaccessible image-based document to an accessible math expression experience on a web page. Along the way they demonstrate tools and techniques to manipulate equations in a variety of languages and formats and how screen readers handle different formats.

The presentation slides and transcript are located at the DAISY Creating and Reading Accessible Math (W) webinar page.

References (click to reveal)
  1. Bellman, S., Burgstahler, S., & Chandler, E. H. (2018). Broadening participation by including more individuals with disabilities in STEM: Promising practices from an engineering research center. American Behavioral Scientist, 62(5). https://doi.org/10.1177/0002764218768864
  2. Bernard, M. A. (2021, July 21). Advancing disability inclusion in the scientific workforce. National Institutes for Health. https://diversity.nih.gov/blog/2021-07-21-advancing-disability-inclusion-scientific-workforce
  3. DAISY Consortium. (2021, October 20). Creating and reading accessible math. Digital Accessible Information System (DAISY). https://daisy.org/news-events/articles/creating-reading-accessible-math-w/
  4. DAISY Consortium. (2021, October 26). Creating and reading accessible math. YouTube. https://youtu.be/wufqq72hhcM
  5. Disabilities, Opportunities, Internetworking and Technology (DO-IT). (2021, April 9). What is MathML? University of Washington. https://www.washington.edu/doit/what-mathml
  6. DO-IT. (2017). Using a screen reader. University of Washington. https://www.washington.edu/doit/videos/index.php?vid=81
  7. Lattin, Z. (2022, February 15). Arbitrarily close to access in STEM [Video]. YouTube. https://youtu.be/VMnZuvTcnkc
  8.  National Center for Science and Engineering Statistics (NCSES). (2023, January 30). Diversity and STEM: Women, minorities, and persons with disabilities. National Science Foundation. https://ncses.nsf.gov/pubs/nsf23315/report/  
  9. National Center on Accessible Education Materials. (2023). Creating accessible STEM materials. CAST. https://aem.cast.org/create/accessible-stem-materials#1
  10. Tanase, I. (2022, August 11). Making math accessible. Microsoft. https://blogs.microsoft.com/accessibility/making-mathematics-accessible/

Math Tool Comparison Table (click to reveal)

This table provides an overview of the types of documents you may encounter, the accessibility of the built-in equation editor in each application, and accessibility of content created with LaTeX, EquatIO, and MathType.

Location Is the Built-In Equation Editor Accessible? LaTeX EquatIO MathType
Canvas

Yes

  • The Canvas equation editor is LaTeX based

Yes

  • You can directly input LaTeX into the Canvas equation editor or copy and paste from other math tools such as EquatIO or MathType.

Yes

  • You can copy LaTeX from EquatIO and insert into Canvas editor
  • You can copy MathML and insert into HTML code for the Canvas page and the equation will be rendered correctly on the page

Yes

  • You can copy the MathML from MathType and insert into HTML editor for the Canvas page
PowerPoint No

No

  • Content created using PPT Equation Editor is NOT correctly read by assistive technology. Often parts of the equation are ignored leaving the spoken math equations meaningless to the listener.

Yes

  • EquatIO inserts images with alt text in PPT files
  • Alt text must be verified by subject matter expert to check for accuracy of spoken text.
  • Math ‘punctuation’ must be specified including hierarchy such as fractions and parentheses or brackets.
  • To edit the equation image, you need to take another screenshot to open the equation in EquatIO

Yes

  • But only if you provide the PowerPoint file (not a PDF version of the PPT file)
  • Equations may appear VISUALLY incorrect in the PPT file when viewed in various browsers, including in Canvas. Brackets, matrices, and vectors are common issues.
  • The equations should be read aloud correctly by the screen reader.
Word

Yes

  • But only if you provide the file as a Word doc, which is LaTeX based

Yes

  • The MS Word editor is LaTeX compatible

Yes

  • EquatIO can insert equations as images with alt text. Alt text must be verified for accuracy.
  • You can also copy LaTeX from EquatIO to insert into Word equation editor

Yes

  • But only if you provide the file as a Word doc, which is LaTeX based
PDF N/A No

Yes

  • Images with alt text

No

 

Output N/A LaTeX code which could be used in other applications such as Canvas, EquatIO or MathType

EquatIO Output Options

  • Image with alt text
  • LaTeX
  • MathML

MathType Output Options

  • MathML
  • LaTeX
  • Image which would need to have alt text added

Note: All equations regardless of program or tool used must be verified for accuracy, including the visual display and alt text of images.

Filed Under: Accessibility, Instructional Design Tagged With: Accessibility, IID, Instructional Design

Universal Design for Learning

What is Universal Design for Learning or UDL?

Whether you know the term Universal Design for Learning or UDL, it can help achieve your goals. Your goal of engaged students with an enthusiasm for learning. Your goal of improved understanding and performance. And your goal to stop feeling ineffective and overwhelmed at reaching your most struggling students.

The reality is with teaching in the COVID era, you don’t have time to learn a new way of planning. If you are an educator, you already know a lot about UDL. Similar to the goals of Backwards Design, Universal Design for Learning seeks to meet every student by rethinking goals, methods, materials, and assessments. Let’s unpack U-D-L first.

UNIVERSAL means that the curriculum can be understood by every student, even though each student is unique and brings diverse life experiences, learning challenges, and attitudes.

UDL and Neuroscience

Neuroscience has discovered that LEARNING requires tapping into 3 parts of the brain for

  • RECOGNITION – the content, or what, of learning,
  • SKILLS and STRATEGIES – the how of learning, and
  • CARING and PRIORITIZING – the motivation, or why, of learning.

So, in order to learn, students need not only knowledge, but skills, and enthusiasm for learning. You knew that already through your own lived experience. You can surely describe that ‘perfect’ lesson where one (or all) of those broke down and learning fell flat.

UDL helps you intentionally address all 3 in the planning stage – the content and how you present it, the learner’s skills and self-efficacy, and the curiosity and motivation needed to learn.

Do you feel like this might be more EduBabble and teacher shaming? How can teachers possibly meet the UNIVERSAL LEARNING needs of so many unique students?

Here’s where DESIGN comes into play!  Take heart!

UDL for Accommodation

Universal Design has been used in architecture and engineering for years to design accessible buildings, products, and services like ramps and automatic doors. Many accommodations address physical disabilities and are often retrofit after the fact. A principle called the curbcut effect means that wheelchair ramps can help not only people using a wheelchair but also people with bikes, strollers, and even Amazon delivery robots.  But how much more functional are these supports when planned for in the first place?

UDL checklists can be used to measure the accessibility of existing courses and materials to retrofit accommodations. For example, adding closed captions and transcripts to videos serves more than just hearing impaired learners. Research shows that 40% of learners use captions when they are in distracting locations, have auditory processing challenges, like multiple modes of input, or just want privacy.

UDL has 3 principles, 9 guidelines, and 31 checkpoints, which sounds completely crazy if you are a K-12 educator. Here’s an example of what not to do to illustrate that throwing in ALL OF THE THINGS without planning for learner diversity is not effective.

UDL Gone Wrong

As a university professor equipping teachers to teach during COVID, I scoured the Internet for ways to help them survive. If you are a teacher, you were probably doing the same thing. 

I’m also a K-12 teacher, so this quest was for myself as well as the teachers in my course. My local school district had a team of curriculum directors develop canned courses for our LMS. Their heart was in the right place and they used the principles of UDL. But In August, when teachers downloaded their courses for the year they were flattened by UDL gone wrong.

Our district had all the right motives and had read all of the books on UDL. They included multiple page, color coded student checklists for every week to encourage student self-management. They had multiple ways of presenting information. PlayPosit videos with embedded questions. PearDecks with embedded video, audio, and comprehension questions. PDFs to annotate using Kami. Discussion boards. Flipgrid video posts.  All. The. Tech.

They created daily LMS folders for each assignment – nested inside each topic – nested inside each unit…you get the idea. Every assignment was linked to Google Drive. Students only had to click through the folders in the LMS, open the document outside the LMS in Google Drive, make a copy, rename it, claim it, DO it, and click 4 or 5 more places to turn it in. 

Have you figured out by now most teachers needed a therapist (uh…I did), and most students just stayed in bed?

You may recognize this scenario. I share this experience not to make you relive nightmares, but to say that UDL has awesome ideas, but it’s more than a checklist to follow.

Allow the purpose to inform the technology, not the other way around. Moving from an essential idea or process to the tool that makes that possible lets you explore the many options and streamline the path for students.

How to get Started with UDL

Now that we have an idea of what doesn’t work, lets look at how we can start small and make a big impact on instruction.

  1. Consider the purpose. Maybe students were recording ideas on Post-Its, forming groups, and organizing Post-Its on chart paper to share.  The purpose isn’t to learn a dozen new EdTech ways to move virtual Post-Its. The bigger goals are individual sense-making, collaboration, and presentation. Start there and allow the purpose to inform the technology. Maybe a breakout room, a discussion board, or if you still love Post-Its, a Jamboard or Padlet.
  2. Streamline the tech tools. Feedback from students, parents, and teachers clearly indicates tech overwhelm. Use a few tools and explicitly teach students how to use them. Many students are using cell phones or have poor Internet connections. Or are sharing computers and do not have the time or mental bandwidth to learn new tech tools. Simple trumps flashy.
  3. Be forgiving. Of yourself, and your students. Research confirms that the pandemic has shortened everyone’s fuse. Give yourself a break. Realize that you cannot possibly have perfect lessons to meet the needs of every student in retrofit mode. Rethink the purpose of assignments, simplify the tech, and keep it simple for your sake and theirs.

Inclusive Instructional Design

In the next post, we will look at Inclusive Instructional Design (IID) and how it is more than retrofitting assignments. IID is rethinking our approach before we break ground and getting the input of our most important stakeholders, our students.  There’s light ahead for all of us!

Universal Design for Learning is often a method or way of doing, whereas Inclusive Instructional Design is a way of thinking.

I’m writing this post on International Accessibility Awareness Day, the third Thursday in May. You can join the movement for digital accessibility at the Global Accessibility Awareness Day website here.

Filed Under: Instructional Design Tagged With: IID, Instructional Design

Engineer to Educator

Ripple Effect of Teachers on Society
Copyright 2020 by The Ripple Effect of a Teacher. www.ditchthetextbook.com

STEM Pioneer to STEM Educator

I love engineering. So why leave engineering for education?

It’s easy to make a buck.  It’s a lot harder to make a difference.

Tom Brokaw

Long before STEM and STEAM were acronyms, few young girls were pursuing engineering as careers.  Influential teachers in my life gave me the confidence to earn two degrees in engineering.  Jerry Martin, my 6th grade math teacher at Ridgeview Junior High School first showed me that I had a talent and interest in mathematics. Thirty years later, he inspired me to use that experience to share my love of math and science with the next generation of future engineers.

In the 20 years since changing careers, I have been influential in the lives of countless children.  I have an MEd in mathematics and science education with a reading endorsement and gifted education minor.

Before attending graduate school, I assisted in two classrooms where the teachers were using random spelling lists and grouping students by level.  Children begged to move out of the lowest spelling group because of the stigma.  I wish I had known about Orton Gillingham’s diagnostic, prescriptive, systematic approach back then.  Not only would it have helped these students with spelling, but with their self-esteem as well.

After graduation I joined the staff at Marburn Academy, in Columbus, Ohio.  Marburn Academy is a private school for students with dyslexia and dyscalculia.  All teachers utilized the Orton-Gillingham methodology for individual tutoring and whole-class instruction.  The Consortium of Literacy Educators (COLE), an Academy of Orton-Gillingham Practitioners and Educators (AOGPE) accredited trainer, provided my training and supervised practicum.

My Dyslexia Story

Let me share a bit about “John”, who arrived at Marburn Academy as a defiant sixth-grader.  Expecting to play football in the public school, he was angry with his parents for sending him to a private school without sports (at that time).  However, he knew that middle school was full of hard knocks and bullying for an intelligent, popular athlete unable to demonstrate his true intelligence and creativity.

John soon realized that we had literacy remediation tools that work, and the competition was on.  Through our writing fluency program, he made astounding progress at getting his thoughts into writing. As his typing and writing abilities soared, he badgered me to print him new graphs to plot his progress.  He left us in 8th grade to attend a top high school where he excelled in academics and football.  Now a proud mechanical engineer, his creativity, inventiveness, and superior math/science skills helped him to design aircraft engines upon college graduation.

Not all students with dyslexia will be able to attend private school for intensive instruction and achieve this type of academic success.  It is my goal is to share resources on dyslexia with teachers, students, and their families.  Many adults, now realizing that they are dyslexic, will find the information useful as well.  My students make me laugh and break my heart at times, but I am grateful daily for the opportunity to help make their lives a bit easier.

Many former students still keep in touch, and seeing where they are today inspires me to continue research into learning challenges and the pursuit of solutions.

My Roles in Education

I have been a classroom teacher, a private tutor and dyslexia advocate, and a university professor. I am now an instructional designer showing teachers how to Design for Dyslexia. These roles allow me to serve individual students and their families, but also to educate and provide resources for teachers worldwide.

I teach Physical Science in the STEM Integrated PreK-6 Classroom in the STEM Instructional Leader Program at Johns Hopkins University School of Education (JHU). This course allows me to combine my experience as an Engineer, a chemistry and physics classroom teacher, and as a special education teacher. JHU has an institutional focus on meeting the individual needs of ALL students, throughout their lives. STEM equity is a major focus in my course and we consider how students’ individual needs are influenced by learning challenges and gaps, cultural differences, educational inequities, and technology access and literacy, among other influences.

Getting educational research into the hands of front-line educators is an ongoing challenge. My goals are to empower educators to design inclusive instruction and help all learners understand and advocate for their own needs.

Filed Under: Dyslexia, Instructional Design Tagged With: Dyslexia, IID, Instructional Design

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