It is recommended that you read this resource on the web but you can also download this resource as a PDF or download this resource as a Word document.
Learning to use a screenreader properly is well outside the scope of this project but having a basic understanding of how a screenreader can interact with a webpage is helpful.
ChromeVox is a screenreader which integrates into the Chrome browser. It is free to use and works with mathematical text encoded in webpages using MathJax. We will use a restricted mode of the ChromeVox screenreader which is easier for a complete beginner.
To install ChromeVox:
When ChromeVox is running you can change or manage ChromeVox options but this tutorial does not depend on any changes. If you have previously installed ChromeVox and the below does not work then you may wish to check that you are using the Classic keymap and Reset current keymap.
Please note that students will certainly have a screenreader more suited to education and employment than ChromeVox and that no student should be asked to change or acquire a skillset in a new screenreader without very good reason and plenty of advance notice.
These are instructions are not intended to teach you how to use a screenreader and they are not suitable for someone who usually uses a screenreader. These instructions exist solely to help you to understand how a structured webpage, equation or interactive diagram might sound to a screenreader user.
To use ChromeVox to read mathematical text correctly you must use the keyboard, not the mouse. Mathematics will be read incorrectly if the mouse is used.
| Key press | What will happen? |
|---|---|
| Enter | Activate current item |
| Tab | Jump to next focusable item |
| Shift + Tab | Jump to previous focusable item |
| Down/Up | Navigate forwards/backwards |
| Right/Left | Navigate forwards/backwards at a more detailed level |
| Backslash | Enter table or equation exploration |
| Backspace | Exit table or equation exploration |
| N | Next (follow by any of the below type commands) |
| P | Previous (follow by any of the below type commands) |
| H | Heading |
| n in {1,..,9} | Heading at level n |
| L | Link |
| T | Table |
| O | List |
| I | List item |
In sticky mode,
| Key press | What will happen? |
|---|---|
| T H | Announce the headers of the current cell |
| T L | Announce the current cell coordinates |
| T [ | Go to the beginning of the table |
| T ] | Go to the end of the table |
| T ; | Go to the beginning of the current row |
| T # | Go to the end of the current row |
| T , | Go to the beginning of the current column |
| T . | Go to the end of the current column |
In sticky mode,
| Key press | What will happen? |
|---|---|
| Down/Up | Navigate forwards/backwards |
| = | Increase granularity |
| - | Decrease granularity |
| M S | Toggle semantic mode |
In semantic mode, in multi-line displayed equations, the reading will not announce the cell location of the current element but will instead read the maths as expressions.
We often need to know the length of a curve between two points, e.g. what is the length of the ropes holding Clifton suspension bridge (see Exercise Sheet 3).
Given a curve \(y=y(x)\)
Accessible interactive graph at https://www.desmos.com/calculator/t8dz6vlmnz
Let \(S\) be the arc length and \(\Delta S\) a short section of it.
Accessible interactive graph at https://www.desmos.com/calculator/g5duc4kmfp
By Pythagoras’ Theorem, \[ \Delta S^2 \approx \Delta x^2+\Delta y^2 \qquad \Rightarrow\qquad \left(\dfrac{\Delta S}{\Delta x}\right)^2 \approx 1+\left(\dfrac{\Delta y}{\Delta x}\right)^2 \] As \(\Delta x\to0\) this becomes an identity \[ \left(\dfrac{dS}{dx}\right)^2 = 1+\left(\dfrac{dy}{dx}\right)^2 \qquad\Rightarrow\qquad \dfrac{dS}{dx} = \sqrt{1+\left(\dfrac{dy}{dx}\right)^2} \] The arclength between \(x=a\) and \(x=b\) is then \[ \begin{aligned} S(a,b) &= \int_a^b\dfrac{dS}{dx}dx\\ &= \int_a^b\sqrt{1+\left(\dfrac{dy}{dx}\right)^2}dx. \end{aligned} \]