Equations for ICT Professionals

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As an ICT professional you can guide the braille reader in using different tools and techniques to understand and solve equations. This instructional guide provides an overview of how braille readers can use a braille display and a screen reader with speech synthesis to solve equations and inequalities. This way of working with equations demands a lot from the braille reader, including mathematical abilities, proficiency in braille, and ICT skills.

Reading and Comprehending the Equation

The braille reader will need extra training to read an equation on the braille display. You can help the student by following these strategies:

Teach the braille reader how to get an overview of the equation by moving their fingers over the expression to see how long it is and whether it contains fractions, brackets, or other mathematical symbols. It is also possible to get an overview by using speech synthesis.
Encourage the braille reader to use both hands when reading, understanding and solving the equation. This will make it easier to keep track of equal signs, brackets, fractions and other symbols.
Teach the braille reader which signs and symbols are commonly used in different equations. For example, both numbers and letters are expected and most likely on both sides of the equal sign. An open bracket is always followed by a closed bracket. If the braille reader knows what signs and symbols to expect, the chances of misinterpretation are reduced.

Solving an Equation

Before starting solving an equation, check that the braille reader is familiar with the keyboard and knows how to write numbers and mathematical symbols. Also ensure that the braille reader has the necessary ICT skills. This includes navigating the braille display and screen reader commands. Teach the braille reader how to use cursor routing buttons and navigation keys on the braille display. If the braille reader needs to check previous steps, he/she needs to know how to leave the cursor at the current step and move the braille display to the previous step. Once he/she has checked the previous step, he/she can just start writing and the cursor will still be at the right place to continue calculating.

Active Cursor and Braille Cursor

Normally, the active cursor follows the braille display cursor when reading, for example when moving to a new line with the arrow keys. This enables the braille reader to read on other lines than where the pc curser is. Then it is possible to start writing even if the reading focus is not the same as the writing focus. Braille displays usually have a shortcut to switch this function on or off, but this varies from model to model. On one of the more common models, the Focus 40 Blue, you press dots 1-2-7 together with the space bar to enable/disable this feature.

Solving Short Equations

When solving short equations, the braille reader can calculate the next step on the same line. This approach is useful for getting a better overview, especially considering that braille displays typically show only 40 characters at a time.

As an ICT professional, your focus is to teach the braille reader how to navigate and edit text in Word. Consult the mathematics teacher for examples of how intermediate steps should appear mathematically.

Although the equations may be short and easily rewritten by the braille reader, it may be beneficial to introduce a strategy of copying the equation from the previous line, pasting it and then modifying the pasted expression. This approach helps to reduce the risk of misreading or miswriting the equation.

Example 1

x + 18 = 25

Move the cursor to end of line of the expression using the End key or the Cursor Routing Button. Press two spaces and start calculating the next step on the same line. Each new step is highlighted, making it easier to follow the solving process.

x + 18 = 25 x + 18 ‐ 18 = 25 ‐ 18

Use the cursor routing button to move the cursor to the first digit or variable (x) in the second step. Press Enter to move this step to the line below.

x + 18 = 25
x + 18 ‐ 18 = 25 ‐ 18

Move the cursor to the end of the expression using the End key or using the Cursor Routing Button. Press two spaces and calculate the next step on either side of the equal sign:

x + 18 = 25
x + 18 ‐ 18 = 25 ‐ 18 x = 7

Use the Cursor Routing Button to move the cursor to the first digit or variable (x) in the second step. Press Enter to move this step to the line below. The braille reader can write three equal signs after the answer to highlight the answer:

x + 18 = 25
x + 18 ‐ 18 = 25 ‐ 18
x = 7===

You can see another example of solving an equation in this video:

Example 2

If the braille reader wants to describe the calculations done, this can be done by adding two spaces after the equation and then adding the steps taken on both sides of the equation:
++ for addition
-‐ for subtraction
** for multiplication
:: or // for division

Using this method for showing the calculations, solving an equation can look like this:

2x ‐ 3 = 7 ++3
2x = 10 ::2
x = 5===

Solving longer equations

When equations are too long to use the strategy described above, the braille reader should copy the previous step to the line below before editing it. In the video, we show you the step-by-step method that is also written out below.

Example

4x ‐ (3x + 5) = 3 ‐ (x ‐ 1)

Copy and paste the equation to the line below: Place the cursor just before the equation using the cursor routing button on the braille display or using Home key. Select the equation (Shift + end). Copy (Ctrl + c). Move to the line below by pressing the right arrow key. Paste (Ctrl + v) the equation.

4x ‐ (3x + 5) = 3 ‐ (x ‐ 1)
4x ‐ (3x + 5) = 3 ‐ (x ‐ 1)

Edit the equation (in this case, start by removing brackets):

4x ‐ (3x + 5) = 3 ‐ (x ‐ 1)
4x ‐ 3x ‐ 5 = 3 ‐ x +1

Copy and paste the simplified equation on the line below, using the same strategy as above.

4x ‐ (3x + 5) = 3 ‐ (x ‐ 1)
4x ‐ 3x ‐ 5 = 3 ‐ x + 1
4x ‐ 3x ‐ 5 = 3 ‐ x + 1

Edit the equation (combine the x terms on the left and integers on the right):

4x ‐ (3x + 5) = 3 ‐ (x ‐ 1)
4x ‐ 3x ‐ 5 = 3 ‐ x +1
4x ‐ 3x + x = 3 + 1 + 5

If the equation is short, the student can do the calculation on the same line after pressing the space bar twice:

4x ‐ (3x + 5) = 3 ‐ (x ‐ 1)
4x ‐ 3x ‐ 5 = 3 ‐ x + 1
4x ‐ 3x + x = 3 + 1 + 5 2x = 9

Move the final step to the line below: Use the Cursor Routing button and move the cursor to the beginning of the last step (after the two spaces). Press Enter to move the equation to the line below:

4x ‐ (3x + 5) = 3 ‐ (x ‐ 1)
4x ‐ 3x ‐ 5 = 3 ‐ x + 1
4x ‐ 3x + x = 3 + 1 + 5
2x = 9

Divide by two on both sides:

4x ‐ (3x + 5) = 3 ‐ (x ‐ 1)
4x ‐ 3x ‐ 5 = 3 ‐ x + 1
4x ‐ 3x + x = 3 + 1 + 5
2x = 9 ::2

Complete the calculation and write the answer on the line below:

4x ‐ (3x + 5) = 3 ‐ (x ‐ 1)
4x ‐ 3x ‐ 5 = 3 ‐ x + 1
4x ‐ 3x + x = 3 + 1 + 5
2x = 9 ::2
x = 9/2===

Solving an Inequality

You can create a table in Word or Excel to solve an inequality. Here is an example of the solution of the inequality $x(x+3)(x-2)\geq 0$ :

	x	x + 3	x ‐ 2	x(x + 3)(x ‐ 2)
x < -3	‐	‐	‐	‐
-3 < x < 0	‐	+	‐	+
0 < x < 2	+	+	‐	‐
x > 2	+	+	+	+

The table shows that the expression x(x + 3)(x ‐ 2) is positive or zero when -3 <= x <= 0 and when x >= 2.

To learn more about navigation in Word and Excel, see the instructional guide on coordinate systems and graphs.

Using Digital Tools to Solve Equations

Digital tools are widely used in schools today. If a screen reader user intends to use a digital tool, it is essential to check that it is accessible to braille readers. An example is GeoGebra, a powerful and flexible tool that allows sighted students to solve equations and manipulate mathematical expressions. This program is not accessible for screen readers. Instead of GeoGebra, braille readers may use other tools such as custom-made Excel sheets and programming.

Excel Sheets

If you have pre-made Excel worksheets, a braille reader can enter the key figures for the equation and the sheet will calculate the result for the equation. In order to obtain good working conditions for the braille reader, the Excel program and screen reading program must have the right settings:

In Excel, the cursor movement must be turned off when the Enter key is pressed. In this case, the braille display will show the result of the input directly, without the braille reader having to move the focus to the braille display.
The screen reader must also be set to display the entire row on the braille display, not just the active cell.

Information on how to adjust these settings in Excel can be found in the instructional guide on coordinate systems and graphs for ICT professionals. You will also discover some useful hotkeys tailored for braille readers.

Programming

Text programming is usually accessible to braille readers. The editor chosen for text programming should have features that allow it to be operated using keyboard shortcuts, so that braille readers can navigate the process independently. An example of an accessible programming editor is Visual Studio Code. For more insight into programming as a braille reader and what ICT professionals need to be aware of, see the instructional guide on computational thinking for ICT professionals.