Jump to:
Understanding the Structure of an Equation
The braille professional can ensure that the braille reader understands the structure of the equation and how to solve it using a braille display. Here, you will find instructions and examples on how equations may look like, and how the braille reader can solve them.
Mathematics often lacks explicit context, and braille readers should use available context to better understand the structure of an equation. They should expect expressions on both sides of the equal sign and ensure that bracket pairs are properly matched. Braille professionals can help by guiding students through these details as they practice solving equations.
Understanding the Structure of an Equation
Braille readers need to understand the structure of an equation to solve it correctly. This requires tactile exploration, where they build up an overview by moving their fingertips from left to right over the braille display. Listening to the equation spoken aloud first can help gain an initial understanding of its structure.
One way to grasp the function of any brackets in the equation is to keep your left index finger on the open bracket while moving your right index finger over the expression inside the brackets. For example, when reading the equation 2(3x + 3), you would linger with your left index finger on the open bracket and use your right index finger to read “3x + 3” until reaching the closing bracket.
Brackets serve multiple purposes in mathematical expressions, both in mathematics in general, and specifically in the linear notation read on a braille display.
Brackets can have multiple meanings that should be explored while reading the expression, as shown in the table:
| Explanation | Example Mathematical Expression | Dutch Linear Notation |
| To change the order of operations |  | 2(x + 3) = 2x + 6 |
| To indicate the beginning and end of a numerator or denominator of a fraction |  | (x + 2)/(x ‐ 3) |
| To indicate the beginning and end of a square root. |  | 2(sqrt(100/4) + 5) |
A step-by-step strategy for understanding an equation could be
- Give the braille reader a general description of the equation. For example, for the equation (x + 2)/(x ‐ 3) = 2/(x ‐ 3), you could say “this is an equation with two fractions. The denominators of both fractions are the same”.
- Have the braille reader read the equation aloud, character by character, to ensure they understand the notation correctly.
- Ask the braille reader to examine the left-hand side of the equation and look for powers, roots and brackets.
- Ask the braille reader to examine the right-hand side of the equation and look for powers, roots and brackets.
The Braille Display
The Size of the Braille Display
Braille displays range in size from 12 to 80 braille cells on a line. If it is too short for an expression or equation, splitting over multiple lines may be necessary. This makes it challenging to get an overview. Braille on paper may offer a better overview, and using worked examples in braille on paper is therefore recommended for braille readers who have difficulty understanding the solving process. Once they have mastered this, they switch back to the braille display. Note that the braille reader works with 8-dot braille on the braille display and that the notation can differ in 6-dot on paper.
Solving an Equation on the Braille Display
Assuming proficiency in ICT skills, the braille reader uses arrow keys, cursor routing, and navigation keys. If lacking ICT skills, seek professional support.
As a braille professional, you can check whether the full equation is visible on the braille display, or whether the equation is split into multiple parts. This is important because it helps the student to get an overview of what he/she can expect when reading on the braille display.
It is important to note that when solving mathematical equations, the braille readers should always select the equation in the last form – which is different from the original equation – and copy and paste this equation on the next line(s). Then they perform new operations on the last equation.
Example
2x + 3 = x + 2
x + 3 = 2
x + 3 = 2
The last line is a copy of the line above. The braille reader can change the last line into x = 2 ‐ 3 etc. You then get:
2x + 3 = x + 2
x + 3 = 2
x = -1
Braille skills – and not only mathematical skills – are important to investigate what should be manipulated and to check whether the manipulations are correct compared to the previous line. In mathematics, small mistakes in reading can lead to a completely different answer or solving procedure.
Using a Screen Reader
When a student uses a laptop equipped with screen reader software, the expression or equation can also be read aloud. This feature serves as a valuable cross-check for the braille reader. The dual approach of reading in braille in combination with speech synthesis, can reduce the challenges associated with mirroring or reversing the braille characters. This may improve the understanding of mathematical content.
The level of verbosity in the punctuation settings of the screen reader software determines which elements will be vocalized. These punctuation settings offer four levels of verbosity: none, some, most, and all. Choosing a higher level of verbosity will cause more punctuation marks and symbols to be read aloud. In the context of reading mathematical content, braille readers must choose the highest verbosity setting since the absence of a single character can significantly change the meaning of the expression.
The appropriate settings will ensure the speech synthesis reads mathematical symbols correctly. However, it is important to remember that these symbols are often also used outside of mathematical contexts. For example, symbols such as ‘-‘, ‘/’, and ‘*’ can have meanings other than just ‘subtract ‘, ‘divide’, and ‘multiply’. Therefore, it may be preferable not to add a mathematical dictionary but to leave it to the students to interpret the meaning in the mathematical context.