Welcome to The Inclusive Math series!
As stated in the intro video on my channel which you can find at [https://www.youtube.com/watch?v=VF3Z_P1ySiA&pp=sAQA], this series is intended for all those looking for accessible solutions to study advance stem subjects. We will be covering all the different sorts of tools available for assistive technology users that have been improved or developed to make it possible for us to read and write equations, that too in a completely inclusive fashion so that our fellow sighted counterparts can see what we’re doing!
For every video I make, I plan to release a textual equivalent of to serve as notes, reference for people who prefer to read rather than listen or want a guide that they can quickly serve through without having to listen to the clips all over again. In part 1 ( the link to which can be found at https://www.youtube.com/watch?v=r6TcHrCakbE&pp=sAQA), we did not specifically dive into a particular tool as such but rather decided to go through some of the key skills (prerequisites of sorts) that we will continue to use throughout this series with all the different sorts of external software and which every student studying maths and science with the use of computers (especially those with assistive technology) should know.
Let’s start with a simple number here.
2
If you are like me and are making use of a screen reader like Nvda, Jaws, etc, all you should have heard there should have been “2”
Yup, and that is exactly what it was!
Let us now try something else.
x=2
In this case, what your screen reader should have read out to you in the line above is “x=2”
What we just wrote is the simplest form of an equation.
However, we can make this equation much more complicated by making use of some of the logical operators that come with most standard keyboards and which can be typed directly in most word processors or text editors without the need of external tools.:
- +: Denotes addition, can be written by holding down the shift key and pressing the equals key, located to the right of the backspace key.
- -: Denotes subtraction, can be written by pressing the key to the right of the 0 key.
- *: denotes multiplication, can be written by holding down shift and pressing 8.
- /: denotes division (also used for fractions), can be written by pressing the key to the left of the right shift key.
- ^: The power symbol, can be written by holding down shift and pressing the number 6.
We can now use these symbols to expand upon the equation from above, like so:
x+y=2
x+y-z=2
x+y-z*c=2
x+y-z*c/b=2
Note – Screen readers usually read these symbols as they are, whether they’re used in English or maths. Therefore, we do have to acclimatise our brains to process these based on all the notations we saw above. It does take a little practice, but is very much doable. Not to mention that once we jump to the more advanced tools things would be much better in this regard-that is to say, screen readers will get much better at the pronunciation of these equations.
Perfect so far, but I’d like you to take another look at the last equation, I’ll paste it again for reference:
x+y-z*c/b=2
Let’s break this one down together.
- We are adding the x and y variables
- We are then subtracting z from it
- Then we multiply (a/b) to it
I realise that this will not be the exact order according to pemdas or bodmas whichever you prefer, but for the sake of sequence let us just think of it as the right approach.
Let us look once more at the final step
Multiply (a/b)
This clearly tells us that a/b is a fraction of its own, that b is a denominator that only belongs to a, that b will divide a and nothing else in the equation. What if however, we want to change this?
What if I say, that we have to construct an equation where in b serves as denominator to all the other terms on the left-hand-side, that the whole thing is a fraction.
This is where the other tool in our toolbox as it were coming in. Something that we’re going to need and use quite a bit in the following few weeks, and which will come in handy with any other external tool as well., brackets.
Therefore, anyone with basic knowledge of mathematics should know what they are and what they are used for. Anyway, I will point out the three sorts that we have available to us regardless, just for the sake of reference and ease:
- Parentheses, also commonly known as round brackets: (), accessed by holding down the shift key on the keyboard and then pressing 9 for an opening parenthesis, and 0 for a closing one.
- Curly braces: {}, accessed by holding down the shift key and pressing the two keys right of the p key, opening represented by the first one, and closing by the second.
- Square brackets: [] Accessed by simply pressing the keys pointed out above to the right of p, except we do not need to hold down shift in this case.
Perfect. We now have access to three different sorts of brackets that we can utilize. Let us try to make use of the round brackets and see if we can come up with a solution to the problem from above.
Here’s the equation once more that needs changing.
x+y-z*c/b=2
Now, we know that the b there, should serve as denominator to the entire left side. Let us try to modify our equation now with the use of these brackets:
(x+y-z*c)/b=2
Good stuff! Using those brackets, we have successfully denoted the entire left-hand side as a fraction. As we know already, no matter what system we use to solve expressions, brackets are taken care of before all the other common operators such as addition, subtraction, etc. Therefore, we know that the entire bracket will be solved before anything else, and the final solution will then be divided by b. So, b divides everything else. Some may wonder why we did not include a bracket for b, but in this case, it wasn’t really necessary, since b is already one term, adding additional brackets where not necessary might make things very confusing especially when we get to much more complex equations, and work with nonconventional tools that may take a while to get used to.
However, here is a situation that might change this for us.
x+y-z*c/b+a=2
At first glance this might seem confusing, so I encourage you to take a thorough look at it before continuing, and for those using screen readers, read it character by character.
Even after looking at this multiple times, it may not entirely be clear what this equation is trying to portray. There could be two possible conclusions drawn:
- x+y-z*c is the numerator, b is the denominator as we depicted above, to which a single variable a, is being added.
- X+y-z*c is the numerator, and b+a is the denominator.
Here is where we need even more brackets!
I stated before that for one single denominator we don’t really need to include brackets, but if we would like to express (b+a) as the complete denominator of the above then we will need to include them:
(x+y-z*c)/(b+a) =2
If we refrain from doing this, then anyone looking at our screen will most likely reach the first conclusion that we drew above. It might also get unnecessarily confusing for us as well when reading the equation with a screen reader.
However, even if it were the first conclusion that we wanted to depict, there is in fact, a better, a lot less confusing way to do that than
X+y-z*c/b+a=2
We might understand how by integrating the things we learnt above, I’d love my readers to think about this one, and write in the comments about how they think it should be done!
That’s, pretty much it! These are all the tools that we are going to need, when we take on slightly more advanced technology in the later parts (which will make use of all this), so I would encourage my readers to practice even more complex questions on their own, and representing their solution using everything we talked about (by utilizing the symbols available to us and possibly making use of multiple brackets if needed) and if there’s anything you’d like to know about, feel free to comment down below, or on the video, and I will try to get back to you as soon as possible!
I hope this article proved to be a good read, and hope you learnt something from it.
Do let me know what you think, feedback is as always, very much appreciated.
Stay safe.
Stay Inclusive.
inclusion the motto! 