Hello everyone and welcome back to What in the World is Dyscalculia, the podcast that
is all about the math learning disability.
I'm your host, Dr. Honora Wall, and the podcast is produced by Educalc Learning.
You can find out more about Dyscalculia at educalclearning.com or at our non-profit
www.thedtri.org which stands for the Dyscalculia Training and Research Institute.
And I'm going to jump in today because I just had a session with a student that really highlighted
a lot of things I want to talk about for classroom teachers, interventionist, tutors, and home
school parents.
I'll be running into this situation that I have today.
And I will preface by saying that most of the situation I ran into today was a conflict
between my prior knowledge as a math educator and the student's lack of prior knowledge
because they're the student and how there's that disconnect between the two.
It is really difficult as an educator to get into the headspace of the student who's hearing
all these terms and doing all this work, learning these concepts for the first time.
We know exactly what we mean when we're talking about these math topics and presenting a lesson.
So it can be hard to know when the student really understands what we're trying to say
and when they don't.
When you work with students who have neurodivergence, dyscalculia, dyslexia, dysgraphia, ADHD, high
functioning autism, or I guess I should say autism in general, I was working with a student
who has high functioning autism and dyscalculia.
These students have a quality I find quite frequently just because I see it a lot does
not mean that they're tied together.
That is an important distinction.
But I do see it quite a bit and it is a great quality in a student and it can be a difficult
or sometimes frustrating quality for a teacher which is why I wanted to talk about it.
So here's the quality.
The quality that I find prevalent in this population of learners is that they're not
interested in taking your first explanation as the answer, they need to know more.
They have so many more questions than a neurotypical student who is more likely to say, okay, I'm
going to do X, I'm going to do Y, and then I get answers E and I move on.
Or I got to do it because they said this is what to do and they move on.
No, neurodivergent students have a lot more questions.
They need to know Y and the way you explain the Y to everyone else is not going to be
satisfactory for these students so they're going to have more Ys.
And I have had students I work with who find that their classroom teachers do get frustrated
and say things like you have to get it.
I just told you what it was.
Or say, okay, that's too many questions.
The class has to move on.
Ask me later.
And I completely get that especially if you have a large classroom, you're trying to meet
a pacing chart or just get through a lesson.
You know the homework you need to assign.
You have to talk about all the things that are going to be on the homework.
So it can take longer to work with students who have more questions.
And sometimes we don't know the answer to their question.
That's exactly what happened to me today.
And I start this lesson.
This particular student of mine is a homeschool student who came to me recently with high
functioning autism and dyscalculia and is old enough, he's 18, old enough to have had
a whole lot of math and were doing mostly grade level work.
But he also did not have the foundation for it because with the dyscalculia using a traditional
math curriculum, he just really had not progressed past second or third grade math.
Which is very common, the worksheets and the traditional curriculum for second and third
grade are a train wreck for students with dyscalculia and without the right support
systems it's just not going to happen.
And that is what the case was here.
So when I met this student a few months ago, I said all right we're going to jump in to
grade level as much as possible, fix the foundation as we go and get this math curriculum complete.
So, today we were talking about complementary and supplementary angles.
All right, if two angles happen to be complementary that is a technical term that means the two
angles add to exactly 90 degrees.
Maybe they are two angles that are part of a right angle, maybe they are two angles that
are not connected to each other.
Maybe you have a graphic of an angle or the two angles, maybe you have a word problem
that just lists the degrees.
You can see this working a lot of different presentations.
But at the end of the day, complementary means two angles add to 90 and supplementary means
two angles add to 180.
I was thinking this would be pretty straightforward, this would be a breeze.
The calculator work, we've already talked about angles, we've already talked even a
little bit about the unit circle and what degrees are, where they come from, what does
that term mean.
We've talked about the semicircle, the 180 degrees.
We've talked about different types of angles, acute up too.
So I thought we had a lot of prep and groundwork laid and this would be a pretty straightforward
extension.
And I could not have been more incorrect in that assumption.
Here we got to with this lesson is that, you know, if you have an angle that's, let's
say 62 degrees and you have to find the complement, the work you do is to grab your calculator
and put in 90 minus 62.
The answer is the measure of the complementary angle.
Okay.
Well, the student really got stuck on why do we care if angles are complementary or
supplementary?
Why do you need to know this?
In what format will you ever use this either in math or in life?
What is the point essentially?
And this is where I think there's an interesting disconnect.
There's big movement in education right now to do kind of the problem-based learning and
put students in a situation where they have to kind of try some things and figure it out
and that is going to develop conceptual understanding.
And that's true for a lot of things and for a lot of students.
I don't find it to be effective in the way we want for students who are neurodivergent
because their conceptual understanding is different and unique.
It is not weak, it is not lower level, it is not incorrect.
It's just different.
And this is a population that will test you as an educator.
They will stretch you and you will have to work in a different way, a unique way.
You're going to have to dig deeper to answer their questions.
I'll give you a spoiler alert.
We got to the end of the session and I said, I will keep searching to try to find an answer
that works for your question but I really don't have one that is satisfactory at this
time and we had to move on.
We'll come back to it later.
If I find a good way to answer the question, I'll let you know in a future podcast.
But for you, you can get this kind of question teaching any topic so I don't want to get
too hung up on what's a good answer for complementary or supplementary.
It's going to happen to you in all sorts of math topics.
So what I really need for you to know is that this is very normal for neurodiverse students.
They have more questions, they need more and different answers.
Telling them the same answer over and over again will not work.
Saying it the way it works for every other student you've worked with will not work.
Saying it just the way it makes sense to you will not work.
You're going to have to keep trying some new things.
And if you have the time and space to do it, it's a really interesting conversation.
You get to think about math in a very different and unique way and you get to think about
the application of math concepts in an interesting and unique way that you have not had to do
before.
If you're finding that it's a source of frustration or aggravation, you want to reflect on your
thoughts about math and your understanding of it.
We can understand math and still not understand how to ask or answer a question about it.
That's okay.
That happens.
We are not robots and a lot of what we're talking about is ephemeral esoteric topics.
I tried to get as close as possible by utilizing, okay, well, if you need complementary angles,
you might need that in building.
Let's say you had a house and the wall was at an 80-degree angle and it really needs
to be at 90 for strength and stability.
So what are you missing, a complementary angle of 10 degrees would help shore that up, things
like that.
But it didn't really satisfy the student in a way that he felt comfortable with the homework
I needed to assign, which was simply what is the complement to a 62-degree angle?
Another interesting point, and I bring this up because this will impact the way you teach
as well.
When I was introducing this lesson, I gave the definition that I thought would make the
most sense complementary means two angles that add to 90 degrees.
Supplementary means two angles that add to 180 degrees.
We talked about it, we wrote it down, we got into our examples, and at the top of this
worksheet you would be given an angle, like I said, the 62 degrees, and you had to find
the complement.
So the work then becomes 90 minus 62.
Even if we had written out the equation, 62 plus x equals 90, you still would have solved
by subtracting 90 minus 62.
Well then at the bottom of the worksheet there were other questions.
Classify the angles as complementary, supplementary, or neither.
And then you were given two angles, let's say 44 degrees and 17 degrees.
You had to add them and decide whether or not they added to 90 or 180 and what kind
of special term that would give it.
So as he's writing down the notes so that he can do this work on his own later, this
was really a sticking point for him.
He was trying to write down what is my formula, how could he explain to himself later, his
future self.
His notes have to be a message to his future self on how to do this work.
And my definition, complementary adds to 90, did not match the work being done.
If you have an angle, you are going to do 90 minus that angle to find the missing complementary
angle.
I said complementary angles add to 90.
The work I told him to do is subtraction.
For people who do not have a math learning disability, this is part of a fact family
situation.
These are inverse operations.
You add and the backwards of that is subtract.
They go together.
For a student with dyscalculia, they do not go together.
These are completely individual, unrelated, separate tasks.
And having the definition adds to 90 does not automatically correlate to solve with
subtraction.
So we really had to dig into that and how to put the right kind of notes for each section
so he knew what to do.
And also discuss a very little bit of the duality, the front and back, top and bottom,
add subtract, the relationship between inverses.
That is why students with dyscalculia also have a lot of trouble with directions and
also have a lot of trouble with those prepositions above, below, front, back, left, right.
These are all difficult concepts because we teach them and think of them as being related
terms.
And for students with dyscalculia, they are not.
It is very much like saying you could have an orange or you could have an octopus.
What?
They are not related at all.
And that is a very different way of thinking about this as an educator.
We might think of things as going together as a unit, doing and undoing each other.
That is not how our students with dyscalculia interpret these concepts.
So just a heads up on some of the things you will definitely find working with neurodivergent
students.
When they're asking questions and they say, but why, but why, but why?
It doesn't make sense to me yet.
I need it to make sense before I can move on.
You really need to take everything that you are thinking about the topic and throw it
up in the air, separate it all out like confetti and start talking about it individually and
separately and differently and try a few things.
And don't be afraid to tell students, you know, that's a really interesting question.
I'm not sure if I'm answering it the way you're looking for an answer.
I'm not sure I understand exactly what you're asking.
Let's dig into this a little more and see if we can get somewhere with it.
Maybe we'll get somewhere that lets you feel better about the topic and understanding it.
We might just get to a point of, listen, for the top half, you're going to do 90 minus.
And for the bottom half, you're going to add and see if it's 90 or not.
Yes or no.
Sometimes we do have to get to that very specific direct instruction.
Do this, do not do that and save the rest of the understanding for a longer or a future
discussion because we have to come up with better explanations.
We have to find that, that route together.
And I do find a lot of students are willing to accept that.
If you are willing to say, listen, I'm not sure, I'd like to find out.
I'm going to research it a little bit.
I'm happy to have this conversation with you later.
Right now we just need to get this part done.
Then that's okay.
It's when we say, no more questions.
Talk to me later.
You're asking too much.
You need to already know.
Now they feel very cut off and that closes the door.
We're limiting the access because of our own experiences, our own frustrations or our
own needs to get some other things done or our own feelings of insecurity, not knowing
how to answer the question that is being asked, not being able to get a satisfactory answer.
And I know that this is true of a lot of educators.
I hear this from teachers at conferences and conventions and during the Q&A and I hear
from the students what they hear from their teachers.
We know teachers are frustrated.
So I want you to understand what to do about that frustration where some of it comes from.
That's just really exciting and different conversation.
It's not the conversation you've had in math class for the last 20 years of your teaching
career.
This is different and be open to that.
And be ready for the surprise.
I truly felt that this would be one of our easier lessons.
I mean, heck, we're using a calculator.
It's only two words and there's only two things to do.
It equals 90 or it equals 180.
That's it.
Those are the only two options.
I thought this would be very straightforward.
And as I said, it was exceptionally difficult to come up with a good explanation that made
my student feel better and more confident about these terms.
I believe he feels confident with the work, but now I'm going to see.
After he's done these worksheets on his own, do his notes still make sense?
Is he still able to complete this work or does he still get stuck because of that conceptual
piece?
Personally, I do not know of any research that's being done in this field yet.
I'm not sure what the research question would even be.
Maybe just a case study or qualitative examination of neurodivergent students and their feelings
about math concepts.
If you've come across anything like that, you have some research for me, please share
it.
I would love to know more.
You can send it to me at Honora, H-O-N-O-R-A at educalclearning.com or Honora at the
dtri.org.
And of course, check out the two websites.
If I do come across some good information in this area, I will put them up as blog posts
and put the links to research or articles on those websites so that we can keep sharing
information about the math learning disability and help our students with any type of neurodivergence.
Thank you very much for listening to the What in the World is Discalculia podcast.
This has been your host, Dr. Honora Wall, and I look forward to speaking with you again
soon.