Hello and welcome back to What in the World is
dyscalculia, the podcast where we talk all
about the math learning disability. I'm your
host, Dr. Honora Wall, and you can probably hear
I have a little bit of a cold or allergies today.
I haven't determined exactly which one it is,
but I set a goal for this year to be truly consistent.
With my podcast and social reels and if you're
going to be consistent, you're going to get the
work done No matter what so here we are The podcast
is really important and I'm excited to be more
consistent with our episodes There's just so
much to talk about and there's a lot of exciting
things happening in the world of dyscalculia
and dysgraphia and dyspraxia and neurodivergence
in general so it's a very exciting time to be
a part of this growing awareness around these
issues and I want to talk today about one issue
that I need all parents and teachers to truly
understand and I need all students to really
buy into what I'm talking about today because
it's going to make a huge difference not only
in your math performance, but also in your comprehension
and your self -confidence around math. Quick
note, the What in the World is dyscalculia
podcast is put on by Educalc Learning and you
can also find information about the math disability
through our nonprofit, the dyscalculia Training
and Research Institute, educalclearning .com
or thedtri .org. Lots of information on those
sites for you as well. So let's get into today's
topic. I want to talk about three very specific
reasons why you should always have students use
their calculator or their external resource of
any kind, I'll talk about them, and write down
their work. Students, if you are not checking
your calculations and you are not writing down
your work, you have exponentially increased the
chance of getting the wrong answer, even when
you understand the math and you know what you're
supposed to do. There's no reason to leave points
on the floor of the classroom simply because
you didn't verify your initial thought. That
is sloppy work. Teachers, I need you to require
precision and don't allow any kind of sloppy
work. And I'll also point out for those of you
who work with high achieving students, this is
a really great habit to get into because everyone
hits their wall when it comes to math. Students
who are struggling are going to hit it earlier.
Students who do Fantastic job and are always
great at math in elementary and middle Sometimes
even in high school. They're still gonna hit
their wall. They could hit it in Algebra or geometry
or maybe they hit it when they get into college
but the older a student is when they hit the
wall in their math performance the harder that
hit is because they've relied on the parlor trick
of mental math and Just getting it super fast
and not having to work at it and now they don't
have the steady skills and the strategies to
back themselves up. And it's very damaging and
disruptive. So we can avoid that by putting in
good habits earlier. And we know that as teachers,
so let's talk about those good habits and the
justification for them. I want students to be
using their grade -appropriate tool to check
calculations. Early grades, that could be a number
line. Could be a 1 to 1 hundredths chart. Could
be a multiplication list. I really hope you've
printed out that old -fashioned times tables
list and you're using that for so many different
topics. Listen to some of our other podcasts
or watch our YouTube channel or get into some
of the monthly training and you'll find out why
and how to use that tool. Then we're gonna move
into a calculator. We're gonna use formula sheets.
to make sure we're writing down the right formula,
putting numbers in their right spot, and we're
checking our work as we go through. That's the
first thing I want students doing all the time,
and here's why. We're going to use that in conjunction
with writing down our work. That is a tough one,
especially if a student has comorbidity with
dysgraphia, so it's going to look like a train
wreck, and that's okay. unless you are the writing
teacher you should not be grading on how nicely
the numbers look anyway you're going to use graph
paper or some lined paper and grids and help
students kind of line up their work and practice
that handwriting skill we're not writing down
work so that it looks beautiful and to improve
writing necessarily but we are doing it to activate
different parts of the brain through that tactile
experience and we're getting into a habit of
writing things down so students can find their
best handwriting, whatever it happens to look
like for them, but we don't just give up on the
skill if we know it's a struggle. We practice
it and we don't grade on that because we know
it's a struggle the student can't really control
if they have dysgraphia or some other fine motor
skill issue. There's more than one thing that
can make a person have problem with handwriting,
but we do want to write down that work because
only doing work in our head It's very difficult.
Super easy to get lost in your thoughts, to overwhelm
your short -term memory, and to get the wrong
answer or lose your place. That's a second reason
for writing down work. Let's say there's a distraction.
There's a noise in the room. Someone comes in
the room. You think about something else. I lose
my train of thought all the time. Every adult
does. So there's no reason we shouldn't expect.
Children will as well. If I've written down what
I'm doing, Then I can go look at what I did and
see where I left off much more efficient Than
trying to keep everything in your head. So the
written work will help you keep track of where
you are in a problem Help you keep track of your
planning. How are you gonna finish this problem
and It's a really useful skill. So here's our
three reasons why we're gonna use that external
tool and we're gonna write down our work This
is a great way to show evidence of our thinking,
which is a big trend in math right now. We've
been doing this, capturing evidence of thinking
through these very strange open -ended questions
on a math problem. Even something as elementary
level math as John has two red marbles, Sally
has three blue marbles, how many marbles do they
have in all? Explain your thinking. Well, the
thinking is that we added 2 plus 3. So if we
need evidence of thinking, showing where we got
those numbers on a number line or 1 to 100's
chart or through manipulatives, that's a demonstration.
Not all demonstration and evidence has to be
written. It could be oral, it could be shown
through using tools, or it could be written down
for a student who prefers using their words and
writing out an explanation. It's also a great
way for you to informally find evidence of thinking.
You can look at what your students are doing.
You can watch them use the 1 to 100 chart number
line multiplication list calculator and see what
buttons are they pushing, in what order, where
are they putting their finger, are they counting
on Or are they starting to count from the square
they're at? Are they able to make some loops
on that number line, kind of hop along, forward,
or backward? Now you can see what's going on
because you're watching them do it. The student
has to be the one doing the work. Otherwise,
you're going to have no idea what the student
actually knows. When they're writing it down,
you can see. Are they using the proper formula?
Are they following the right steps and procedures?
Which step is a stumbling block for different
students? So for example, let's say I'm working
with formulas at any grade level. We really start
using formulas very early and I'll go with a
straightforward one. Let's say I'm finding perimeter
and I've been working a couple of days on adding
different sides to get a total perimeter, but
now We're doing an extension. We're doing the
reverse. I have the perimeter. I'm looking for
a missing side. Well, first of all, working backwards
like that is an entirely different skill for
a student with dyscalculia. It's not a forward
and back connection. It's not like a fact family.
Those inverse operations can be separate and
unique situations. Separate and unique math topics
for a student with dyscalculia. Understanding
that can change your approach to teaching that
lesson and having the student write down the
formula put the numbers where they go and you
can look over their shoulder watch them do it
on a dry erase board and Hold those up so you
can scan everyone in the class before they get
started Did they put the total perimeter where
the P is in the formula or did they put it somewhere
else? Now you can see evidence that they are
using a formula appropriately putting numbers
where they go, and that's going to set them up
for success. That is true of our most basic to
our most complex formulas. And if you are an
older math student, hold on, make it through
some of those complex formulas like distance
or quadratic formula, because if you can get
to physics, those formulas are much easier, much
more straightforward. The ones in statistics
aren't actually that bad. We just use a lot of
weird notation at that point. And using notation
or not for students with dyscalculia is something
we've talked about in other podcast episodes.
And you can read about the research from Dr.
Katie Lewis out of Washington State for reasons
why you as a teacher need to understand where
students with dyscalculia struggle with those.
Written math notations any who getting back to
our topic today first reason why I want you using
an external tool in written work is because it
gives evidence of Thinking and it can help you
correct students on the fly right away. Oh you
put this number here. It's actually gonna go
right here and Now we're set up more for success
our second reason why we're going to do this.
It lets the student confirm their prediction
of what they think they're supposed to do, what
they think the answer might be, what they think
the next step is. If you have read any of the
work about the way people think, the way the
brain works, any of our other podcasts, we've
talked about this before. The human brain is
constantly predicting what it thinks will happen
next. in every situation, not just in math class.
This is how the human brain operates. We like
to predict what we think is going to happen,
and when we get confirmation that our prediction
is accurate, we strengthen those neural pathways.
When we get a confirmation that our thinking
was incorrect, we weaken those neural pathways.
If we never get confirmation, or if the confirmation
comes the next day, or Monday after the test,
or maybe never, then the brain doesn't really
know what to do with that information. So an
easy way for you to help strengthen some of the
pathways and connections in the thought process
for your student is to make sure they immediately
check their work by using those external tools.
And really by fourth grade. There are topics
where you can start introducing a calculator
to reduce cognitive load, allow the student to
transfer the formula or the concept in the long
-term memory without stumbling through numeracy
issues, and now we're creating a very strong
math foundation for the student. So we know they're
going to predict. We want them to confirm either
way immediately. For a student who's struggling,
this can be the key to some really immediate
growth. If they have low numeracy, weak math
foundation, they're a multi -language learner,
so they're trying to translate vocabulary in
their head from one language to another, we want
these external tools. It's going to strengthen
the number part, so they can focus on the other
parts that are important for them. And if they
have dyscalculia, Their parietal lobe is going
to lose math information over time, especially
those basic facts. We know it to be true. So
if you're teaching a student with known or suspected
dyscalculia, here's an easy fix. Let them use
their external tool, including the calculator,
to check their work. If you don't, then what
you're really assessing is their disability.
You're not assessing their actual comprehension
of math and their ability to do math, so That
might be my strongest case personally, but even
if they don't have dyscalculia the constant confirmation
Ensures that the thing they remember is the right
answer what they always have is the right answer.
It's not a lot of wild guesses They have to be
precise, and this is our third reason for using
these external tools and for writing down our
work. It's not just to take up a lot of extra
time or to add to the workload. There are specific
reasons tied to learning why this is important.
And our third one is we're building a habit.
We are requiring precision and accuracy. And
that's vital. Trust and believe that if someone
keep studying math and science and becomes a
chemist or starts working at NASA, I want them
to be precise and accurate in their work. There
is a stage where human lives truly depend on
it. If they go into medicine, I want them to
be precise and accurate. If they go into nutrition,
I want them to be precise and accurate with the
advice that they're giving. We need precision
and accuracy. That doesn't come down from the
ether. We don't become precise and accurate through
osmosis. We do it through habit. These habits
are built when we're younger. Do it in school.
Get into the habit in first, second, third, fourth
grade of writing down work, checking answers,
and being precise before you hand things in.
Don't take the work! until the student has written
something down, until they have confirmed all
of their answers. It should be very easy grading
for you as a teacher for all of your classwork
and all of your homework because you don't accept
it until they've gone through and confirmed.
Hand it back. They can get a late score if they
don't do it on time. We've got to do that early
to build the habit. And then by middle school
and high school, we have a much larger group
of students who know they have to show their
work, who know they have to go check their answers.
They already are doing it. So my elementary teachers,
if you can start doing it now, then my middle
school and high school teachers are gonna have
a nicer experience in a couple of years. Middle
and high school, it's a struggle to build those
new habits. Hard stop. I usually don't like to
put more work on our classroom teachers. But
let's face it, that's work that's going to be
important. It has to be done. And for struggling
students, it might be the thing that saves them.
It's certainly at any age going to be the thing
that increases math performance, both in the
classroom and on those ever important end of
year state tests. So if you're looking to increase
test scores, your school if you're trying to
change your performance rating at your school
then as an administrator You better be getting
into every single math class and making sure
everyone's writing their work and using Whatever
external tool is best for them and for the topic
to check their work If you always have an a because
you're always writing out your work and you're
always checking your accuracy of your answers
then You're going to continue that anytime you're
doing math work. If you're constantly guessing,
and you really have no idea if you're right or
wrong, and you kind of get the broad strokes,
you have the basic idea of what's going on, but
you're not looking for the little tiny details
that are part of accuracy, well that's why you're
failing algebra 90 % of the time, even for students
with a math learning disability. My students
do very well in algebra because we use external
tools like a calculator to handle the numeracy
part we write things down and we verify that
our numbers are in the right place and then with
that habit we have the mental space to look for
negative signs we have the mental space to remember
the rules of combining like terms and we have
the capacity to look for inverse operations and
we're not exhausted by the time we get to the
end of the work, we can go back to the original
problem and say, did I find what they wanted?
Did they ask for the value of x? Or are they
asking for the measure of this angle? Do I need
to apply the value of x that I found? This kind
of work with longer steps and procedures can
be exhausting. So if we want students to be complete
with their answer, then we need to make sure
they're not mentally exhausted. And the habits
of precision and accuracy are the tools that
get us there. So, to recap, we've got to have
students using their external tools longer than
we think they should. You've got to get over
this idea that mental math and speed is some
kind of indicator of math accuracy and ability.
They're not Mathematical thinking should be efficient
and it should be precise I don't want to eat
a muffin from a baker who said, you know, I'm
pretty sure it was a quarter teaspoon of Baking
powder like I don't know I put it in there No,
I'm if I'm paying for a muffin. I want it to
be really good I'm gonna need you to be a little
more precise with your measuring Same thing in
math class. If I want students to be really good
at math and to feel good when they're doing math
and to understand and perform well in math, I
need to let them use their external tools. I
need to have them write down their work. If I'm
going to be accurately grading what someone knows,
I need to see it. I need to hear it. I need to
have them show me and tell me. Ridden work. Here's
why you're going to do it. It gives you better
evidence of student thinking. For the student,
it lets them confirm their predictions and create
stronger neural pathways for the right answers.
And over time, it builds the habit of being precise
and accurate. Very important, not only in math,
but really in any field. If you would like to
know more about this topic, Or if you want to
know more about the research behind these ideas,
get on Google Scholar, find some research articles.
We're always trying to build more of these onto
the website so that you can go back to the original
source material and check out our websites, educalclearning
.com or you can look at thedtri .org for more
information. I'm Dr. Honora Wall. I appreciate
you being part of the What in the World is Dyscalculia
family, and please send me your questions, comments,
concerns, and ideas for future podcast episodes.
Thanks for listening. Talk again soon.