Hello, Happy New Year, and welcome to What in
the World is Dyscalculia? The very erratically
produced podcast about the math learning disability.
But in 2026 we have a new team, we have some
new people in place, and hopefully some new systems
and processes that will help me be more consistent
with getting these podcasts out to you. What
in the world is Dyscalculia is produced by EduCalc
Learning and hosted by me, Dr. Honora Wall, Executive
Director of the Dyscalculia Training and Research
Institute. We added some staff this year at the
DTRI. And I like to say we are for the neurodivergent
by the neurodivergent. Every one of us either
has a diagnosis or, in my case, some very clear
signs and symptoms. Although I'm too old to have
gotten testing when I was younger, we really
didn't talk about these things in school back
in the day. That's one of the reasons why leaning
into the research is really important in this
work, understanding neurodivergence and how it
impacts the life experience of a person with
dyscalculia, dyslexia, dysgraphia, dyspraxia,
ADHD, autism, so many things that fall under
this neurodivergence umbrella. Understanding
these unique traits. is a new and complex field.
Very interesting. The neuroscience is fascinating
and that is one of our goals here at what in
the world is dyscalculia. To bring you some of
that research and to direct you where you can
go learn more on your own. Always encourage that.
And if you don't have time or you're not a fan
of reading dense research articles, we can at
least summarize and get you some key points.
But I I'm a big fan of geometry, love teaching
geometry so much. And of course, our big thing
in geometry is prove it. So you should never
take my word for anything. You should go back
and read original source material yourself. And
if you want to read the original source material
for today's podcast, you're going to look up
a learning math article. Just type in learning
math by Das and Janzen. It should pop right up.
J .P. Das and Chris Janzen out of the University
of Alberta. And this article was published in
2004. I really like this article because it breaks
down domain general versus domain specific in
a way that's really easy to understand. So that's
what we're going to talk about today. And then
we're going to talk about how that applies to
the four main things that the researchers say
learning math requires, the components of learning
math. So only four things that we need to learn
math and only two domains that we're going to
talk about. Very simple and accessible information
but really crucial to understanding where and
when and why a student struggles with math and
how we can help them. So let's start with the
domains. There are two things that we talk about
in education, domain general and domain specific.
And it comes up a lot in neuroscience too, not
just education, but there's a lot of overlap
between those two fields. So what do they mean?
Domain general refers to processes that apply
to lots of different things. So short -term memory,
that is domain general. We need short -term memory
for pretty much everything that we do, and that
governs our moment -to -moment experience throughout
the day. And that information may or may not
get transferred into long -term memory. Another
domain general idea is successive processing.
And we really see that a lot in pattern recognition.
So if you're looking at plus plus minus, plus
plus minus, plus plus minus, that is successive.
There's a process, it's repeating, we can predict
it, and it's one right after the other. And it
happens in all sorts of different patterns, not
just the ones that we study in math. So successive
processing and that pattern recognition happens
to all people all the time in all sorts of ways.
So those are general because they apply to more
than just math, but they're a very big part of
mastering math. So when we're looking at domain
general issues, we find that chunking helps,
breaking things down into smaller bits. That
way we're not overwhelming short -term memory.
which can also overwhelm cognitive load. We'll
talk about cognitive load theory in future podcasts.
And we know that chunking can be a really great
intervention and accommodation for dyscalculia.
And then also transferring domain general ideas
onto a new problem, something that's similar
but slightly unexpected. So for example, we talked
about those. patterns recognizing a pattern like
plus plus minus plus plus minus and now looking
at a pattern like let me see if I can remember
all of the Fibonacci sequence off the top of
my head one one two three five 8, 11, recognizing
that there's a pattern in there and taking the
idea of pattern recognition and applying it to
this new set of numbers and figuring out what
the pattern might be. That transfer is very difficult
for people with a math learning disability. So
we can see in the classroom that there's a difficulty
transferring knowledge to a problem that looks
at all different. If you've changed around the
word problem, if you've changed the order of
information, for example we've been finding perimeter
because we have all the sides but now all of
a sudden we have perimeter, we're finding a missing
side, even that shifts the problem enough that
transferring that domain general knowledge is
very difficult. So as teachers we want to help
build those bridges, we don't expect the transfer
to occur automatically. So that's domain general.
Let's take a look at domain specific, which is
going to be things that apply absolutely, definitely
to math. So counting, very domain specific. Counting
is something we do in math. It's not something
we do in necessarily history or English unless
we're talking about mathematical piece. Estimating
is domain specific. Estimating is something we
do with numbers and with quantity and with time.
So estimating is a specific skill. And planning,
problem -solving planning, is domain specific.
And it's a big part of approaching a math problem
deciding how you're going to solve it. The issue
for people who have the math learning disability
is that this kind of planning requires flexible
thinking and flexible strategies before we can
really be efficient at doing this kind of planning.
If you've worked with people who are neurodivergent,
or who have dyscalculia specifically, or even
as they're struggling, maybe they have low numeracy,
but this is a skill set they can improve, you
probably see that there are some issues with
flexible thinking. That can happen a lot if you
have a touch of either autism spectrum or sometimes
ADHD, but sometimes just in dyscalculia, very
rigid thinking, very linear. thinking. I also
find a lot of times students with dyscalculia
can be overwhelmed with the different options
and strategies and ways to solve a problem, and
especially when they're learning skills in the
classroom, they wish we would just pick something
and stick with it. And of course, we want them
to learn all of the different ways, find the
one that works best for them, play around, land
on something that's effective for you. and now
you have different options. But we have to remember
that for a student with rigid thinking or linear
thinking, or who's struggling, those choices
can feel overwhelming. It's very much like when
I walk into any kind of hardware store, whether
it's local or a big box store, there's just so
many things I can't even figure out which thing
is the wrench. Which thing, I can pretty much
nail down a screwdriver, but it's going to take
me a while and is it the right kind of screwdriver
for the project I have at home? I don't know.
It's too much, too many choices. So those are
some domain specific issues. People with dyscalculia
have problems in both areas, so we want to be
aware of both and support them differently. For
a domain general issue, using things like chunking,
reducing cognitive load, and helping build transfer.
That's going to support a domain general issue.
For domain -specific issues, like counting, estimating,
planning, that's where we're going to use number
lines, 1 to 100 charts, multiplication lists,
worked examples, or notes that really stay. Step
one. distribute the two to everything in the
parentheses use multiplication step to combine
like terms and you might need more explanation
about that step three like this we really want
to help with that planning and when possible
you want to teach and then assess one strategy
at a time then you know for sure which strategies
have been mastered and which have not. When we
try to teach all of the strategies and then test
all of the strategies at once, which commonly
comes up when we're teaching systems of equations,
it's just too many things to remember, too many
options and it gets overwhelming. And then we
really don't know which strategy the student
understands and which part of the problem they
understand. And that's where we can support domain
specific issues. And if you want to know more
about either of those, Google domain general
versus domain specific in math, and a lot of
articles will come up. So the next really important
piece from this article. And then there might
be another podcast out of this article. It was
very rich, lots of information. But they talked
about the four things that learning math requires.
So we're going to touch on them briefly today
and then we might dig deeper in future podcasts.
But here are the four things all humans need
in order to learn math. First is magnitude. Second
is value. Third is procedures. And the fourth
thing we need is conceptualizing. So let's break
those down. Magnitude is an innate skill. Everyone
has it. We can measure it in infants. And magnitude
refers to size, but also relationships between
size. So magnitude is thinking of one thing being
bigger or smaller than another, which is the
biggest toy, which is the smallest cookie, things
like this. However, you can't really have big
without having small. You can't have larger without
having tinier. So they do go together. Magnitude
is something that we can automatically do from
infancy. And we can see that in infants where
they'll sort things by size and they're kind
of putting things together. If you give one child
a small bag of treats and another child a very
large bag of treats, you're going to have an
issue because those children are going to know
right away who got more treats. So magnitude
is an innate skill and that happens first. The
second thing we need for learning math is to
understand value. Value refers to quantity, how
many, on its own, not in relation to anything
else. And that's the basis of our counting. That's
where we really start looking at value. And of
course, that gets very complex because now we're
coding words and Arabic numerals and a number
line onto quantity, but we'll save that for another
day. All of that is wrapped up in value. The
thing about value and quantity is that it is
not an innate skill. We do know that across the
globe even tribal communities with very little
interaction with the outside world have an understanding
of 123 more or 123 many but in a collective society
you really don't do a lot of counting beyond
that so quantity has a different interpretation
different usage depending on where you are And
here's where it's not an innate skill. If you
look at the numbers in the article, they used
29 versus 45. These are both two -digit numbers.
The 2 and the 9, and the 4 and the 5. They're
both odd numbers. One ends in 9, one ends in
5. They have a lot of similarities. If you were
writing them out in word form, they would both
have a dash in the middle. 20 -9, 40 -5, so there's
a lot of similarities. Understanding their value
that having 29 pencils means you have fewer than
if you had 45 pencils, that quantity is something
we have to teach. And that is very much tied
to a number line, 1 -100 charts, We know that
it can be problematic for people with dyscalculia,
so we want to use external number lines, 1 -100
charts, manipulatives much longer than we would
for a neurotypical student because we know that
could be an issue, a place of slower development,
if you will. A lot of students with dyscalculia
don't develop a mental number line in the same
fashion or at the same time as a neurotypical
student. The third piece of learning math involves
procedures. That comes down to how do we add,
how do we subtract, what are the steps for problem
solving, what are the algorithms of multiplication,
especially with multi -digit numbers, the procedures
that we follow. And here's the thing about procedures.
You have to learn them and learn them. and learn
them again. You have to over learn procedures
before they become anywhere near automatic. You
need extra time with procedures and I do think
that's something that is missing in most of our
K -12 schools in math class. Does not mean that
we should not have fun projects and exploration
and discussion We absolutely should but we cannot
throw out the procedural baby with the bathwater
Procedures have to be learned over and over and
over again for all students neurotypical or neurodivergent
However, we do know that people with dyscalculia
of any age do have more trouble remembering and
recalling steps and procedures. They can get
lost in complex procedures. If you've taught
long division to a student with dyscalculia,
you know exactly what I'm talking about. And
a lot of our larger problem -solving steps in
algebra, we run into these procedural issues.
So procedural fluency is not something to put
to the side. It's very, very important, and it's
a huge part of learning math. The fourth piece,
is conceptualizing and this one is a trending
keyword in math instruction these days making
sure students conceptualize what's happening
in a math problem with the goal that they will
then remember the concept and this will help
them remember the procedures and it will help
them intuit what they might do for a strategy.
So conceptualizing has a lot of rich benefits.
However, how do we really know what someone else's
concept of anything is? This is some higher level
thinking that we may or may not be able to explain
very well, especially for young children, but
I know plenty of adults who have problems explaining
themselves, so conceptualizing and communicating
are not innate skills. And also, even with the
best class discussion, We really don't know how
much a person understands or if they understand
and interpret the same way we do. Are they using
vocabulary in the same way? Does that conceptualizing
really fire procedural memory and fact fluency?
That's something that we really need more studies
on. So the jury is still out on that. Of course
conceptualizing is important. Of course it's
something we need to include in math class. Is
it something we need to include in an assessment?
I'm not sure about that. I think that's part
of a much larger discussion which I'm sure we'll
have in future podcast episodes. So to wrap up,
this excellent learning math article by Das and
Jansen, two domains we're concerned with, domain
general and domain specific, and how those affect
a person with a math learning disability. You
can use things like chunking. You can use things
like reducing cognitive load stress on short
-term memory. You can help with planning and
have more discussions about how a problem might
be solved. You can help the domain specific by
using external tools like a 1 to 100 chart, number
lines, manipulatives, multiplication lists, to
support those domain -specific issues and get
to know your students and how rigid or flexible
they are in their thinking. That will help you
know how many strategies they can choose from
at one time. The four things we need to learn
math. First, magnitude. We get that already.
It's just a bonus of being alive. Value. That's
a quantity we have to teach. Procedures. Whenever
you're teaching them, you gotta teach them more,
you gotta say them again, you gotta make a poster
and put it up on the wall. You have to discuss
the procedures you're gonna follow at the beginning,
middle, and end of class. You cannot drive home
procedures too many times. That's exactly how
a procedure becomes automatic through over -learning
that skill. And then finally, conceptualizing,
which is the holy grail of any math instruction,
but... My two cents, I don't think it needs to
be the holy grail of math assessments. Okay,
so that's everything I got out of that article
so far, but there's more. I want to dig into
that, and we might revisit this article in a
future podcast episode. Thank you so much for
listening to What in the World is Dyscalculia?
I would love to hear your comments, questions,
and suggestions for future podcast episodes.
You can find me at or you can find me at honora
at eduCalcLearning .com. Visit our websites eduCalcLearning
.com and thedtri .org and find me at conferences.
I've got a whole bunch already lined up for 2026.
I'm super excited to go around the country talking
about dyscalculia. If you know of a good conference
near where you live, send it to me. I will do
my best to get there. And as always thank you
for your support in increasing awareness and
support for people with the math learning disability
dyscalculia.