Hello there and welcome back to the What in the World is Dyscalculia podcast.
I'm your host, Dr. Honora Wall, and the What in the World is Dyscalculia podcast is sponsored by
Educalc Learning, where we offer a wide variety of training for educators, advice for families,
and now, very exciting, online math classes for students who have dyscalculia.
Those can be used as part of your homeschool program or at your local school.
We're making some inroads with schools in different states.
If you're interested in that, please reach out to me at honora@ededucalclearning.com.
If you're just looking for more information about the math learning disorder,
you can check out the Dyscalculia Training and Research Institute, www.thedtri.org.
We have lots of free information there for you, including some brochures you can download, print, and share.
That talk more about Dyscalculia.
And one thing that I'll definitely be getting a blog post up about as soon as I can,
but I want to talk about it today, is a research study that I am so excited about.
It's just fascinating, and this was a research study conducted by Dr. Michelle Mazzocco,
who is with the Institute of Child Development at the University of Minnesota.
And she and a team did a research study looking at the fraction piece for students with a math learning disability.
This research study is phenomenal, and coming out of the U.S., I'm so excited because, as you know,
we need more research into this field.
And the work that Dr. Mazzocco is doing is so topical, so timely,
and really can help us develop that classroom piece, making that bridge to application.
What do we do with what we know?
So let me share with you what we know from this study.
There was a lot going on in this study.
They took students, both typically developing, non-struggling students,
and neurodivergent students with Dyscalculia, also just any kind of math struggle.
And they looked at these students from fourth grade to eighth grade, specifically in the world of fractions,
which, as we know, make most adults cry, not to mention students.
What they were looking for is what they call the one-half fraction advantage,
the idea that we can look at a fraction,
written with Arabic numerals, numerator and denominator, or a visual representation,
and immediately know when we're looking at half of something.
So one over two, one-half.
Four over eight, one-half.
Three over six, one-half.
And seeing any image where one-half is shaded, knowing,
ah, okay, that relates to half of something,
dividing by two, one over two, all of those things coded together.
Well, here's what they found with their research study.
I'm going to highlight three things that popped out the most for me.
But if you go to Google Scholar and read the article, you'll find even more.
It's a fascinating study.
So key finding number one.
Everybody is struggling in math in grade four.
Okay, that one's not surprising.
We're just starting to introduce fractions.
We're working with them in a lot of ways and learning anything new is difficult.
So if you're looking at one-half versus one-third versus two-fifths,
we have a lot of teaching going on in grade four and it's difficult.
We expect that typically developing non-struggling students are going to level out.
By grade five, definitely maximum grade six,
and they're going to really understand fractions very well.
They're going to recognize numerators and denominators,
match those two amounts in a real-world setting or in something visual.
And definitely by grade five, latest grade six,
they can recognize one-half in virtually any setting.
And that gives them a strong basis for everything else we do with the fractions that aren't one-half.
That helps compare and order and all the different work that we do with fractions
in that conceptual piece that is the holy grail of teaching math.
However, students with the math learning disability do not.
Now, a student with low numeracy who is not neurodivergent might still struggle
and they could struggle all the way through grade seven or eight
or maybe they just really, it doesn't click for them and they don't like fractions
and they will a lifelong avoidance or lack of mastery with fractions.
The students who have dyscalculia, it's a different ballgame,
even though they're trying their hardest and working diligently on understanding fractions,
they do not develop that half fraction advantage until maybe, if we're lucky, grade seven or eight.
And even then, they reach a maximum ceiling of 75% mastery.
So, meaning you have a student in seventh grade or eighth grade,
they're still struggling with fractions and you're thinking,
I've got to figure out what is going on with the student.
You do some interventions, then you give them a worksheet
and you ask them to circle all the fractions that show one-half
and that could be with Arabic numerals or it could be with visuals.
After an intervention, the student with low numeracy should show some improvement
and if you're focusing only on that one-half piece and that was your intervention
and that was your assessment, you should really see a lot of growth in that.
The student with dyscalculia, even after the intervention and a lot of diligent work,
at best might score 75% on that assessment, only looking at fractions that represent one-half.
That is really astounding.
It's a great way for educators to have another tool in the classroom
to kind of differentiate between low numeracy or weak math foundation
versus a neuroatypical development issue, a math learning disability
which needs to be addressed through accommodations and extra support.
Key finding number two, students with the math learning disability
do not develop strategies they can use for any kind of fraction.
So a typically developing student or a struggling student who's had some great interventions
and is increasing their comprehension and mastery, they're going to develop strategies
that they can use for any fraction.
Maybe they're looking at Arabic numerals and thinking about it as a pizza pie
that's been sliced into different kinds of slices and they're comparing that way.
Maybe they're turning fractions into decimals and comparing things that way.
Maybe they're understanding different denominators and how does that change
the amount of the thing your fraction represents?
Lots of strategies, but they are developing them and they are using them.
Students with dyscalculia are not.
Each question is brand new. Each question is unique and each question
requires them thinking about what can I possibly do to answer this question.
There's something that for me really points to some future research.
How do we get that idea of transfer, taking a strategy and applying it to different kinds of fractions?
How do we increase that feeling of confidence and mastery with tying a strategy
to different types of math problems?
That's one for another day.
I haven't found any research on that yet.
If you have some, please email it to me, Honora at thedtri.org.
If I find some, believe me, I will come back and share it with you.
For those of us who are not researchers, it's important to understand this really
underscores the need for extended time during assessments.
If you have to go find a brand new strategy for every single question on a 10-question test,
it's going to take you a lot longer than a student who has one strategy
they can apply to all 10 questions.
It also underscores, again, the need for those accommodations, having some kind of worked examples
or a reference sheet that explains those steps and procedures, that has an example problem,
and here's what you do with it.
Whatever it takes, using multiplication lists or calculators to support the work
because a student who has to come up with a brand new strategy every single question
is going to be mentally exhausted and have a much harder time going to find those basic facts
for multiplication and division or simplifying fractions,
and if they have dyscalculia, their parietal lobe lost half that information anyway.
So again, please, accommodations at all times.
Key finding number three.
Oh, I should say the accommodations at all times.
That's me. That's my opinion.
That was not an opinion stated by this research study because that was not the focus of the study.
The focus was to examine what the reality is for students with and without math learning disabilities
while they work with fractions.
I just threw in my opinion at the back end.
Okay, key finding number three.
When we start teaching fractions, we set up the Arabic numerals with the numerator and denominator,
and we tie that to a visual image.
So the fraction one third might be paired with a rectangle cut into three pieces,
and one of them is shaded.
This is helping the student code the visual with the numbers and then develop the conceptual understanding
that a fraction represents part of a whole,
and you can think of one third versus one fourth
and know which fraction is giving you more of the rectangle.
Well, students with discount code and they use the term math learning disability.
So that can be a little broader depending on whether or not you have a diagnosis
and what your diagnostician was trained to do or what they like to look for when they're testing.
But don't get me started on that soapbox.
Students with the math learning disability do not code those two things together.
They do not automatically match a visual image with those Arabic numerals,
even by the end of eighth grade.
This is a coding issue, which makes a lot of sense because dyscalculia is a type of neurodivergence.
It's a different kind of brain wiring, a different way of thinking and processing math information.
So, of course, coding the math information would be impacted.
I mean, that one makes a ton of sense.
But as educators for us to know in the classroom, that's a key thing to remember.
Our older students who have had excellent instruction, great interventions,
and have done the work, they are not automatically creating the mental image
between Arabic numerals and the fraction and a visual representation.
So for students who are typically developing or who had a math struggle
and they've overcome it through interventions and instruction,
now they have that mental imagery, they have that visual coding in place,
and they can use that going forward.
Students with dyscalculia do not.
So, again, accommodations, this part is my opinion, need to continue throughout the lifespan.
They don't go away after eighth grade or after eleventh grade or after a college placement test.
So college professors, please, your students deserve different accommodations than you're giving.
Just give it to them.
And also, the accommodations should not be taken away after excellent instruction and intervention,
because that's not the problem.
The problem is a wiring difference.
I can't underscore this enough, mostly because I'm recording this in November
and I've had nine to twelve weeks of working with students across the country and their teachers who are unaware of dyscalculia
and why it is different than what they thought math instruction would be all about.
So I hope you share this message with your colleagues.
There is clear published research that shows dyscalculia is different
and it's not a condemnation of their teaching style.
It is not, hey, use this intervention and then you never have to do it again.
There's a reason why we're asking for accommodations in IEPs and 504s.
I would argue, and this is 100% my personal opinion,
I would argue that the specialized instruction required in an IEP speaks more to the direct instruction
that students would dyscalculia need, not exploratory or project-based instruction,
but being very explicit, very direct and specific with what to do and how to do it.
And that instructional piece is really beneficial to students who have low numeracy
or a weak math foundation or a trauma background or they're brand new to the states
and they're an ELL student and we need differentiated instruction to kind of bridge them,
get them to the next space.
However, the accommodations are the much more impactful piece in either an IEP or a 504
for a student with dyscalculia because the accommodations are going to carry them across grade levels
and across math topics because in the same way wearing the right prescription glasses
to actually read the font and see the text, therefore you can comprehend
in the same way the accommodations do that same work for students with dyscalculia.
Okay, so to recap, one of the ways you can differentiate between low numeracy
and the math learning disability is to look at that one-half fraction advantage.
In grades seven or eight or even later, if you gave a student an assessment
that only asked them to find the fractions that showed one-half through Arabic numerals
and visual representations, how well are they doing with that?
If you give them an intervention and then you reassess, have you seen a noticeable change
and is it greater than 75% mastery?
If not, then you have some pretty clear indications that this student is not a struggling math student.
This is a student who has a learning disability and needs something different.
If you are not in the position, maybe you're not the interventionist, maybe you're not part of the child find team,
maybe you're just trying to teach, maybe you're a homeschool parent trying to teach,
you're a tutor working with a student after school, you're just trying to get them through the unit.
Understanding that they do not have the same mental imagery and the same connection
and the same strategies as other students can really help you find effective ways to work with that student.
So again, to recap, this was a research study conducted and published through Dr. Michelle Mazzocco.
It's amazing, it's one of my favorite dyscalculia research studies.
I'm sure if you reach out to her, you can get a copy if you don't find it on Google Scholar,
but I found it on Google Scholar, so I'm sure you can too.
She's with the Institute of Child Development at the University of Minnesota.
And I plan on reaching out to her, I'm hoping maybe I can meet with her or talk with her more.
I'd love to read more of her research studies and see what other exciting things are coming out of Minnesota.
And I promise to get some kind of summary about this onto the websites as soon as I possibly can.
A little bit overwhelmed by saying yes to too many projects,
but there's really a lot of exciting things happening in the world of dyscalculia right now.
I know it can feel overwhelming and a little disappointing to try to make headway with this
when there are so many people for whom this is new information.
But that awareness piece is growing and the opportunity for new insights and therefore new help for students
is really a very exciting time to be working in the field of math.
That's my opinion based on this lovely research study I read.
And I'd like to bring you more of these studies, I think that's really important,
so that you know what is evidence-based, what does the research say,
and let's have a conversation about how to make that a practical application.
It's part of why I got that doctorate in curriculum and instruction,
because that I think is the most important piece building that bridge.
I'm Dr. Honora Wall and I really appreciate you listening to What in the World is Dyscalculia.
If you have questions, comments, concerns, or other topics you'd like to hear on the podcast,
please reach out to me anytime.
And until then, thanks for listening.