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Hello there and welcome back to the What in the World is Dyscalculia podcast.

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I'm your host, Dr. Honora Wall, and the What in the World is Dyscalculia podcast is sponsored by

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Educalc Learning, where we offer a wide variety of training for educators, advice for families,

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and now, very exciting, online math classes for students who have dyscalculia.

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Those can be used as part of your homeschool program or at your local school.

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We're making some inroads with schools in different states.

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If you're interested in that, please reach out to me at honora@ededucalclearning.com.

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If you're just looking for more information about the math learning disorder,

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you can check out the Dyscalculia Training and Research Institute, www.thedtri.org.

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We have lots of free information there for you, including some brochures you can download, print, and share.

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That talk more about Dyscalculia.

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And one thing that I'll definitely be getting a blog post up about as soon as I can,

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but I want to talk about it today, is a research study that I am so excited about.

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It's just fascinating, and this was a research study conducted by Dr. Michelle Mazzocco,

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who is with the Institute of Child Development at the University of Minnesota.

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And she and a team did a research study looking at the fraction piece for students with a math learning disability.

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This research study is phenomenal, and coming out of the U.S., I'm so excited because, as you know,

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we need more research into this field.

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And the work that Dr. Mazzocco is doing is so topical, so timely,

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and really can help us develop that classroom piece, making that bridge to application.

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What do we do with what we know?

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So let me share with you what we know from this study.

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There was a lot going on in this study.

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They took students, both typically developing, non-struggling students,

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and neurodivergent students with Dyscalculia, also just any kind of math struggle.

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And they looked at these students from fourth grade to eighth grade, specifically in the world of fractions,

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which, as we know, make most adults cry, not to mention students.

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What they were looking for is what they call the one-half fraction advantage,

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the idea that we can look at a fraction,

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written with Arabic numerals, numerator and denominator, or a visual representation,

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and immediately know when we're looking at half of something.

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So one over two, one-half.

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Four over eight, one-half.

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Three over six, one-half.

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And seeing any image where one-half is shaded, knowing,

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ah, okay, that relates to half of something,

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dividing by two, one over two, all of those things coded together.

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Well, here's what they found with their research study.

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I'm going to highlight three things that popped out the most for me.

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But if you go to Google Scholar and read the article, you'll find even more.

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It's a fascinating study.

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So key finding number one.

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Everybody is struggling in math in grade four.

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Okay, that one's not surprising.

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We're just starting to introduce fractions.

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We're working with them in a lot of ways and learning anything new is difficult.

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So if you're looking at one-half versus one-third versus two-fifths,

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we have a lot of teaching going on in grade four and it's difficult.

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We expect that typically developing non-struggling students are going to level out.

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By grade five, definitely maximum grade six,

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and they're going to really understand fractions very well.

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They're going to recognize numerators and denominators,

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match those two amounts in a real-world setting or in something visual.

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And definitely by grade five, latest grade six,

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they can recognize one-half in virtually any setting.

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And that gives them a strong basis for everything else we do with the fractions that aren't one-half.

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That helps compare and order and all the different work that we do with fractions

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in that conceptual piece that is the holy grail of teaching math.

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However, students with the math learning disability do not.

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Now, a student with low numeracy who is not neurodivergent might still struggle

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and they could struggle all the way through grade seven or eight

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or maybe they just really, it doesn't click for them and they don't like fractions

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and they will a lifelong avoidance or lack of mastery with fractions.

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The students who have dyscalculia, it's a different ballgame,

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even though they're trying their hardest and working diligently on understanding fractions,

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they do not develop that half fraction advantage until maybe, if we're lucky, grade seven or eight.

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And even then, they reach a maximum ceiling of 75% mastery.

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So, meaning you have a student in seventh grade or eighth grade,

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they're still struggling with fractions and you're thinking,

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I've got to figure out what is going on with the student.

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You do some interventions, then you give them a worksheet

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and you ask them to circle all the fractions that show one-half

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and that could be with Arabic numerals or it could be with visuals.

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After an intervention, the student with low numeracy should show some improvement

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and if you're focusing only on that one-half piece and that was your intervention

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and that was your assessment, you should really see a lot of growth in that.

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The student with dyscalculia, even after the intervention and a lot of diligent work,

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at best might score 75% on that assessment, only looking at fractions that represent one-half.

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That is really astounding.

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It's a great way for educators to have another tool in the classroom

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to kind of differentiate between low numeracy or weak math foundation

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versus a neuroatypical development issue, a math learning disability

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which needs to be addressed through accommodations and extra support.

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Key finding number two, students with the math learning disability

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do not develop strategies they can use for any kind of fraction.

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So a typically developing student or a struggling student who's had some great interventions

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and is increasing their comprehension and mastery, they're going to develop strategies

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that they can use for any fraction.

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Maybe they're looking at Arabic numerals and thinking about it as a pizza pie

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that's been sliced into different kinds of slices and they're comparing that way.

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Maybe they're turning fractions into decimals and comparing things that way.

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Maybe they're understanding different denominators and how does that change

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the amount of the thing your fraction represents?

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Lots of strategies, but they are developing them and they are using them.

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Students with dyscalculia are not.

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Each question is brand new. Each question is unique and each question

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requires them thinking about what can I possibly do to answer this question.

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There's something that for me really points to some future research.

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How do we get that idea of transfer, taking a strategy and applying it to different kinds of fractions?

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How do we increase that feeling of confidence and mastery with tying a strategy

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to different types of math problems?

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That's one for another day.

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I haven't found any research on that yet.

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If you have some, please email it to me, Honora at thedtri.org.

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If I find some, believe me, I will come back and share it with you.

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For those of us who are not researchers, it's important to understand this really

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underscores the need for extended time during assessments.

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If you have to go find a brand new strategy for every single question on a 10-question test,

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it's going to take you a lot longer than a student who has one strategy

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they can apply to all 10 questions.

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It also underscores, again, the need for those accommodations, having some kind of worked examples

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or a reference sheet that explains those steps and procedures, that has an example problem,

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and here's what you do with it.

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Whatever it takes, using multiplication lists or calculators to support the work

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because a student who has to come up with a brand new strategy every single question

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is going to be mentally exhausted and have a much harder time going to find those basic facts

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for multiplication and division or simplifying fractions,

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and if they have dyscalculia, their parietal lobe lost half that information anyway.

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So again, please, accommodations at all times.

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Key finding number three.

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Oh, I should say the accommodations at all times.

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That's me. That's my opinion.

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That was not an opinion stated by this research study because that was not the focus of the study.

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The focus was to examine what the reality is for students with and without math learning disabilities

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while they work with fractions.

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I just threw in my opinion at the back end.

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Okay, key finding number three.

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When we start teaching fractions, we set up the Arabic numerals with the numerator and denominator,

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and we tie that to a visual image.

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So the fraction one third might be paired with a rectangle cut into three pieces,

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and one of them is shaded.

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This is helping the student code the visual with the numbers and then develop the conceptual understanding

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that a fraction represents part of a whole,

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and you can think of one third versus one fourth

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and know which fraction is giving you more of the rectangle.

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Well, students with discount code and they use the term math learning disability.

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So that can be a little broader depending on whether or not you have a diagnosis

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and what your diagnostician was trained to do or what they like to look for when they're testing.

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But don't get me started on that soapbox.

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Students with the math learning disability do not code those two things together.

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They do not automatically match a visual image with those Arabic numerals,

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even by the end of eighth grade.

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This is a coding issue, which makes a lot of sense because dyscalculia is a type of neurodivergence.

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It's a different kind of brain wiring, a different way of thinking and processing math information.

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So, of course, coding the math information would be impacted.

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I mean, that one makes a ton of sense.

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But as educators for us to know in the classroom, that's a key thing to remember.

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Our older students who have had excellent instruction, great interventions,

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and have done the work, they are not automatically creating the mental image

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between Arabic numerals and the fraction and a visual representation.

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So for students who are typically developing or who had a math struggle

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and they've overcome it through interventions and instruction,

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now they have that mental imagery, they have that visual coding in place,

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and they can use that going forward.

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Students with dyscalculia do not.

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So, again, accommodations, this part is my opinion, need to continue throughout the lifespan.

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They don't go away after eighth grade or after eleventh grade or after a college placement test.

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So college professors, please, your students deserve different accommodations than you're giving.

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Just give it to them.

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And also, the accommodations should not be taken away after excellent instruction and intervention,

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because that's not the problem.

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The problem is a wiring difference.

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I can't underscore this enough, mostly because I'm recording this in November

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and I've had nine to twelve weeks of working with students across the country and their teachers who are unaware of dyscalculia

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and why it is different than what they thought math instruction would be all about.

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So I hope you share this message with your colleagues.

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There is clear published research that shows dyscalculia is different

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and it's not a condemnation of their teaching style.

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It is not, hey, use this intervention and then you never have to do it again.

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There's a reason why we're asking for accommodations in IEPs and 504s.

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I would argue, and this is 100% my personal opinion,

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I would argue that the specialized instruction required in an IEP speaks more to the direct instruction

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that students would dyscalculia need, not exploratory or project-based instruction,

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but being very explicit, very direct and specific with what to do and how to do it.

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And that instructional piece is really beneficial to students who have low numeracy

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or a weak math foundation or a trauma background or they're brand new to the states

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and they're an ELL student and we need differentiated instruction to kind of bridge them,

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get them to the next space.

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However, the accommodations are the much more impactful piece in either an IEP or a 504

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for a student with dyscalculia because the accommodations are going to carry them across grade levels

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and across math topics because in the same way wearing the right prescription glasses

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to actually read the font and see the text, therefore you can comprehend

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in the same way the accommodations do that same work for students with dyscalculia.

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Okay, so to recap, one of the ways you can differentiate between low numeracy

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and the math learning disability is to look at that one-half fraction advantage.

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In grades seven or eight or even later, if you gave a student an assessment

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that only asked them to find the fractions that showed one-half through Arabic numerals

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and visual representations, how well are they doing with that?

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If you give them an intervention and then you reassess, have you seen a noticeable change

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and is it greater than 75% mastery?

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If not, then you have some pretty clear indications that this student is not a struggling math student.

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This is a student who has a learning disability and needs something different.

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If you are not in the position, maybe you're not the interventionist, maybe you're not part of the child find team,

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maybe you're just trying to teach, maybe you're a homeschool parent trying to teach,

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you're a tutor working with a student after school, you're just trying to get them through the unit.

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Understanding that they do not have the same mental imagery and the same connection

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and the same strategies as other students can really help you find effective ways to work with that student.

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So again, to recap, this was a research study conducted and published through Dr. Michelle Mazzocco.

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It's amazing, it's one of my favorite dyscalculia research studies.

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I'm sure if you reach out to her, you can get a copy if you don't find it on Google Scholar,

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but I found it on Google Scholar, so I'm sure you can too.

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She's with the Institute of Child Development at the University of Minnesota.

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And I plan on reaching out to her, I'm hoping maybe I can meet with her or talk with her more.

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I'd love to read more of her research studies and see what other exciting things are coming out of Minnesota.

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And I promise to get some kind of summary about this onto the websites as soon as I possibly can.

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A little bit overwhelmed by saying yes to too many projects,

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but there's really a lot of exciting things happening in the world of dyscalculia right now.

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I know it can feel overwhelming and a little disappointing to try to make headway with this

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when there are so many people for whom this is new information.

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But that awareness piece is growing and the opportunity for new insights and therefore new help for students

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is really a very exciting time to be working in the field of math.

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That's my opinion based on this lovely research study I read.

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And I'd like to bring you more of these studies, I think that's really important,

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so that you know what is evidence-based, what does the research say,

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and let's have a conversation about how to make that a practical application.

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It's part of why I got that doctorate in curriculum and instruction,

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because that I think is the most important piece building that bridge.

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I'm Dr. Honora Wall and I really appreciate you listening to What in the World is Dyscalculia.

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If you have questions, comments, concerns, or other topics you'd like to hear on the podcast,

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please reach out to me anytime.

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And until then, thanks for listening.