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Hey everyone. Welcome to this episode. We are talking all about math disorder intervention.
My guest, Adrianne Meldrum, is the founder and owner of Made for Math, an all-online math center focused on serving students with dyslexia, dyscalculia, and math learning disabilities. She’s a certified Multisensory [00:01:00] Math Instructor through Marilyn Zecher. She holds a Master’s degree from Bridges Graduate School of Cognitive Diversity.
Adrianne is married with three boys and lives in Mesa, Arizona, where she enjoys soaking up gorgeous sunsets.
Adrianne is here to talk with us all about math intervention. We talk a lot about dyslexia and other reading issues, but math learning disorders are out there as well, and these kids need services. So I’m so grateful to have her here.
These are just a few things that we talk about. We talk about the different subtypes of math learning issues. We talk about the differences between big-box intervention and one-to-one intervention for math disorders, the core components of successful math intervention, and specific interventions for different types of math concerns.
I really liked talking to Adrianne. She’s very open, very personable, and clearly knows her stuff. I hope [00:02:00] that you enjoy our conversation as well.
Hey Adrianne, welcome to the podcast.
Adrianne: Hey, good to be here, Jeremy.
Dr. Sharp: I’m excited to chat with you. We’ve talked about math disorders a little bit on the podcast. I think I’ve done one episode but we didn’t really talk much about intervention. So that is a wide-open topic, and I know you have a lot of expertise in that area. So I’m thrilled to have you here. Thanks again.
Adrianne: Yeah, I’m excited. This is one of my favorite things to talk about.
Dr. Sharp: Well, that’s a nice segue to my first question, which is why this is important to you, out of all the things that you could do in your life and spend your time on, why math and math intervention?
Adrianne: Oh, well, I think what’s [00:03:00] interesting, a lot of people like to assume, oh, Adrianne must be a math whiz. She must be amazing. No, actually, I think I spent a lot of my life running away from math and they often say that you’re happiest when you serve who you used to be. I was that kid, growing up, that struggled with math greatly, so much so that I would cheat on my math tests. My friends and I would work together because I knew I couldn’t pull math facts out of my head or keep up with some of the stuff that the students were doing.
And it did ultimately catch up with me in middle school. There’s no more hiding. I had to do remedial math, and that was devastating. I also knew that’s where I belonged. And so I didn’t say anything to my parents. I don’t even think they knew that I was in remedial math. This is back when parents are just like [00:04:00] go to school, go away.
Thankfully, I had a teacher that was very influential and he saw me because I liked to fade in the background, but he wouldn’t let me do that. So he took good care of me, brought me up to the front of the classroom so he could be close enough to point and gesture and take a few moments when he had a moment, to coach me and help me. That really helped me see that he saw value in me. And thankfully each teacher after that really worked hard with me.
I did become a good math student, however, it was a source of anxiety for a very long time. In fact, when I was in college, they tried to recruit me into the mathematics department to do student teaching there. I flat out told them no, because I didn’t think I had what it took.
So really interesting segue into that, anyways [00:05:00] but I did have a stint of working in autism for a while, and I really fell in love with that one-to-one intervention world. I found myself tutoring and guess what, everyone asked for tutoring. They want help with math. And so I had to, okay, I can do this. I can give the same thing that other teachers have given to me.
And I did, but there was always this selection of students that I worked with that I couldn’t reach and that never sat well with me. So I dive into the research and figure out what’s going on and come to find out. I learned a lot of things like how dyslexia affects mathematics, and I couldn’t unsee that. And then also this whole dyscalculia thing.
I was looking around who’s teaching about this. No one seems to be teaching about this, but I did manage to find Marilyn Zecher, who was my mentor. And when I learned about her methodology for intervention, I went all in. I have been a diehard nerd ever [00:06:00] since. I am obsessed. This is what my expertise is. I enjoy helping these students that feel largely unseen and helping them get their needs met and taught in a way that really helps them and changes their life drastically.
Dr. Sharp: I feel like math is the redheaded stepchild of the learning disorder world. We spent so much time on reading and dyslexia and different disruptions to reading and math get pushed to the side a bit. There’s much less research on it and we don’t have a great idea of, well…
Adrianne: For sure. I think culturally, it’s okay to be bad at math. I can’t tell you how many people, when they hear what I do for a living, will tell me their horror stories of math or parents will excuse what the kids are doing, well, oh, no surprise, they’re bad at math. I’m bad at math too. [00:07:00] Just kind of brushing it off.
There’s this study that I was reading recently where it’s saying 58% of American adults cannot calculate a tip which we’ve seen now. And when you go to the restaurants, what do you see now? They have 10%, 15%, 20% because adults cannot calculate this. It’s interesting how it is bleeding into our society but yet it’s such a hindrance to adults. And the more modern our society gets, the more we need these math skills.
I think it’s a real detriment that it’s not getting the attention it needs. I hope that maybe by having chats like this, we can help people get their research funded so we can get it back to the students and get them the help they need.
Dr. Sharp: Right. Yes. I’m going to ask a question right off the bat that goes off of our script, but [00:08:00] I do that sometimes. That statement you just made about, hey, we’re moving into more of a modern society and math is even more important than ever, there is a little voice in my head that was like, really? Why is math more important as we get more modern?
It seems like we have lots of tools to help with math. We have calculators. We have smartphones in our pockets. We have the tip printed on the receipt. What was behind that statement for you?
Adrianne: Sure. One of the things I’m thinking about is the spread of misinformation is prevalent among social media. There was a really great example of this. When someone’s reporting in the media and they say the majority of Americans feel this way but when you look at the statistic, it says 51%. That’s not a majority. That’s a split.
And so if you are struggling with mathematics, you would be susceptible to thinking, well, the majority of people will [00:09:00] think this, when actually you need to challenge that and say, no, that’s actually not true. That number doesn’t make sense with a majority.
So there’s a lot of misinformation going around. I think a lot of us are susceptible to maybe not reasoning through some of the things that are thrown at us. And we have to be careful with that. The more modern our society gets, the more information that’s shared.
And also I think some of the economics that we’re dealing with is partially because we don’t understand what we’re committing to sometimes. We take on too much debt because you don’t understand this debt-to-income ratio as well as we probably should.
Dr. Sharp: That’s a great example. Yeah, I think that’s a huge problem these days. I don’t think most folks think about financial literacy in the way that we should. There’s a lot of folks out there who are getting punished by debt and interest rates.
Adrianne: They really are. [00:10:00] They’re hurting them drastically, right?
Dr. Sharp: Yeah.
Adrianne: When you are a kid with dyscalculia, it can affect things like your sense of time even, your ability to manage your time, to know what the days and the weeks and the months mean. All of those things can really impact you as an adult.
And yes, software might be able to get you close to what you need but at the same time again, going back to that reasoning, do they know that that’s correct? Can they challenge it if like the date was given to them wrong and know that it was wrong? There’s some issues around that. So it’s important to have these skills.
Dr. Sharp: Absolutely. Yes. Well, let’s lay some groundwork here for our conversation, and then we’re going to talk about math issues and intervention quite a bit over the next hour or so. I’d love to just get some basics on the table. I think we all know there are [00:11:00] different types, so to speak, of math learning issues. I would love to hear you articulate the different types that you see and compare and contrast these math learning issues a little bit. Can we start there?
Adrianne: Yeah, sure. Absolutely. Dyscalculia is a word that most people don’t even know about or hear often. And sometimes in like a professional setting, like yourself, you’re giving a diagnosis of a learning disability with an impairment in mathematics, and then you’re labeling it, mild, moderate, or severe. So there’s that. It’s complex in giving the diagnosis but also in understanding the student’s profile because no two students are alike.
It’s really tricky and just because you’ve seen a kid with dyscalculia doesn’t mean every kid with dyscalculia looks like that child. It’s drastically different and all of them have [00:12:00] little things that are different. There was some research done back in 2014 and I believe Dr. Ansari was part of it. He’s in Canada. He’s excellent. If you’re not following him, I would suggest you follow him if you want to stay up to date on some research.
They found that there were some clusters with these math learning disabilities of how they might present in a student. One was that these students just have a weak mental number line. A lot of us are unaware that we have this mental number line in our minds, and students who struggle with mathematics might have a weak one. And so part of intervention would be to build that.
The other thing they could be struggling with is an approximate number system. It’s poor, it’s weak, meaning being able to look at a quantity and get close to how much that is, so that can be difficult.
Spatial [00:13:00] difficulties- if you put in a blank number line in front of the student and ask them to plot between 0 and 50 and then some numbers in between, it’s clear you can see these students are going to struggle with that task. There’s a lot of pen in the air when they’re working because they’re not really sure where to put that pencil. They struggle with directionality too. It’s a really big topic, this idea of spatial issues.
Some of them struggle with accessing numbers and they read their quantity and their relationship with the symbolic form- we call that understanding the fiveness of five. What does it look like? What does it feel like? How do we write that numeral? What are all the forms that it could take on? They struggle with that.
And then there’s also those that have just a [00:14:00] numerical cognitive deficit. And then there’s kids that have a garden variety, all sorts of these things going on.
So those are what they found, and I would agree with that that we see a blend of those things, but we also see a lot of students coming to us who have dyslexia. That’s their main diagnosis. And then they’re there for math help because they’re struggling with math. 50% of kids do, that have dyslexia are struggling with math as well.
But what’s interesting about their learning profile is they have really strong visual-spatial skills. It’s like off the charts when we look at their testing but it’s other things like the procedural, the verbal, pulling information from their memory that they really struggle with. Those are the profiles that we’re dealing with. And so obviously there’s a certain way you want to work with these students that can be really complex.[00:15:00] Dr. Sharp: Sure. There are so many layers to it. I think every time I get into these discussions, I forget. It is so striking though, how many cognitive processes are involved in math.
Adrianne: So many. If you’ve got issues with just some regular cognition stuff with the math issues on top, it makes for a very complex situation.
Dr. Sharp: Yeah. Who are you seeing as presenting most frequently for math intervention? Out of all those types, what comes up the most for you?
Adrianne: In our practice with our students, right now, the majority are kids with dyslexia, probably closer to 60%. However, the bigger Made for Math, we’re finding kids with really complex profiles are coming to us. So we’re seeing a lot more of those kids with [00:16:00] that weak number line, the weak approximate number system.
So even adult students are coming to us who cannot grasp numbers even within 10. We get some pretty severe things. And so the majority are dyslexia but we’re starting to see a trend of that uptick of more difficult, tricky kids coming our way.
Dr. Sharp: I hear you. You talked about the impact of being “bad at math” on society. I guess we’re on individuals. We talked a little bit about the adult impact. What are you seeing with kids as far as how they’re conceptualizing being “bad at math” or some stigma involved?
There’s a little bit of a personal bend to this question because my daughter is 10 and historically has not [00:17:00] been great at math and then certainly developed that script in her head that she’s “bad at math”. I’m just curious what you’re seeing with that and how you address that a little bit with these kids or if you address it.
Adrianne: Yeah, we do. Yes, kids, typically when they come to us, two scenarios have happened. Either they’ve had just repeated failure both at school intervention, going to other big-box tutoring centers like a Kumon or Mathnasium or something like that.
By the time they make it to us, that poor kid is just convinced that they’re never going to be able to learn math. And that’s because of that repeated failure. It’s because of the mix and match, if you will, of different types of approaches people have tried just more or the same and louder, over and over. And so they’re just certain that there’s [00:18:00] no hope for them.
So our goal, when they come to us is to reduce the anxiety they feel about math as fast as we can. When they come, we do an assessment. However, it is more game-based because it will reduce the anxiety. So we’re just playing games with them and making notes about what’s going on with this student. And we also have some of those neuropsychological reports to pull in some of that data but we are taking notes about what’s going on with this student.
The student doesn’t even know that they’re being assessed, but they’re able to show us better than a traditional standardized test would because they feel unthreatened by this game that they’re playing. So that’s a really important piece and part of what we do.
And then when we’re working with students, we try to get them to the quickest wins as possible, and they set goals. Some of our students will come to us and say, I just really want to learn my 7 times table. Okay, let’s do that.[00:19:00] We involve them in their learning in this way, and they start to see, like, oh my goodness, I can do this because it’s being presented in a way that makes sense. And once they have that quick win, then they start being more open to other experiences, and they start having more wins all around.
But I will say, it’s not a fast process. It takes a lot of time, and I think parents are shocked at how far back we have to go because math builds upon itself. So a lot of people ask like, well, where do you begin? And usually, the answer is, well, at the beginning. We’re back at the beginning, usually, and they’re surprised by this, but we move kids too quickly through the curriculum and the public schools, and they don’t have time to really have a deeper understanding of how numbers work and build that foundation out.
Dr. Sharp: Got you. Well said. I’m curious about this assessment game that you’re playing. Can you give us any insight into what that looks like?[00:20:00] Adrianne: Yeah. There’s all sorts of games. There’s this game we play called BUMP where it’s got numbers on the board and they’re rolling dice and they’re either adding two facts together or subtracting two facts. And so they’re just showing us what they know how to do. And it progressively changes over time. As they’re getting comfortable, it’s less and less game-like and more just like, Show me what you know about fractions. Here’s a problem but we display everything one problem at a time to give that child adequate time.
The other thing too, is we don’t keep marching through the assessment like a neuropsychologist would, where you need to get the full picture. For us, we march forward until that student has repeatedly failed at a task three times, and we stop. That’s our instructional start point.
So the games can be like I said, a bump game, cards, you’ll see lots of little manipulatives and blocks and things just watching the students build and play with the numbers to see [00:21:00] how they’re doing with it.
Dr. Sharp: That’s great. Anything we can do to take away some of that stigma and pretend that we’re not doing math is helpful.
Dr. Sharp: I’ve done a few episodes on a variety of topics that are related here. Stereotype threat is certainly at play and just how kids think of themselves, the messages that they send themselves, and the messages we send as evaluators. And so doing anything that we can do to take it away from that route back and forth assessment process can go a long way.
Adrianne: And really giving them positive feedback about creative ways that they may be solving. There’s some kids that actually do quite well with math facts but because they’re solving it in a creative way, it’s not route really quick recall. They think that that means they’re dumb, [00:22:00] but actually the amount of flexibility they’re showing in that assessment is really impressive. That they can come up with different ways to tell me what 6 x 8 is. That’s valuable information to have that might not show up if it’s a time test because that kid didn’t have time to process.
Dr. Sharp: Well, I know we are primarily talking about intervention. I would love to shift to that because I think that’s the missing piece from a lot of these discussions. We’re pretty good at identifying math disorders. I think it is harder to identify how to intervene afterward.
Adrianne: Absolutely. I think it’s difficult to point parents in a good direction as to where to go because this is still kind of my new thing. What we’re doing is still relatively new. It’s not as established like an Orton–Gillingham reading curriculum would be. We’re not there yet. It’s coming. It’s just taking a lot longer for [00:23:00] that very reason. So yeah, let’s dive into it. What do you want to know about intervention?
Dr. Sharp: Well, let me start with a bait, I don’t know what kind of question it is. I can’t think of the right word. I’m just going to ask it then. You mentioned this contrast to what you called big box intervention a little bit ago. So maybe we start there. What is big box intervention? And then why is that not sufficient enough sometimes?
Adrianne: Sure. There’s a model of intervention in schools that’s tiered. So Tier 1, Tier 2, Tier 3. What we do at Made for Math is Tier 3, where it’s all one-on-one and it’s intensive, whereas Tier 2 would look like something you would experience at Mathnasium or Kumon. [00:24:00] Often, what these programs have is a scripted out curriculum with lots of practice and honestly not too much difference from what they’ve already experienced in school.
In fact, to my horror and sadness, I see giant binders given to children and they just show up to these centers with a tutor that’s sitting by them who coaches them to work through the worksheets. And if you’re a kid with dyscalculia or dyslexia, that is punishment in itself. I can’t imagine being given a binder like that and being told, yeah, you’re going to work through this.
A student that’s average, that would probably be fine. More practices praised and that would be good. But a kid that’s had that repeated failure, that just continues to beat in the message, you’re not smart enough to do this work. And then if you look at the pages themselves are overwhelming, there’s too many problems on the page. It’s just too much [00:25:00] so that when parents come to us and say, yeah, we tried that. That was a joke, and my kid got worse, not better, it’s because it’s just more of the same higher repetition, louder and it’s no good.
Dr. Sharp: I was actually talking to a client yesterday, just a client of mine. This individual’s partner got a temporary job at a local tutoring center. The job training was basically non-existent. They just said, here’s our script. Read the script. That’s the tutoring. We have lots of scripts. My client and partner were horrified and the partner ended up quitting relatively quickly because they’re like, what is happening here?
Adrianne: Yeah. What is happening here? And the people that they’re hiring, [00:26:00] typically, if they have a math background, they’re out of there pretty quick because they’re bored to death. Imagine what the kids are thinking. So the turnover rate is really high, whereas if you contrast that with what we do, it’s actually difficult to get hired where we work. You have to have a really good background, plus, you’re getting tons of training. You’re not even seeing a student until you pass a student teaching with us to make sure you’ve got the solid plan down. And then we’re constantly mentoring and helping you be successful because that’s what impacts the students. So it’s very different.
Some people will say, well, when I compare the cost of you versus a big box tutoring center, you guys are a lot more. Well, yes, this is why, because of the ongoing training that we’re doing, the constant mentoring to help them stay up to float with all this research that is [00:27:00] coming out and making sure we’re using it to benefit the students.
Anyway, so when we contrast those two, I am not necessarily saying don’t use big-box tutoring and only come to someone like us. No, they have their place. How you would decide that is, is your kid getting a B- in mathematics and you want them to have an A, I would take your kid there.
But if they have a C or lower, and you’re seeing diminished confidence, a lot of negative self-talk, a lot of avoidance behaviors, running away from the table when it’s time to do homework, throwing it away, maybe, even. We see that. Just avoid it altogether. They would have a good chance of being able to overcome those things here at Made for Math. That’s what I was trying to say with that contrast with the big box tutoring.
Dr. Sharp: Well said. Thank you for digging into [00:28:00] that graciously.
Adrianne: I don’t want to bad mouth.
Dr. Sharp: Right. No answer, I think it was a nice way to split the difference. I would love to talk about the intervention itself. Is it possible to generally describe this kind of intervention you’re doing or should we approach it more from a specific lens depending on what the student’s coming in with or the type of math issues, how would you tackle it?
Adrianne: No, I think there’s some general hallmarks that we could talk about that a good math intervention would include- you would know you had found a quality person if you were looking for someone. I think that’s helpful for any parents that are listening and providers that are looking for people.
There’s about six of them. I’ll go into each of them if that’s okay and feel free to stop me. [00:29:00] I have a list of notes just so, that’s one of my hacks. Nearpoint references, guys, that’s one thing you should have in your reports. Recommend kids get near-point references.
One of the first things, the hallmarks that you should be seeing in intervention is that it’s multisensory, meaning that we’re using the senses. So the visual, the auditory, the kinesthetic tactile, but it’s not that they’re a visual learner. We know that that’s been debunked. That’s not true.
What we’re doing is we’re using all of these simultaneously to help increase access points in the brain. Some days it might be that the auditory and the kinesthetic together really helped the student understand what’s going on. Sometimes it might be the visual and the auditory that made the difference that day. So it just helps increase the chance of the memory picking those things up and making it stick in that long-term storage.
So you’re going to be seeing that [00:30:00] with blocks. You’re going to be seeing hands-on stuff. We use beads. We have base 10 blocks. We have craft sticks. You should see the kids that we send out. They are massive and enormous. The goal is to get the student touching lots of different types of manipulatives so that they’re generalizing this concept of number so that they’re not always associating one block means one.
You would be surprised. We have kids who can be that granular or if you write in purple and someone else writes it in pink, now the numbers are different. So we really have to work hard to generalize those things so that the manipulatives make a big difference.
Another important piece of intervention is that it’s systematic. The instruction, it follows a logical order. So we’re starting with the most basic knowledge and progressing to the more advanced. We work from what a student knows to what is new.
And so in our lessons, you’re always seeing a review at the beginning [00:31:00] of a previous learned concept and then we’re building towards the new concept as the lessons going on and we only work on a new idea for about 10 minutes in a lesson. That may not sound like that’s enough, but it is because we’re building in this review and this practice for the students. And so it’s systematic.
The other thing is direct instruction. There’s a lot of research how important it is for us to directly teach the student why something is working and how it’s working. We don’t want to leave students to infer or explore just to arrive at some connection independently because it might not be complete or accurate, especially with a student with a math learning disability. They’re taught directly and they’re coached and they’re giving feedback from their interventionist. And so it’s really important for us to have that direct instruction model.
The other thing that you want to see is diagnostic. So we’re going to be pulling [00:32:00] information from a neuropsychologist to get a general idea of the learning profile, but also we’re using an ongoing assessment to guide and direct our instruction as we’re working with the students and making sure that we’re revisiting topics frequently to make sure it’s being retained by the student and shored up if not. So it’s really important that it’s diagnostic.
Another interesting hallmark is that it’s synthetic and analytic, meaning that we see how the parts of math work to build a whole or how the whole is broken down into parts. That’s a really important piece. A lot of kids with dyslexia, they love to see the whole picture. They need that road map of where they’re going. When math facts are taught in isolation, they’re so meaningless.
My theory and feeling is that kids’ brains, when they have dyslexia, they’re just quick to discard it because it has no meaning to them. It doesn’t really build the picture that they [00:33:00] need to see. But if we work from that big picture idea and break it down for them, they can see how the pieces and parts work together. So that’s really important.
And then some of the other things that we want to see in a session would be like a heuristic. Remember PEMDAS. Did you have PEMDAS growing up?
Dr. Sharp: Yeah. Please Excuse My Dear Aunt Sally.
Adrianne: So that would be considered a nearpoint reference. We also have these things called long division buttons, where it’s got the symbols for the steps and long division and kids can use their non-dominant finger to help guide them down the buttons so they can remember the steps because a lot of them get lost in the weeds with the procedural, especially with division. So we use things like that, but they’re guided. They’re directed. The student knows how to use those things, and so we’re giving that constant feedback.
Those are the hallmarks that you should be seeing in a really good intervention situation and that [00:34:00] research and evidence has backed up that you should be seeing these things in an intervention situation.
Dr. Sharp: I love that. That’s a great list. Thank you. So now I wonder if we could drill down and be more specific in terms of how the intervention might change depending on the “type of math issue” that we’re seeing.
Let’s take a break to hear from our featured partner.
The Feifer Diagnostic Achievement Tests are comprehensive tools that help you help struggling students. Use the FAR, FAM, and FAW to hone in on specific reading, writing, and math learning disabilities, and figure out why academic issues are occurring. Instant online scoring is available via PARiConnect, and In-Person e-Stimulus Books allow for more convenient and hygienic administration via tablet. Learn more at parinc.com\feifer.
All right, let’s get [00:35:00] back to the podcast.
Adrianne: The profile, yeah, absolutely. I would love to share a link with your audience. I’ll make sure to pass them on to you. We actually have this document that’s for neuropsychologists that helps, based on your testing, what recommendations you could give to parents in that document. So we could drill down into just three of those subtypes.
Dr. Sharp: Let’s do it.
Adrianne: Okay, great. One assessment I really like as an interventionist is the Feifer Assessment of Mathematics. Of course, there’s some people that are like, no, don’t use that test, but I find that their reasons are silly. Honestly, it’s a great test but you wouldn’t use it alone to make a diagnosis. You’re going to use it in a battery of tests, but it holds up really well compared to other assessments like the WISC and whatnot.
I love the FAM because it has buckets subtypes. One of those is [00:36:00] the Procedural Index, and then we have the Verbal and then we have the Semantic. I’ll share a few from those but mostly I would encourage your listeners to go check out the document because it’s free for you to use, copy and paste what you want from your computer into your documents that you’re writing to families, because my goal is that more families have a better direction of where to go. It’s very overwhelming to receive a diagnosis and then feel lost as to what to do.
Dr. Sharp: Absolutely.
Adrianne: Procedural, when I hear of Procedural Index, I’m thinking of step by steps. Sometimes vocabulary can be part of that. We talked about nearpoint references, but we like checklists. A lot of checklists can be helpful combined with visuals to help students remember what steps. So we’ve got that.
Like the long [00:37:00] division, we divide first, and then we multiply, we subtract, and then there’s an interesting step here that a lot of people don’t think about, which is compare. Compare meaning, now with what’s left over, is there enough to divide again? And if there is, that means I should have went up one more group. And so that compare step’s really important.
So in our checklist for students, you’ll see these buttons, but also written out sentence to one side that’s got these prompting questions for them. And the language is super clear and simple, which is important. So a lot of kids with dyscalculia, if they don’t have the dyslexia present, they actually have really high verbal skills. They’re excellent at reading usually. So something like this would be great for them because it helps them keep track of these steps and they can read and reference those things on their own.
But over time, we want to change that near-point reference to the point where the student [00:38:00] could just make it themselves on the side of a piece of paper with the symbols or the letters to help them remember, because they don’t need all those prompting questions they’ve done in enough time. So that’s where we are going bigger and narrowing it down into something more manageable.
Another thing that we can do is help students with the vocabulary of mathematics. If you think about third, the word third carries a tremendous amount of different meanings. What then comes to your mind when you hear third?
Dr. Sharp: Third? The first thing that comes to mind is a birth order situation or what order something is. Is it first, second, or third? I guess second would be like a fraction. So a portion, maybe.
Adrianne: Yes. Absolutely. It’s a little tricky, right? We have to teach these kids explicitly; what are these differences? How do we do this? And then also words [00:39:00] like perimeter and area. Kids intermix those all the time. They can’t seem to remember the difference between them because they know they’re related but they’re not really sure how. And so again, creating a visual card for them, doing a word study, helping them break down the parts of the words.
With perimeter, peri means around. A meter is a measure of distance. So we involve the gross motor and we have the kids go around in a rectangle. Area is the space covered. And so this gross motor really helps these kids. So having a visual, having the gross motor, as you can see now, they’ve got two different things that it can relate to as far as accessing that information again. Those things are really important.
Another piece of Procedural Index intervention that you could do would be to help kids build that mental number line I was talking about earlier. And the easiest one to start with is actually a vertical one. A lot of us start with horizontal, but [00:40:00] vertical makes sense. You go up and down. The numbers are getting bigger as I go up and they get smaller as I go down. And so that can be helpful.
And so my recommendation for interventionists, if they’re listening, would be to get a big old tube from wrapping paper and put the number line on it with rubber bands going up so they tactilely when they’re moving numbers, they can feel the difference. And so that helps them start to build this internal number line, but it has to be explicitly taught. That is a really valuable tool.
Another common thing you’ll see us using is a lot of dice and dominoes and subitizing. Subitizing is the ability to see a quantity suddenly. So you’re seeing it in a dice pattern or a domino. And it’s a really useful skill to have up to about the quantity 6 or 7 in a subitized dice pattern. Anything beyond that, a student [00:41:00] typically is going to get their finger out and start counting those little pips on the domino. And that is not efficient.
So we want to make sure we’re teaching subitizing in a way that’s helpful to them for grasping the quantity and mapping it to that symbol as quickly as possible. So you’ll see a lot of side by sides of dice and dominoes and the written numerals for the abstract so that we’re making the connections between the two. I could just keep going on and on about those, but do you have questions about any of those things?
Dr. Sharp: No, this is great. These are fantastic examples. I know a theme of our conversation is the multi-sensory approach. And it’s cool to see some of that come to life in these different interventions. No, this is good.
Adrianne: Okay, good. The Verbal Index is interesting. And when I’m looking at two profiles and let’s say a kid with dyslexia comes across to our desk, [00:42:00] you usually see a much higher visual-spatial and then a more depressed Verbal Index scores. They’re struggling with that recall of math facts is what we’re typically seeing.
One thing that you can do intervention-wise to really help these kids, its stop teaching all of the math facts in large chunks, because that’s what you saw, Jeremy, at school, and that’s what I saw, and so that’s what we think we should be doing. That’s not what we should be doing. We do what’s called focus facts.
So if we’re going to teach a student the 4 times tables, we’re not going to start out with all of those facts. We’re going to start with maybe up to 4 x 3 then we’ll add in 4 × 4. And then we just keep adding in a little bit as they start showing mastery of those others until we build up to that 4 × 9, 4 × 10. That makes a really big difference.
Another interesting piece that when we hire people and train them about this that is huge, this is a [00:43:00] huge game changer, we need to give these math facts utility. So when you give students a new concept to learn, it can be anything; fractions, even pre-algebra concepts, If we can keep those focus facts intact for that student, they can learn these higher level, age-appropriate concepts because they’re not bogged down trying to remember and retrieve all these random facts that they may or may not have learned.
So instead, we’re freeing up that working memory for them so that they can learn the new concept and be practicing those same facts that they’ve been working on. That’s a huge game changer for a lot of students, and they start to feel that success again. And so focus facts, that’s where it’s at. It’s my favorite tip, and it’s easy to implement. I promise you it’s worth it. It’s worth doing.
The other thing you could be doing, we talked a little bit [00:44:00] about math vocabulary but for a student, create a binder that has this vocabulary in it with visuals and involve them in creating the visuals around it. Because if the students’s involved, it’s more meaningful to them to be drawing the pictures and making the connections about how these words work together.
So with our perimeter example, tying it to other words that have peri in it, like a periscope; It goes up and around and looks around, and peripheral vision; we can see things around us because of that. So those kinds of things are really helpful to students and help them tie and make more meaning of the language side of mathematics. So that’s really important for students.
And then again, I can’t emphasize enough how important it is to use clear and concise language when you’re talking to students. There’s the language that the student will use. There’s the language that you use. And then there’s a language of mathematics, and we don’t want to shy away [00:45:00] from teaching them a language of mathematics. We’re going to build that together. We take what the student knows and we start building them towards using the correct terminology for things.
One fun fact, we’re actually working on writing a book right now, with the goal of helping people teach children to add and subtract than 10. There’s nothing that goes deep down in like we need it to. In these lessons, we’re teaching children language like compose, decompose, equal, near, consecutive.
These are big words. A lot of people might not know what they mean but they’re really important and they’re part of mathematics and can be super helpful. So we have these word maps that we’re talking about here, where we’re helping students build the visuals and tie it to a gross motor activity. So these kinds of things make a big difference in there, what we’ve been doing consistently over at Made for Math to help these students.
Dr. Sharp: Very cool. [00:46:00] So let me go back just a bit and talk about the focus facts. I know I asked you in our pre-podcast chat about math facts and drilling on math facts. And just to emphasize that it seems like it is important but you have to do it appropriately for it to be helpful.
Adrianne: Yes, absolutely. It’s not helpful to a student with dyscalculia or dyslexia to be sitting and being timed on math facts at random. That increases their anxiety. And as we know, the amygdala is what’s blocking some of that function that you need in your brain to go pull that information because it’s feeling threatened by math. It’s literally out to get you in that moment.
So we don’t want to create environments like that, but I do think timing things does have its place. It does help [00:47:00] you see how the student’s doing, but they don’t necessarily need to know that you’re timing them because it does change the outcome. When we’re practicing with students, we’re not timing them. They’re using those focus facts in every single lesson. We see that that act alone, it’s way better because we’re practicing over a long haul instead of short bursts and thinking they’ve got it right. That’s really important.
There is a lot of debate about fluency. The NCTM recently came out talking about drilling kills over. We shouldn’t be doing it. And I’m saying, please drill students but don’t do it with those parameters of timed flashcards, all the things that you and I know instead use games.
Just play as many different games as you can find to practice [00:48:00] those math facts and then give students opportunities to use that math in a meaningful way in something that they’re actually going to use, whether that be cooking or building something with their hands or sewing or whatever it is, give it some utility and you’ll see these math facts will start to stick.
Dr. Sharp: Very cool. I like to make it a fun game with my kids. I think it’s fun. Maybe they think it’s fun to work math into day-to-day life where we’re talking about, is it cooking and measuring things or is it, right now it’s the allowance and how much money they have and how much they might need to save each month to reach us to buy something. So just trying to make it super relevant whenever possible and force them to absolutely think through math concepts.
Adrianne: My kids will see me doing silly things and they know this. I’ll use it. An approximate [00:49:00] measurement tool on my body, which is my feet, and I will walk around the perimeter of some room with my feet and come up with a close enough estimate. Oh, it’s about 13 Adrian feet long. That’s my unit. And so it helps me estimate. And so there’s lots of ways that we can interject this mathematics into everyday life. I love that.
Dr. Sharp: Nice. So the third area that we could tackle.
Adrianne: Semantic, yes. This is a really interesting one. So working on lots of decomposing, meaning we’re breaking numbers down. Remember how I talked about the whole and breaking it down. Kids can get stuck in a rut thinking that the best way to make 10 is 5 and 5. And they just get stuck. And so teaching them how to decompose in several different ways is really important, but also with bigger numbers beyond 10. Decomposing 13, for example, that there’s multiple paths [00:50:00] to making 13.
One of my favorite games to play with students is actually Pyramid Solitaire, which that’s what you’re doing in this game is constantly making groups of 13. There was a time when I was playing that game so much, but instead of adding to 10, I was always adding to 13 when I had columns and numbers to add because I was just in the zone. So that’s a really great skill to have.
Another thing we can do to help these kids that have more struggles in the semantic area is to limit how many problems we’re giving. How much drill and kill? Giving a student 40 problems of homework is not necessarily an efficient way to help them really master the content.
So limiting how many problems we’re giving and how many problems are actually on a page. We talked about that earlier. Our recommendation is no more than 2 to 4 problems on an 8.5 by 11. These kids, again, they have some visual-spatial issues. They need [00:51:00] lots of room.
When I think about the worksheets that are usually given, there’s very little room, or they tell the kids to transfer the problem to a piece of paper, which also creates lots of problems for students because they might not even get it copied correctly to the page. So limiting what you have visible on the page is really helpful.
Graph paper is huge to help students with alignment with place value. Try to find graph paper with really big boxes too. That is extremely helpful and gives those students the ability to get everything aligned the correct way. If you don’t have access to that, you could take normal notebook paper and flip it, instead of writing left to right, you flip it. Now you’ve got these columns that can be helpful for organizing your work and use each column for a place value.
Other things you could be doing is obviously, in this index, lots of [00:52:00] manipulatives, lots and lots of hands-on things. Even in the secondary world, algebra tiles are popular, and we like them, please use them, but also use some of those lower-level skills that maybe you have never thought of, like subitizing these algebra tiles to help the student grasp and see the quantity quickly, those kinds of things. Find those zero pairs really fast.
Manipulatives are huge part of being able to help these students understand and grab, that knowledge of how numbers are working together and generalized to different kinds of situations.
And then another thing that you’ll see recommended for this is color coding. Color coding is huge for students. It’s so easy to do. Teaching them the color code or use shapes to help them break different things apart. This is especially applicable for those older students. So that’s really important for these students. So anyways, [00:53:00] the document I’m going to share has mountains of examples for you, so I don’t want to bore everyone with every detail that’s on there but those are some of the main ones that we are using constantly.
Dr. Sharp: That’s great. I know my audience is probably like, no, bore us. We love examples because I think people often ask about specific recommendations for our reports for math and many other things, but specific recommendations are always helpful. So that document sounds awesome.
Adrianne: If they’re really that nerdy, I’ll tell you two of my favorite books, but that’s nerdy. So you’ve got to read Mathematics for Dyslexics and Dyscalculics by Steve Chinn and Ashcroft, really good. I think it’s the 4th version. And then there’s a brand new one that’s called Effective Teaching Strategies for Dyscalculia and Learning Difficulties in Mathematics. That one’s by Marie-Pascale [00:54:00] Noel and Giannis and his last name, I struggle to pronounce. I’m going to get it down one of these days. It’s Greek.
What I love about these books, there are detailed diagrams, and it’s all backed by evidence. So these are ideas that have been tried and found to be helpful. And so we treat them like Bibles. On my team, we read them a lot and we practice because obviously no two kids are alike, but they’re really helpful to help us make sure we’re giving students that quality learning experience that they need.
Dr. Sharp: Yeah. Love it. We are just a bunch of nerds around here. We like reading books.
Adrianne: Good. I’m glad I’m at home.
Dr. Sharp: Yeah, absolutely. Well, I have two random questions for you before we wrap up, if you’re willing.
Adrianne: Yeah. I’m down.
Dr. Sharp: I’m curious if you have any thoughts on kids who [00:55:00] don’t want to show their work when they’re doing math. I’m sure you’ve run into these kids where they’re doing the math in their head. Let’s say, they’re pretty good at it. And so theoretically, maybe they don’t need to show their work for their sake but is there a benefit to that from a learning standpoint or from a procedural standpoint with math?
Adrianne: Yes. That behavior typically shows up anywhere from 4th grade up to 8th grade. We see that behavior that they just think, oh, there’s no big deal. I can do all of this in my head. Yes, but as math progresses, this is something we have to explain to them, you’re going to get to the point where you can’t see it, the answers.
At this point, you are beholden to following those procedures and making notes about what you’re doing because otherwise, you can’t see the solution that might be right there in front of you [00:56:00] normally. A more real-world example that we’ve used before, we had a student that was really interested in being a pilot but did not want to show his work. And so I have a lot of pilots in my family. So I reached out to them and I said, hey, guys, give me a concrete reason why.
I had no idea that when you are a captain of a plane, your co-pilot has to do the loads for the luggage and the people inside. They have to calculate it and they have to write it out, and they give it to the captain who then verifies that yes, these are the correct loads. When I explained that to the student, this is basic math. This is just adding numbers but they have to write it out to make sure that they have got the correct loads. And it’s also something that’s going to [00:57:00] guide and make the flight safe for everybody.
Nurses are doing things like this. They have to write out a lot of their calculations to cover their back, if that makes sense, when they’re at work to say, hey, I did administer the correct dose of this. And if I didn’t, here’s show of what I did. So there is reason to be doing those things.
And we have to just keep tying it back to real-world application because how many adults have you heard say, well, I never use algebra now. I know that yada yada. We have to give them real-world experience so that they can see the utility of why we want to do these things.
Dr. Sharp: Great. So showing your work is important. That’s what you’re saying.
Adrianne: It is.
Dr. Sharp: It is. Okay, that’s fair. We’ve covered a lot. I know that you are [00:58:00] working on a book though to help students. Can you tell us a little bit about that?
Adrianne: Sure. So in addition to getting lots of requests for us to work with kids, we also get lots of requests for, well, don’t you have something that you can teach us with? Isn’t there, can I have, there’s all these requests that come at us. And so we decided as a team, maybe this is naïve and maybe it’s not, but we’re trying to put together some of that solution.
We talked about scripted programs earlier that maybe Mathnasium has, so our goal is to create a book that has the research and evidence but also suggested progression of lessons. It’s not that it’s scripted, meaning you’re going to say this, then this, then this. It’s like, here’s the suggested progression that hits on all those things that we covered earlier about the language and [00:59:00] the multisensory experience and building that internal number line.
And so our first book is just about adding and subtracting within 10. Our goal is to help educators and parents who are really struggling with those tricky kids that are just not grasping these basic concepts and naively, maybe optimistically, we’re going to keep marching forward in the mathematics curriculum. That’s Volume 1 and there will be many more to come, but that’s the goal is that we want to give people a starting point so that there isn’t so much pain in coming up with that lesson. These are based on the lessons we’ve done.
Dr. Sharp: That sounds wonderful.
Adrianne: Yeah, thanks. We’re really excited and there’s going to be fun games. So many games in there plus digital games that anybody on the internet can access and play, Pyramid Solitaire being one of them.
Dr. Sharp: Great. I’m going to go look up Pyramid Solitaire.
Adrianne: That’s super [01:00:00] fun. Your daughter would love it. Play it with your daughter.
Dr. Sharp: Okay, will do. We’ve got some homework tonight. Fun homework.
Adrianne: Fun homework, yes.
Dr. Sharp: That she won’t know is math. Well, thanks so much for being here and talking through these things. I know that there is so much more that we could get into with intervention and math, and this is just a broad overview, but I appreciate you sharing some specific ideas and interventions. I know that I wrote down a lot of things and have learned a lot from our conversation so I really appreciate it.
If people want to reach out, want to find you, want to talk to you, what’s the best way to do that?
Adrianne: Probably the easiest way is to head over to our website at madeformath.com. If you want to get in contact with us, you can email but you also can hit us up on social. We’re on Instagram, Facebook and YouTube. I don’t know if YouTube is considered social but we have a lot of content [01:01:00] over there.
If you want to get really nerdy, we have a web series called Unlocking Dyscalculia where we are talking to researchers, interventionists, we’re talking to parents, and we’re trying to get some kids to come on and talk about it from their perspective but that’s a very vulnerable thing. Anyway, connect with us over in those places and you can message anywhere and we will respond to you.
Dr. Sharp: Love it. Well, thanks for your time and your knowledge today, Adrianne, love it.
Adrianne: All right, thanks so much.
Dr. Sharp: Take care.
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