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Ep 28. Autism and evidence-based math instruction
with Katharine Beals

This transcript was created with speech-to-text software.  It was reviewed before posting but may contain errors. Credit to Jazmin Boisclair.

You can listen to the episode here: Chalk & Talk Podcast.

Ep 28. Autism and evidence-based math instruction with Katharine Beals

[00:00:00] Anna Stokke: Welcome to Chalk and Talk, a podcast about education and math. I'm Anna Stokke, a math professor, and your host. You are listening to episode 28 of Chalk and Talk. My guest in this episode is Dr. Katharine Beals. She is a linguist who teaches several courses on autism at both Drexel University and the University of Pennsylvania. She is also the author of several books on autism, including one focused on autism-friendly curriculum and instruction.


I was eager to learn from Katharine about autism and how it relates to learning math. We begin the episode with an overview of autism, where Katharine explains some of its defining characteristics. She tells us what skills are typically affected by autism and where math fits in. We then discuss how some common math instructional techniques may negatively impact autistic students and what research suggests are the most effective instructional methods for these learners.


Along the way, we discuss facilitated communication, and Katharine offers her recommendations for math programs that are particularly well-suited for autistic individuals. One key takeaway from this conversation is that many instructional techniques that are most effective for autistic students also benefit the majority of students.


However, students with autism are more adversely affected by poor instructional methods. I found this conversation with Katharine to be both fascinating and highly informative. As someone with limited knowledge about autism, I gained a deeper understanding of what makes for autism-friendly instruction, and I hope you find our discussion equally enlightening.


In addition to this episode, I recommend checking out Katharine's book, Students with Autism. and I will include a link in the show notes. Now, without further ado, let's get started.


I am excited to be joined by Dr. Katharine Beals today, and she is joining me from Philadelphia. She has a Ph.D. in linguistics. She specializes in language and literacy acquisition, in autism, language technologies for autistic individuals, and educational challenges for students with autism.


She's an adjunct professor in the autism program at the Drexel University School of Education, where she designed two of the program's five courses. She also teaches an autism course in the School of Education at the University of Pennsylvania, and she teaches several courses in evidence-based instruction at Temple University.


She has written and lectured extensively about the education of students with autism. She's the author of several books, including Raising a Left-Brain Child in a Right-Brain World and Students with Autism: How to Improve Language Literacy and Academic Success.


Welcome, Katharine. Welcome to my podcast.


[00:03:18] Katharine Beals: Thank you for having me. I'm excited to be here.


[00:03:21] Anna Stokke: I just read your book, Students with Autism, and I've read a lot of books for the podcast. And I have to say, I learned probably more from this one than any of them, just because I didn't know, don't really know much about autism or educating students with autism. So I highly recommend that book to listeners because it's really well written.


It's very accessible and I certainly learned a lot. So, you have a background in linguistics. So how did you become interested in autism?


[00:03:54] Katharine Beals: Great question, and a very fair question because they're not obviously related at all. I wouldn't have thought they were related at all. I, it began with my having a son with autism and noticing that he was having a lot of trouble picking up language.


There's an additional complication. He is also profoundly deaf, and he has a cochlear implant, but once we got to the point where he could hear, there was still an additional issue with picking up language, and that got me really interested in what it is about the autism spectrum and the behavioural symptoms that we know about that affect it.


The ability to pick up language. And so then I became an autism linguist in the process of working on that question and trying to figure out solutions for him.


[00:04:43] Anna Stokke: Okay. So it was very personal to you, but you've also written a lot and educated a lot of people on autism. So that's really helpful. So can you just sort of explain for the listeners, what is autism and what are some characteristics of individuals with autism?


[00:05:03] Katharine Beals: Sure. So, it's an odd diagnosis in terms of the symptoms that are given in the DSM. And these symptoms, by the way, have been pretty stable since the term was first coined back almost 70, 80 years ago at this point by Leo Kanner. The two symptom categories that have been then observed separately by various other people or early pioneers are the social category, which involves less tuning in and less social back and forth, less engagement, that's one category.


And then the other category that is seemingly quite different is the restrictive repetitive behaviors category, where there is, and you don't need to have all four symptoms, but a combination of hyper-focus on small parts of things as opposed to the big picture. Stimming, self-stimulatory activities, and an all-encompassing focus on very, you know, very narrow interest, which sort of is like the focus on parts rather than holes.


And then there's an optional sensory sensitivity category that you don't necessarily need to have. So, the restrictive repetitive, I think the one way to think about that is it's an overall narrow focus, whether it's on parts of objects or a very strong interest in something that then excludes other interests, potentially.


[00:06:31] Anna Stokke: So when thinking in terms of the autism spectrum, my understanding is that verbal knowledge and skills are affected by autism severity. So can you explain the difference in terms of verbal knowledge between individuals with mild, moderate, and severe autism?


[00:06:50] Katharine Beals: Sure. So, the spectrum that's relevant to this is the social part of it. And the social symptoms overall are a pretty good marker of autism severity. So, the question is, how often does an individual child tune in to speech and social interaction and engage with it? And so, a child who almost never does that is a child who will end up with very little spoken language, language in any form, including comprehension.


A child who does a lot of the tuning in, just less than average will end up potentially seemingly normal levels of language skill, eventually, it may, there may be a slow start to it. However, there's still an issue with social uses of language. So there may be difficulty, even with perfect syntax, big vocabularies, which a lot of people do have, there may be difficulty doing a conversational back and forth, staying on topics, staying on other people's topics as opposed to going to your topic, if you're a narrow interest, that sort of thing.


In the middle, and this is where my son is, and it's kind of odd because it's like, it's almost like a, a bimodal distribution. There's, there seem to be fewer people in the middle than there are at both ends. So, which makes you kind of wonder what's going on here. But in the middle, you have people who have, you know, language and reasonable vocabularies and abilities to express themselves but have difficulty putting words together into more complex sentences.


And that seems to correlate with being in the middle in terms of socially tuning in. And, you know, there's a certain amount of that, but not as much as a milder case, which would once have been called Asperger's or certainly with neurotypical, what's called neurotypical or nonautistic.


[00:08:44] Anna Stokke: What does it mean to be high-functioning autistic, because I often hear that phrase, and where does Asperger's Syndrome fit in?


[00:08:52] Katharine Beals: Right. So, Asperger's syndrome fell out of favor for various reasons, and it's probably never going to come back because of the association that has been uncovered between Hans Asperger, the person it was named after, and some collaboration with the Nazis way back when. So that term is probably not going to come back, although it's still used informally.


The distinctive characteristic with Asperger's is fluent language, you know, no, no issues with getting the words out, getting the syntax out, getting the vocabulary out. However, issues with that social use of language. High functioning seems to be used to include Asperger's, but also to include IQ scores, at least the nonverbal IQ, is at normal or above.


The verbal IQ for anyone who isn't fully fluent is going to be somewhat lower than average, but you could still end up with overall average or above average IQ scores if the performance IQ is high enough. And so those are the people who are going to generally be high functioning, considered high functioning.


Another marker of that is that higher functioning individuals are those who are most likely to end up in general education classrooms where they're getting the same, most of the same subjects as everybody else. They might have some pulling out for speech or other things, but they're in general education classrooms.

[00:10:20] Anna Stokke: Okay, so the main difference would be, if I'm understanding correctly, is the language is perfectly normal, right? With high functioning Asperger's.

[00:10:31] Katharine Beals: Asperger's the language is normal except for the social use. For the rest of the high functioning, the language may not be normal, but the. Nonverbal IQ is high enough, that there's not an overall intellectual impairment that's measured. And people will draw the lines in different places.


So, I don't know, I would say it's a fuzzy category where it's a combination of pretty good language and normal to above normal IQ and or placement in general education.


[00:11:02] Anna Stokke: So, often placement in general education, but still some sort of diagnosis of autism. And so, what sort of difficulties does that cause for a student who's high-functioning autistic? Like are there difficulties with being distracted by other students, things like that?


[00:11:23] Katharine Beals: Yeah. So there are a bunch of challenges in the regular ed classroom. So for one thing, the flip side to being less tuned into voices and social stimuli is a tendency to be easily distracted by non-social stimuli and to be more sensitive to things like buzzing fluorescent lights, if those are still around, or outdoor noises or bustle in the classroom, kids moving their, belongings around and doing hands-on activities.


So there's that, and then there is difficulty with the social interactions that might be expected in the classroom. And then anybody who has who's a little more towards the moderate part of the spectrum will have challenges with comprehending what's going on verbally in the classroom.


They might have difficulty with the reading, but difficulty understanding oral directions and explanations, and also difficulty expressing themselves verbally as readily as other students do.


[00:12:26] Anna Stokke: So, while verbal skills are often affected by autism, my understanding is that some other things are not affected. So, can you say something about that and discuss where math fits in?


[00:12:39] Katharine Beals: Sure. So, math would seem at first glance to be a subject that should not be affected by any of the things I just described. Now, the caveat is that there are comorbidities that occur with autism, particularly more severe forms of autism, for example, intellectual impairment, and that, of course, will have an effect on any subject, potentially, right?


A general intellectual impairment. In the absence of that, however, there's no reason why someone with an autism diagnosis should have any difficulty with math. In as much as math is operations on numbers and spatial stuff, right? Because none of that should be affected by autism, by the diagnosis. The only thing that potentially is affected, some researchers have found that even higher functioning people with autism have disproportionate difficulty with complex information.


So when there's a lot of moving parts and a lot of disorganization. That can disproportionately undermine someone on the spectrum. There may be some secondary cognitive things that are going on, or maybe it's somehow related to the social. But the point is that if you had a subject that's maybe not that verbal but is not well organized in terms of how it's presented, then that might cause additional challenges for the autistic students more than for other students.


[00:14:16] Anna Stokke: Okay, so it sounds sort of like there's a need for structure.


[00:14:20] Katharine Beals: Absolutely. That's a big, big one. And you even hear that in autism memoirs, you know, testimonials from autistic people. “I need structure,” higher-functioning individuals say that.


[00:14:32] Anna Stokke: I need structure too.


[00:14:33] Katharine Beals: The more you learn about autism, the more you think, “Hey, I'm kind of like that too, right?”


[00:14:38] Anna Stokke: So, speaking of which, now, I'm going to read a quote about mathematicians, and I understand that your dad was a math professor. Right?


[00:14:49] Katharine Beals: He's retired, but he even this past semester he taught a course. So he's somewhat active, but yes, he's a math professor,


[00:14:57] Anna Stokke: So in one of your articles, you discuss some work done by autism researcher Tony Attwood, who observed that math has special appeal to individuals with autism as it is often the subject that best matches their cognitive strengths. In fact, he wrote in his book, The Complete Guide to Asperger's Syndrome, that the personalities of some of the great mathematicians include many of the characteristics of Asperger's syndrome.


Now given that math can be a strength for students with autism, yet verbal skills can lag behind, what is the impact of language-heavy math programs for these students?


[00:15:38] Katharine Beals: Not good. So what's unfortunately happening is you have a subject that is potentially autism-friendly, autism accessible, a way for these kids to feel successful, potential entry point to a career that is being made less autism-friendly, less accessible that potentially is a subject where someone who even someone who could be quite successful in math may not get good grades, may not get good test scores if the tests require verbal explanations, may not get mathematically challenged may not get opportunities that perhaps they once had. So that's a huge concern.


[00:16:22] Anna Stokke: Okay, so are we talking about things like “explain your answer?”


[00:16:27] Katharine Beals: Yeah, absolutely. That's a big one. So, it's an increasing requirement, you know, I first, I first became aware of this actually - so I didn't really know what was going on in math until, you know, I hadn't checked in in many, many years and then suddenly my son is in school and he was in a, you know, kind of a situation at a regular public school, but he was at that point able to do double digit addition and subtraction and some multiplication I think as well.


So we were thinking, "Oh, well obviously they're going to be willing to put him in a regular third-grade math class" to just be pulled out from his special classroom. And we sat down with the powers that be at the school, and we were told, well, you know, “Math is different now.” We, those were the principal’s words.


“Math is different now. There's a lot of group work, and students are journaling, writing journals…” and so on. And I'm thinking, wait a sec, I've grown up kind of around math, and math is different now? I'm hearing this for the first time, what is going on in math?


So yeah, so this issue of having to explain his answer, continued to dog him throughout his, certainly throughout arithmetic is early elementary years and even as later elementary years and there would be questions like, you know, explain your thinking, which is particularly a challenge for kids with autism.


There is a tendency, going along with the lack of the lowered verbal skills in autism, is a tendency not to be working problems through in a verbal fashion. Actually, I'm not sure if anyone really works through arithmetic by thinking in words, but certainly someone who isn't autistic can kind of guess what the teacher wants you to say with words and has the words to say it.


Whereas, someone on the spectrum told to explain their thinking is going to have no idea what's expected and won't even be able to kind of fake their way through that process, and then points get taken off. In, certainly in Pennsylvania, in the state tests, there are sections where you will lose points if you do not explain your answers.


That was one of the reasons we were told, even by teachers who might in principle have been willing to waive that requirement, they would say, “Well, but on the state tests, he's going to have to explain his answers.”


[00:18:50] Anna Stokke: Okay, what about “show your work,” though?


[00:18:53] Katharine Beals: Well, that I think is a completely different thing. So, and I think it's a good thing for hard problems, not for, you know, simple problems that you might do in your head. These kids can do a lot in their head and there's a lot of rote learning that they just do on their own without any necessarily any encouragement by teachers.


They just may have memorized a lot of stuff. So I think that it's something that, that is not a productive requirement in, in arithmetic, but certainly by the time you get to things like algebra and trigonometry and calculus, I wanted him to show his work. He often did make silly mistakes, and if he had shown his work more that would have been a good idea.


I think that one thing that for him was missing was any kind of penmanship instruction. So I think that, you know, to be able to fluently write out your math and show your work and actually be able to read what you wrote down and see a problem, you need to have had some sort of instruction in penmanship or have a natural ability.


Penmanship is not something that individuals with autism are naturally good at. There's, there are fine motor challenges in autism. So the problem we ran into with showing your work, later on when it actually made sense to do that, was that he couldn't see what he couldn't understand what he'd written and so he couldn't see the silly mistakes he'd made here or there.


[00:20:20] Anna Stokke: Okay, so what is it about math then that may make it more appealing to some individuals with autism then? Is it the structure, is it the logical nature of math, is it that there isn't normally a lot of language involved?


[00:20:37] Katharine Beals: Yeah, I think it's those things because I think we want to be careful to not generalize and so there are plenty of people like Temple Grandin, for example, who didn't like math or maybe who like geometry but not other aspects of math. I mean, the one way to look at it is that people with autism probably have just the same range of non-autism-related strengths and weaknesses of everybody else.


And so what that means is that you're going to have people with autism who have strengths in math, yet they may not be able to fully realize those strengths because of deafness. The way things are currently practiced in schools, and so for those people, the appeal of math is a) that they just have a natural inclination towards it, but also b) that it potentially doesn't have the barriers to entry that some other subjects do the language barrier, especially.


[00:21:30] Anna Stokke: And so you've alluded to this a little bit, so we should probably talk about this because in your book you have an entire section titled “Problems with Progressive Math,” and so we should talk about that. First off, what do you mean by progressive math?


[00:21:45] Katharine Beals: Well, it's hard to come up with the perfect term because I think it used to be called reform math, and then I was encouraged by, I think my colleague, Barry Garelick was the one who said, just progressive math is a better term for it for now. One way to look at it from an autism perspective is it's got, all the autism-unfriendly traits it could possibly have.


So there's a lot of group work, there's a lot of child-centered activity. So unstructured, multiple solutions and emphasis on multiple solutions to problems. Tony Attwood has actually written about that. Also, that individuals with autism don't find it satisfying to keep doing the same problem over and over again using multiple solutions.


You know, “I solved the problem, why do I have to do it again a different way?” And then there is the, of course, the language-intensive components of math, not just the you know, the group work is going to involve a lot of speaking, but also the word problems, the story problems have more words than ever.


They deliberately add excess terminology that's not related to the problem because people seem to think now that part of being good at math is knowing which words in the word problem to ignore, which is, was not always the case.


And then there's the, all the verbiage that is expected for explaining your answer. And then one of the consequences of having a child-centered approach and a multiple-solutions approach is that everything is less systematic. Textbooks themselves are less systematic to the extent that people are still using textbooks. So one way I see this is that individuals with autism are kind of like the canaries in the coal mine.


None of this is good for anybody in math, right? We know that from the research, but individuals with autism, as we noted earlier, especially need structure. They especially need organization, direct instruction where appropriate. They especially need the language to be factored out of the math and address the language separately.


 Let them do the math.


[00:23:54] Anna Stokke: So let's talk about some of the specific things and, and actually in my episode with Tom Loveless, we talked about the history of reform math is what he refers to it as, and the shift that sort of started in 1989 to focus on some of the things that you were just mentioning. And one of those things was more of a focus on conceptual understanding, not that we’re against conceptual understanding, but there is an overemphasis on it, in my opinion.


So, let's start with that emphasis on conceptual understanding over procedural skill. So, can you discuss how that might impact autistic students?


[00:24:36] Katharine Beals: Okay. So one of the interesting findings in the research on the cognitive challenges with complex information processing in autism is that individuals with autism have disproportional difficulty with one particular sort of activity that's that people tend to associate with conceptual understanding and that is to apply a concept to a new situation.


So, like, you might learn one type of math problem, perhaps in the abstract, and then you're given a word problem to apply it or a new situation to apply it to, for example. And what, the people who have been successful with this population and students in general have found is that you will get conceptual understanding with a lot of procedural stuff first, right?


And in fact, there's an interaction between doing a lot of so-called rote problems and gradually getting a handle on what the underlying concept is. I believe you've had people talking about precision teaching on, or if you haven't, you probably will, but anyway, you should because there's a lot of interesting things to say there.


The precision teaching people are based in Seattle. There is a school called the Morningside Academy. They work with students with various issues, whether overall disadvantage or specific learning issues. They don't so much focus on autism, but they do work with kids who have had lack of success in the public schools, in the general public schools.


And what they have found is that with an emphasis on rote, not just rote, but also fluency, you, what you work on is getting automaticity in the mechanical stuff so that with that automaticity, you then can devote all your cognitive resources, so this is like cognitive load theory, to the conceptual stuff and applying the algorithms that you have automated to new situations.


That is the kind of approach that they have found to be very successful with their population. Again, autistic students are kind of like the canary in the coal mine. This is the way to work on that issue with complex information processing that individuals with autism have. Automate as much as possible then you get to apply things to new situations and get that particular conceptual understanding in place.


[00:27:03] Anna Stokke: You're kind of talking about, some things I've talked about with other guests and in the podcast, which I think we refer to maybe as explicit instruction or direct instruction, which could be with a capital D and a capital I or not, but a lot of it just means teach students explicitly, get them lots of skills, lots of fluency, and then they're able to apply that mathematical toolbox to new situations, right?


[00:27:33] Katharine Beals: Yeah. And I think it's important to also keep emphasizing to the world that direct instruction does not mean a passive lecture. It's very interactive back and forth, back and forth call and response lots of hands-on, you know, actual doing problems with pen and paper.


The one thing, though that the precision people add that I think is useful is the fluency component. So the precision teaching people believe in all of those things, but they also believe in the importance of tracking fluency and actually keeping track of a student's progress, so that you have a sense of when someone is fluent enough to move on to something else.


So that's, that's the one thing I would add to what you said is that it's interactive, it's structured, it's sub-skill by sub-skill, all of those things, but it's also additionally an emphasis on, tracking and an emphasis on fluency.


[00:28:23] Anna Stokke: That's a fantastic idea. So yeah, I definitely should have someone on to talk about precision teaching then, but you've told us a lot about it here today.


You use the phrase, the canary in the coal mine, and I hear you saying something that reminded me of something that Pam Snow kept saying, and I can't remember it perfectly. And she's much more eloquent than I am, but it was something like direct instruction: it works for all, it's essential for some and it harms no one.


[00:28:52] Katharine Beals: And I also think it puts an interesting spin on this fashionable notion of universal design, right? So I don't know if that term has come up yet in your podcast, but the idea behind universal design is we should be able to have any student with any issue, any disability, all in the same classroom if we only could just find a way to have adequate entry points for every student.


Somehow that's theoretically possible and a great idea. Well, I would say that it's actually that's very logistically unfeasible in a lot of ways. The one thing, the one grain of truth here, what flips everything around is that actually what works for special ed kids is often what works for everybody.


It's just that the special ed kids are the canaries in the coal mine. So if we want universal design, what we should be doing is taking all these things that people have found to work for kids with autism and with other special needs and having everybody undergo these things. One of the most successful autism therapies is this applied behavioral analysis approach, which is very much akin to both precision teaching and direct instruction.


If you had classrooms that were run basically like that, you would have classrooms that worked for multiple populations. That would be the ideal kind of universal design.


[00:30:12] Anna Stokke: And I also had Daniel Ansari on the podcast, and he knows a lot about dyscalculia. And he was saying exactly the same types of instruction that you're talking about, exactly the same type of instruction is required for students with dyscalculia.


[00:30:30] Katharine Beals: And same with dyslexia. It's just everything. Like, it turns out that not only is learning styles wrong, but we all kind of need the same ingredients to be successful. And those ingredients are not going to be harmful. You know, the only thing that would be harmful would be holding someone back, you know, someone who's ready to move on, but we all benefit the most.


And if you think about any other activity that you've, you engaged in, you know, whether it's martial arts or how to play a violin or how to swim, that's how you learn. People break it down and you practice sub-skill by sub-skill until you're automatic.


[00:31:04] Anna Stokke: Absolutely. So you mentioned a few things in your book about concrete materials. So that's something we also see a lot of in math class. So can you tell us a bit about that?


[00:31:20] Katharine Beals: Sure. So there's nothing about concrete materials per se that is sort of problematic or, or beneficial one way or the other in as much as doing something with concrete materials bypasses language. That's a good thing. So you could certainly learn a fair amount by working with manipulatives and building things and doing experiments and so on if you're on the spectrum.


The issue that what can become problematic is when it's unstructured or so there is just a lot of amorphous exploration and the kids don't really know what they're doing. Or in a classroom where you have 25 to 30 kids all kind of manipulating objects on their desks and building things, there can be a lot of clutter, a lot of auditory clutter and distraction that can be hard for kids on the spectrum who have those sensory sensitivities and challenges.


[00:32:20] Anna Stokke: They can be helpful, right? That's what you're saying. But over-emphasis again, over-emphasis can be very distracting and actually not helpful.


[00:32:30] Katharine Beals: Yeah, and you want to embed it in some sort of organized structured program with a real goal and measurements and so on.


[00:32:36] Anna Stokke: So what about the focus on real-world problems?


[00:32:40] Katharine Beals: An additional initial problem that comes up, which I haven't mentioned yet, is that when you have a language impairment that affects comprehension, you also are missing out on a lot of incidental information about the world, a lot of background knowledge, not just the kind of background knowledge people talk about for reading comprehension, but just even background knowledge about the everyday world around you.


So as soon as you have a word problem that has a real-world situation in it, like, you know, there's some sort of discount and you're getting a t-shirt or whatever. Suddenly you have all this stuff that doesn't necessarily make sense to someone with a language comprehension impairment, including an individual with autism.


It's also of course going to be problematic for someone coming over from another culture. And that's actually, one way to look at students with autism. It's almost like they're not full members of either their language or their culture. They're not picking up as much as other kids do.


So that's where the real world, the real-world problems have both the language component and the background knowledge component problem for kids with autism.


[00:33:54] Anna Stokke: Okay. And what about group work?


[00:33:56] Katharine Beals: That just goes right to the social challenge in autism. And so there is difficulty being in a group, there's difficulty contributing to the group appropriately understanding what's going on. You could have anything from a student just completely checking out to a student who maybe knows, say it's a math group, who knows the math really well and wants to kind of take over and doesn't know how to be diplomatic about it then getting shunned by everybody in their group.


Teachers can't keep track of every group. You might have an impression that you're keeping track of all the groups in your classroom, but there's a lot of subtle social shunning that can happen that flies below the radar. And so the entire process, the entire experience of being in a group can be very challenging and potentially upsetting to someone on the autism spectrum.


[00:34:48] Anna Stokke: So what would you recommend then if that's part of the way a teacher is supposed to be teaching, what would you recommend?


[00:34:58] Katharine Beals: Well, it's tricky when you are being monitored as a teacher and someone can open the door and see that you're not, you don't have everybody in a group, but logistically you could easily have someone, a student in your, an autistic student in your class who, provided they have a certain amount of self-motivation and interest, say, in math, you could have them doing a separate, you could just have them doing independent math on their own, whether in a textbook or in a good online program.


And you then would have to make a case for what you're doing if someone challenges you, say your principal. And I think that the case to make is that these kids need to have their language skills addressed separately, you know, so why not have speech-language, the school's speech-language pathologist pull the kid out for, for language instruction and not let that hold back the student in math.


And same with social skills, you can have social groups that are perhaps done at the school or perhaps done elsewhere, but the school doesn't have someone who is qualified to run a social group for social skills then certainly the teacher isn't qualified. And so we need to point out that these teachers are not trained in how to help - a general education math teacher is not trained and how to help someone with autism navigate a social group and therefore, perhaps better solution is to not have the person in a group.


[00:36:35] Anna Stokke: Okay, and so I can sort of see how this might go, and I can imagine being a parent, and you go to the school and say, “I don't want my child in a group my child doesn't function well in a group because they've been diagnosed with autism,” and the school says, “but it's part of our job to teach children how to work together.”


So what you're saying is math class is not the place to teach that.


[00:37:05] Katharine Beals: Yes, and general education teacher is not a social skills specialist right, especially with autism.


[00:37:12] Anna Stokke: I teach at the university level, and we often get accommodation letters. So in other words, we've got to accommodate students in various ways. So, for instance, an accommodation might be that the student gets extra time and our accessibility services center would work that out.


But one of the accommodations I have seen come through in recent years is the student shall not be required to participate in group work. I was kind of surprised by that and it's actually not a big deal for me because I usually don't have group projects in my calculus class. Say, you know, they can work together in the lab and that sort of thing, but I certainly don't force groups.


So you've helped me understand this accommodation quite a bit more today. I think that that makes a lot of sense that why should the actual academic piece be compromised over being required to participate in a group, which would be really difficult maybe for this individual.


[00:38:17] Katharine Beals: It's interesting that your school had that accommodation because we attempted to get that accommodation for my son when he was a student at Drexel, which is where he went afterwards. And he, by the way, majored in math and computer science there. But he was faced with these. These general ed requirements, including an English requirement where there was group work, and I could not get the disability office to agree to exempt him from this.


It was very frustrating because they have a lot of kind of boilerplate accommodations, extra time, and so on and so forth that were only so helpful. So what ultimately solved that problem was the pandemic. Because all of a sudden, the groups were online groups, and that reduced a lot of the problem for him.


And I think it was largely because of the pandemic that he was able to graduate.


[00:39:08] Anna Stokke: Oh, wow. So he got his math and computer science degree?


[00:39:12] Katharine Beals: Yes, took him, took him a little bit longer than average, and now he has, he's employed. And it's been great, and Drexel has been very helpful. I have to say other components of Drexel have been very, very helpful for us.


[00:39:23] Anna Stokke: Oh, well, congratulations.


[00:39:26] Katharine Beals: Yeah, we're, it's beyond our, any expectations, and the initial diagnosis with moderate autism, even moderate autism at the time he was diagnosed was considered to be so impeding of his life trajectory and his ability to take regular classes that he was predicted to end up in life skills classes and essentially not be employed in anything like the capacity he's employed now. So we're very happy.


[00:39:58] Anna Stokke: Well, you’ve been a great mother.


[00:39:59] Katharine Beals: Being a linguist, you know, that we did a lot of work on the language there.


[00:40:02] Anna Stokke: Okay, so I wanted to ask about accelerated programs and gifted programs and just in general, for students who excel in math, I feel that it's important to have accelerated options available. And I'm wondering your, what your thoughts are on that.


[00:40:21] Katharine Beals: I think in theory, they're a great idea. And again, it's one of those things that in practice has gotten problematic. So in Pennsylvania, for example, to get into a gifted program, you need to have an overall IQ of overall, of a certain level, right?


Like mentally gifted, whatever that means. And that, so what that means is that someone on the spectrum, people on the spectrum are often going to have IQ scores, sub-scores that are all over the map, and they might have very high math skills and yet not have a high enough IQ to make it into a gifted program.


So that's one problem. And I would just say as an aside that we are a surprisingly IQ-obsessed society. What the focus really ought to be on is readiness, academic readiness. And if a kid is academically ready in math then there should be something for them. But then the other problem with the gifted programs in this country is that they tend to be not necessarily programs that put you ahead in math or any other subject, but add-ons where you're doing projects, group projects.


And so actually it's a bunch of stuff that kids on the spectrum aren't good at. So what would be really great would be a way, you know, people have arranged this kind of on the side, but a kind of systematic pathway for kids who are really good at math, whether or not they're on the spectrum to get ahead, regardless of what else, you know, what the general expectations are of other people, and not with this general barrier to gifted education that many may not be able to get through.


[00:42:05] Anna Stokke: Your book actually, you know, you've got a lot of research references in there. your statements are research-backed. And so I think I understand that you would say that in general, the best way to teach students with autism is through explicit instruction or precision teaching, as you were talking about, but another thing you talk about is facilitated communication, and I'm wondering if you can tell us a bit about that.


[00:42:32] Katharine Beals: This is actually a major activity of mine at this point. Facilitated communication is a pseudoscience. It was debunked in the 90s by probably more studies than pretty much any other pseudoscience has had, multiple times. There are probably 20 studies in the 90s debunking it. What it is is the initial version of it was you had a nonspeaking or minimally speaking person, typically with autism with an assistant who would hold their wrist or hand or elbow or even shoulder over a keyboard of some sort.


And what appeared to happens is that this nonspeaking person who appeared to show very little signs of comprehension, let alone literacy is suddenly typing out perfectly or near perfectly spelled words and sentences with a vocabulary beyond what anybody thought they had.


And to some people, this looked like a miracle. So you have people who appeared to have no language suddenly typing out full sentences. But what studies showed was that, and this was the really interesting thing about this is that it was unwitting, unconscious, the facilitators, the people holding the hands, the elbows, whatever, and the board were unaware of the fact that they were queuing, they were directing the movements of the, it's usually an extended index finger. It's not ten-finger typing. It's like this, right?


The slow one letter at a time and the way they established this surprising fact was by blinding the facilitator to the answer to a question that was asked of the facilitated person, or more, more devastatingly, you would show the facilitator one picture at the same time that you showed the facilitated person a different picture, and then you would ask, “What did you see? What's in the picture?”


And what happened again and again and again is that the individual, the nonspeaking individual, would type out not what they saw, but what they couldn't see, what the facilitator saw. How could that happen except if the facilitator were controlling the messages? And what was really interesting about those studies was that - and there's a documentary called Prisoners of Silence that is no longer on PBS, but you can get it through the way back machine, the Internet Archive, and what you see in that documentary, which I would say is one of the most fascinating documentaries out there, just even in the grand scheme of documentaries.


You see facilitators reacting to the test when they see what happened and they are just totally taken aback. They had no idea that they were directing these messages. It's devastating because they realized that they were essentially having conversations with themselves. Imagine finding that out. Okay, so you would think that this would have gone away. It hasn't. It has come back. Not just this version is still around, but there are newer variants of this that are called things like rapid prompting method and spelling to communicate.


And the variation is that often now there isn't much touching that happens. Instead, the facilitator holds up, and they're called a communication partner, they might be called a helper or assistant. They're holding up a laminated letter board to the person's extended index finger. Again, it's extended index finger, slow typing, not ten-finger typing.


You hold up the board, the board kind of moves around the person prompts and will say things like “You almost got it, you almost got it.” You know, as the finger moves towards a letter. There is queuing that still happens. It's, it's auditory and it's movement rather than touch, but all the available evidence suggests that the same, there's the same control by the facilitator that there is in the touch-based facilitated communication.


Tricky things that people now don't want to test. So there's a mantra in the communities that use this. Don't test, don't test, don't test. And so we don't have a lot of direct evidence that's been published, that this method is as facilitator controlled as, as the traditional one was.


But we know from private experiments, and we know from the capacity for queuing, it doesn't have to be tactile, it could be auditory and movement-based, and it's the same mysterious phenomenon. Somehow, someone who is minimally speaking, and has not had any phonics instruction, and has not had any direct instruction because they, in academics, because they've been in special ed, somehow these individuals have perfectly typed sentences with sophisticated words like amber and Pluto and orbit, things like that, out of nowhere.


And the explanation is supposedly that these kids are somehow absorbing information from the environment without the instruction.


[00:48:12] Anna Stokke: It kind of sounds like a Ouija board, right?


[00:48:15] Katharine Beals: Yeah, well, certainly the touch-based stuff is easily understood that way.


[00:48:19] Anna Stokke: So this is commonly used?


[00:48:21] Katharine Beals: It seems to be on the rise. There's a movie called Spellers, which is basically a documercial for this. There's a clinic not far from me that promotes it. There are people suing the school districts around here for the school districts to pay for this sort of thing.


I've been involved in some of this. I'm starting to see students of mine go out and do field experiences where there are students using this method and they, they don't my students don't know enough to know that this is a problem. So now we've changed the curriculum a little bit and there are a whole bunch of news stories now about this. every month or so there, there, there's a feel-good story in the newspaper about some kid who was unlocked.


So there's a lot of very irresponsible reporting. And we know that from that happens with education as well, and even PBS. So PBS now has two facilitated communication promoting movies on its website.


So they got rid of the documentary from the nineties. That's no longer on PBS. But they have instead, so mainstream media has fallen for this. It's hard to keep track, it's hard to know what the numbers are, but it's starting to seem to me as if nearly every parent who has a minimally speaking child a) is going to hear about this and b) is going to be extremely tempted to try it out.


[00:49:47] Anna Stokke: Okay, so basically, a similar thing was used in the 90s, and there had been some research done at that time, fairly easy to check like you explained exactly how you could just check if this works or not, right? Fairly easy to check. They did some research on it, showed that it actually wasn't doing anything.


And of course it comes back because this is very typical in education, right? That, you know, we get these fads, they go away, they come back they sound really good and so people kind of jump on the bandwagon. So how do you think its current popularity fits in with some of the broader fallacies in education then?


[00:50:26] Katharine Beals: Well, that's one of the really interesting things about it. You know, why now, why is it making such a comeback? And I do think that it very much fits into our current educational ethos because for one thing, the initial explanation by the guy who first brought it to the U.S., a guy named Douglas Biklen, who then became dean at Syracuse later, at Syracuse University, when he was asked, how is it these, these kids are literate suddenly, he said, “Well, they learn to read the same way everybody else does just by being in a print-rich environment, right?”


So that sounds familiar, doesn't it? So this idea that we don't need direct instruction in literacy, we just need to surround kids with books. And then where does the math skills come from? Well, they just sort of absorb stuff somehow. You know, there, there are stories of kids somehow learning Spanish because they hear their siblings practicing Spanish at home, they're doing their Spanish homework.


They somehow learn physics because they could hear a physics class through the cafeteria wall, and one of my favourite examples with math, so there's this one, you know, some of these accounts are unwittingly telling. So there's a kid who purportedly, you know, it's really actually presumably his facilitator, but there's a blog or some sort of post on the internet where this kid talks about how he was having trouble with his calculus class.


I don't know if it was calculus or trig or some high school math class. He was having trouble with it because his facilitator had math anxiety. And so the problem was solved by replacing that facilitator by a facilitator who didn't have math anxiety.


And then all of a sudden he was able to do his math, but anyway, I think that part of why it's popular is because there isn't sufficient skepticism about how these kids have acquired already have these skills, because we saw a lot of people think that kids can just pick skills up by being kind of surrounded, they don't need direct instruction.


So that's part of it. And then the other big picture has to do with this reluctance to really look intellectual disabilities squarely in the face and this assumption that, everybody has the capacity in them to communicate. Everybody has the capacity in them to succeed. It's just a matter of providing some sort of an entry point.


And I, and you hear that kind of talk a lot in at least in special ed, but I think in general ed, where, it's like, you need to provide multiple entry points. And so the metaphor seems to be to allow what's somehow already there in the student to come out and flourish.


[00:53:17] Anna Stokke: And certainly to help people and to help students learn, sometimes we do have to recognize those differences. I think that's kind of what you're saying.


[00:53:25] Katharine Beals: Yeah, and you know, another interesting mantra that you hear all the time in the pro-facilitated communication world, and perhaps also in the education world I don't know if the term sounds familiar, but it's presumed competence. So this is the idea that the starting point should be to presume that someone has competence.


Well, I have taken some hard math classes. I am not a mathematician, but I have taken some hard math classes. And there are some professors I had where I honestly wish they had presumed incompetence. At least be diagnostic about it, like slow it down. We don't know this yet, we need examples, we need more homework, we need more trying out on our own.


And there's a little bit too much of assuming that, well, you know, a little hand waving and some fast proofs and we're all going to get it. So I, as a student would have preferred a little bit more of that in some of the classes I took.


 I just think it's a really bad pedagogical idea to just assume that students already know stuff. You need to find out first and act accordingly.


[00:54:29] Anna Stokke: We've talked quite a bit about some of the issues with reform math and the best type of instruction. So just to sort of sum up, what does an autism-friendly classroom look like?


[00:54:43] Katharine Beals: It partly depends on whether you're talking about an autistic support or a general ed classroom. And of course, there, there are constraints on just how much you can adjust a general ed classroom. But some very basic things are in terms of the distractions, you know, minimize the clutter, minimize the noise if possible and then in terms of the instructional mode and the great thing is these are things that will benefit everybody, right? So structure, focus on the direct instruction and the precision teaching sorts of elements that are good for everybody.


Try to factor out the language and the social from the stuff that doesn't require inherently the language and the social, like math. Allow these kids to excel at the stuff that they can excel in and feel good about because so much of school is going to be challenging for them. Let those on the spectrum who are able and motivated to get ahead in math. And just in general, find ways to create structure, spell things out, minimize the group activities, and, to the extent possible, get the language and the social components addressed separately and instead of having them be barriers to the learning process.


[00:56:03] Anna Stokke: Okay. That's a fantastic summary. So are there math programs, or I think in the US, you often refer to this as math curriculum, that is well-suited to students with autism that you can tell us about or recommend, maybe for parents or teachers who are looking for good math programs?


[00:56:25] Katharine Beals: The programs that I used with my son and my kids in general are Singapore Math, number one. I guess we need to make sure now that it's the older version of it because my understanding is that the kind of Americanized standards version is not what it is. You certainly don't want the version where the bar graph bar diagrams are drawn for you and you're just filling things in.


So the great thing about Singapore Math is it's got this approach called bar modeling that makes things visual. That is a very powerful tool that also eliminates some of the language aspects of the problems. They do have a lot of word problems, but the words are minimal. The number of, you know, the problems go on for maybe one or two lines of text as opposed to like a whole paragraph.


So in those respects, and it's systematic. Very, very systematic and very much builds skill by skill and very clever curriculum. So I absolutely recommend that, but make sure to get the older versions of it. And anything published before 1950 is probably a good idea.


And, you know, geometry proofs, which are so, scarce now, like it doesn't seem like people are doing those, which is quite ironic given that they're very conceptual, those are great and if you can get like a Dolciani geometry book from, or is it, I forget now who, anyway we have a, we have a geometry book in our house from the 1960s and we have a bunch of books from the 1920s that also have been great for math instruction.


And the great thing about those is they're in the public domain to some extent so, you know, they're not going to be expensive.


[00:58:00] Anna Stokke: You're talking, I think, about the Singapore Primary Math Series. That's the series. We use that actually, parts of it, in the after-school program that I run. And so I will put a link to that on the website. resource page for this episode. As for geometry proofs, that was my favorite part of Grade 10 math.


I loved that. And then they took them out of the curriculum. They don't do geometry proofs in Manitoba anymore. So it's the same in the US?


[00:58:31] Katharine Beals: That seems to be, yeah, very minimal. You know, not, not those multi-step ones where you really had to think about the, you know, the shapes and their relationship to each other and sort of step by step, you know, first you figure out how long this line is or what the angle is, and then you have a whole bunch of steps to finally figure out what this angle is.


That's gone. And I have no idea why, actually. That's, what is the justification for that, given the emphasis on conceptual understanding and higher-level thinking? What is the explanation for that?


[00:59:01] Anna Stokke: Good point. And I also have a copy of Dolciani so I could probably list that on the resource page too.


[00:59:09] Katharine Beals: It's such a great book, yeah.


[00:59:11] Anna Stokke: Final question. So, what thoughts or advice would you like to leave listeners with related to our conversation today?


[00:59:22] Katharine Beals: I think, so if you're a teacher, I think that what you want to do is to neither presume competence nor incompetence. Like, I think, you know, to really refine what I said earlier, be diagnostic and keep in mind that an autistic student, so the grain of truth in the kind of presumed competence idea is that an individual with autism may look less capable than they actually are because we do tend to judge people to some extent by their verbal skills and by how much they seem to be tuning in and reacting.


And so you could have a child who actually is, say, very, very gifted in math, but you might not look at, you might look at the child and just think, “Oh, they're, they're not that sharp in general. So maybe they're not good at math.” So I think the important thing is to realize that these kids defy a lot of typical expectations and you really need to take a close granular look to see where they have capacities and to keep in mind that with autism you can have a lot of specific strengths that are very productive to work on in addition to weaknesses.


[01:00:36] Anna Stokke: That's a great way to end on that nice high note. So thank you so much for coming and talking to me today. I learned so much and you're doing great work. And I'll put a link on the resource page to your books and people might want to check that out. I highly recommend it. So, thank you very much.


[01:00:55] Katharine Beals: Thank you so much, Anna. It was a pleasure to be on and you asked great, great questions and, it was just a pleasure to cover so much ground in so little time. That was great.

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[01:01:04] Anna Stokke: As always, we've included a resource page for this episode that has links to articles and books mentioned in the episode.


If you enjoy this podcast, please consider showing your support by leaving a five-star review on Spotify or Apple Podcasts. Chalk and Talk is produced by me, Anna Stokke, transcript and resource page by Jazmin Boisclair, social media images by Nicole Maylem Gutierrez.


Subscribe on your favourite podcast app to get new episodes delivered as they become available. You can follow me on X for notifications or check out my website,, for more information. This podcast received funding through a University of Winnipeg Knowledge Mobilization and Community Impact grant funded through the Anthony Swaity Knowledge Impact Fund.

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