Memory, Learning and Theory Pedagogy with Leigh VanHandel

Notes from the Staff

Dr. Leigh VanHandel joins us to talk about the science of memory and learning, and how it can help us better structure our teaching. We also chat about her new book, the Routledge Companion to Music Theory Pedagogy, which recently received an Outstanding Multi-Authored Collection award from the Society for Music Theory, and about the Workshops in Music Theory Pedagogy series she coordinates.

Links:

Leigh VanHandel's faculty page at the University of British Columbia

The Routledge Companion to Music Theory Pedagogy:

Workshops in Music Theory Pedagogy

Ask Dr. Van

uTheory

Chapters:

00:00:20 Introductions

00:01:45 Editing the Routledge Companion to Music Theory Pedagogy

00:07:56 How math pedagogy research can inform our teaching of music theory

00:12:34 Long term, short term and working memory.

00:15:24 The relationship of working memory and visuo-spatial skills

00:19:00 How learning happens, neurologically. (Schema forming)

00:21:21 The implications of schemas for how we teach

00:24:13 The curse of expertise, and working memory

00:32:30 The value of memorization vs. deriving concepts

00:34:30 Using schema to teach for fluency

00:44:58 Strategies for identifying and helping students with working memory limitations

00:50:20 Reducing cognitive load to help students focus on what they're learning

00:55:31 Workshops in Music Theory Pedagogy series

00:59:50 What else are you up to, now that the book is out?

1:00:00 Where can we follow you?

1:03:18 Wrap-up

Transcript:

[music]

0:00:21.2 David Newman: Welcome to Notes from the Staff, a podcast from the creators of uTheory, where we dive into conversations about music theory, ear training and music technology with members of the uTheory staff and thought leaders from the world of music education.

0:00:34.5 Gregory Ristow: Hi, I'm Greg Ristow, founder of uTheory and associate professor of conducting at the Oberlin Conservatory.

0:00:40.3 DN: And I'm David Newman. I teach Voice and Music Theory at James Madison University and I write code and create content for uTheory.

0:00:48.7 GR: Thank you, listeners, for your comments and episode suggestions. We love to read them. Send them our way by email at [e-mail] and remember to like us and subscribe wherever you get your podcasts.

0:01:00.1 DN: Our topic for today is music theory and working memory and joining us to talk about this as well as her new book, The Routledge Companion to Music Theory Pedagogy, is Dr. Leigh VanHandel. Dr. VanHandel is associate professor and chair of the Division of Music Theory at the University of British Columbia. Her primary research areas are music theory pedagogy, music cognition, and the relationship between music and language. Her research is published in Music Perception, the Journal of New Music Research and the Journal of Music Theory Pedagogy. She is co-director with Gary Karpinski of the Workshops in Music Theory Pedagogy program, a week-long summer intensive where teachers can learn from six experts in the teaching of music theory. Leigh, it's an honor to have you join us.

0:01:46.2 Leigh VanHandel: It's an honor to be here. Thank you so much.

0:01:48.6 DN: And especially right after you won this award at SMT for, what is the... The award was for?

0:01:54.7 LV: Outstanding Multi-Author Collection.

0:02:00.5 DN: Fantastic.

0:02:00.6 LV: Yeah. So The Routledge Companion to Music Theory Pedagogy had an insane number, 68 authors and contributors. And so I think that qualifies as multi-author. [laughter]

0:02:17.6 GR: It's a delightful book, I have to say. We had a chance to speak with Melissa Hoag a couple of weeks ago and Stefanie Dickinson just about a week ago. And I have been just really loving going through the articles in it. It's a really... I think so many pedagogy textbooks come from one author's perspective and I've just been delighted by the variety of perspectives offered. Could you maybe talk a little bit about the origins of the book?

0:02:50.7 LV: Yeah, sure. So I'd been approached by Routledge about putting together some essay collection and the Norton Music Theory Pedagogy book was in its final stages. We knew what the format was gonna be, we knew who the authors were gonna be. And I had that moment where I went, "Well, why do we need another one of those? What can I do that's gonna be different?" And it was literally a shower thought, you're in the shower, you're washing your hair and you go, "Well, wait a minute, what if, what if I did this crazy thing where instead of these long essays, we put together a bunch of lesson plans and made something that's practical and useful and immediately relevant to people?" And so I pitched that to Routledge and I don't think they knew what to make of that idea at first, but somehow I managed to convince them to go along with this crazy idea.

0:04:00.0 LV: And I sent an email out, some people I targeted specifically, I also sent emails to the SMT mailing list and things like that and just said, "Send me your best lesson plan. Send me the lesson plan that you look forward to teaching every year that works every time you do it." And people responded. And I wasn't sure what the response was gonna be. I thought maybe I'll get 40 and maybe I can choose 30 of them or something. I got over 220.

0:04:41.1 GR: Oh my gosh.

0:04:41.4 LV: Yeah. [laughter] And so I kept having to go back to Routledge and going, "Okay, so what are the limitations of the print again? What... How many... [laughter] How many pages am I allowed to have?" And there were just so many amazing, amazing lessons and it was so exciting to go through all of them and figure out what to include and it was just... The contributors were amazing, that they were willing to share their best lessons and let people see what they do and then allow people to replicate it also. So it was just... It was an amazingly big project, but it was also really, really rewarding and in a very nerdy way, a lot of fun.

0:05:33.5 GR: And also there are the wonderful companion materials that so many of these lessons have as well, can you talk a bit about that?

0:05:42.8 LV: Yeah. So I think that was another innovation for the book is that, authors, when they talk about assignments that they might give or scores or analyses or whatever, they provided the materials and I created a website where all of these materials are on the website and you can go and say, "Oh, here's the assignment that this person uses after making that... After doing that lesson." And so there's links to recordings and there's all of this material that people can use to make these lessons happen. And that was really the goal was I wanted to make it as easy as possible for someone to read the chapter and implement the lesson in the way that the person was recommending. And there's... I also wanted it to be accessible to specialists in music theory, but there's a lot of non-specialists who are teaching music theory.

0:06:45.3 LV: There's a lot of schools these days that are hiring the bassoon/theory or trumpet/aural skills instructor and having them have these resources and materials was really important for me and having them be able to use them easily and right away. So that was the goal behind the supplemental materials was just making everything available as much as possible for everyone.

0:07:14.5 GR: That's great. We've been saying on the past few episodes, we are just in love with this book, I have to tell you. I'm [laughter] decidedly a fan and really have just been thrilled to, I mean, as you say, to have this window into these really excellent teachers' best lesson plans. It's just delightful.

0:07:35.8 LV: Yeah. Yeah. It's... I'm incredibly proud of the volume and I'm also incredibly grateful that I was allowed to come up with this crazy idea and see it through to completion and even more grateful that it's being recognized because that's just... That means a lot to me.

0:07:56.3 DN: So I have loved talking with you and Betsy Marvin about your work in music cognition. And your chapter in this on music theory and working memory opens by talking about the connection between success in math and music and how math pedagogy research can inform our teaching of music theory. Can you talk about that a bit?

0:08:17.9 LV: Sure. So I wrote an article in, I guess, it was published in 2012 in the Journal of Music Theory Pedagogy about what music theory pedagogy can learn from mathematics pedagogy. And I have a really good friend who is a excellent mathematics teacher at the university level and he and I would have conversations about how people learn math and I... And he was also a musician. And so we started seeing relationships between these things. And so I just took it and ran with it. What happens is that the best predictor for how someone is going to do in a freshman level music theory class turns out not to be how good of a performer they are or how good of an ear they have, whether they have absolute pitch or anything like that, it's their score on the math portion of the SAT or ACT, depending on which exam they take.

0:09:21.9 GR: Wow.

0:09:23.0 DN: Wow.

0:09:25.5 LV: Yeah. And there's... I think there's a lot of work that needs to be done on why, but the article basically says, "Look, assuming that there is this relationship between these things, how can we borrow how we understand mathematics is best taught and adapt that into music theory pedagogy?" 'Cause mathematics pedagogy is a very, very well-funded field. Music theory pedagogy is not. So when we can steal research from anywhere, we should, I think. [chuckle] So I did a lot of reading on how people learn mathematics. And in order to make the relationship between fundamentals and math, you have to go back to first principles of mathematics, which is basic principles addition and subtraction and things that. And of course, the problem is most people learn those things when they're very young.

0:10:30.9 LV: And so the learning process, people are usually concerned that it's a little bit different. There's actually evidence that adult learners go through the exact same processes that children do just at a slightly faster rate. Not slightly, just at a faster rate. And so if you have someone who is still struggling with mathematics when they enter college, they go through the exact same processes learning basic math as a third grader does essentially. So then I thought, "Okay, if that's the case, then we can take these principles and apply them to our adult learners in freshman theory or so on, who are trying to learn these very complicated systems of music theory."

0:11:22.1 LV: And one of the challenges is that mathematics is a well-formed system. If you add four plus four, you're always gonna get the same thing. Music is what's called an ill-formed system, which I find hilarious [laughter] because sometimes in one context, the answer to something is this and sometimes in another context, the answer is this. And so it's actually even more complicated than learning mathematics in that way. So yeah, so that got me thinking about what are the different processes that we go through when we're learning to do basic mathematics? How can we apply that to basic music theory skills like spelling intervals or chords or scales? And all of that got me thinking about the cognition of teaching and learning and about what are the best, most efficient and effective ways of teaching this material to adult learners. And then that led into the working memory stuff and that led to the chapter in the Routledge Companion.

0:12:35.3 GR: That's great. And in that chapter, you talk about three kinds of memory. You talk about long-term, working and short-term memory. Can you tell us a bit about these?

0:12:45.7 LV: Sure. So long-term memory is essentially the facts, the declarative knowledge or the procedural knowledge that you have stored away in your head and it's material that's there and is available for retrieval and you don't have to walk around rehearsing that information all the time. It's there. You can... If you wanna make the filing cabinet analogy, you can go to the filing cabinet, pull out that information when you need it, and then put it away and you don't have to constantly be thinking about it. Short-term memory is our ability to hold a certain amount of information in our memory for a short period of time.

0:13:27.7 LV: So short-term memory is the thing that kicks in if you are trying to remember a phone number or if somebody tells you, "Okay, turn to page 221 and look at example 4.3," you're holding 221 and 4.3 in your head and you have that in your short-term memory. Working memory is when you are holding a short amount of material in your memory, but you're manipulating it. And so if I said to you, "Here's my phone number," and then you had to remember it long enough to run over and write it down, that would be short-term memory. If I said to you, "Here's my phone number, now repeat it to me backwards," that would be working memory because now you're having to manipulate that information in some way. Or if I said, "Add one to every number of my phone number," or something like that, that would be having to manipulate that information.

0:14:25.3 GR: And how consistent is, do we... Is there a base level of working memory that everyone has, or do we vary in our ability to use our working memory?

0:14:39.0 LV: The answer to both those questions is yes, [laughter] which seems contradictory. But in the 1950s, there was a psychologist named George Miller and he did a famous memory study in which he determined that the short-term memory limits for most people are, as he described it, five plus or minus two items. So there's a range in which most people fall, but some people have more abilities and some people have fewer abilities. And so yes, the answer to both questions is yes. There's a limit, but there's also variation within that.

0:15:26.1 GR: Yeah. And then you talk in your article a bit about the relationship between working memory and visual spatial skills or visual spatial skills. First off all, what are visual spatial skills and what is that relationship?

[laughter]

0:15:41.9 LV: So yeah, visual spatial skills are the ones that are hardest to describe. It's essentially like direction finding, the ability to rotate a figure. If you've ever taken an online test or something that where it says, "Here's an F and here's another F," but it's rotated and you have to say which direction it's been rotated or something like that. It's essentially the ability to manipulate spatial information. And your podcast listeners can't see it, but I'm rotating my hand around in circles in very bizarre ways right now because I talk with my hands. So it's that ability to manipulate spatial information, keeping one version of something in your head and then manipulating the other one to see how it changes. My theory, and I have not yet had a chance to test this and I really, really, really want to, my theory is that visual spatial memory comes into play in music theory fundamentals, especially when we're talking about things like interval inversion and things that or chord inversions, because students have to be able to spatially manipulate chord members that are out of order basically.

0:17:05.4 LV: If they're in open position or if they're inversion, they have to be able to go, "Okay, I have a G on the bottom and then I have an E, and then I have a C. Wait a minute, how do I rotate those around in my head to get them in the right order?" And I've encountered a number of students in my career who struggled with that in a way that was more than I would have expected them to. And so I have this crackpot theory that I really wanna test at some point, which is that if you have a visual spatial working memory deficit or memory deficit, then things like chord rotations or open position or things like that might be a little bit more challenging.

0:18:00.6 DN: There's a clear example of that if you're playing on the piano because it does, it feels very much... It looks like a rotation, how you position your right hand, for example.

0:18:12.6 LV: Yeah, yeah. And that's actually a really good point because one of the ways you can combat that if it's happening is through some other sensory input. Sometimes if somebody has trouble doing that mentally, the kinesthetic reinforcement of thinking about a piano keyboard, if it's something they're familiar with, if they're struggling with the piano keyboard as well, this just adds another layer to the complication. But if it is something that they're familiar with, then that can be a kinesthetic reinforcement of the rotation or representation of the rotation and can help them figure that out. But if they're having that trouble, yeah.

0:18:56.0 DN: Alright. So in the context of these kinds of memory, how is something learned? How can we solve this problem?

0:19:08.3 LV: That's a great question. So when we are learning material, the first thing it does is it goes into our working memory and our short-term memory. If we're manipulating it, it's working memory. If we're processing it for knowledge, it's short-term memory. But as it's becoming knowledge and as we're trying to get it into our long-term memory, we're creating what's called a schema. And a schema is basically an interconnected network of basically all of the things that we know. And this is a gross simplification, but there's this network where when a new piece of information comes in, our brain goes, oh, wait, that's connected to this and to this and to this. So I'm going to put that there, and I'm going to build these connections out to this other material so that this piece of information partially recalls these other pieces of information when I pull it up. So you can have isolated bits of knowledge. The example I always give is, you can tell someone who's a non-musician over and over that the key of A major has three sharps. And you can repeat that enough to them that they'll be able to repeat that piece of information back to you.

0:20:30.3 LV: And that is now a piece of knowledge that they have. It may even be living in their long-term memory if you've said it to them often enough. But they have no context for what that information means or what they can do with it. So the schema is the network that helps you figure out, oh, okay, the key of A major has three sharps. I know what those three sharps are because I know this information. I know what that means in terms of scale because I know this information. And I know what that means in terms of intervals and chords because I know this information. And all of those things are connected. And that's the goal that we want to get people to when we're teaching them fundamentals is we want them to have this schema where every bit of information that we're giving them reinforces every other bit of information.

0:21:27.9 DN: That is cool.

0:21:29.1 GR: I think, just right away about the implications for how we teach as well, just how important that means it must be to think about when we're introducing a new concept, proactively tying it into things that we've already covered and making the back connections and setting up the forward connections as well.

0:21:51.9 LV: Absolutely. Absolutely. That's the critical thing. Some students are able to make those connections on their own. And they're the ones whose schemas are pretty robust. If someone's schema is shaky to begin with, they need that explicit connection to be made for them. And even if they don't need it, it helps. It helps them to go, oh, this is how this connects to the material I already know. It helps reinforce that material. And like you said, it helps lead forward to whatever other way we're going to expand that information in the future.

0:22:28.8 DN: And this is a little off topic, but it makes me think of how does one deal with remediation? But a good description of what you're trying to do is trying to help find where the holes in someone's mental map are and maybe help patch them.

0:22:47.1 LV: Yeah, exactly. Exactly. I've been teaching fundamentals for a really long time because I absolutely love it. But one of the things that happens is if a student is struggling with some material, they're usually not struggling with that material. They're struggling with one of the steps on the way to it. And so you have to investigate their schema a little bit and figure out where are they having that struggle? Where are they failing to make that connection between something and then help them make that connection. And I can't count the number of times I've spent time with a student doing that. And when you finally find that fundamental misunderstanding or that thing that never quite clicked for them and you work through that with them and then they go, oh, wait. And then all of a sudden, you see the metaphorical light bulb go on over their head and they go, wait, now I get it. And this means this and this means this. And they get really excited because suddenly all of these things fall into place. And quite honestly, those are the moments that I love. I love watching that light bulb go on and I love watching them see that connection and see this connected world of fundamentals opening up in front of them and them seeing how to navigate through that path. And those are the wonderful, wonderful moments.

0:24:15.0 GR: That's great. That's so great. I think for me, sometimes one of the challenges of that and probably for a lot of teachers is, and you talk about this in your article, is the curse of expertise. This idea that especially when we're teaching basic concepts in our field, we know those so well that it doesn't tax our working memory at all. Could you maybe give an example of this and help us with how we can work through that curse of expertise as teachers?

0:24:47.2 LV: Sure. Sure. So yeah, so the curse of expertise is basically when you've gotten good enough at something that you don't remember what it's like to not be good at it. And as a result, what that means is that you forget how many steps a non-expert has to go through to get to that point. So my favorite example of this is, because we are all experts, we do not have to tax our working memory at all if we're trying to remember how to spell common chords, for example. If somebody says to us, what's a D major chord? We go DF Sharp A. There's no... Yeah, exactly. And we don't have to use any cognitive load on that. There's no working memory burden. It just pops out, right? And it pops out immediately. What we forget is that for someone for whom this is new material, there's a tremendous number of steps that they have to go through because the number of steps that are involved in figuring that out, if we don't already know it, are really quite big. So if you go, okay, what's a D major chord? Then somebody would have to go, okay, so wait a minute, which notes are in, if a D is the root, so it would be A, B, C, D, E, F, G, A.

0:26:09.3 LV: Okay, D, F, and A. So I'm going to have some kind of a D, some kind of an F, some kind of an A. Now they want major, so major, let's see, where is that on the circle of fifths? Okay, that's two sharps. What are the order of sharps? So I'm going to have F sharp and C sharp. And wait a minute, what were the notes of my chord again? I had a D and an F and an A, and I had F sharp and C sharp. Oh, F, F sharp, F sharp. Aha, it's DF Sharp A, right? And I'm exaggerating a little bit for comic purposes or demonstrative purposes, but those are the steps. And if any one of those things is not really that solid, if they had to spend more time thinking about the key signature and the order of the sharps and whatever, by the time they came back to what were my notes that I had, they might have forgotten which the notes were, if they don't have those things set together as a chunk. And so it's really a quite working memory intensive task that we're asking someone to do if it's not already in your schema. Whereas we just go, DF sharp A, no problem. So one of the horrible things that I've asked people to do in presentations on this is I've said, okay, we are all experts at the A, B, C, D, E, F, G system, so let's take that away. You're not allowed to use A, B, C, D, E, F, G. We're now going to use H, I, J, K, L, M, N, right?

0:27:52.9 GR: Yeah. As I see you're counting them out on my fingers, yeah.

0:27:55.1 LV: Exactly, exactly. And think about your fundamental students who are doing the same thing on their fingers, A, B, C, D, E, F, G, right? They're experiencing the same thing.

0:28:06.3 GR: Or even worse, they're doing C, D, E, F, G, A, B and struggling with the wraparound after G.

0:28:11.6 LV: Yeah, exactly, exactly. So then in this exercise that I do, I say, okay, we've got H, I, J, K, L, M, N, those are our new note names. Let's keep the conceit of root, third, and fifth of a chord. We'll alternate to spell chords and so on and so forth. Wrap around when you reach the end and don't write this down. Do it in your head. And so then I'll give them some examples and I'll say, okay, in that system, what if I is the root? How do you spell the chord?

0:28:45.7 GR: I, K, M.

0:28:50.0 LV: Yes.

0:28:50.7 DN: I, K, M. But yeah.

0:28:53.9 LV: But you have to count it out on your fingers.

0:28:56.1 GR: Yeah, exactly. Yeah, people can't see that, but yes, I'm sitting here and yes, absolutely counting out on my fingers.

[laughter]

0:29:01.1 LV: Yeah. And then if H is the third.

0:29:09.0 GR: M, H, J.

0:29:12.1 LV: Yes. Why was that one harder?

0:29:14.0 GR: Because I had to wrap around. I had to work backwards from H, which is the start of the alphabet, and I couldn't wrap backwards because I couldn't remember what the end of the alphabet was, so I had to go all the way forwards to the end of the alphabet and then count backwards.

0:29:32.6 LV: Exactly. Exactly. So yeah, so that's a really challenging exercise. And then I make it harder. I add different things in where you have to... So you have to spell the chord and then you have to look at what I call a target word and figure out how many letters the target word has in common with the chord that you just spelled and manipulate the chord in some way, which is essentially the process of figuring out your letter names, thinking about the circle of fifths, thinking about what the order of sharps and flats is, and then applying that to what you're doing. It's really a humbling experience for a lot of experts. Some people don't find it that difficult, but they're still taking 10 seconds per chord to do it, whereas if I say, what's a D major chord, you go DF sharp A, and it takes you one second.

0:30:35.2 LV: And so where this creeps in is that as expert musicians with our cursive expertise, we forget the number of steps that someone has to go through in order to solve these problems that we're giving them. And so we go, oh, okay, here's 10 intervals. You can do this in a minute, forgetting that we can do that in a minute because it's six seconds per interval. But they're having to go, okay, so wait, they want a major sixth above E. Okay, so six, E, F, G, A, B, C. Okay, so it's some kind of a C. Now, let's see, major six. Oh, god, what's the key signature for E? And all of a sudden, now we're already at 20 seconds for this one interval, whereas we look at that and go, C sharp, done, next. Right? So one of the things that we have to think about when we're designing assessments or when we're trying to assess fluency is, we have a different level of expertise than our students do. We are able to come up with this information much faster because it's in our schema. That is the goal for the students. We do want them to be able to have that material, that available.

0:31:56.6 LV: But if they're just learning it, it's going to take them time to get there. And so we have to allow for, for example, more time than we think on timed tests. We can't go by how fast we can do it, basically. And then we also have to remember that it is really going to help the students if we make those explicit connections that help them develop that schema so that they can then develop that expert recall that we want them to have.

0:32:29.4 GR: As you're talking about this, I'm thinking a lot about this idea of a schema and the interconnections between pieces of information within that schema. I wonder, does this tell us anything about the value of memorization versus saying understanding processes for deriving ideas?

0:32:53.6 LV: Yeah, it does. So if you are memorizing information, yes, you're getting it into your head and you're able to pull it back out. But it's usually not connected to other information as well as it should be. A good example of this is think about someone who's memorized a piano sonata or something like that, any piece of music. What happens if they make a mistake and have to stop? They usually have to go back to the beginning of some section because that's where they've created a mental, here's where this starts and I have to go through. It's harder to pick up in the middle. And that is if they memorized it by rote, right? I do this thing after I do this thing after I do this thing. And then if you stop in the middle and go, okay, what comes next? They go, I have to go back to the beginning and work through all of this. Whereas if you have the information memorized, but you have it connected to other information, then you can go, okay, this is where I am. This is what comes next and start back up from where you left off. And the same thing happens in spelling chords or intervals or whatever. If you get a problem and suddenly you get distracted and then you go, "Wait, where was I?" Oh, right, I remember this. And then pick back up and go where you left off from.

0:34:31.6 GR: And in a topic like music fundamentals where we do want students to eventually gain that fluency and ease and speed that really only comes at the point that a lot of these things are, as you said, immediate knowledge accessible in long-term memory. Does that have implications then for how we teach to get them to that speed?

0:34:58.1 LV: Very much so. You're about to open up a rant on how we teach intervals. Is that okay?

0:35:03.9 DN: Please. Yes. Yep.

[laughter]

0:35:09.2 LV: Okay. There's a number of different ways that people think about teaching intervals and one of the ways that people teach intervals is by teaching students to count whole steps and half steps. The benefit of teaching whole steps and half steps is that it's a algorithmic process. The bad thing about it is that it is not connected to any other piece of information. If you get a student who is going, okay, every time I see a major third, I'm going to count four half steps, then they're not necessarily learning how these things connect to one another or how these are connected to the bigger schema. So I cringe internally a little bit when I see people teaching intervals by whole steps and half steps just because it's memorization of an algorithm, not of, not adding it to the system. And so there's a number of different ways that you can take students who are relying on doing that and move them towards more sophisticated understandings of how these things relate. Obviously, one way of thinking about it is if you're asked to spell a major third above F, you can think of F as the tonic of the scale and then go, okay, what's my key signature? How does this relate? And so on and so forth.

0:36:52.4 LV: And that works, but the problem with that method is what happens when the bottom note is a D double sharp and you don't have that as a tonic and so on and so forth. Then when that happens, what expert musicians do is they go, oh, okay, let's see, you're asking me for... The interval I always give when I give this example is a minor sixth above D double sharp. And that is because pretty much nobody has that interval stored in their memory anywhere. And so you actually have to think about it. What happens is if we meta-cognate about how do I solve that problem, expert musicians do what's called decomposition. They go, all right, D double sharp. No, I am not thinking about D double sharp. Mentally, I'm covering up that double sharp and I'm thinking about D. Now, let me think of a minor sixth above D. If we have it in our memory, we go, okay, minor sixth above D is B flat. Otherwise, we go, now I can think of the scale of D and now I can think of D minor and figure it out that way. And I go, "Okay, now I know that this is B flat." But my interval was above D double sharp. Now I re-manipulate that and I go, I'm going to raise my D by two half steps. I'm going to raise my B by two half steps. And now my answer is D double sharp to B sharp, which is a ridiculous interval and nobody should ever encounter that in their lives, but it's a good example how we can move people through a strategy.

0:38:34.4 LV: If somebody is spelling the interval by counting half steps and whole steps, they have to remember that there are eight half steps in a minor six and then they have to count up from D double sharp. And if they're just counting, there's a really good chance that they're going to land on C and go, oh, my answer is a C and that's not a minor sixth then other problems come about. If they're just relying on that scale method, then they're going to run into trouble because they're going to have to think about what the key of D double sharp is and nobody should ever have to do that. The more sophisticated steps are these decomposition steps, which is where you take a piece of information you already know and manipulate it into the piece of information that you need to find out mixed with this idea of immediate recall.

0:39:32.3 LV: We couldn't immediately recall a minor six above D double sharp, but we probably could because we are expert musicians immediately recall what it was above D. We did the immediate recall for that and then the decomposition to manipulate that information. What we want to do is when we're teaching students to spell intervals, we want to move them as close as we can to that immediate recall. But we also want them to have the other strategies in place for when the immediate recall doesn't work. And I talk about this some in my 2012 article. What we want to do is we actually want to show students that these strategies work because if they're stuck on using half step and whole step method to count intervals, it's because they don't trust their schema to give them the right answer otherwise. They're going back to the version of this process that they think is the most reliable for them. One of the things that I do in the classroom when I'm doing this is I very, very deliberately talk about process for every single question that I ask them. When I was in the theory classroom, I had teachers who would point at you and go, "What's a major third above A flat?"

0:41:09.7 LV: And you had to answer immediately and then point at the next person and point at the next person and point at the next person and bark out intervals. You had to answer as quickly as you could. And A, it was terrifying and intimidating, but B, if you got the wrong answer when he was barking at someone else, if you even were practicing these intervals along or if you were just sitting there in terror waiting for your turn, you didn't know why you got the wrong answer. One of the things that I do is I will always say, okay, so what is a minor third above F? I'll let people think about it for a second and then I'll call on someone. If someone goes, oh, it's A flat, how did you get that answer? And if they say, I just knew it. I'll say, okay, what if you didn't just know it? It's great that you knew that, but what if you didn't just know it? How could you get that answer? And then make them go through the steps of saying, well, I could have thought of the F minor scale and realized that the F minor scale has four flats and that A flat was one of them, so the third above F is going to be A flat.

0:42:25.8 LV: Okay, great. What's another way? And then somebody will go, well, I thought of the F major scale and then lowered the third by a half step. Okay, great. I'll do that so that the students who are struggling with these processes see how that works. And more importantly, they see that students are being successful with those more sophisticated strategies because ultimately what it is is they don't trust the strategy yet because it's not quite... Their schema isn't quite built up enough so that it's working for them. You have to work on the schema, but you also have to work on that confidence. And so that's where making that schema explicit, making those connections explicit is super, super helpful. Ironically, the other type of student that this helps, it helps the student whose schema is not fully formed yet. It also helps the overachieving perfectionist student who has the immediate recall, but has to double and triple check to make sure that their answer is correct. And so they end up spending way too long on every answer. If you get interval quizzes back where two-thirds of the questions are answered but they're all correct, you've got someone who is double and triple checking their answers to make sure that they're correct, which means that they're not getting through as many as they should 'cause they don't trust their process.

0:44:03.9 LV: Having those students see, okay, I'm using this process. This other person used this process. They got it right. I should trust my process more. I should trust my schema more. Also helps those perfectionist students who are afraid of making a mistake.

0:44:23.0 DN: I love this reminder that perhaps we need to be mindful of what our goals are and that the goal is not necessarily to know the piece of information, but to build the schema.

0:44:39.7 LV: Exactly. Exactly. That is the piece of... Building that schema is the thing that's going to help students moving forward. Having the isolated bit of information that a minor third above F is A flat will be useful in some circumstances, but does not help them with anything else really going forward.

0:44:58.3 GR: And related to that, you talk in your article on working memory a lot about ways that we can use our knowledge of working memory to improve our teaching. I wonder if you could talk about some of the strategies you identified, specifically identifying and intervening with working memory issues and also reducing cognitive load.

0:45:22.6 LV: Sure. When I present on this, the question I always get is, okay, how do we figure out who's having those working memory problems? The easiest way to tell if someone is having a working memory problem is, I think we've all had students who brain dump a whole bunch of information on the top of a task store in assignments. They'll write out the note names and they'll draw the piano keyboard and they'll draw the circle of fifths and they'll do all this stuff on the test. And the reason they're doing that is because that is reducing the burden on their working memory. They've now offloaded this information onto the page so that they have something to reference and they don't have to do the mental calculation each time. Those kind of things are crutches, basically, and they will help the students at the beginning and then they will hinder them as they move forward because they are not developing quickly enough the schema that they need and they're relying on this offloading of information. And they're doing it because they're having trouble developing that schema. This actually relates to both working memory and schema and cognitive load because essentially, they're trying to lighten the load on their cognitive burden in order to calculate these things.

0:46:50.5 LV: That's one way of identifying them. Obviously, another way is if a student is struggling with material then they probably have some weak link in their schema somewhere and you have to spend a little bit of time with them to drill down into that. But there's other cues as well other than performance on assessments. So if students are exhibiting trouble in processing information simultaneously or keeping information in their heads or forgetting what the next step is in a complicated process, for example, if they're like, okay, wait, wait, wait, what do I do after I do this? It has to be a constant thing. But working memory deficits are also implicated in things like ADHD or other attention deficit disorders. It's not the cause of it, but it's implicated in it. And so they might be easily distracted, especially if an activity is challenging, they might try to avoid completing the activity just because it's become hard for them and they don't want to acknowledge that it's hard for them. So they go, oh, look, a squirrel and they get distracted by something. So students who have ADHD or other neurodivergences like that, they tend to exhibit behavioral problems.

0:48:38.0 LV: Students with low working memory exhibit some of the same symptoms, but they typically don't exhibit any of those behavioral problems. So if there's no other issues, then working memory might be implicated in something like that. So the thing is there's no real way that we can train our working memory. So if you listen to National Public Radio for any period of time, you'll hear ads for Lumosity or something like that, train your brain kind of things. And studies that they fund talk about how this helps you with your working memory or with brain processing and so on and so forth. Independent studies find that that's really not the case. The tasks that something like Lumosity are asking you to do, you can get really, really good at those tasks, which are things like swipe on the direction of the center bird or things, there's these different exercises that Lumosity gives you. You can get really, really good at swiping in the direction that the center bird in a group of five birds is facing, but that's not going to help you spell chords. [laughter] So there's no transfer from the type of task that something like that is asking you to do into music theory fundamentals.

0:50:11.3 LV: You have to practice music theory fundamentals, and you have to develop that schema of music theory fundamentals in order to get better at it. And you mentioned cognitive load, and that's a really, really important thing for instructors to think about because if a student has a working memory deficit and you are standing in front of them going, okay, so everyone, let's turn to page 88. Let's look at example 12. I want you to identify passing tones, neighbor tones, appoggiaturas. If you're listing a whole bunch of things, by the time you're done with that list, they've forgotten what page you asked them to turn to because they've been trying to keep all of this material in their head as you've been going, and that's when you get the what page, what example, what are we doing? And so this is one of those universal design for learning principles that it's better for everyone not just people with working memory deficits. If you give instructions very, very clearly, if you provide time for processing, if you write it on the board so that they can reference it when they have questions, it's the cognitive load of... If the cognitive load of the task you're asking someone to do is very high and you're dumping more information on them as they're trying to do that task, they're going to fail at the task.

0:51:48.7 LV: There's going to be some an interrupt, whether they've forgotten the instructions, whether they've forgotten the task or how to do the task. So there's a lot of principles in learning about the best way to reduce cognitive load on students so that they can put most of their cognitive load on the task that you're asking them to do. Clear instructions, instructions that are in the same place as the question. So for example, don't design an exam where the instructions for a question are on one page and the question is on the next page because then they're flipping back and forth and they have this split attention issue where they're not able to read the instructions and immediately look at the thing that they're being asked to do. The other thing, I've observed people in the classroom where they will play music during some kind of a test. Music unrelated to the test, they will play music during the test. And their feeling is, well, students to listen to music when they study, so I should do this when they... But that's a huge cognitive load drain because students with working memory issues or with attention issues are going to be distracted by this thing that you're doing.

0:53:17.6 LV: And so that's always something I did, don't play extraneous music while students are concentrating on something. And one of the things that I figured out also was, if students are doing a test and I have a musical example that I wanna play for them, for example, it's really intrusive of me to go, okay, everyone, turn to example three. I'm going to play the example now and then play the example because they were in the middle of a task. They were in the middle of something and they had their thought processes going and they had all of that stuff where they were trying to remember, okay, I'm doing this and I'm doing this and I'm doing this. And suddenly I barge in and go, okay, pay attention to this now. So what I'll do is I'll tell them I'm going to play this music example at 10 after, at 15 after, at 20 after, and I will give you 30 seconds notice before each time I play it. And so when it gets to that point, I will very quietly say, okay, finish up whatever task you're on. I'm going to play this musical example in 30 seconds.

0:54:25.9 LV: That gives them time to make notes to themselves or finish that thing and then get that gone so that they can now concentrate on this new thing. And it's worked really, really well because one of the things I noticed when I was not doing that was that students would leave questions blank or half completed because they forgot that they were working on it. They looked at it and they went, oh, I've got an answer there that must be right and then moved on to the next question. And I don't see that as much anymore when I'm mindful of directing their attention in specific ways and carefully asking them to finish up what they're doing and now let's pay attention to this.

0:55:14.2 GR: Yeah, I'm learning so much just talking with you now.

[laughter]

0:55:15.0 GR: This is wonderful. I have the sense we could go on talking for hours, but of course, time is always...

0:55:24.7 LV: That's probably my fault. I'm sorry.

0:55:27.8 GR: It is such a gift to us. Really, it's just delightful. But for people who would like to learn more from you, there's certainly that opportunity. You and Gary Karpinski coordinate the Workshops in Music Theory Pedagogy series. Could you tell us a bit about that, about who that's for and if people want more information about that, where they can find it?

0:55:50.4 LV: Yeah, absolutely. So the Workshops in Music Theory Pedagogy have been a workshop series that's been hosted every three years. They've been hosted by Gary Karpinski at the University of Massachusetts at Amherst. Gary has retired and he's asked me to step in as director. So this year is his last year. We're co-directing this year and we're moving them to the University of British Columbia. And they are June 26th through 30th of 2023. The workshops consist of four faculty that are brought in who are expert music theory pedagogues and it's a week-long workshop where each faculty member talks about their strategies and things that they're specialists in. And then there's also small group workshops with each faculty member each day so you can choose who you want to go work with and get more information and feedback from each person. So this year we have six faculty. It's Gary Karpinski, me, Michael Callahan from Michigan State, Nancy Rogers from Florida State, Jena Root from Youngstown State, and Jenny Snodgrass from Lipscomb University. And so it's an amazing, amazing group of music theory pedagogy scholars who are going to have a ton of information that they can share with people.

0:57:29.3 LV: We're in the process of finalizing the registration like financial stuff, just getting the ability to have people make payments. But there is a website that you can go to which is just workshopsinmusictheorypedagogy.com and that will take you to the UBC website where the information is and that website will eventually include links for registration and housing and meals. And basically, you just live on campus for a week and do these workshops, these interactive workshops. And it's a wonderful type of nerd camp which is perfect for people who are... Like grad students who are studying to be music theorists, music theorists who just want to hear other people's perspectives. It's wonderful for faculty who maybe are non-specialists in theory who are being asked to teach music theory. Every single time it's offered, we get somebody who comes in and goes, I'm the flute instructor. I've just been told I'm teaching aural skills in the fall. What do I do? And it's the perfect...

0:58:44.0 GR: What about high school teachers who maybe are starting to teach AP theory or something?

0:58:51.1 LV: Absolutely. Absolutely. Yeah, that's actually a great population for it as well because if you're a music ed person you had theory classes but you probably haven't had them in two or three years and now you have students who want to do an AP class and you're terrified, come to us. Come to us.

0:59:11.8 GR: Great. And we will link to that site in the show notes as well.

0:59:16.0 LV: Excellent. Excellent. Yeah, so it's really exciting that it's being hosted in British Columbia now. Late June in Vancouver is an absolutely stunning time to be in Vancouver. And I know a lot of people are planning on taking a couple of extra days at the beginning or at the end to do some sightseeing around Vancouver's area and I'm super excited to have it in here and to be part of it now.

0:59:52.1 DN: Cool. [laughter] And aside from that, what else are you up to these days?

0:59:58.5 LV: Well, I'm still relatively new at UBC. I started in September of 2020 in the middle of the pandemic, so to me I feel that first online year didn't really count. I feel like I'm still figuring out how things are going here but I've managed to get a really good music cognition lab going and so I'm doing lots of music cognition research. My main interests there are meter, rhythm and tempo and so we've been running a whole bunch of experiments on perceived rhythmic complexity and rhythmic patterns and what makes people feel something is complex. And yeah, so that's probably the primary thing that I've been working on recently is that project.

1:00:54.8 DN: Cool.

1:00:54.9 GR: I just can't wait to hear what you have to say as well.

1:00:58.7 DN: I know we need to have you on again. [laughter]

1:01:00.7 GR: This has been just such a delight talking with you today. I wonder if listeners are interested in keeping up with what you're up to, where can they find you?

1:01:10.2 LV: So they can search for me on the University of British Columbia website. I have my own website. You'll eventually find it if you search for Leigh VanHandel Music Theory. It'll probably take you right to it. On that website, you'll find information about my research lab. You'll find information about the Routledge Companion to Music Theory Pedagogy. There's also a blog that I have that I call Ask Dr. Van where I get a lot of emails from middle school students who have to do some a research project where they email a faculty member and ask a question. And so I started answering the questions and then putting them up on the website with the identifying information redacted of course. And some of the questions are really great, really sophisticated that take multiple iterations of questions to answer. And some of them are just wonderful questions why is Stairway to Heaven the best song ever?

[laughter]

1:02:19.3 LV: And I had to sit down and figure out how to answer that question. So that's really fun also looking at that and seeing that even younger students are really interested in music and what it means to them and how they think about music. Some of the questions are theory oriented. Some of them are cognition oriented. And it is really fascinating to see that kids are thinking about this and hopefully these are the students that we can get interested in it, keep them interested in it and they're going to be our fundamentals theory students and our music theory and cognition students in the future.

1:03:06.6 GR: Excellent.

1:03:07.3 LV: And people can also email me, [e-mail].

1:03:13.4 GR: Awesome.

1:03:14.2 LV: So if anyone has questions, they can email me.

1:03:16.8 GR: Great. Well, thank you again for joining us. Really just such a delight to learn from you. I feel I've come away from this with 100 ideas that I'm going to have to just sit down and process as I start to incorporate them into my teaching. So really thank you.

1:03:31.8 DN: Thanks so much, Leigh.

1:03:32.0 LV: Thank you for having me. This was a lot of fun.

1:03:38.5 DN: Notes from the staff is produced by utheory.com.

1:03:41.2 GR: uTheory is the most advanced online learning platform for music theory.

1:03:45.4 DN: With video lessons, individualized practice and proficiency testing, uTheory has helped more than 100,000 students around the world master the fundamentals of music theory, rhythm and ear training.

1:03:56.9 GR: Create your own free teacher account at utheory.com/teach.

[music]