How People Learn, Dr. Lindsey Richland

- Okay, so, consider the learner's thinking process not your own performance when planning a class.

Consider not just what you want those students to learn, but also how you want the students to engage with the subject matter.

So what sort of thinking do you actually want them to be doing, with this material, rather than thinking to yourself of a list of facts that you wanna make sure you cover, and you're expecting that, of course, they'll be thinking about their interconnections and sort of the bigger picture.

And also, consider the students' and your own cognitive load.

And I'll say a little bit more about what I mean by cognitive load, in a minute, and how you can do so.

This is something that probably many of you have done, but I think it's important to first think about your own metaphors for your learners.

The way that learning happens in your learners, so, you know, we often imagine that if we create the perfect lecture or the perfect set of materials, students will record it, you know, they'll remember everything that you've said, or maybe they'll file it away in some sort of nicely-categorized structure that you've sort of given them, the title and this PowerPoint, and then they'll remember all the pieces that go in that slot.

But this tends to not be a great metaphor and when we actually see people's learning, we see something much more dynamic, dynamic happening.

Even with computers, this has been sort of a big metaphor for the way we envision students.

We talk about them sort of processing inputs, you know, what are the inputs they're getting, what is their processing capacity, and I'll talk about, I'll use that metaphor a little bit today.

But again this is misleading because it really separates out your information that, you know, the input that you have full control of, and whatever you want the input to be, that actual thing will go into a computer, whatever you actually put in, and their processing capacity is sort of this limited set.

And we have a, humans are actually much more dynamic and so you have less control over what input is actually hitting their sensory motor system than you imagine.

And there's lots of evidence, biological evidence, suggesting that even your sensory neurons are actually really processing information in a very, very higher order, top down way, so they're doing lots of processing of that information before it even gets to their explicit conscious thinking.

So we can't really control what they're getting.

We need to be thinking about what they're doing with that information.

What is higher order thinking?

With this model, we often think about higher order thinking as using this sort of model developed by Bloom originally in 1956.

It was actually developed as a, an assessment tool, so to help people creating assessments so that they could designate different types of questions, that would evaluate things like creating being kind of the top of the line.

People really understand information if they can create something new with it, but a less good, but also important, would be evaluating, analyzing, down all the way applying, understanding, down to remembering.

And this has been a taxonomy that's taken on a life of its own.

When we talk about higher order thinking from an educational perspective, often we're talking about trying to move up in this triangle, to these richer, better ways of thinking.

But it's hard to know exactly what that means, right.

You're probably thinking about this and you maybe you've seen these.

These are really everywhere.

You're thinking about, "Well, do I do "evaluating in my class?

"Or do creating?

"What does that mean?

"What is the difference between applying "and evaluating and analyzing?

"And, well, don't they all, "really isn't understanding what I really care about?"

It's not necessarily a clear translation between this and what you would actually put into practice.

I'm gonna argue that one way of thinking about this that I think is really powerful is to really draw on this model of structure mapping, that we just heard from Deirdre, so thinking about higher order thinking as, in particular, a reasoning about relations, and sort of looking for relationships and privileging the relational information in the way that you

would present information.

Part of the rational for this is that expert-like thinking and innovation, particularly in STEM domains, this is where my research comes from, but I think this is true in lots of other ones, really relies on deep relational reasoning.

So when we're talking about experts, experts tend to see the deep, underlying relational structure in lots of different contexts and lots of different systems rather than lots of separable information.

What we're trying to do with developing one model here, thinking about relationships, is to develop coherence across teachers and disciplines about what counts as higher order thinking.

And I think that can be done if we're really focusing on relations.

Also, there's a huge body of research on relational reasoning, some of which we saw today, which we can then build on, in order to actually develop interventions that are clear and really grounded in theory, but also very relevant to actual practice.

We know already from laboratory work some successful strategies for supporting relational thinking, so one being reducing cognitive load, and I'll, sorry I keep hinting on that, and then the second piece is improving coherence and narrative links.

So this is really about making people aware that they're supposed to be doing relational thinking here and creating sort of narratives, making this a clear progression, as you're moving through multiple relational contexts.

Okay, so what do we mean by higher order thinking?

Well, too much introduction so far.

Focusing on relationships versus objects.

So this comes from a middle school example, that's where much of my research lies, but I think the relations are clear to undergraduate learning as well.

So what we really want to think about in, some instances not necessarily understanding and looking at a volcano, in particular, you know, this is a lab lots of students do.

But we don't want people to learn about volcanoes per se.

You really wanna learn much more about the whole system, right, and so this broader system of relationships.

And so we don't want to just know what is the definition of erosion, we wanna know, okay, how do these whole processes contribute to each other and build out that way.

In psychology, you might have things like the scientific method, right, developing science is about having two contexts that are almost the same except for some key variable, and you wanna manipulate, you know, one variable at a time, let's control our variable strategy, which is something that turns out to be hard to learn.

And so, really, what we're doing when we're doing science is really all about developing higher order relations and comparing contexts.

We also do lots of theory comparison, right.

So, in psychology, we have Piagetian stage theory versus core knowledge theory.

These are two theories about child development that when you have an undergraduate class on psychology very often you go through Piaget's stage theory and then you say, "Well, there are some "problems with that, so here are some other "theories that have been presented," and it becomes a sort of long list of theories, right.

And part of that is practical, so you only have one PowerPoint slide, so you kind of go through a few, but you end up doing this serial progression.

Now, as an expert, you know what's interesting about these is how they relate to each other, how one built from one to the other, and that's kind of what you're hoping that students are getting out of it, but they may be missing that part, unless you make it really explicit.

Higher order thinking in mathematics.

This is an example of exponential growth.

Sorry these are kind of dark and kind of hard to see, but, you have, these are screenshots from an actual classroom, so you have this example of, you can't even see that, but two to the X, so you have two to the one is two, you have two is four, two to the three is eight, and you wanna be able to see the underlying structure that this set of symbols is the same thing as

the quantity change represented by these blocks, as well as in this graphical representation.

You also wanna be able to see differences, so higher order thinking comparing differences.

You wanna know the difference between these two kinds of, these two slopes, right.

These are very different kinds of lines, but they may not immediately appear that way to a student.

They look perceptually quite similar.

So you say, "Well, my students are undergraduates.

"They've moved beyond those kinds of simple topics.

"They understand these broader concepts "of exponential growth and things."

But, actually, I'll tell you little bit about a study of community college students.

So they're community college students, maybe you have some differences, but I think, you know, these are students who have completed high school and through a mathematics curriculum, in particular, I'll tell you about math data.

These students were given a bunch of questions, like this, so they get this set of problems, and I'll give you a second.

Do a couple of these.

When asked to do this, 77% of these community college students calculated the answer to each one of these separately.

So they sat there and they had 10 times three, and then, like, 10 times 13, and they wrote out a whole different one.

And then 20 times 13, and I'm guessing that some of you, looked at the relationship between your first answer and then you thought about what you would, you know, the second one you can build on that.

And so you're probably oriented to seeing these kinds of problems as related, while these students were oriented towards seeing math as a set of procedures to be calculated.

When asked this problem, "Why do we put a zero here?"

most of these students could do this algorithm, though when asked about the zero, less than half of the students referred to place value at all.

And most gave really good mathematical response, and they said things like, "I really don't know.

"I really don't know why it's done that, "way like that, but it's the way I was taught to do it, "and I always just did it like that.

"I don't know the answer to that, though."

So most of them didn't have these deep concepts of things like place value, which feels very fundamental and very straightforward, and it's something that they're actually using.

When community college faculty were told about this, they said, "Whoa, that's really strange."

So the students also said lots of things, like, "Math is about memorization.

"I don't know why you do things in math, "it's just about things to be learned."

The community college, by contrast, said things like, "I went into math specifically because I didn't "have to memorize anything."

So yet they had this really different orientation towards the content, than their students were.

Very many of your students may have these kinds of orientations towards math, which is fundamental to understanding it, but also in other domains, that looks different than yours, so they're, again, taking these inputs that you're providing and seeing them as, maybe, things to be memorized, where you're seeing them as things to be reasoned through, right.

And we know that domain experts and novices vary on the dimension of relational reasoning very systematically.

We see that in history.

Sam Weinberg has done really neat work looking at proficient novices, so students who have just gone through a history class.

They know lots of facts about a period, but they engaged with primary documents from that period in a very different way than experts do from that period, so experts may not have the facts, but they do this deep relational thinking, trying to embed and think about how this primary document is embedded in the larger relational context of the period.

Mathematics, so there's a famous quote from a mathematician, Polya.

He's arguing that mathematicians are people who do analogies between analogies, you know, in math, so this is, it's really, it's not about this memorization.

It's about seeing these relations, using them broadly.

Physics, the same thing, in terms of identifying, you know, this is a classic study where they had people classify problems and so experts did it based on the underlying concept, the novices did it by what these problems look like.

So we know that this is sort of a fundamental piece, so this is very likely to impact the way that we construct our lessons.

I think it's interesting that I consulted, before this talk, and actually I happen to be teaching a summer class at my institution.

I asked some people who have been rated as highly expert teachers by their students, "What do you do?"

And the answer that I got almost every time was, "Well, I try to teach my passion.

"I try to really embed this with my passion."

And I think that part of what they're doing, what they mean when they're doing that, is teaching their way of thinking about this information, so teach this relational information, teach it as this exciting narrative that it is, and why these things are all, these pieces are all important.

So I would say, "Teach your way of thinking, "as well as the content."

'Cause you may be presenting the content and you're seeing it as this large, interrelated, interconnected set of relationships, where they may be not getting that.

Now, in terms of why are there maybe differences in the way you teach and the way that you think, when we asked people about their intuitions, in terms of how to teach science, we asked preservice teachers, undergraduates, and middle school students, about how they would prefer to learn.

"Would you prefer to learn from simultaneous, "seeing two representations at the same time "and having to think about similar," we didn't say having to see similar ideas or differences.

We just said, "Would you like to see "multiple things, "representations of systems at the same time "or would you like to see them serially?"

And we asked them, "If you were gonna teach "middle school students, or if you were a middle schooler, "if you were gonna teach 5th grade students, "how do you think they would benefit?"

Interestingly, at teaching themselves, everyone said, "I want them togeth."

Not everyone, 75% of them said, "I'd like to see them together."

They were wanting to see these and be able to, I think, they wanted to grapple with these relationships, but they always said that, not always, but significantly more often, said that they thought middle school students would learn best a different way.

So, in the simultaneous condition, most often.

This was, people in the simultaneous condition thinking that middle school students would learn better if presented serially, and when we asked them what the different benefits were, of these different strategies, serial presentation was deemed easier to interpret, you could avoid confusion more often.

Now it didn't let you do comparison and contrast, but if you wanted to do that, you could do simultaneous presentation.

What I think that this gives us some insight into, is if we have, if, as an instructor, if you have a very clear interest in producing comparison and contrast, you might decide to use simultaneous models, but if your aims are otherwise, you know, things like making class easier and avoiding confusion,

you might tend to do serial presentation.

However, in the larger scheme of things, maybe it's okay to have some confusion and maybe, you know, this conflict in interpretation is actually part of getting the richer, more relational understanding, so this more higher order thinking kind of a model.

So our intuition may be to move towards a serial presentation while if we're thinking maybe the design of a difficulty model will suggest that actually having to grapple with these, this confusion a little bit is okay.

Now, partly they're right.

Analogies are hard, right.

We just saw with the Donker radiation model.

I mean we don't just get analogies right away, we really need some support to do so.

And, why are they hard?

Well, there're a couple things.

One is knowledge.

So you need to have enough prerequisite knowledge to be able to represent and map these relations.

And I think this knowledge can happen at that same time, so as an instructor, if you provide enough support for really understanding these relations you're okay.

But they need to be, students need to be ready enough to grapple with them.

And there is some evidence that students who are too outperforming do benefit from a serial presentation versus a relational presentation, I think, if they don't get enough support.

But then the second piece is limited processing capacity, so back to a little bit of this computer metaphor, so this idea that we have a limited cognitive control system which is required in order to do relational structure mapping.

So in order to represent one system and another system and think about them as systems, and then think about how those systems are related and figure out what that higher order relationship would be, all of that takes working memory.

And so this is the ability to inhibit irrelevant things and bring into your set what are the relevant relational pieces of information, and then, you need to sort of actively organize them in your mind and draw these relations.

And so executive function is a well-researched model many of you are familiar with it, those of you not from psychology and education fields maybe not.

We seem to have these three parts to our executive function system.

So one is the inhibitory control piece, which is the ability to modulate attention and suppress your immediate impulsive responses to things.

The second piece is being able to manipulate and hold things active in this memory set.

And then the other piece is being able to shift between tasks.

So, in a class context, where you're trying to attend to what's on the board you have to filter through what the person is talking about in order to think about what are the relevant elements of this relational system, and map them together.

This can be a very heavy load, a heavy cognitive load.

And what it turns out to be that if people are overloaded, what they'll end up doing is remembering some of the surface information, so it kind of looks like they're getting the knowledge that you're producing, but they're not necessarily doing this relational higher order thinking piece.

How do we teach without overloading these resources?

One, we want to aid students by drawing attention to the relational structure.

So highlighting these in particular and making sure that they have working memory load to do this.

Oh gosh, am I, oh no I started this, okay, I'm not running out of time, sorry my time counter was started before I started.

Okay, so what are teachers doing now to support relational thinking?

One of the ways to try to get some strategies is, for doing these things in a really practical way, is to look at what teachers are doing in places where you have high-achieving students.

One study we did was looked at teachers in mathematics and in higher-achieving countries than our own.

So looking at US, Hong Kong, and Japanese classroom lessons, and trying to understand what teachers are doing when they're teaching relational comparisons.

We found 520 relational comparisons, this happens all the time.

We have equilateral and equiangular polygons up there.

And basically we found some strategies that seemed to differentiate teaching across these countries.

One is whether or not the source was visually presented.

So one thing that happens is there, you know, you're teaching something, you're teaching a system and then you say, "You know, it's just like "something else," and you describe that other thing, verbally, but you didn't really go through a lot of work to make sure that they knew what you're meaning by that other representation.

And that takes a lot of work for the student to pull that back out of memory, hold it in their working memory, and trying to reorganize it and see what you mean by this relational comparison.

And then keeping this source visible the whole time, while you are making this comparison, happened less often in the United States than these higher-achieving regions.

Spatially aligning these representations.

So if you make them visible but they're sorta haphazard that takes a lot of inhibitory control, maybe, to say, "Oh, which parts of these should be related?"

And so you have to be saying, "Okay, wait, not the fact that it's higher.

"What I really mean is that this part's the same," using comparative gestures, so gestures that move back and forth between the things you're trying to teach.

Using familiar sources.

Very often teachers you'll see here actually presented two things that were pretty new and that seems to work okay, but presenting something that's really familiar, again, was less often done by US teachers and, I think, is a tool for making sure that the knowledge doesn't overwhelm the learner.

And using some other kind of imagery, so it can be movement in a computer design or some other kind of mental imagery that's really salient.

Basically, you see, these are a bunch of strategies that seem to be correlated, at least, with higher learning outcomes.

And we see that US mathematics teachers are using relational comparisons frequently, but they're providing fewer of these kinds of extra supports to make sure that their students are noticing and using these things.

And we see the same thing in science teachers, and I'll just go quickly through these.

These are US teachers that were designated as having strong conceptual linked lessons and weak conceptually linked lessons.

These are by the Tim's group, so we didn't do this rating, but then we looked at how they were using analogies and connections, and so they found that in the weak conceptual linked, well, in the lessons with strong conceptual links, most of the time these things were happening, this didn't happen that often and it happened less often in the lessons with weak conceptual links.

And another piece that's important here is the breaking down of whether the teacher's doing all of this or whether the teacher's engaging the student in these things.

And so we go back to this expert, novice distinction.

If you already know how these pieces should be related, you're not gonna have to do a lot of work, so you might say, "This one is just like that one."

Or you maybe say a little bit, you know, "Well, this built from that," you know, "This theory came out of this other theory."

But you don't need to provide a lot of support because you really understand it, and also the student, so the student is just listening to you, they may miss it.

Also, if they're not being forced to actively engage with this, they may be not having to actually do the work of doing this relational structure mapping.

So you see the teachers and the students, together, are doing this much more often in these stronger lessons.

And we also see consecutive, 53% of the lessons with weak conceptual links only had consecutive presentation, while 94% of the lessons with strong conceptual links had concurrent presentation of these visual representations.

And then we looked at whether these were, oh and when they had multiple representations, whether these were compared at all, so 65% of the time they weren't compared at all even in the weak conceptual link lessons, and the teacher and students did them together more often in the strong conceptual link lessons.

Overall, this is maybe not something that students are getting a lot.

This might be part of an explanation for why students are coming in to college classrooms without this sort of deeper, more relational way of representing at least math.

And I think the evidence is that they feel that way in science as well.

So then, do these support strategies that I outlined actually help, though?

If we wanna look experimentally, we've done this in a few different ways, but one of the ways is that's, I think, closest to real classroom learning is videotaping a lesson where you have a relational reasoning opportunity, like comparing problems or solutions, we teach it once in a real classroom with real students and we videotape those lessons with multiple cameras simultaneously.

And then we edit all those video in order to create two matched conditions, or three matched conditions, that have exactly the same lesson, all the unexpected things that happen in a real lesson, but they vary on some particular piece.

They look like this.

It's the same lesson, but one of the things we looked at is, is it important to provide these visual representations right.

I laid out some reasons why it might be important and what you see is here, this is either a camera that zooms in on the teacher and doesn't capture the board, or that's the not visible condition, and in the all visible condition, the videos were edited so that there was a camera that caught all of them, and then in the sequential one, you saw one solution and then the next solution, and then the next solution.

If that makes sense.

And basically we looked at procedural understanding, flexibility, and conceptual understanding.

Here, I just have procedural knowledge, procedural flexibility, and basically here there's some evidence that simultaneous presentation is particularly important for procedural flexibility.

There were no differences here on procedural knowledge, which I think is interesting in that, as I said, people tend to get some information if you're teaching in a way that is not making use of all this higher order opportunities, but they're not necessarily getting all of it.

But, in the sequential condition, we actually see the lowest performance.

And we actually found that they end up picking up misconceptions somewhat times in the sequential presentation model, so this seems to be really not an effective mode.

Overall, the experiments like that suggest that having simultaneous visible and structurally aligned representation in adults is really important.

It's also important in 5th graders, and making them visible improves, making them both visible is effective and improves learning flexibility and transfer, but only if they're visible simultaneously.

So using lots of visual representations serially may actually be producing some misconceptions.

We see benefits for using these linking gestures, and interestingly, new data were suggesting that students under stereotype threat, so people who are worrying about their performance, may end up showing reduced learning from these relational reasoning opportunities, because that is another working memory load, and so it's actually taking some of the resources away from doing this higher order thinking.

Overall, I'm hoping to convince you that relational thinking is essential for learning expert-like disciplinary skills.

So if you're trying to teach students to look like you, to look like experts, you wanna really be drawing their attention to these relations.

Better supported instructional analogy leads to more flexible learning and transfer, in particular reducing processing demands on the learner by doing things like making visual representations available simultaneously, making them spatially aligned, and using linking gestures to move in between.

Be aware of stereotype threat.

Quickly, I'll just end with looking at these classrooms, right.

This is you as an instructor looking at your classroom.

You can't see that there's this huge screen with all these, board with all these (inaudible) on one of them.

There are all these students looking at you.

When you're teaching, you're under high cognitive load, too.

You're worrying about other people's opinions, how the students are feeling.

Are they engaged or are they not engaged?

You wanna be trying to get at assessing their thinking.

You're also worrying about what you're doing and so you're under your own cognitive load.

And so the more you can prepare ahead of time, and reduce your load, the better you'll be able to do higher order thinking in the classroom and be able to draw out these comparisons for the students a little bit more.

And I'll end with that, 'cause I think I'm going long.

(applause)