How People Learn

tt_icon_170Here’s my latest Science Teaching Tips podcast — As any teacher knows, the ability to ask good questions — and use students’ questions — is a valuable skill to have in your teaching toolbelt.  In this podcast, TI staff biologist Karen Kalumuck describes how she tries not to answer every question that’s asked during a class, however tempting it may be. Instead, she’s learned how to guide her students to discover ideas for themselves.

Episode 66:  That’s a good question!

Karen Kalumuck’s Web site


That long blog post title is the summary of a very interesting piece of research just written up in Cognitive Daily.  This is worth going over and taking a peek at the original post, because it’s quite an interesting piece of research.

The research question was whether people’s memories follow a predictable pattern.  After all, we seem to remember more stuff from our 20’s and 30’s than, say, our 60’s.  The researchers found, basically, that more life-defining events happen in our 20’s and 30’s (like marriage, having kids) and those events create more long-lasting memories.  I’m grossly paraphrasing here, so take a look at the original post for the clearer picture.

Cognitive Daily says:

This corresponds well to other researchers who have found that immigrants remember more details about the years surrounding their time of immigration than non-immigrants. So if you immigrate in your 30s, you’re more likely to have memories from your 30s than someone who immigrated in her 20s. Other studies have found a memory bump in people from Bangladesh corresponding to a period of political unrest in that country. So it seems that our memories are affected more by the events in our lives than just the physical development of our brains. We’re not all destined to remember more of our teens and 20s than other years; we’re just more likely to experience significant, life-changing events in those years than others.

This is the last in a series of three posts on Dan Schwartz’s work on preparation for future learning, or helping students learn skills instead of rote facts so that they can apply their knowledge to new situations. All pictures in this post are courtesy of Dan Schwartz.

Contrasting cases

In the previous post, I showed Dan’s use of contrasting cases in helping students understand density and ratios. Why is it important to show students different cases, instead of the best single example of something? Well, he said, think about perception. Consider this circle:


We immediately recognize it as a circle. It is, after all, not a square.

untitled9But, in fact, it is many things. It’s a empty circle. It’s a circle created with a black line. It’s a largish circle. Here are a bunch of contrasts to this circle:

untitled11 untitled10 untitled81

We’re abstracting “circle-ness” from the single example, but that’s because we recognize circle-ness already. These contrasting cases would be important if we were first learning about circles.

Here are some contrasting cases of something familiar to us:


After all, what is the best way to teach Japanese speakers to say the sound “L,” which doesn’t exist in their language? Give them the purest example of an “L” sound that you can find? No, it’s to let them hear “R” and “M” and all the other sounds, so they know what the “L” is NOT in addition to what it IS.

But, this is what we do in instruction! We give students the purest example of something that we can. Consider, for example, this picture.

untitled13This is a perfect example of this breed. Now, tell me which one of the following is the same breed?

untitled14An expert will look at the width of the ears, the curve of the nose. But a novice can’t look at these pictures and see the immediate resemblance to the example picture. (I forget which one was the correct answer, but I think it’s the last one. The hair length is an extraneous feature, the ear shape is most important.)

It would have helped if, first, an expert had used the following picture with contrasting cases to help you learn about ear shape (what does “rounded” ear shape look like? How wide is “wide”?). You need to be oriented to understand the key structures in what you’re seeing. You can’t just look at the picture below and learn from it, though — a bunch of different examples are confusing to a novice. The expert’s role is to help them make sense of the different cases.

untitled15An example activity

Here, for example, is his activity where he asks students to invent a reliability index for a pitching machine. He gives them several different cases so they have to find a general solution which fits all these cases. This, after all, is what we do in science – to find a general solution that fits many cases.

untitled16In my previous post, I gave his activity for teaching density using clowns in buses.

The way he uses these in the classroom is to have students explain their classmates’ solutions to each other. That means that each student’s solution has to be written clearly enough so that someone else can understand it. This act of public “publishing” of the results gives students a bit more motivation to come up with a good solution. On the other hand, the goal of this task is NOT to come up with the “right” solution! It’s to prepare students to understand the expert solution (in this case, the idea of variance) when it’s presented.

Expert blind spot

As experts in a subject, we know an amazing amount. What we’ve learned has been compressed into a bunch of huge steps. We don’t recognize the huge number of things that we’re doing when we do what seems to us to be a single step (such as computing a ratio). We need to decompile our knowledge for the novices. In order to do this, it’s good to have an intelligent novice around — someone to ask us a bunch of questions at every step so that we can see what it is that we are doing in any task. Once you’ve discovered some key, fundamental idea that is needed to solve the problem, that’s a great place to put an invention activity. Examples are density, vectors, variance, and other fundamentals.

What these activities are not:

  • Not just brainstorming
  • Not puzzlers
  • Requiring a flash of insight to solve
  • Not pure “discovery” tasks
  • Not to replace standard instruction

What these activities ARE:

  • Students make answers for one case, and recognize it doesn’t generalize to the others
  • Learning is incremental
  • Students don’t have to find the right solution to benefit from them
  • Students should start to notice the variables that matter
  • Students are told to invent a form of representation
  • They are visual
  • These activities are used strategically to communicate fundamental key ideas (like density). Not used for everything.
  • Prepares student for standard instruction

To make these cases yourself:

  • Think about your own knowledge to isolate key concepts
  • Think of each case as an experimental treatment to isolate a key variable
  • Or, think of formulas or units and make sure they contrast for each case
  • Have some sense of likely misconceptions so you can create cases that will highlight probable “traps” students might fall into
  • Make them approachable. You don’t have to be as frivolous as the clowns example, but it should be done in a context that’s different from what you want students to learn (like physics). Then you can help students map it into the new context.

What about assessment?

Dan’s main point is that our assessments need to change in order to use this kind of instruction. If we value students’ showing that their learning is adaptive, we have to give them a chance to demonstrate this on a test, to demonstrate an expert level of perception.

What do I mean by expert level of perception?

What do the images below say to you?

untitled17 untitled18

The novice answer (“car,” “bird”) is not very precise.

The expert answer (“2007 BMW X5” or “indigo bunting”) is much more precise, and relies on deep recognition of various features. We should test students on this more broad ability to apply their knowledge. For instance, geology students should be able to extract some important features from this picture of a landslide:


This doesn’t have to be a perceptual test — in the previous post, the “green people” vs. “blue people” example relied on students ability to recognize the variability in a data set.


I think this stuff is incredibly powerful. Let me know of any more activities that you come up with or you know about!

In my last post, I wrote at length about Dan Schwartz’s work about teaching students how to learn by having them create a solution to a problem before you give them the standard lecture about how to solve that kind of problem. I wanted to give you an example of this kind of “Preparation for Future Learning” activity, in addition to the batting machine example in the previous post. All images are courtesy of Dan Schwartz at AAA Lab.

This one is to help students learn about density. The task is below.


And here are the graphics for the task.


The key to notice here (and in the previous batting example, though I only showed you one example of the batting machines) is that he uses contrasting cases to teach this concept. There are different buses with different amounts of clowns. These cases are chosen carefully so that the student must come up with a solution that satisfies all these different cases. For example, the number of clowns in the bus does not distinguish between the very first and very last cases shown on this sheet (for which the answer would be “2” for both cases, which are clearly different).

He found that those students who first invented this density ratio were better able to then use this knowledge to understand spring constants (another ratio) than those were were just told the formulas for density. That data is shown below.


More on how to write your own preparation for future learning activities in the next post….

We had a visit from Stanford education researcher Dan Schwartz last week, and what he told us about how people learn just rocked my world. I always enjoyed his work (and it was a real pleasure to tell him how much he’s influenced my thinking about education), and have blogged before about his A Time for Telling paper. Still, spending many hours with him over two days was a transformative experience for me. Let me try to tell you why.

All images in this post are courtesy of Dan Schwartz. His research website is here.

This is a problem of transfer (or so we say).

For example, students can learn how to do permutation problems using, say, cars or marbles as examples. But when you ask the marble-trained students to answer a question using cars, they struggle. Similarly, we see our own students do well on homework and chapter-level tests, but not on the final. They know the formulas and ideas, but don’t know how to apply them. This has been called a problem of transfer from one domain to another.

But, he argued, how is it that we could fail to transfer what we know? After all, we learn something at home and we bring it to work, or we learn something at home, and we bring it to school. We seem to transfer all the time. And, as my colleague Noah Finkelstein has argued, in order to believe in transfer, we have to believe that there is some thing to be transferred. What is transferring? Some static little packet of knowledge? There’s no tangible chunk of knowledge that we can bring from place A to place B. Knowledge is about skills and process and understanding, it’s not a static thing.

Efficiency over Adaptation

So, Schwartz argued, it’s not really a problem of transfer. The problem is that we’ve trained people to do things quickly – efficiently – not to adapt to new situations. We train people to recall lists of words quickly, or take timed tests, or tell us what causes the seasons when asked on the street. So we’ve trained efficiency over adaptation. While efficiency is important for routine tasks, experts readily adapt their knowledge to a new situation.

Preparation for Future Learning

Schwartz did a fascinating study to see what helps students learn to adapt to new situations.

  1. One set of students read a chapter and then hear a lecture about it
  2. Another set of students analyze and graph data, deciding what they think is important to graph
  3. A third set played around with graphing the data and then heard a lecture about

So, how did they each do on assessment? On a traditional factual test, group 1 (reading and lecture) and group 3 (graphing then lecture) do equally well. Group 2 (graphing only) did very poorly — without some expert guidance they didn’t really learn much from just playing around. Those data are to the right.

OK, so does that mean that it’s equally good to have studentsbarchart2 read and hear a lecture as to play around with the data before hearing the lecture?

Nope… he then gave them all a test that required them to use their understanding in a new situation, and those data are to the right here. Those who first played around with the data and then heard the expert lecture did much better on that test. They were approaching adaptive expertise more quickly than the others! The differences in performance on this test, above, are stunning — these students (who, he argues, were prepared to be able to learn during the test by the instruction they were given) did more than twice as well on this test.

So the message here is that there is a time for telling (ie., lecture) — just not too soon!

This is particularly appropriate to remember in math and science. Math, for example, is usually presented as an efficient way to solve problems. What if, instead, students found that math helped them understand science and manage complex problems? For example, he took a class of 9th grade students and taught them statistics by asking them to find a way to rate the reliability of pitching machines. Below are two examples of student approaches to this problem.


This forced them to create ways to deal with variability in data before being given a formula for computing variability (eg., standard deviations). He found that, even a year later, these students did better than college students in understanding formulas for variability, and were much better able to understand variability in data and its importance. Below is the task that he gave these students — those who had struggled with variability before hearing the lecture were able to recognize that the IQ scores of the green people had more spread, even though the IQ of the blue people was higher, on average.


He argued that this emphasis on efficiency is very American. We train people to become expert at routine tasks, but what we need to emphasize instead is innovative experiences. Let go of what you’re told, and try something new. For one, when students innovate a solution first, then they have a context for what they’re learning. When given the solution first, they don’t have a context for it. Telling people the answer works if they have a lot of prior knowledge (and that’s why talks at conferences, for example, can still be decent ways to get a lot of information across). But when you’re learning something new, don’t tell too soon!

You can find out more about Dan Schwartz’s work here.

I’m siting right now in a fascinating meeting for my physics education group, and we’re hearing about research on stereotype threat, which I’ve written about before. Stereotype threat is the idea that when you spark cultural stereotypes (like “girls aren’t good at math”) then those people get very stressed about their performance, feeling that however they do (say, on a math test) will reflect poorly on their group (women).  That makes them perform worse on that task than they might.

It turns out that if you give women the same test and say that it’s not diagnostic of their ability (for instance, by saying that it’s just a pilot test and you’re looking for feedback to improve it), then women and men do similarly on the test.  That’s because women don’t feel threatened in that case, it’s a low-stakes test.

Similarly, when you tell subjects that men and women perform differently on the test, women score worse.  You’ve made them aware of the stereotype by doing that.

Interestingly, when you tell subjects that men and women perform the same on the test, women score better and men score worse (closing the gap between their scores)!  For some reason, when men feel that they’re not getting some advantage from their gender, they don’t perform well.

They’ve seen similar results with:

  • The elderly and memory. (Flash words like “senile” and “florida” to bring the stereotypes to the forefront of their mind, and they’ll score worse on a memory test)
  • White men can’t jump (Remind men of stereotypes of race and athletic ability and white men won’t jump as high.  If a black experimenter is present and provides feedback on jumping ability, white men will improve less than black men.  That doesn’t happen if there’s a white experimenter.)
  • Asian men and math. (Remind people of the stareotype that asians are better at math, and white men do worse on math problems
  • Poverty and test performance (Remind people that economically disadvantaged people do worse on tests, and they will handily uphold the stereotype).

They’ve done some work to see how understanding and knowledge of this stereotype threat can be used to help close the gap between some of these traditionally lower scoring groups.  Psychological processes can have a significant impact on students’ performance — we need to be aware of that as teachers, and address it.  They did some work on mentorship, for example, and found that motivation is fairly malleable based on whether the mentor gave strict negative criticism, vs negative criticism that’s buffered with positive feedback.  The positive feedback appeared to help.  Sparking students’ positive ideas about themselves also seem to help.  Basically, it is important to highlight factors other than the stereotype that are relevant in performance.

“A Time for Telling” is the title of one of my favorite papers of Dan Schwartz (Professor of Education at Stanford). In it, he argues that lecture isn’t all bad. We complain that lecture (or “direct instruction” in ed-speak) doesn’t result in a lot of learning for our students. This has been shown again and again, in a lot of studies. But it’s pretty hard to completely eradicate lecture from our universities (or high schools, etc.) — it’s a pretty efficient way of communicating information. But if students first struggle with the ideas and concepts, then they’re prepared to learn from it. This is called Preparation for Future Learning.

For example, you could imagine (and it’s been shown) that students who first invent the idea of density (by being given the task of coming up with a way to describe how many clowns there are per square foot at a circus) will be better able to answer a question about the density of water than, say, a student who was just given the formula for density and shown a worked problem using gold. And a recent study by Schwartz shows just that, that those students who first invented the solution were better able to transfer the idea to a new situation. He writes:

Direct instruction is important, because it delivers the explanations and efficient solutions invented by experts. To gain this benefit without undermining transfer, direct instruction can happen after students have engaged the deep structure, per the Invent condition. [The students who invented the solution on their own] performed just as well on a subsequent test of word problems about density and speed. Direct instruction becomes problematic when it shortcuts the appreciation of deep structure. Across conditions, students who encoded the deep structure of the clown problems were twice as likely to transfer. It is just that fewer students in the Tell-and-Practice condition encoded the deep structure, because they had received direct instruction too soon.

Similarly, he later cites a study that found:

For example, college students learn more from lectures and readings when they first work with relevant data compared to when they write a summary of a chapter that explains the same data .

In some instances, he says, it is useful to just receive direct instruction because the goal is to build rote, routine skills. But in math and science, this isn’t the case:

In math and science, instruction cannot exhaust all possible situations. Transfer and adaptation are important. Although automaticity is important for some facts such as “2 x 3 = 6,” real situations rarely come with formulas attached, so students need to learn to recognize the relevant deep structures. Moreover, the cumulative curricula of math and science mean that students should build a base of knowledge on deep structures from which future learning can grow and adapt.

But teaching this way brings up the problem of assessment:

In the current milieu of high-stakes testing, standardized assessments largely measure routine expertise; namely, efficient recapitulation. If educators want students to become adaptive, innovative citizens who keep learning through changing times, current assessments do not fit. A better fit would map students’ trajectory towards adaptive expertise. Ideally, assessments would examine students’ ability to transfer, particularly for new learning. Such assessments would include resources for learning during the test (for example, a simulation that students can freely manipulate).

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