Tag: problem solving

Situated Learning

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[I wrote this review of situated learning, also known as situated cognition, in 2009 for the internal communications discussion board we use in the Carl Wieman Science Education Initiative. I go back to it often enough, mostly to find the reference for the amazing paper by James Paul Gee, that I’m reposting here.]

We’ve all seen it, and probably done it, too. An instructor has a really interesting problem to tackle in a course, a problem that synthesizes many concepts. So the instructor carefully presents each concept, one after another, building anticipation and excitement for the big day when everything comes together. And when the big day arrives, a month into the term, the students don’t seem to get it. “But we just spent a month getting ready for this! Why aren’t you excited? Can’t you remember concepts A, B, C, D, E, F and G?”

Uh, no. The problem is, concepts A thru G were presented without any context. They are disembodied or decontextualized knowledge.  There’s no scaffolding, no motivation to grab the students’ attention. The promise of excitement a month from now isn’t enough. As this is a scenario I’m facing, I needed some research to support my argument for change. At Carl’s suggestions, with great help from Wendy Adams (CU Boulder), I put together a brief summary of what we know about the failures of decontextualized knowledge, or better yet, the profound benefits of situated cognition.

For thousands of years, novices have become experts through apprenticeship: the master trains the novice, not just with reading assignments and homework, but by teaching the craft in situ. The novice accumulates the craft’s concepts as needed. The novice learns simultaneously, both the knowledge and how to use it. As Brown, Collins and Duguid (1989) write,

by ignoring the situated nature of cognition, education defeats its own goal of providing usable, robust knowledge.

This paper is an excellent discussion. The authors describe two benefits to situated cognition:

  1. “Learning from dictionaries, like any method that tries to teach abstract concepts independently of authentic situations, overlooks the way understanding is developed through continued, situated use.” This echoes Chapter 3: Learning and Transfer of How People Learn. Teaching in context (and then in slightly different situations) increases the “flexibility” of students’ knowledge, aiding transfer.
  2. “[Students] need to be exposed to the use of a domain’s conceptual tools in authentic activity – to teachers acting as practitioners and using these tools in wrestling with problems of the world.” This one surprised me because it didn’t even occur to me and it’s probably more important than the first. Students in a situated learning environment get “enculturated” (Brown et al., 1989) into the practice of how to study the field, not just the field’s concepts.

Okay, great. But how do you do it? How do you “enculturate” your students? What kinds of activities or curricula work?

Mayer and Wittrock, in Chapter 13: Problem Solving of the Handbook of Educational Psychology (Winne and Alexander, 2006) describe a wide range of methods for teaching problem solving, many of which have a flavour of teaching and learning in context.

Donovan and Bransford in How Students Learn (2005), a follow-up to How People Learn, collect together a number of case studies about teaching and learning science.

Sabella and Redish (2007) give some advice for physics instruction, but the messages are much more general:

[C]onceptual knowledge is only one part of what students need to know in order to solve physics problems. They also need to know how and when to use that knowledge.

Finally, if you read only one more paper after Brown et al., read this fantastic how-to article by James Paul Gee. He studies literacy and he’s a (the?) video gaming guru. This article, “Learning by Design: good video games as learning machines” (2005) lists 13 principles that education should have. Each principle is matched to a video game where that skill or activity is best exemplified (they’re all long, role-playing games like Halo and Tomb Raider where you must accumulate skills to win). And for us, he kindly translates the principles into what educators need to do to incorporate these principles into our teaching, like

skills are best learned as strategies for carrying out meaningful functions that one wants and needs to carry out.

In conclusion, situated cognition (or situated learning) has benefits far beyond helping students hang concepts onto the scaffold in the right places. It introduces them to how experts in the field practice their craft.

References

J.S. Brown, A. Collins, and P. Duguid, “Situated Cognition and the Culture of Learning,” Educational Researcher 18, 32 (1989).

J.D. Bransford, A.L. Brown, R.R. Cocking (Eds.) How people learn: Brain, mind, experience, and school. (National Academies Press, Washington, DC, 2000).

R.E. Mayer and M.C. Wittrock, in Handbook of Educational Psychology (2nd ed.), edited by P.H. Winne and P.A. Alexander (Mahwah, NJ: Lawrence Erlbaum Associates, 2006), 287.

M.S. Donovan and J.D. Bransford (Eds.) How students learn: Science in the classroom. (National Academies Press, Washington, DC, 2005).

M. Sabella and E.F. Redish, “Knowledge activation and organization in physics problem-solving,” Am. J. Phys. 75, 1017 (2007).

J.P. Gee, “Learning by Design: good video games as learning machines,” E-Learning 2, 5 (2005).

Is going over the answers negative reinforcement?

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My wife works with people with developmental delays, like autism and fetal alcohol spectrum disorder. Her niche is sexual health.  Imagine the hormones of a teenaged boy with the impulse-control of a 5-year-old. She often gets called in when some Grade 6’er starts whippin’ it out – either for the reaction he gets or because he doesn’t realize that’s not what typical Grade 6ers do.

The other day, we were talking about how to change people’s behaviours and she gave me an example of positive, no wait, negative, erm, reinforcement. I’m out of my depth when it comes to psychology so let me remind me (and you) about the difference, in overly-simplified terms I can get my head around. Oh, and when I’ve mentioned I’m writing this post, everyone I’ve spoken to gives a different definition of negative reinforcement, so it’s possible the one below is different than yours…

Positive reinforcement is something that’s added, typically by the person in authority – a parent, teacher, boss – after a person does something good. Like a high-5 by the coach after a good play, for example. That action strengthens the person’s motivation to repeat the behaviour.

Negative reinforcement strengths the unwanted behaviour. Your kid is having a fit because she doesn’t want to clean her room. Suppose you say, “Okay, I understand you don’t want to do it. Why don’t you watch TV for half an hour, calm down, and then clean your room….” It reinforces the undesired behaviour.

Every source I googled made sure to point out negative reinforcement is not the same as punishment. Getting grounded because you haven’t cleaned your room is not negative reinforcement.

(Geez, this is subtle. I can imagine some amazing clicker questions about positive reinforcement, negative reinforcement and punishment. [Update March 19, 2012: A couple of days after I wrote this post, Derek Bruff wrote about a clicker workshop he gave, including some pos/neg reinforcement clicker questions created by one of the participants.]  Okay, back to the conversation with my wife.)

Scene 1: Grade 6 classroom

There’s this boy, let’s call him John. John like to strip his clothes off at school. Like in the middle of class. His teacher intervenes. Frustrated with John’s continual stripping, the school decides they have no choice but to send John home when he strips, punishing him for his behaviour. But here’s the thing – John might have a developmental delay but he knows what’s what: he doesn’t like school. He strips so he can get sent home. In fact, John has started stripping on the school bus on the way to school so he doesn’t even have to go through the charade of going to class. Sending John home, which the staff feel is punishment for his behaviour, is, in fact, a reward for John. What they think is punishment is, in fact, negative reinforcement for John.

“So what are they supposed to do?” I asked her.

They shouldn’t send John home. And they shouldn’t praise him for keeping his clothes on. Instead, throughout the days when John is at school, the teachers should say, “We’re so glad you’re here with us today, John!” That’s positive reinforcement, something added to John’s school day that strengthens the good behaviour of keeping his clothes on.

What I’ve left out is what to do during the difficult transition time between he continually rips off his clothes and when he keeps them on. The teacher needs to intervene somehow. Calling my wife is a good start!

Scene 2: University physics lecture hall

The physics instructor has realized that his traditional, “all lecture, all the time” style of teaching does not promote learning like he wants.  He’s decided to make the class more student-centered. He gives 10-15 minute mini-lectures and then hands out worksheets which are supposed to guide and scaffold the students through the next stage of the development of the concept. The problem is, the students don’t do the worksheets. They just sit there, staring at the empty spaces on the page or desperately scribbling down formulas like I described here, biding their time, because they know he’ll be going over the answers in a few minutes. Sure enough, after a while, he goes over the answer to Question 1. The students madly scribble down his solution or, increasingly, grab their phones and start snapping pictures.

He’s not punishing them for not doing the worksheets (“Why have you not answered the questions!? You will all Remain. In. This. Classroom. Until I see some work!”) Rather, he’s reinforcing their behaviour of not doing the worksheet. They get what they want (the answers) and he thinks he’s helping. This seems to be an example of negative reinforcement, at least according to the definition I posited earlier.

“So what is he supposed to do?”

Good question.

Let’s look at this top down: What do the students need to get out of the activity? They need feedback on their answers in a timely manner. “Timely” because feedback a month later when they fail the exam is too late. One way to give them feedback is to go over the answers so they can check. That’s not the model used by the significant portion of the astronomy education community who use the Lecture Tutorials worksheets. Instructors do not go over the answers. Instead, the worksheets have built-in feedback and most instructors follow the worksheets with a sequence of peer instruction questions. If you get those questions correct, you know you’re okay on the worksheet. If you don’t get the questions correct, your peers will straighten you out. At the very least, you’ll know which concepts you didn’t get and can talk to the prof or TAs about them. More positive reinforcement comes when you ace those identical or “identical except some parameters changed” questions on the exam.

I’d love to create a sequence of clicker questions to follow the worksheets in this physics class but that’s not the simplest alternative because it requires the instructor to be agile with worksheets AND with peer instruction. One thing at a time…

What about this? The instructor watches the students doing the worksheet questions, monitoring their progress. If everyone is getting along just fine, don’t stop them. When it looks like students are stuck, and individual attention by the instructor or TA can’t handle the widespread confusion, intervene with a class-wide discussion. Don’t begin with, “I’m so happy you answered Questions 1 and 2 by yourselves!” (“John, I’m so glad you kept your pants on today!”) Instead, work together to get past the sticking point. Get the students to contribute to the solution, using the work they’ve already done to chip away at the problem. A pat on the back or a high-5 for a good tidbit of problem solving. The students are praised and rewarded for the work they’ve done, even if it’s not complete. That’s positive reinforcement for good behaviour, right?

(Unless that’s an example of “intermittent” negative reinforcement which, according to my wife, is even stronger than continuous.)

Yes, there will be difficult transition period, when students are not solving the problems and the instructor is not going over all the answers. Sorry, tough it out.

What if the students were never allowed to get into the habit of not doing the questions? What if, from Worksheet 1 on Day 1, this collaborative solution approach was the way it’s done. Ahh, now that would be something, wouldn’t it?

Alright, I’m not exactly sure where I’m at. I know the current method of going over the answers isn’t working. And that if we make changes, there will be a difficult period of transition. I like the collaborative problem solving approach — I’ve seen it happen in a physics class of about 30, where the agile instructor knew everyone’s name and kept track (in his head) of who hadn’t contributed yet, calling on them for input.

One other thing I know:  I should learn some more psychology.

Image: RaaksBeton2 by Dan Kamminga on flickr CC. In my mind, it shows people working together to reinforce what they’re building.

Problem solving like a physicist

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In my role in the Carl Wieman Science Education Initiative at the University of British Columbia, I am often “embedded” in an instructor’s course, providing resources, assistance and coaching throughout the term. This term, I’m working with an instructor in a final-year, undergraduate electromagnetism (E&M) course.

The instructor has already done the hard part: he recognized that students were not learning from his traditional lectures and committed to transforming his classes from instructor-centered to student-centered.  Earlier, I wrote about how we introduced  pre-reading assignment and in-class reading quizzes.

This course is heavy on the math. Not new math techniques but instead, math the students have learned in the previous 3 or 4 years applied to new situations. His vision, which he shared with the students on the first day, was to introduce some key concepts and then let them “do the heavy lifting.” And by heavy lifting, he means the algebra.

The vector for this heavy lifting is daily, in-class worksheets. The students work collaboratively on a sequence of questions, typically for 15-20 minutes, bookended by  mini-lectures that summarize the results and introduce the next concept.

We’re making great strides, really. After some prompting by me, the instructor is getting quite good at “conducting” the class. There are no longer moments when the students look at each other thinking, “Uh, what are supposed to be doing right now? This worksheet?” It’s fine to be puzzled by the physics, that’s kind of the point, but we don’t want students wasting any of their precious cognitive load on divining what they should be doing.

With this choreography running smoothy and the students participating, we’re now able to look carefully at the content of the worksheets. Yes, I know, that’s something you should be planning from Day 1 but let’s face it, if the students don’t know when or how to do a worksheet, the best content in the World won’t help them learn. Last week’s worksheet showed we’ve got some work to do.

(Confused guy from the interwebz. I added the E&M canaries.)

The instructor handed out the worksheet. Students huddled in pairs for a minute or two and them slumped back into their seats. You know those cartoons where someone gets smacked on the head and you see a ring of stars or canaries flying over them? You could almost see them, except the canaries were the library of equations the students are carrying in their heads. They’d grasp at a formula floating by, jam it onto the page, massage it for a minute or two, praying something would happen if they pushed the symbols in the right directions. Is it working? What if I write it like….solve for….Damn. Grab another formula out of the air and try again…

After 10 minutes, some students had answered the problem. Many others were still grasping at canaries. The instructor presented his solution on the document camera so he could “summarize the results and introduce the next concept.” The very first symbols at the top-left of his solution were exactly the correct relationship needed to solve this problem, magically plucked from his vast experience. With that relationship, and a clear picture of where the solution lay, he got there in a few lines. The problem was trivial. No surprise, the students didn’t react with “Oh, so that’s why physics concept A is related to physics concept B! I always wondered about that!” Instead, they responded with, “Oh, so that’s how you do it,” and snapped some pix of the screen with their phones.

Scaffolding and Spoon-feeding

We want the worksheets to push the students a bit. A sequence of questions and problems in their grasp or just beyond, that guide them to the important result or concept of the day. Here’s what doesn’t work: A piece of paper with a nasty problem at the top and a big, blank space beneath. I’ve seen it, often enough. Students scan the question. The best students dig in. The good and not-so-good students scratch their heads. And then bang their heads until they’re seeing canaries.

There are (at least) 2 ways to solve the problem of students not knowing how to tackle the problem.  One is to scaffold the problem, presenting a sequence of steps which activate, one by one, the concepts and skills needed to solve the nasty problem. The Lecture Tutorials used in many gen-ed “Astro 101” astronomy classes, and the Washington Tutorials upon which they’re modeled, do a masterful job of this scaffolding.

Another way, which looks the same on the surface, is to break the nasty problem into a sequence of steps. “First, find the relationship between A and B. Then, calculate B for the given value of A. Next, substitute A and B into C and solve for C in terms of A…” That’s a sequence of smaller problems that will lead to a solution of the nasty problem. But it’s not scaffolding: it’s spoon-feeding and it teaches none of the problem-solving skills we want the students to practice.  I’ve heard from number of upper-level instructors declare they don’t want to baby the students. “By this stage in their undergraduate studies,” the instructors say, “physics students needs to know how to tackle a problem from scratch.”

This is the dilemma I’m facing. How do we scaffold without spoon-feeding? How do we get them solving nasty problems like a physicist without laying a nice, thick trail of bread crumbs?

Fortunately, I have smart colleagues. Colleagues who immediately understood my problem and knew a solution: Don’t scaffold the nasty problem, scaffold the problem-solving strategy. For a start, they say, get the instructor to model how an expert physicist might solve a problem. Instead of slapping down an elegant solution on the document cam, suppose the instructor answers like this:

  1. Determine what the problem is asking. Alright, let’s see. What is this problem about? There’s A and B and their relationship to C. We’re asked to determine D in a particular situation.
  2. Identify relevant physics.  A, B, C and D? That sounds like a problem about concept X.
  3. Build a physics model. Identify relevant mathematical relationships. Recognize assumptions, specific cases. Select the mathematical formula that will begin to solve the problem.
  4. Execute the math. Carry out the algebra and other manipulations and calculations.
    (This is where the instructor has been starting his presentation of the solutions.)
  5. Sense-making.  Sure, we ended up with an expression or a number. Does it make sense? How does it compare the known cases when A=0 and B goes to infinity? How does the order of magnitude of the answer compare to other scenarios? In other words, a few quick tests which will tell us our solution is incorrect.

Wouldn’t it be great if every student followed a sequence of expert-like steps to solve every problem? Let’s teach them the strategy, then, by posing each nasty problem as a sequence of 5 steps. “Yeah,” my colleagues say, “that didn’t work. The students jumped to step 4, push some symbols around and when a miracle occurred, they went back and filled in steps 1, 2, 3 and 5.” Students didn’t buy into the 5-step problem-solving scheme when it was forced upon them.

So instead, for now, I’m going to ask the instructor to model this approach, or his own expert problem-solving strategy, when he presents his solutions to the worksheet problems. When the students see him stop and think and ponder, they should realize this is an important part of problem-solving. The first thing you do isn’t scribbling down some symbols. It’s sitting back and thinking. Maybe even debating with your peers. Perhaps you have some insight you can teach to your friend. Peer instruct, that is.

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