Which is a better way to teach?

a) The teacher shows how to do a problem, explains the concepts behind the problem, and then the students do problems on their own.

b) The teacher shows how to do a problem, does not explain the concepts, and the students start doing problems on their own.

c) The teacher explains the concepts necessary to solve problems, and then the students attempt solving problems.

Schools have been around for over 400 years, shouldn’t we know the answer to this question? Not just by asking teachers or academics what they think works. By now, shouldn’t we know what really works?

I had the fortune to attend the first conference of the Pittsburgh Science of Learning Center (PSLC) at Carnegie Mellon University on February 18, 2009. The PSLC is a joint program of CMU and the University of Pittsburgh, and its purpose is to leverage cognitive theory and cognitive modeling to identify the conditions that cause robust student learning.

Researchers at the PSLC create learning tools and devise and conduct experiments to test learning theories. They want to find out how to help students learn faster, retain more, and better transfer what they learn to new situations.

The PSLC conference brought together researchers and people (like me) from the business of education to exchange ideas and learn from each other.

The next two blog entries will summarize what I learned. This entry will focus on a talk I had with one of the researchers, and the second entry will report on a talk I had with the PSLC director.

Ron Salden is one of the post-doctoral fellows who presented at the PSLC conference. The way he conducted his research and the insights he obtained are representative of the high quality findings presented.

Dr. Salden’s experiment involved testing how to present worked examples, specifically in a computer-tutor situation in geometry, although the conclusions apply to other disciplines and to pen-and-pencil and lectures. He used three different ways of presenting information:

1. Present the students with problems only. This was the control group.

2. Present an example with explanations of how to solve it, then present subsequent examples, but over time, display fewer and fewer of the steps, making the student fill them in. For example, if it takes four steps to solve a particular type of problem, for the first problem, all four steps would be displayed. The second time, perhaps only the first three steps would be displayed, and the student would have to fill in the fourth step. The third time, perhaps only the first two would be displayed, and so on. This was called “fixed fading” because all students in this group were presented with the same sequence of examples and steps.

3. Present an example with explanations of how to solve it, then, for subsequent examples slowly fade the steps of each solution, but based on how well the students understood how to solve the problem. This was called “adaptive fading” because it was dependent on the student’s growing understanding as they were working on the learning material.

This experiment was conducted with two different student populations. In Germany, students participated in a lab study and learned one lesson, and then were tested a week later. In the US, students participated in a classroom study of about five weeks of lessons, and then were tested a month later.

Overall, the results indicated that the adaptive fading group was able to remember the lessons significantly better than the control group and the fixed fading group. In the classroom study the group with adaptive fading fared slightly better than the group with fixed fading, but the differences were not significant.

What does this teach us about teaching or creating content? Rather than merely show students how to solve a problem, we should present multiple examples to students, but increasingly have them provide the problem-solving steps before we ask them to go and do problems on their own.

In another series of experiments, Dr. Salden measured the effect of cognitive load on learning. What’s cognitive load? The amount of effort it takes the student to solve a problem. Think about driving. When you learned how to drive, you had to think about every aspect, turning the wheel, pressing the accelerator, etc. Today, you can drive 20 miles and not think about what you did at all. When you were learning, driving imposed a large cognitive load, today, you are most likely cognitively efficient when you drive. As such the amount of cognitive load experienced by the learner is highly dependent on how much experience s/he has performing a task.

Typically, when we measure student performance, we give students problems and assess whether they answer appropriately. Dr. Salden and his colleagues claim that in addition to performance assessment, it is also important to measure the cognitive load students experience while solving problems. Take two students of which the first one aces a problem with little effort while the second student also aces the same problem but has a much harder time to solve the problem. You would not give these students the same new problem after taking the difference in cognitive load into account. The first student can be presented with a more complex problem whereas the second student should be given a problem of equal complexity of the one he just solved.

In the series of lessons, there were 10 levels of complexity in the problems. Dr. Salden took one group of students and gave them problems, assessing their answers (the control group). With another group of students, he not only assessed their answers, but had them describe how hard the problem was for them to solve. So now, a student not only had to perform well but also should not need to experience a hard time solving the problem. The higher the student’s performance and the lower the student’s experienced difficulty to solve those problems would lead to a faster progress through increasingly more challenging problems.

In the control group, not everyone got through the 10 levels. The group where cognitive load and performance measures were combined got through the material more quickly, made bigger jumps to more complex problems, and remembered the material longer.

The implication for learning is that there is a distinct advantage in having students do problems until the process is easy for them before having them move on to more difficult or advanced material. But, instead of just giving every student a large number of problems, it is more ideal to determine how hard they find the problems, and then advance when they find the problems easy.

Going back to the question at the beginning of this article, which is a better way to teach?

a) The teacher shows how to do a problem, explains the concepts behind the problem, and then the students do problems on their own.

b) The teacher shows how to do a problem, does not explain the concepts, and the students start doing problems on their own.

c) The teacher explains the concepts necessary to solve problems, and then the students attempt solving problems.

PSLC research shows that none of these is optimal.

C is the worst, presenting the concepts and having students solve problems results in students taking longer to learn the material, not remembering at long, and being less able to transfer their knowledge to new situations.

There is no significant difference in B or C. Having the teacher explain the concepts has almost no effect on students learning the material. What seems to be important is for the teacher to show how to do something.

But, what worked much, much better was to first present how to solve a problem as a worked example, and then make each student describe why each step worked. This process of making the students think about why the solution worked resulted in them learning the material much faster, remembering it longer, and being better able to apply it to new situations. Additionally, taking the individual student’s learning progress into account and adapting the learning materials to this progress, for instance by fading examples or by changing the complexity of the problems, can make education much more efficient.

In the next article, I’ll present some of the other findings from the PSLC, summarize my talk with the PSLC director, and point you to other resources.