If the Shoe Fits: The Instructional Fit Hypothesis

Take a look at the map below. Suppose you live on Jackson Avenue, and you need to go to the store to buy a new pair of shoes. What route will you take? 

Once you've planned your route, how will you remember it? Will you:

• Form a mental map, position yourself on that map, and update your position as you travel
• Form a mental list of verbal directions (e.g., head toward Main Street; after Main, turn right on 1st; then, take a left on Madison; the shoe store will be on the right). 

In the unlikely event that you take a wrong turn, which strategy will be more helpful in getting you to your destination? Which representation is easier to store in working memory? Which one is easier to use while driving? 

Connecting Instruction to Learning

In this blog, we've discussed many different types of representations that the mind uses to store and organize information. We also have talked about various learning strategies that help us acquire new information. One aspect of the discussion that's been missing is how these pieces all fit together. Are there some learning strategies that are more likely to give rise to one type of representation over another?

To answer this question, my collaborators and I set out to test the hypothesis that certain forms of instruction inspire learning events that translate into specific types of representations. We called it the instructional fit hypothesis, in that instruction should match the type of learning that we want to elicit. Before we talk about how we tested the instructional fit hypothesis, let's review the assumptions on which it is based.

Our Assumptions

First, we assume there are different types of mental representations that we use to reason about the world and to solve problems. This assumption is supported by plenty of evidence that people construct and use many different types of representations. For the purposes of the present discussion, let's focus on two representations: mental models and problem-solving schemas. As we saw, a mental model is an image or dynamic simulation that allows the individual to make inferences based on that model. For example, we might not know how many windows there are in our house, but we can mentally walk from room to room and count them. A mental model can also be incomplete or incorrect, in which case I can add details to or correct my model as I encounter new relevant information. A problem-solving schema, in contrast, can be thought of as a recipe for solving a problem. In a previous post, we introduced the idea of a production rule, which is an if/then statement that says what to do when certain conditions are met. A problem-solving schema links multiple if/then statements so that a problem can be solved.

Second, we assume that certain types of representations are better suited to solve specific types of problems. It is more expedient to use a mental model of the circulatory system to diagnose a heart problem than it would be to use a problem-solving schema in which several production rules have to be tested to find one that matches the symptoms to the root cause. Likewise, it is easier to solve a multi-step math problem using a problem-solving schema than by constructing a mental model of that particular problem. To be effective and efficient, the representation and the problem-solving demands should match. 

Our third and final assumption is that certain types of instruction lead students to engage in specific types of cognitive processing. For example, suppose I instruct one of my classes to write a summary of a passage about the circulatory system. For my other class, I ask them to answer difficult questions like: Why would the distribution of oxygen be less efficient if there is a hole in the septum? The first class would concentrate on a surface-level understanding of the text because the task requires them to remember the sentences of the text rather than the underlying meaning. The second class would need to understand the interplay of multiple structures as well as their functions within the system as a whole.

Now that we've laid out all of our assumptions underlying the instructional fit hypothesis, let's put it all together. First, we start with the question: What do we want our students to be able to do or know? These are the task demands. Once we know what they are, then we ask, which representation is best suited for our learning goal? Then we figure out which cognitive processes are most likely going to lead to the generation of that representation? Finally, we ask, which instructional activity will most efficiently give rise to those cognitive processes? If we sketch it out, the chain of events might look like something like this:

Figure 1. The hypothesized chain of events.

The Study and the Evidence

To test the instructional fit hypothesis, we asked high-school students to learn about an advanced topic in physics (electrodynamics) under a couple of different experimental conditions. The first condition nicely mapped all of the steps from Figure 1. The instructional activity inspired the cognitive processes that we believed would lead to a useful representation to solve electrodynamics problems (i.e., a problem-solving schema). For the other experimental condition, the fit wasn't as nice. The instructional activity prompted the students to build and modify a mental model. While useful to visualize the problem situation, a mental model does not specify how to arrive at a numeric solution.

We asked our participants to solve their electrodynamics problems with a computer tutor called the Andes Physics Tutor [2]. Students can ask Andes for a hint to help them when they get stuck. As one measure of how difficult it was for students to solve the problems under the two different conditions, we counted the number of hint requests. It turned out that students who were prompted to form a problem-solving schema asked for fewer hints than the students who received the mental-model instructional activity. This provided preliminary evidence in favor of the instructional fit hypothesis.

The STEM Connection

The implication  of the instructional fit hypothesis for STEM education is fairly straight forward. The bottom line is: try to align instructional activities to cultivate the mental representation(s) that will be most useful to your students as they work to achieve specific learning objectives. Fitting instructional activities to the task demands, however, can sometimes be a challenge. One way to accomplish this would be to begin designing a new lesson by conducting a rigorous task analysis. If you're fortunate enough to know someone who is already an expert in the target domain, consider asking her to talk through her process while she solves a problem similar to one you would like your students to be able to master. After she is done, go back and ask, "How did you know to take this step?" or "What knowledge did you rely on to figure this out?" The goal is to figure out which representations an expert in the area relies on to produce an efficient solution. 

Once you have a handle on the task demands and the representations an expert uses, the hard part is to figure out what instructional activities can most effectively inspire those types of representations. In our study, we relied on 20 years of research on self-explaining to come up with our activities. That literature was robust enough that we could theorize about a potential match or mismatch between the instructional activities and the representations that are needed.

Obviously, this is a time-consuming process. But if we can understand the chain of events a little better, then we will certainly be able to improve our instruction! 


Share and Enjoy!

Dr. Bob

For More Information

[1] Nokes, T. J., Hausmann, R. G., VanLehn, K., & Gershman, S. (2011). Testing the instructional fit hypothesis: the case of self-explanation prompts. Instructional Science, 39(5), 645-666.

[2] VanLehn, K., Lynch, C., Schultz, K., Shapiro, J. A., Shelby, R., Taylor, L., et al. (2005). The Andes physics tutoring system: Lessons learned. International Journal of Artificial Intelligence and Education, 15(3), 147–204.