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.

You Got Some Explaining To Do!: Self-explaining

Here's a fun question for you: How detailed is your mental model of a toilet? If I had to guess, I would say you generally know how a toilet works, but haven't written a thesis on the topic. To test yourself, read the following passage and try to assemble a mental model of the modern flushable toilet.

The toilet has several working components. The tank (or cistern) holds clean water, and it is located above the toilet bowl, which holds the flushable content. Connected to the tank is a handle that, when pressed, releases the water from the tank. Gravity drains the water into the bowl through a small cistern tube. The water then exits the bowl at the bottom through the S-trap. 

Inside the tank are several additional components that control the flow of water into and out of the tank. At the bottom of the tank is a flapper valve, which is connected to the handle by a chain. When the handle is pressed, the chain raises the flapper valve to let the water out. As the water level decreases, the float ball, which is connected to the float rod, drops and opens the inlet valve. When the inlet valve opens, clean water rushes in to fill the tank. When the water reaches the top of the tank, the float ball closes the inlet valve. 

There's a lot of information crammed into those paragraphs [1]; however, it is also the case that a lot of information is missing. For example, how does the float ball and rod open and close the inlet valve? To make sense of the description as currently written, you still have to do some work. First, you have to spatially assemble all of the components in your mind's eye as you learn about them. Second, you need to supply any information that may be missing. Finally, you might have to resolve contradictions that arise between the information you are learning and the mental model you are building as you engage in the first two activities [2].

What do good students do when learning something new? 

When students read a text about an unfamiliar topic, their first priority is to make sense of each and every word. Once they decode the words, their next task is to assemble them into larger chunks of meaningful information. For example, you probably know what the words handle, chain, and tube mean. But you need to connect all three concepts together to form a working model of the flush mechanism in a toilet. The mental process of hooking these concepts together is what we will call self-explaining, or the generation of inferences that are required to construct an accurate mental model.


Evidence for self-explaining was first observed by asking students to read a passage about a branch of physics called statics [3]. In statics problems, balanced forces are acting on a body, which means there is no acceleration (see Fig. 1 for an example). Statics problems can become quite complex, as you can probably imagine. Researchers noticed that students who best understood statics were the ones who explained to themselves how to solve these types of problems. In other words, the best students naturally engaged in self-explaining. They also generated several self-explanation inferences to fill in the missing pieces of information that are not stated explicitly in the text. These missing pieces are necessary to fully understand the problem's solution.

Fig 1. An example statics problem.

Can you motivate students to self-explain? 

It's really interesting to read transcripts of students as they attempt to make sense of a complex topic. They might not understand it at first. But as they explain it to themselves, they are then able to see how to correct their current understanding with the model presented in the text. Good students naturally self-explain, but can we get all students to engage in self-explaining? The answer, as it turns out, is a qualified "yes." 

In one of the first studies to demonstrate that self-explaining can be prompted, researchers asked eighth grade students to read a passage about the human circulatory system [4]. Before students read the passage, the researchers asked them several questions about their understanding of the circulatory system. Because they were so young, it was no surprise that students generally had an impoverished understanding of the circulatory system. Most knew that the heart beats, but they didn't know why or what purpose the heart served. Some of the better students knew that the heart circulates blood, but they didn't understand pulmonary circulation. That is, they didn't realize that the heart has a special circuit of blood that goes to the lungs for oxygenation (and back).

After the pretest phase of the experiment, the students were asked to read a text passage that described, in detail, all of the steps of circulation. The student was verbally prompted by the experimenter to self-explain after reading each sentence of the text. After a while, merely turning the page was a prompt to self-explain. In other words, the researchers trained the students to self-explain, and then they reminded them over and over to self-explain. It was a pretty heavy-handed approach, but it worked. It paid off because the students who were prompted to self-explain demonstrated a more robust mental model of the circulatory system on the post-test than students in control condition who were only prompted to think about or reread the sentences.

Why was prompting students to self-explain a qualified success? Like most educational interventions, there were individual differences in the amount and effectiveness of the prompting. Some students generated several self-explanation inferences, whereas others generated only a few. Since the original study, researchers have designed new ways to help students become better self-explainers. For example, one study gave students an incorrect solution and asked students to debug the fictitious student's reasoning process [5]. This helped take the pressure off the student so that they could focus their attention on reconciling the differences between the correct and incorrect solution paths.

The STEM Connection

The connection between self-explanation and STEM education is extremely straightforward. Students should be trained on the definition of what self-explaining is. Then they should be prompted, periodically, to engage in self-explaining. To help them get started, here is a list of prompts that were used in the original study [4]: 

1. What new information does each line provide for you?
2. How does it relate to what you’ve already read?
3. Does it give you a new insight into your understanding of how ______ works?
4. Does it raise a question in your mind?

Also, students should be shown evidence of the utility of self-explaining. Students will probably be more likely to self-explain if they understand what it will eventually buy them. Moreover, students should be given an opportunity to develop the skill [6]. In fact, there is an intelligent tutoring system that was developed to do precisely that. The iSTART system gives students the opportunity to self-explain while reading complex textual passages [7]. Because self-explaining can be mentally taxing, the iSTART system was even outfitted with a bunch of mini-games to help build fluency in self-explaining [8].

Self-explaining is a powerful learning mechanism. It can be time-consuming and mentally exhausting, but the end result is definitely worth the effort. Like other concepts covered in this blog, self-explaining is a skill, which means it can become automatized over time. Thus, we need to get students started with self-explaining as early as possible because when they get to college, they will thank us for giving them the tools to make sense of tough concepts like organic chemistry (and flushable toilets). 


Share and Enjoy!

Dr. Bob

For More Information

[1] Here is the resource I consulted to write this description. To further enhance reading comprehension, it's typically to include a diagram. I intentionally omitted the diagram because I wanted you to attempt to assemble a mental model without a visual aid. 

[2] Chi, M. T. H. (2000). Self-explaining expository texts: The dual processes of generating inferences and repairing mental models. In R. Glaser (Ed.), Advances in Instructional Psychology, Hillsdale, NJ: Lawrence Erlbaum Associates. 161-238.

[3] Chi, M. T. H., Bassok, M., Lewis, M., Reimann, P., & Glaser, R. (1989). Self-explanations: How students study and use examples in learning to solve problems. Cognitive Science, 13: 145-182.

[4] Chi, M. T. H., de Leeuw, N., Chiu, M. H., & LaVancher, C. (1994). Eliciting self-explanations improves understanding. Cognitive Science, 18: 439-477.

[5] Booth, J. L., Lange, K. E., Koedinger, K. R., & Newton, K. J. (2013). Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 25, 24-34.

[6] Hausmann, R.G.M., & Chi, M.T. H. (2002). Can a computer interface support self-explaining? Cognitive Technology, 7(1), 4-14.

[7] McNamara, D. S., Levinstein, I. B., & Boonthum, C. (2004). iSTART: Interactive strategy training for active reading and thinking. Behavior Research Methods, Instruments, & Computers, 36(2), 222-233.

[8] Jackson, G. T., & McNamara, D. S. (2013). Motivation and performance in a game-based intelligent tutoring system. Journal of Educational Psychology, 105(4), 1036.

Have You Gone Mental?: Mental Models

Using Models to Reason and Infer New Knowledge

Let me ask you a question: How many windows are in your house or apartment? It's entirely possible that nobody's ever asked you this before. At least, that's what I'm banking on. If you've never been asked "How many windows are in your home?", then that means you aren't answering from memory. Instead, the question requires that you compute a value on the spot. How did you accomplish this task?

My prediction is that you visualized your home, and then started a walk-through, counting each window as you moved from room to room. In other words, you used a mental simulation, or a mental model, to answer my question. As it turns out, mental models are great for more than just answering random questions. They are just one instance of a class of mental representations that we use everyday. Mental models are simulations or images that we use to reason about the world and/or infer new knowledge.

What do toilets and light beams have in common? 

Consider another example of a mental model: the flushable toilet. If you know how a toilet works, then you can use your mental model to debug it when things go wrong. For example, a well-constructed mental model will help you figure out why the water keeps running (i.e., the filler float is stuck or the flush valve is stuck in the open position). Or why nothing happens when you depress the handle (i.e., the chain that connects the handle to the flush value fell off or is broken).

In addition to reasoning about the world, mental models are also useful in generating new knowledge through the process of inference. In a previous post, we talked about the power of inheritance to derive new information. This is similar in the sense that you infer new facts by "running" a mental model. 

One of the more famous examples of this is Einstein's claim that he used a mental simulation of riding a beam of light and asking all sorts of questions about what he might observe at that speed. Good thing he interrogated his mental models because it gave birth to the special theory of relativity!

A STEM Example

There are so many examples of mental models in science and engineering that I won't even attempt to catalog them here. In fact, one could argue that STEM education is primarily focused on helping students build detailed and accurate mental models. Here are a couple of illustrative examples.

First, the astute reader probably noticed that a recent post, entitled "Midnight in the Garden of Encoding and Retrieval," attempted to create a mental model of memory. That model proved to be useful when we started asking questions about what happens during encoding, storage, and retrieval. The answers to those questions helped us debug potential reasons why a student might fail to learn a new fact or skill. 

Another example, that I've used in my own research, is the human circulatory system. In one of our studies, we asked about the thickness of the muscle for the right ventricle versus the left ventricle of the heart. If you know that the right side of the heart sends the blood to the lungs, and you know that the lungs are proximal to the heart, then you know it doesn't need to pump very hard; therefore, the muscle in the walls of the right ventricle do not need to be as thick as the muscles in the left ventricle. This is useful knowledge that doesn't need to be taught directly. Instead, it can be inferred by the student through a series of leading questions. 

The final example I will give is one of my favorites [1]. It has to do with the development of the mental model for the Earth. When kids are little, they know, via observation, that the Earth is flat. Later on, they learn that the Earth is round. To make the observation compatible with the authoritative knowledge that they hear from adults, children then reason that the Earth must be round, like a pancake. If you ask them leading questions, such as, "What will happen if you walk for days and days?", they will answer that you will come to the edge of the Earth. 

If the goal of education is to help students develop accurate and complete mental models, then there is a pretty interesting implication for assessment. It is difficult and time-consuming, but developing generative questions is a excellent way to evaluate your students' mental models. Generative questions ask the student to reason about his or her model model. The "muscle thickness of the ventricles" and "walking the Earth for days and days" are good example of generative questions. 

Share and Enjoy! 

Dr. Bob

For More Information

[1] Vosniadou, S., & Brewer, W. F. (1992). Mental models of the Earth: A study of conceptual change in childhood. Cognitive Psychology, 24, 535–585.