By: Kelsey Gilbert

Learning new concepts in a math class at any level of education can be challenging. To learn these concepts well, it is important to use an effective strategy that strengthens your understanding of the material. Self-explanation is a learning technique in which you not only provide the explanation of the problem that you’re faced with, but you are also the one who is benefitting from the explanation (1). So, self-explanation is explaining the concept, the steps, and the solution to yourself in order to develop a deeper understanding of the material.

How is self-explanation effective for learning mathematical concepts?

Self-explanation can deepen your understanding of the concepts you are trying to learn, and it can also draw attention to the errors you make while solving the problem, so that you can correct them (2). Additionally, one of the main benefits of self-explanation is that it can increase your ability to transfer the knowledge and skills learned with one concept to different situations that call for the same knowledge (3).

What exactly is this “transfer of knowledge”? For example, I know how to find the mean (or average) of a set of numbers, and when I was taking a statistics class in college in order to find the standard deviation in a data set I had to find the mean in one of the steps. I was able to transfer my skills of finding the mean from a basic algebra class to finding the standard deviation in a statistics class. This ability to transfer knowledge and skills from one situation to another ultimately benefits your ability to learn new concepts in different areas of math. (For more on transfer and how difficult it is to achieve, see here and here).

Here’s an example of a study that has looked at self-explanation in a real student population. In this study, elementary school students tried to solve mathematical word problems (4). Students were assigned to one of three groups: the self-explanation group, the self-learning group, or the control group. Those in the self-explanation group were told to self-explain each step of a worked example, those in the self-learning group listened to the teacher explain the worked example and the studied it, and those in the control group studied the worked example without explanations. Performance was measured immediately and a month later. Students in the self-explanation group did reliably better than students in both the self-learning and control groups on the immediate test, and reliably better than the control group on the test a month later. The authors believed that self-explanation improved the understanding of elementary students’ word problems because the students were able to reconstruct information into complete mental models.

In another study, high school students tried to learn a geometry theorem (5). The students were placed in one of two groups: the self-explanation group, or the control group where they studied as they usually would. The students who used self-explanation outperformed the control group in a posttest when solving more difficult problems.

How can you use self-explanation in math?

This is an example of how I use self-explanation when finding the mean of a set of numbers. In each step I wrote out what I would be explaining to myself as I went through the calculation.

Step 1. To find the “mean” of a set numbers means I am finding the average.

Step 2. The numbers I have in my number set are 8, 12, 5, 10, 13.

Step 3. To find the mean I first need to add all of these numbers up… I got 48.

Step 4. Then I need to divide the sum of these numbers by the count, which is how many numbers there are in this set. There are 5 numbers in the set so I will divide 48 by 5.

Step 5. The mean is 9.6!

What are the limitations of self-explanation?

When students focus on improving their understanding of a concept, their skills can transfer to other problems in the same domain. Sometimes, however, students focus solely on restating the steps of one particular problem, which does not improve understanding of the problem as a whole, and in turn their skills will not transfer. Additionally, if students’ self-explanations are conceptually incorrect, they can acquire incorrect knowledge (1). This could be even more detrimental to their education than not understanding a concept at all, because they think they’ve learned something and are unable to see their errors.

Finally, although self-explanation is associated with improved concept acquisition, spontaneous self-explanations are uncommon, meaning that students do not tend to self-explain on their own (6). Since self-explanation is not a natural study habit, teachers might want to consider instructing their students in this technique.

References

(1) Berthold, K., & Renkl, A. (2009). Instructional aids to support a conceptual understanding of multiple representations. Journal of Educational Psychology, 101, 70-87.    

(2) Richey, J. E., & Nokes-Malach, T. J. (2015). Comparing four instructional techniques for promoting robust knowledge. Educational Psychology Review, 27, 181-218.

(3) Lombrozo, T. (2006). The structure and function of explanations. Trends in Cognitive Sciences, 10, 464-470.

(4) Tajika, H., Nakatsu, N., Nozaki, H., Neumann, E., & Maruno, S. (2007). Effects of self-explanation as a metacognitive strategy for solving mathematical word problems. Japanese Psychological Research, 49, 222-233.

(5) Wong, R. F., Lawson, M. J., & Keeves, J. (2002). The effects of self-explanation training on students' problem solving in high-school mathematics. Learning and Instruction, 12, 233-262.

(6) Renkl, A. (1999). Learning mathematics from worked-out examples: Analyzing and fostering self-explanations. European Journal of Psychology of Education, 14, 477-488.