Self-explanation is the technique of explaining to another person (or yourself) what you are doing whilst you work and why e.g. precisely detailing why you are times the numerator by 7 and the denominator by 2 or what happens in a synapse when it fires to transfer a signal from one neuron to the next.
This can be put in to practice by asking yourself or another person to explain exactly what it is they mean when they are writing an essay or what they are doing when solving a maths problem. The prompt questions you can use can be either "content-free" or "content-specific"; they can include no information about the question at hand (e.g. "Explain what the sentence means to you. That is, what new information does the sentence provide for you? And how does it relate to what you already know?") or they can contain relevant information to the question (e.g. "Why do you calculate the total acceptable outcomes by multiplying?").
There have been many different studies examining the efficacy of self explanation and the circumstances in which it works best. Bielaczyc et al. (1995) conducted an experiment on 24 students (a very low number of participants) embarking on a programming course and divided them into two groups; those who received explicit instructions on how to effectively use self explanation and those who just received written instructions. They found (unsurprisingly) that those who were given explicit instructions used self explanation more and this increased use of self explanation was associated with greater performance gains. However this positive result should be taken with a pinch of salt as both conditions were actually told to use self explanation (with the experimental group actually being shown how to do it and the control group just receiving written instructions) and the fact it has a very small number of participants.
Aleven & Koedinger (2002) found that 15 and 16 year old children taking a geometry class scored higher in a subsequent test after using self explanation than the children who (during practice) just provided the correct answer. During practice, the students used a Cognitive Tutor (an interactive computer program that helped students) across all conditions e.g. participants in the self explanation condition explained each step they took and got feedback from the program as to whether it was correct. Whilst they found a positive effect for self explanation, this study also suffered from a low number of participants (41 participants, only 24 of whom actually completed the experiment).
Rittle-Johnson (2006) looked whether self explanation helped students with maths problems they had not encountered yet. There were two variables; instruction vs no instruction and self explanation vs no self explanation. She found that students who were given instructions on how to get the correct answer and those who (after getting the answer) had to explain why one answer was correct and another was incorrect, had greater procedural knowledge (the steps they had to do in order to get the correct answer). There was no interaction between instruction and self explanation. This study had enough participants per condition to have sufficient power (so you can be more confident that the finding isn't a false-positive; Simons, Nelson & Simonsohn, 2011). This study also tested the students after a two week delay and found that participants who used self explanation scored the highest. However the participants were tested immediately after the intervention so practice testing may have had some effect on understading (Dunlowsky et al., 2013)
However, it should be noted that the utility of self explanation is massively diminished when students are provided with explanations of the answer; presumably because students put in little effort before looking at the answers (Schworm & Renkl, 2006, as cited in Dunlowsky et al., 2013).
Overall it would seem that self explanation can be effective for learning, but more research needs to be done to determine how much of an effect it has and how long its effects last.
Aleven, V. & Koedinger, K. (2002). An effective metacognitive strategy: learning by doing and explaining with a computer-based Cognitive Tutor. Cognitive Science. 26 (1), 147–179.
Bielaczyc, K.; Pirolli, P. & Brown, A.. (1995). Training in Self-Explanation and Self-Regulation Strategies: Investigating the Effects of Knowledge Acquisition Activities on Problem Solving. Cognition and Instruction. 13 (2), 221-252.
Dunlosky, J.; Rawson, K.; Marsh, E.; Nathan, M. & Willingham, D. (2013). Improving Students’ Learning With Effective Learning Techniques: Promising Directions From Cognitive and Educational Psychology. Psychological Science in the Public Interest. 14 (1), 4-58.
Rittle-Johnson, B.. (2006). Promoting Transfer: Effects of Self-Explanation and Direct Instruction. Child Development. 77 (1), 1-15.
Simons, J.; Nelson, L. & Simonsohn, U. (2011). False-Positive Psychology: Undisclosed Flexibility in Data Collection and Analysis Allows Presenting Anything as Significant. Psychological Science. 22 (11), 1359–1366.
Schworm, S. & Renkl, A. (2006). Computer-supported example based learning: When instructional explanations reduce selfexplanations. Computers & Education, 46 (1), 426–445.