Brief statement of principle
Post-practice reflection involves activities that follow successful completion of a quantitative problem aimed at helping students to understand the concepts associated with that problem and to develop abstract problem-solving schema. Such schema are a kind of knowledge component that if acquired with high feature validity will help students with solving similar (near transfer) problems, and perhaps also far-transfer problems.
Post-practice reflection activities often involve some kind of dialogue between the student and another agent (teacher, peer, or computer tutor).
Here is a sample Reflective Dialogue, incorporated within the Andes physics tutoring system (VanLehn et al., 2005):
TUTOR: Which major principle did you need to solve the problem? [Just the name, please]
STUDENT: Newton's 2nd law
TUTOR: Yes. The main difference between this problem and most of the previous N2L problems is the fact that the direction of acceleration is __________. (fill in the blank)
TUTOR: Correct. All else being the same, how would the velocity at the lowest point of the swing change if the length of the rope were doubled to 4.0 m?
STUDENT: it would also double
TUTOR: Well, it would increase, but it would not double; recall that the formula for centripetal acceleration involves the square of the velocity. If the radius doubles, the square of the velocity would double also, to maintain the same centripetal acceleration.
All else being the same, how would the velocity at the lowest point of the swing change if the mass of the ball were doubled to 10 kg?
STUDENT: it would decrease...
Katz, S., & Allbritton, D., & Connelly, J. (2003). Going beyond the problem given: How human tutors use post-solution discussions to support transfer. International Journal of Artificial Intelligence and Education, 13 (1), 79-116.
Katz, S., Connelly, J., & Wilson, C. (2007). Out of the Lab and into the Classroom: An Evaluation of Reflective Dialogue in Andes. In K. Koedinger and R. Luckin (Eds.), Proceedings of AI in Education 2007.
Katz, S., Connelly, J., & Wilson, C. (2007). An Evaluation of Reflective Dialogue in Andes. Poster presented at the Physics Education Research Conference (PERC 2007), Greensboro, NC.
Lee, A. Y., & Hutchison, L. (1998). Improving learning from examples through reflection. Journal of Experimental Psychology: Applied, 4 (3), 187-210.
VanLehn, K., Lynch, C., Schulze, K., Shapiro, J.A., Shelby, R., Taylor, L., Treacy, D., Weinstein, A., & Wintersgill, M. (2005). The Andes physics tutoring system: Lessons learned. International Journal of Artificial Intelligence and Education, 15 (3).
VanLehn, K., Lynch, C., Schulze, K. Shapiro, J. A., Shelby, R., Taylor, L., Treacy, D., Weinstein, A., & Wintersgill, M. (2005). The Andes physics tutoring system: Five years of evaluations. In G. McCalla, C. K. Looi, B. Bredeweg & J. Breuker (Eds.), Artificial Intelligence in Education (pp. 678-685). Amsterdam, Netherlands: IOS Press.