Flexible Solving Strategies in Algebra Remain in the Long Term

Abstract

Reduced teaching hours of mathematics in primary and secondary schools in Japan seem to enhance surface learning among Japanese students. If a student surface-learns mathematics, he/she simply memorizes formulas, and uses them without understanding the embedded mechanisms. His/Her solving strategy depends on symbolic calculations and quite rigid. His/Her answer sheet hardly includes any qualitative analysis, numerical confirmations, graphs, or explaining sentences. Flexible solving strategies and rich descriptions on answer sheets, we think, make a useful measure if the student has overcome surface learning. In this preliminary study, we tried to confirm if flexible solving strategies, which they learned with the use of our web-based instruction system two years ago, still remain in their engineering problem solving procedures. We selected a problem of a basic electrical circuit, where it takes time if a student sticks to symbolic analysis, but it is easier to answer if he/she uses graphs or analyzes qualitatively. Almost all the students could write the key formula for the problem in their answer sheets, but some students stopped there without adding any meaningful descriptions. They apparently have rigid solving strategies, which might be related to surface learning. On the other hand, the students, who have learned flexible solving strategies in algebra, seem to have more flexibility in their problem solving. We think it makes a small evidence to support that flexible problem solving strategies in algebra remain in the long term.