Flexible Solving Strategies in Algebra Remain in the Long Term
Hitoshi Nishizawa nisizawa@toyotact.ac.jp
Electrical & Electronics Engineering
Takayoshi Yoshioka
yoshioka@toyotact.ac.jp
Toyota National College of Technology Japan
Abstract
Reduced teaching hours of mathematics in primary and secondary schools
in Japan seem to enhance surface learning among Japanese students. If a
student surfacelearns 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 webbased
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.
