Multiple solution problems and mathematical thinking: Wasan geometry example

Abstract

Wasan geometry flourished in Edo period of Japan as arty, multiple solutioned and systematic. Teachers are not open and papers are not evaluated. Multiple solutions are seen in parallel with advanced mathematics thinking. 80 middle school and 37 high school pre service math teachers were given a Wasan problem and grouped according to correct answers, different answers, and originality. 24 different answers (equality of diagonals of a square, symmetry, equality of tangent lines, auxiliary lines and auxiliary shapes, cosines’ theorem, tan (67.5), similarities, types of triangles etc.) were detected. Answers were also coded for composite answers (who include two different rules), or simple one ways, first answers, similar solution ways and 5-6 different solutions.