A Study and Development on Learning Environment that used “Multiplication Cross” on Lower Secondary School

Abstract

　　The purpose of this study is to consider the unit about multiplication and factorization of polynomial in lower secondary school, and to develop a learning environment about this unit.

　　Especially, to achieve this purpose, we focus attention on a calculation format that is called“Multiplication Cross”.　This calculation format has been introduced in“Das Zahlenbuch”by E. Ch. Wittmann.　And this concretizes trial-and-error method in student’s learning activities.　So we used this calculation format as a problem for designing learning environment of multiplication and factorization of polynomial.

　　As empirical study, we designed learning environments of 6 unit times, and practiced experimental lessons in grade 9 class.　In consequence, we got following 4 suggestions for this design of learning environment.

1）“Multiplication cross”can be a scaffolding for students to solve problems of multiplication and factorization of polynomial.

2）“Multiplication cross” induce more inquiry learning in students learning activities.

3）“Multiplication cross” give students the ability to solve evolution problems of multiplication and factorization of polynomial.

4） We have to pay attention to how the formulas are introduced in learning of multiplication and factorization of polynomial.

　　In accord with these suggestions, we would like to continue to investigate how this learning environment in lower secondary school can be redesigned.