ANALYSING STUDENTS’ MISTAKES WHEN SOLVING DIVISION AND POLYNOMIAL PROBLEMS FROM THE “DIDACTIC CONTRACT” APPROACH

Thiện Chí Nguyễn

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Abstract

 

 

In this article, we use the concept of “didactic contract” introduced by Guy Brousseau in 1980 as a tool to analyse students’ mistakes.

From the analysis of Math textbooks and exercises for Grade 8 volumes 1, this article proposes two rules of “didactic contract” related to solving division and polynomial division problems: design situations to verify “didactic contract” and conduct an experiment.

The research results show that many students commit mistake of solving these problems, which derived from the “didactic contract” approach:  

“When students solve problems proving that A(n) (n is a natural number or an integer) is divisible by a natural number other than 0 and 1, students commit a mistake by not considering the condition of variable n depends on new variables” and “Students’ mistake in thinking that the quotient of a polynomial division of a variable with an integer coefficient is a polynomial with an integer coefficient”.

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References

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