
05616348
j
2009e.00472
Choi, Sangki
Le, Jee Hae
Teaching factorization in school mathematics.
J. Korea Soc. Math. Educ. Ser. A, Math. Educ. 48, No. 1, 8191 (2009).
2009
Korean Society of Mathematical Education (KSME), Seoul
KO
H24
H34
I24
U24
elementary algebra
solving equations (theory)
divisibility
factorization of polynomials
Summary: This paper focuses on two problems in 10th grade mathematics, the rational zero theorem and the content (the integer divisor) of a polynomial. Among 138 students participated in the problem solving, 58 of them (42 \%) has used the rational zero theorem for the factorization of polynomials. However, 30 of 58 students (52 \%) consider the rational zero theorem is a mathematical fake (false statement) and they only use it to get a correct answer. There are three different types in the textbooks in dealing with the content of a polynomial with integer coefficients. Computing the greatest common divisor of polynomials, some textbooks consider the content of polynomials, some do not and others suggest both methods. This also makes students confused. We suggest that a separate section of the rational zero theorem must be included in the text. As for the content of a polynomial, we consider the polynomials are contained in the polynomial ring over the rational numbers. So computing the gcd of polynomials, guide the students to give a monic (or primitive) polynomial as an answer.