On Understanding of Multiplicative Identites in Junior Secondary Students.

• Main Authors: Sheng-Ho Chang, 張勝和
• Other Authors: Sou-Yung Chiu
• Format: Others
• Language: zh-TW
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/27007810703477574400

碩士 === 國立彰化師範大學 === 科學教育研究所 === 83 === It is to explore junior secondary students''''understanding of mul- tiplicative identities,especially when the students fall short of competence inmathematics.The attempt is to answer the following three questions:1.What are students''''errors in solving problems of multiplicative identities and the related mathematical tasks? 2. How do students achieve conceptual change about multiplicative identities and related mathematical knowledge? 3.How to probe into suitable remedial instruction? Qualitative method is used in data collection and analyses, including one-to-one interview and field-note-taking,video and audio taping while students solve problems.Protocols are made afterwards and analyzed.It''''s found : 1.Students often commit systematic errors.(1)Answers are impro- perly expressed,such as: X+X=X^2, X．X＝2．X.(2).Meanings of operations are confused,or, coefficients and exponents are mis- placed,such as:X+X=X^2; X^2+ X=X^3.(3)False analogy or mal- generalization,such as:(ab)^2= a^2 b^2 implies (a+b)^2=a^2＋b^2. (4)Misconception of"common factors",such as:3X．3X=(3．3)X=9X (X as common factor),or 3X．3 X=3(X．X)=3X^2(3 as common factor) (5)False composite of different terms or the coefficients of different terms,such as:4+3N=7N. 2.Misconceptions are robust to change.Basing on prior knowledge and encountering cognitive conflicts,students may produce conceptual change.Through numerical substitutions or geometric diagrams,students appreciate the meanings of letters and algebraic expressions and visualize the missing terms and imcomposables in the alleged contradictions. To sum up,it is necessary to provide familiar problem situations and to shed light on students''''prior knowledge in the remedial remedial instruction . More research waits to be headed on how to make students aware of the founding princples of algebra through analogical reasoning.