Using calculators to teach algebra : from numbers to operations to structure

• Main Author: Murphy, Maureen
• Language: English
• Published: 2009
• Online Access: http://hdl.handle.net/2429/5884

The problems of teaching mathematics to unmathematical high school students are described and analyzed in terms of differences in language, especially syntax, between arithmetic and algebra. There follows a detailed description of a demonstrably successful alternative to so-called regular mathematics courses which depends essentially on the use of electronic calculators. Over three years, 274 students in 11 of the author's own mathematics classes, where algebra was taught in this alternative way, were observed for signs of mathematical insight. Relevant anecdotes were recorded, analyzed, and categorized and are discussed so as to justify the claims that, by using electronic calculators, teachers can shift the attention of students from numbers to mathematical operations and from operations to the overall structure of algebraic expressions, and that students who are taught algebra in this way reveal spontaneously, both orally and in writing, that they have an understanding of algebra. Finally, it is suggested that the difficulties encountered by many students in high school algebra could be reduced or eliminated if unmathematical students were taught in this way alone and mathematical students were taught in this way first, before proceeding to so-called regular mathematics courses.