NOMAD 11(3), 2006. Defining moments in the graphing calculator solution of a cubic function task

Skapad: 2006-10-31. Ändrad: 2006-11-02  

NOMAD 11(3), 2006. Defining moments in the graphing calculator solution of a cubic function task

JILL BROWN and GLORIA STILLMAN

Abstract

A case study investigated cognitive, mathematical, and technological processes undertaken by senior secondary students as they searched for a complete graph of a difficult cubic function using a graphing calculator. Intensive qualitative macroanalysis identified several defining moments in the solution process. Those related to use of scale marks and identification of key function features are presented. Students' understanding of scale marks varied and this impacted on the efficiency and elegance of their solution. A range of calculator features was used in identifying key feature coordinates. These were not always used successfully or with an understanding of the mathematics underpinning their operation.

Sammenfatning

Denne artikel rapporter et case-studie til undersøgelse af kognitive, matematiske og teknologiske processer hos gymnasieelever (11. og 12. klassetrin), der arbejder med at tegne en fuldstændig graf for et vanske-ligt 3. gradspolynomium ved hjælp af en grafregner. Intensive analyser af elevernes virksomhed har identificeret en række "defining moments" (afgørende momenter) i elevernes løsningsprocess, der er bestemmende for forløbet af deres virksomhed og for deres brug af grafregneren. I artiklen præsenteres og analyseres "defining moments" knyttet til elevernes brug af skalering og enheder ved tegning af funktionens graf samt til elevernes udnyttelse af grafregnerens faciliteter til bestemmelse af koordinater for funktionsgrafens karakteristiske punkter. Der var stor variation i elevernes forståelse af skalering og dette havde indvirkning på effektiviteten og grad af elegance i elevernes løsningsstrategier. Eleverne brugte en række af grafregnerens forskellige faciliteter til bestemmelse af koordinater for grafens karakteristiske punkter, men ikke altid på en succesfuld måde og heller ikke altid baseret på forståelse af den matematik der ligger til grund for deres operationer på grafregneren.

JILL BROWN
Jill Brown was a secondary mathematics teacher for over two decades and has recently joined the staff at Australian Catholic University where she is a lecturer in mathematics education. Research interests include use of graphing calculators in the teaching of function at the secondary level. Jill is currently undertaking her doctoral studies within the field of technology-rich teaching and learning environments at the University of Melbourne. The research presented in this article was undertaken for Jill's research masters thesis at the University of Melbourne.

GLORIA STILLMAN
Gloria Stillman is a senior lecturer of mathematics education in the science and mathematics education cluster within the faculty of education at the University of Melbourne, Victoria, Australia. Research interests include teaching and assessing higher-order thinking through applications and mathematical modelling, metacognition, technology use in mathematics teaching at the secondary level, curriculum change, and ethnomathematics.