Using computer algebra systems in mathematical classrooms

This paper describes a research whose main focus is the use of Computer Algebra Systems (CAS) in mathematical classrooms and the didactical possibilities linked with its use. The possibilities of integrating Self-Regulated Learning (SRL) within the CAS environment are brought into focus. Forty-three Israeli students (mean age 13.3) were assigned to two learning algebraic groups. The first group received explicit meta- cognitive SRL with CAS (CAS + SRL); the second group was exposed to CAS without SRL (CAS). Empirical results from the experimental and case study designs revealed that (CAS + SRL) students outperformed (CAS) students on algebraic thinking and that (CAS + SRL) students regulated their learning more effectively.

[1]  Susan N. Friel,et al.  Navigating Through Algebra in Grades 6-8 , 2001 .

[2]  Margaret J. Kenney,et al.  Communication in mathematics, K-12 and beyond , 1996 .

[3]  Kaye Stacey,et al.  STUDENTS' UNDERSTANDING OF ALGEBRAIC NOTATION: , 1997 .

[4]  A. Sfard,et al.  The gains and the pitfalls of reification — The case of algebra , 1994 .

[5]  Z. Mevarech,et al.  Improve: A Multidimensional Method For Teaching Mathematics in Heterogeneous Classrooms , 1997 .

[6]  Candace S. Bos,et al.  Cognitive and metacognitive characteristics of eighth grade students' mathematical problem solving , 1990 .

[7]  Orit Zeichner,et al.  Using Technology to Enhance Mathematical Reasoning: Effects of Feedback and Self-Regulation Learning , 2001 .

[8]  E. Corte,et al.  ENHANCING LEARNING AND PROBLEM SOLVING SKILLS: ORIENTING AND SELF- JUDGING, TWO POWERFUL AND TRAINABLE LEARNING TOOLS , 1999 .

[9]  B. Kramarski,et al.  The effects of metacognition and email interactions on learning graphing , 2002, J. Comput. Assist. Learn..

[10]  S. Stein What's All the Fuss About? , 1996 .

[11]  Bracha Kramarski,et al.  Effects of Multilevel Versus Unilevel Metacognitive Training on Mathematical Reasoning , 2001 .

[12]  Elsbeth Stern,et al.  Interaction between Knowledge and Contexts on Understanding Abstract Mathematical Concepts , 1997 .

[13]  D Kerslake,et al.  Children's Understanding of Mathematics: 11-16 , 2004 .

[14]  Mark Huisman,et al.  Self-regulated learning as a cross-curricular competency , 1999 .

[15]  Kaye Stacey,et al.  STUDENTS' UNDERSTANDING OF ALGEBRAIC NOTATION: 11–15 , 1997 .

[16]  Douglas J. Hacker Definitions and Empirical Foundations , 1998 .

[17]  Joe Garofalo,et al.  Metacognition, Cognitive Monitoring, and Mathematical Performance. , 1985 .

[18]  K. Hart,et al.  Children's understanding of mathematics: 11-16 , 1981 .

[19]  Bracha Kramarski,et al.  Enhancing Mathematical Reasoning in the Classroom: The Effects of Cooperative Learning and Metacognitive Training , 2003 .