A Toolkit for Analysing Approaches to Algebra

This chapter presents a toolkit for analysing approaches to algebra which was developed as a response to the diverse views of members of the Working Group on Approaches to Algebra (APPA) with respect to both what school algebra is and theories about teaching and learning. The interrelated dimensions of the toolkit incorporate a focus on the problem domain, the teaching approach, the theoretical perspective and the community of students. Within this context three approaches to algebra are analysed using the toolkit to illuminate differences which are grounded in classroom practice. The Working Group maintains that such differences often remain implicit within meta-level discussions of the mathematics education community.

[1]  James Aczel.  Towards a theoretical synthesis of research in the early learning of symbolic algebra , 2001 .

[2]  Ricardo Nemirovsky.  Mathematical Narratives, Modeling, and Algebra , 1996 .

[3]  J. Mason.  Expressing Generality and Roots of Algebra , 1996 .

[4]  A. Treffers.  Three Dimensions: A Model of Goal and Theory Description in Mathematics Instruction ― The Wiskobas Project , 1986 .

[5]  Jean-François Nicaud,et al.  Syntax and semantics in algebra , 2001 .

[6]  Proto-mathematics and/or Real Mathematics. , 1996 .

[7]  Helen Chick,et al.  The future of the teaching and learning of algebra : proceedings of the 12th ICMI Study Conference : The University of Melbourne, Australia, December 9-14, 2001 , 2001 .

[8]  Thomas J. Cooper,et al.  Moving from Arithmetic to Algebra Under the Time Pressures of Real Classrooms , 2001 .

[9]  Paul Cobb,et al.  Developing Mathematical Reasoning within the Context of Measurement , 1999 .

[10]  L. Brown,et al.  Poster 22: Complex Decision-Making in the Classroom: The Teacher as an Intuitive Practitioner , 1999 .

[11]  Thomas J. Cooper,et al.  Same Teacher, Different Teaching Behaviours When Students Are Using an ILS to Learn Algebra , 2001 .

[12]  R. Sutherland,et al.  Key Aspects of Teaching Algebra in Schools , 2002 .

[13]  Alf Coles,et al.  Needing to use algebra: a case study , 1999 .

[14]  James J. Kaput,et al.  Teaching and Learning a New Algebra , 1999 .

[15]  Alf Coles,et al.  Developing Practice: Teachers' Inquiry and Educational Change , 1997 .

[16]  Carolyn Kieran,et al.  Approaches to Algebra , 1996 .

[17]  S. Engel.  Thought and Language , 1964 .

[18]  L. Vygotsky.  Mind in Society: The Development of Higher Psychological Processes: Harvard University Press , 1978 .

[19]  Carolyn Kieran,et al.  Approaches to Algebra - Perspectives for Research and Teaching , 1996 .

[20]  Frances R. Curcio,et al.  Developing Mathematical Reasoning in Grades K-12. 1999 Yearbook. , 1999 .

[21]  Rosamund Sutherland,et al.  A Comparative Study of Algebra Curricula , 2002 .

[22]  B. Davis,et al.  Engaging minds : learning and teaching in a complex world , 2000 .

[23]  P. Boero.  Transformation and Anticipation as Key Processes in Algebraic Problem Solving , 2001 .

[24]  K.P.E. Gravemeijer,et al.  Developing realistic mathematics education , 1994 .

[25]  Patrick W Thompson,et al.  Quantitative reasoning, complexity, and additive structures , 1993 .

[26]  R. Sutherland,et al.  Perspectives on School Algebra , 2002 .

[27]  Alan H. Schoenfeld,et al.  In Fostering Communities Of Inquiry, Must It Matter That The Teacher Knows "The Answer"?* , 1996 .

[28]  Kaye Stacey,et al.  Curriculum Reform and Approaches to Algebra , 2001 .

[29]  Gl Claxton,et al.  The Intuitive Practitioner: On the value of not always knowing what one is doing , 2000 .

[30]  Keith O. Geddes,et al.  Solving Systems of Equations , 1992 .

[31]  Eugenio Filloy,et al.  Propositions Concerning the Resolution of Arithmetical-Algebraic Problems , 2001 .