Based on a longitudinal study of beginning teachers struggles conveying algebra in the classroom, this review uses didactical situations theory to analyze the constraints on student understanding, and provides practical suggestions for teaching and research.
Describes three separate analytic categories for teaching and learning algebra
Introduction. -Theoretical Framework.- Theoretical Foundation for a Pattern Based Approach to Algebra.- Methodology.- Epistemological and Didactical Analyses of the Mathematics Potential in Tasks on Generalisation of Shape Patterns.- Constrained Feedback Potential in Adidactical Situations.- Complexity of Turning a Situation of Action into a Situation of Formulation.- Complexity of Operating in the Situation of Validation.- Synthesis.- References.- Appendices._
The book is based on a longitudinal study of beginning teachers' struggles with algebra, with strong foundation in the theory of didactical situations (Brousseau, 1997). The focus is on factors that constrain students engagement with algebraic generality in shape patterns. Participants in the study are six student teachers and two teacher educators of mathematics. The empirical material consists of videotaped classroom observations and the mathematical tasks with which the students engaged. Three analytic categories emerged from an open coding process which show that the students algebraic generalization is constrained by: 1) a limited feedback potential in situations where the students are supposed to solve the mathematical tasks without teacher intervention; 2) obstacles the students face when they shall transform into algebraic notation formulae they have expressed informally in natural language; and, 3) challenges with justification of formulae and mathematical statements that the students have proposed. This book provides many practical and concrete examples to guide mathematics education researchers, mathematics teacher educators, and mathematics educators in teaching algebra in a variety of contexts and environments.