Learning Mathematics From Classroom Instruction: On Relating Lessons to Pupils' Interpretations

Abstract

How do students learn mathematics from classroom instruction? We propose a framework in which we assume that a student must form a coherent mental representation of the events that take place in a lesson and then use this representation to construct new knowledge. The process of representing the events of a lesson as a coherent whole is assumed to be affected by characteristics of the lesson (e.g., the clarity with which goals are expressed), as well as by characteristics of the student trying to learn from the lesson (e.g., background knowledge, lesson schemas). This framework is applied (a) by assessing both the nature of the mental representations students form of lessons and what they have learned from the instruction and relating the two, (b) by manipulating the way a lesson is taught and seeing how this affects how it is represented, and (c) by seeing how students who differ in various ways represent the same lesson. A description of four empirical studies is supplied by way of illustration.