Factors Affecting Pre-Service Teachers' Evaluations of the Validity of Students' Mathematical Arguments in Classroom Contexts
Cognition and Instruction
2007, Vol. 25, No. 4, Pages 479-522
Anne K. Morris
University of Delaware
This study was designed to identify the types of understandings, skills, and beliefs that affect pre-service teachers' evaluations of students' mathematical arguments in classroom contexts. Thirty-four pre-service teachers read a transcript of a third grade lesson in which the students were expected to prove a generalization. To investigate whether pre-service teachers evaluate students' arguments in a consistent way across different classroom contexts, pre-service teachers' evaluations of the responses were examined in two experimental conditions. In the first condition, one student made a valid argument that proved why the generalization was true, and in the second condition, this student's response was omitted from the transcript. Findings included the following: 1) Pre-service teachers' evaluations of students' inductive arguments differed dramatically across conditions; 2) Pre-service teachers rarely used logical validity as a criterion for evaluating arguments; 3) Pre-service teachers exhibited a wide variety of conceptions about the relationships among mathematical proof, explaining why something is true in mathematics, and inductive arguments, and these conceptions affected their evaluations of students' arguments; 4) Many pre-service teachers were able to distinguish between student responses that did and did not explain why a generalization was true; and 5) Pre-service teachers used their own knowledge to fill in "holes" in students' arguments which led to inappropriate evaluations of students' arguments and understanding. Implications for teacher preparation programs are discussed.