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.
doi:10.1080/07370000701632405
