Are Teachers Amenable to Increasing Students' Scope of Work in Doing Proofs? Estimating Teachers' Decision-Making Using a Diagnostic Classification Model

Abstract

We investigate teachers' decision making in contexts where they could choose to provide students more authentic experiences with proving. Specifically, we investigate their preferences to depart from norms about what proof problems to assign to students. Scenario-based instruments consisting of two sets of items reflecting two hypothesized norms in doing geometric proofs, the given and prove norm and the diagrammatic register norm, were used to operationalize teachers' preference to depart from instructional norms in order to increase students' share of labor. By applying a diagnostic classification model (DCM) to classify teachers with respect to their depart from two norms, this study shows that teachers' decisions depend on the norm at issue. To examine individual factors associated with preference profiles, we use scores of teachers' mathematical knowledge for teaching, beliefs on the importance of student autonomy, and confidence in mathematics teaching. This study also illustrates methodological benefits of a DCM model in estimating a binary construct (i.e., teachers' preference), which has more than one sub-construct, with a small number of items.

Keywords

• doing proofs
• instructional situations
• scenario-based assessments
• high school geometry
• teacher decision making
• instructional norm
• diagnostic classification model