A Collective Case Study of the Influence of Teachers’ Beliefs and Knowledge on Error-Handling Practices During Class Discussion of Mathematics
Wendy S. Bray
This collective case study examines the influence of 4 third-grade teachers’ beliefs about and knowledge of their error-handling practices during class discussion of mathematics. Study findings suggest that, although teachers’ ways of handling student errors during class discussion of mathematics are clearly linked to both teacher beliefs and teacher knowledge, some aspects of teacher response are more strongly linked to knowledge and others are influenced more by beliefs.
Understanding Prospective Mathematics Teachers’ Processes for Making Sense of Students’ Work With Technology
P. Holt Wilson, Hollylynne Stohl Lee and Karen F. Hollebrands
This study investigated the processes used by prospective mathematics teachers as they examined middle school students’ work solving statistical problems using a computer software program. Ways in which the model may be used by other researchers and implications for the design of pedagogical tasks for prospective teachers are discussed.
Using Dynamic Sketches to Enhance Preservice Secondary Mathematics Teachers’ Understanding of Limits of Sequences
Beth L. Cory and Joe Garofalo
This study investigates 3 preservice secondary mathematics teachers’ understandings of limits of sequences and their changing conceptions of limit during and after instruction involving interactive, dynamic sketches embodying the formal definition of the limit of a sequence. Manipulating a coherent visual representation of the formal definition in the contexts of various sequences, coupled with answering carefully chosen questions and completing interview tasks before, during, and after technology-enhanced instruction, gave the participants opportunities to investigate and reflect on their own concept image as they compared their understandings to the results of the actions they performed on the sketch.