# Knowledge and motivation as mediators in mathematics teaching practice: the case of drawn models for fraction arithmetic

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## Abstract

Past studies have suggested that in light of recent curriculum standards, many US teachers make limited use of drawn models in their mathematics instruction. To gain insight into this phenomenon, we investigated relationships between US teachers’ opportunities to learn about, knowledge of, motivation for, and instructional use of drawn models for representing multiplication and division of fractions. A national sample of 990 practicing middle-grade teachers was administered a three-part survey that contained a knowledge assessment; a professional history and teaching practices questionnaire that included questions about opportunities to learn to use drawn models; and a motivation questionnaire that measured teachers’ value, anxiety, and self-concept of ability for using such models in instruction. In regression models without motivation, opportunity to learn significantly predicted the teachers’ knowledge, frequency of use, and purpose for use of drawn models. In structural equation models that included motivation, knowledge and motivation substantially accounted for relationships between the teachers’ opportunity to learn and their self-reported use of drawn models in instruction. These findings are consistent with the general hypothesis that teacher’ opportunities to learn teaching practices indirectly affect their instructional practices. Teachers’ knowledge and motivation also play a central role.

## Keywords

Teacher knowledge Teacher motivation Mathematical knowledge for teaching Practicing teachers## Notes

### Acknowledgments

This research was supported by the National Science Foundation (NSF) under Grant DRL-0903411. The opinions expressed are those of the authors and do not necessarily reflect the views of NSF.

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