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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.

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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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Authors and Affiliations

  1. Department of Curriculum and Instruction, Indiana University, 201 N. Rose Ave, Bloomington, IN, 47405, USA

    Erik Jacobson

  2. Department of Mathematics and Science Education, University of Georgia, 110 Carlton Street, Athens, 30602, GA, USA

    Andrew Izsák

Authors
  1. Erik Jacobson
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  2. Andrew Izsák
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Corresponding author

Correspondence to Erik Jacobson.

Appendices

Appendix 1: motivation questionnaire for using drawn models

The following questions ask about drawn models. Drawn models include number lines, area models, arrays, and other drawings or diagrams that represent mathematical concepts. Please answer the following questions (circle ONE for each question.)

figure a

Appendix 2: correlation table

The following three tables (Tables 5, 6, 7) list the correlations between the 30 variables used in this study: the purpose for use indicators (purp1, purp2), the frequency of use indicators (freq 1, freq 2), the opportunity to learn variable (otl), the logit of overall knowledge probability (know), the thirteen motivation indicators (motv1–motv13), a binary indicator for black (raceB), male (male), native English speaker (english), the number of math classes (mclass), the number of methods classes (medcl), a binary indicator for mathematics credential (mcred), for high school credential (hscred), the log years of experience teaching mathematics (teach), binary indicators for teaching Grade 6 (cur6) and Grade 8 (cur8) at the time of the survey, and amount of mathematics-focused professional development (mpd).

Table 5 The correlations between the variables 1–9 and variables 2–11
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Table 6 The correlations between the variables 1–14 and variables 12–20
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Table 7 The correlations between the variables 1–29 and variables 21–30
Full size table

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Jacobson, E., Izsák, A. Knowledge and motivation as mediators in mathematics teaching practice: the case of drawn models for fraction arithmetic. J Math Teacher Educ 18, 467–488 (2015). https://doi.org/10.1007/s10857-015-9320-0

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