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Sustainable changes in teacher practices: a longitudinal analysis of the classroom practices of high school mathematics teachers

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Abstract

This study examines the effects of professional development on various aspects of teachers’ mathematics instruction. Using data collected between 2005 and 2009, we examined the extent to which the instructional practices of 49 US high school teachers who participated in content-based, sustained professional development changed over time. We found that changes in several aspects of their instructional practices followed somewhat different patterns. Teachers made statistically significant and steady changes in mathematical discourse, instructional clarity, and the development of students’ mathematical habit of mind, but not in student interactions or in the use of multiple representations.

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Notes

  1. By reform-based mathematics teaching, we are referring to inquiry-based teaching in which teachers create an environment where students actively engage in problem-solving activities and make sense of mathematical concepts through investigation and discussion.

  2. This study included only the first two cohorts because the goal of the study was to investigate the long-term effects of the program. Classroom observations conducted with the teachers in the third cohort were not longitudinal.

  3. Depending on the needs of the cohort, the content covered in summer institutes varied by cohort to some extent.

  4. Throughout the duration of the program, the external evaluator of the project reworded or replaced some items. However, the 40 items that stayed the same in all versions of the instruments were included in the data analysis.

  5. Given that factor analysis is dependent on correlations among items, using tetrachoric correlations is more appropriate for binary items. Therefore, we preferred to use two separate factor analyses. In both analyses, we used principal components analysis with varimax rotation and retained only factors with eigenvalues >1.

  6. Classroom climate scale measuring the climate of respect of teachers and their students for each other was not included in the data analysis because teachers’ average score on the baseline measure was .9 out of a maximum of 1, which did not leave room for growth on this scale.

  7. Teachers’ grade levels were not included in the analysis because many teachers were teaching multiple grade levels in a given year.

  8. Analyses were also conducted separately for the two cohorts to investigate whether the overall observed trend was similar for both cohorts, which was similar across all five scales. In addition, an alternative two-level model with cohort added as a Level 2 variable resulted in similar coefficients for the “time” variable.

  9. All models were fit using the mixed methods procedure (PROC MIXED) in SAS/STAT software (SAS Institute Inc., 2008). Additionally, given that the data were collected from the same teachers over time, residuals within teachers were correlated. Hence, the autocorrelated error needed to be taken into consideration in addition to the random error (e.g., measurement errors and missing variables; Hedeker and Gibbons 2006). The autoregressive structure was used to test whether a serial correlation needed to be taken into account.

  10. The residual correlation was not significant for any of the models for all scales, which indicates that the correlation between errors was not significant. Neither teachers’ scores on the content knowledge instrument nor years of teaching experience were related to the improvement in their mathematics instruction; therefore, they were excluded from the data analysis and from the final models reported here.

  11. Teachers’ scores on the Multiple Representations scale did not change noticeably throughout the program (p = .30).

  12. The coefficient for semester2 in Table 3 represents a quadratic change on the Student Interactions scale.

  13. Because the coefficient for semester was positive (p < .001) but for semester2 was negative (p < .002), teachers’ scores on the Student Interactions scale initially increased and then gradually decreased.

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Acknowledgments

This study is based upon work sponsored by a grant from the National Science Foundation under the Grant No. EHR 0412072.  Any opinions, findings, and conclusions expressed herein are those of the authors and do not necessarily reflect the views of the National Science Foundation.

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Authors and Affiliations

  1. Department of Curriculum and Instruction, University of Houston, 434 Farish Hall, 4800 Calhoun Rd., Houston, TX, 77204, USA

    Yasemin Copur-Gencturk

  2. Rice University School Mathematics Project, Rice University, Houston, TX, USA

    Anne Papakonstantinou

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  1. Yasemin Copur-Gencturk
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Correspondence to Yasemin Copur-Gencturk.

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Copur-Gencturk, Y., Papakonstantinou, A. Sustainable changes in teacher practices: a longitudinal analysis of the classroom practices of high school mathematics teachers. J Math Teacher Educ 19, 575–594 (2016). https://doi.org/10.1007/s10857-015-9310-2

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