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Prospective teachers’ learning to provide instructional explanations: how does it look and what might it take?

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Abstract

Several studies have documented prospective teachers’ (PSTs) difficulties in offering instructional explanations. However, less is known about PSTs’ learning to provide explanations. To address this gap, we trace changes in the explanations offered by a purposeful sample of PSTs before and after a mathematics content/methods course sequence. Consistent with prior research, our study reveals the limitations in PSTs’ explanations at their entrance to the course sequence. It also documents PSTs’ progress in providing explanations, thus providing existence proof that this practice is learnable. Using evidence from multiple sources, we also propose a component entailed in this learning—learning how to unpack one’s thinking through the use of representations as explanatory tools—and four factors associated with it, including PSTs’ subject-matter knowledge, active and deliberate reflection on practice, productive images for engaging in this work, and productive dispositions about engaging in this practice. We discuss the implications of our findings for teacher education and offer directions for future research.

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Notes

  1. Although taught by a single instructor, these courses were the result of a collaborative effort of mathematics educators, mathematicians, practicing teachers, researchers, and graduate students, who, over the past 15 years, have worked together to design, teach, reflect on, and refine the courses (see more in Ball et al. 2009).

  2. The letters denote whether the excerpt comes from a pre-coursework (PE), post-coursework (PO), or a post-program (PP) interview; the numbers represent the transcript lines from which the excerpt was drawn.

  3. We use the term as defined in Ball and Bass (2003, p. 11): in contrast to mathematicians, who often present the content in compressed formats, teachers need to decompress the content to make it accessible to learners.

  4. The letters denote whether the excerpt comes from notebook class-notes and reflections (NC), notebook homework (NH), comments on reflection cards (RC), the survey administered at the beginning of the content course (SC), or the survey administered at the beginning of the methods course (SM).

  5. The remaining 12 PSTs for whom we had complete data displayed analogous learning paths: five PSTs started in places anywhere between Suzanne’s and Nathan’s pre-coursework performance and, by the end of coursework, provided explanations that resembled those of Nathan’s and Suzanne’s; four PSTs started in a similar place as Vonda and Suzanne and improved in providing explanations, although, not as dramatically as Suzanne; like Nathan, a PST learned to unpack his mathematically valid, yet condense, explanations; a PST displayed a remarkable learning growth tantamount to Suzanne; and another PST exited coursework with limitations in her capacity to provide explanations similar to those documented in Vonda’s case.

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Authors and Affiliations

  1. Department of Education, University of Cyprus, Theofanides Building, Room 508, Dramas 11-13, 1077, Nicosia, Cyprus

    Charalambos Y. Charalambous

  2. Harvard Graduate School of Education, Gutman Library Rm 445, 6 Appian Way, Cambridge, MA, 02138, USA

    Heather C. Hill

  3. School of Education, 610 E. University Avenue, Rm 1110, Ann Arbor, MI, 48109-1259, USA

    Deborah L. Ball

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  1. Charalambos Y. Charalambous
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  2. Heather C. Hill
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  3. Deborah L. Ball
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Correspondence to Charalambos Y. Charalambous.

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Charalambous, C.Y., Hill, H.C. & Ball, D.L. Prospective teachers’ learning to provide instructional explanations: how does it look and what might it take?. J Math Teacher Educ 14, 441–463 (2011). https://doi.org/10.1007/s10857-011-9182-z

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