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Algebra-focused features of instruction: an integrated investigation of curricular guidance and instructional enactment

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Abstract

To be successful in algebra, students need access to high-quality instruction that includes opportunities to develop their algebraic understanding. Yet research on algebra teaching suggests that instruction remains procedurally focused, indicating that teachers may need additional support to provide students such opportunities. One possible lever for improving instruction may be through curricular guidance provided to teachers, specifically through educative materials that provide support for teacher as well as student learning. This study aims to understand how curricular guidance supports teachers to enact the types of instructional practices that support students’ learning opportunities in algebra specifically, and how teachers enact that guidance. We draw from a sample of 29 video observations from six teachers of the same three textbook lessons and use aligned analytic frameworks to examine the curriculum materials and enacted lessons in tandem. We investigate how the curricular guidance provides opportunities for algebra-focused instructional features, how these opportunities are taken up by teachers, and how and in what ways differences in instructional enactments might be related to the curricular opportunities. We find differences in which instructional features varied more by lesson and which varied more by teacher and describe sources of this variation. Curricular guidance supported teachers’ enactments, but teacher-level variation was largely due to teachers going beyond the support provided. This study suggests how curriculum materials can better support teacher learning and provides insight into taking a content-focused approach to studying curricular enactment.

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Fig. 1
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(Source: Dietiker et al. 2013, pp. 330–333)

Fig. 5

(Source: Adapted from Dietiker L et al. 2013, p. 330. ©2022 CPM Educational Program. All rights reserved. Used with permission.)

Fig. 6

(Source: Dietiker et al. 2013, p, 752. ©2022 CPM Educational Program. All rights reserved. Used with permission.)

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Data availability

Data are not available due to information that could compromise the privacy of research participants.

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Not applicable.

Notes

  1. We use the term “lesson” to refer to the textbook curricular material for a given class session and the terms “enactment” and “lesson enactment” to refer to a teacher’s instructional instantiation of that lesson in their classroom. Each video represents an enactment of one of the three focal lessons. Three sample lessons from six teachers over two years yields a potential sample of 36 lesson enactments; variation in the number of lessons per teacher are due to differences in study recruitment, teacher absence, and technical issues, resulting in an analytic sample of 29 enactments. The analytic sample includes at least one enactment of each lesson from each teacher.

  2. Lesson enactments from four teachers averaged approximately 45–50 min in length. Two teachers’ enactments were approximately 70 and 75 min in length. While differences in lesson length might allow for more opportunity to enact lesson guidance, our analysis of lesson enactments did not indicate considerable variation in whether (or how long) teachers engaged in the main activities of the lesson as suggested by the materials.

  3. Procedures were taught in 97 of these segments; segments in which procedures were not taught were omitted from analyses around Making Sense of Procedures and Supporting Procedural Flexibility.

  4. Given the exploratory nature of our analysis and that we were not aiming to make broad claims regarding instructional quality, we felt this was a sufficient level of interrater reliability and consensus coding was appropriate.

  5. We note that interviews with teachers regarding their instructional vision and instructional decision-making are missing from this analysis. Although interviews would provide rich information on how and why teachers enacted (or did not enact) curricular guidance, because this was secondary data analysis, conducting such interviews was not possible.

  6. We note that while we did not have a measure of curricular fidelity or the extent to which teachers used the curricular guidance, we observed that all lesson enactments followed the structure laid out in the guidance, indicating that teachers were aware of and relying on the materials. For example, while the tasks appeared in both the student- and teacher-facing materials, the guidance for how those tasks should be structured and suggested questions to ask students appeared in the teacher notes (see Fig. 3 for an example). All teachers in the sample enacted these questions and activities to some extent, indicating a level of attention to the guidance.

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Acknowledgements

The authors wish to thank Leslie Dietiker, the EPIC research team at Boston University, and CPM Educational Program for collecting these data and access to lesson videos for this study.

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  1. College of Education and Human Development, University of Delaware, 105D Willard Hall Education Building, Newark, DE, 19716, USA

    Erica Litke & Kateri A. Sternberg

  2. Illinois State University, Normal, IL, USA

    Julien Corven

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Litke, E., Corven, J. & Sternberg, K.A. Algebra-focused features of instruction: an integrated investigation of curricular guidance and instructional enactment. J Math Teacher Educ (2023). https://doi.org/10.1007/s10857-023-09573-8

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