Abstract
The purpose of this study was to develop and test the viability of a conceptual framework for analyzing mathematics instruction and mathematics teacher development within the context of policies regarding district-wide adoption of curriculum. The framework takes three dimensions of curriculum-based instruction into account independently: use, congruence (the extent to which instruction aligns with district and curricular guidelines), and quality (the extent to which instruction maintains the cognitive demand of appropriately challenging tasks, takes account of and builds on student thinking, and situates intellectual authority in mathematical reasoning). Based on analyses of multiple observations of 36 teachers across two districts, teachers were classified into one of four implementation profiles (flounderer, mechanical, canonical, maverick) that were created by crossing the three dimensions; in addition, their trajectory through those profiles was traced over a two-year period. Results suggest teachers were more likely to use the district-adopted curricula as the source of their lessons than to align their practice with curricular and district guidelines. Teachers’ demonstration of high-quality lessons was less frequent. Differences across the two districts in the percentages of teachers falling into each of the implementation profiles suggests that district actions may have shaped teachers’ uptake of the curriculum. Finally, results suggest a more uneven pathway toward high-quality instruction than had been initially conjectured.
An earlier version of this paper was presented at the 2011 annual meeting of the American Educational Research Association, New Orleans. This work was supported by a grant from the National Science Foundation (IERI Grant REC-0228343), as well as support by the Institution of Education Sciences and the U.S. Department of Education (Award R305B1000012). The content or opinions expressed herein do not necessarily reflect the view of the National Science Foundation or any other agency of the U.S. Government.
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Notes
- 1.
In this manuscript, we use the term, “curriculum” to mean a textbook series.
- 2.
Non-US readers may prefer the term “didactical.” The features to which we refer are those that relate to how to teach the mathematics content.
- 3.
Because the two curricula used in this study were standards-based and at least partially funded by the National Science Foundation, the presumption (supported by some prior analyses [see Stein and Kim 2009]) is that the tasks—as they appeared in the curriculum—were high-quality.
- 4.
This is possible because, in the context of district-paced implementation, teachers on the same grade level should be implementing the same lessons at roughly the same time, thereby allowing the district to “preview” an upcoming unit to teachers across the district on the same date.
- 5.
Judgments about congruence are necessarily district and curriculum specific.
- 6.
A mathematical task is defined as a classroom activity, the purpose of which is to focus students’ attention on a particular mathematical idea. An activity is not classified as a new or different task unless the underlying mathematical activity toward which the activity is oriented changes. Standards-based lessons typically consist of one or two tasks.
- 7.
Judgments about teachers attending to student thinking and about intellectual authority were made based on the entire lesson.
- 8.
We have identified 4 profiles instead of 8 possible profiles because only 4 profiles were conceptually meaningful. Two profiles (either high or low quality crossed with low use and high congruence) were unlikely because it is difficult to imagine a teacher implementing materials with pedagogical fidelity without actually using the materials. The other two profiles are actually represented in the flounderer and maverick categories which stipulate that (along with either low [flounderer] or high [maverick] quality) the teacher implements with low congruence and either high or low use. Conceptually the dimension that carries the weight of both the flounder and maverick categories is having low congruence with the pedagogical guidance of the curriculum and district.
- 9.
Pseudonyms.
- 10.
The individuals who were selected to conduct the observations and create the write ups had expertise in either mathematics education or a social science field that relied heavily on observation (e.g., anthropology). They participated in a 2-day, in-person, group training at the start of the project. This training involved watching videos of mathematics lessons and creating write ups that were critiqued by project leaders and their peers. During the course of the project, the observers were provided feedback on their write-ups and participated in at least one follow up group session.
- 11.
Because one pre- and one post-interview were conducted per set of 3 contiguous lessons, the coded data based on those interviews is the same across all lessons in one set.
- 12.
Inter-rater reliability was computed as the number of agreements divided by the total number of possible agreements/disagreements.
- 13.
This seemed reasonable because it is not unusual for teachers to do non-textbook activities for a small portion of a class period. For example, they might review a skill such as “telling time” because an early dismissal has been announced for the day. On the other hand—because Investigations and Everyday Mathematics are comprehensive curricula with daily lessons—a teacher who failed to use them at all for one or more lessons (of the six observed lessons) would be considered to be an inconsistent user.
- 14.
Either from a “doing mathematics” task to a “procedures-with-connections” task or from a “procedures-with-connections” task to a “doing mathematics” task (Stein et al. 1996).
- 15.
Fall 2005 where 82Â % of Region Z teachers were high users and 79Â % of Greene teachers were high users.
- 16.
There were no flounderers that led to mavericks.
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Stein, M.K., Kaufman, J., Kisa, M.T. (2014). Mathematics Teacher Development in the Context of District Managed Curriculum. In: Li, Y., Lappan, G. (eds) Mathematics Curriculum in School Education. Advances in Mathematics Education. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-7560-2_17
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