Fidelity of implementation: bringing written curriculum materials into the equation

Abstract

Fidelity of curriculum implementation (FOI) is an important area of research because of the critical role it plays in understanding how and why curriculum materials work and how they can be improved. This analysis explores written features within the Math Trailblazers curriculum that may influence the ways teachers implement mathematics curriculum materials. In particular, we examine FOI data from prior research in order to identify features within the materials themselves that may influence why teachers adhere to the intended curriculum to varying degrees. This paper reports on our analysis of examining five whole number lessons previously analysed for level of FOI alongside an analysis scale of written curriculum features. Our purpose in this analysis is to examine features of the written curriculum that potentially mediate teachers’ implementation of the materials in line with the intended curriculum. In doing so, our analysis further emphasises the critical role teachers play in curriculum implementation, and thus may provide some insight for curriculum developers as they consider ways in which to design the written curriculum that increase the likelihood that teachers will adhere to the intended curriculum.

Keywords:

• curriculum
• curriculum development
• mathematics
• textbook analysis

Notes

1. The phrase ‘innovative mathematics curricula’ refers to curriculum programs that reflect inquiry-based visions of teaching and learning, similar to the ideas underlying several Standards-based mathematics curricula. Standard-based curricula refers to mathematics curriculum programs that received funds from the National Science Foundation in the early 1990s to develop curricula that reflected the teaching and learning ideas in the Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 1989). Such curricula are in use in classrooms in the United States.

2. To be sure, researchers have analysed the information and language used in curriculum materials in ways that offer certain insights into the relationship between the language in the written curriculum and the intended curriculum (e.g., Herbel-Eisenmann, 2007; Stein & Kim, 2009). This research, however, has not focused specifically on the role of the written curriculum in supporting teachers in implementing the curriculum as intended.

3. Cognitively demanding, or higher level, tasks are those tasks categorised as Doing Mathematics (DM) and Procedures with Connections (PWC). DM tasks are those that require non-algorithmic thinking and afford multiple strategies whereby the solution is typically not immediately obvious to the student, and thus require considerable cognitive effort (Stein & Smith, 1998). PWC tasks are those that entail the use of procedures to understand the underlying meaning of the concepts embedded in the task and generally require some cognitive effort on the part of the student. Conversely, lower level tasks are those tasks categorised as Procedures without Connections (PWOC) and Memorisation tasks. PWOC tasks are those that require the use of algorithms or procedures, have little connection to the concepts underlying the tasks, and require limited cognitive effort on the part of the student (1998). Memorisation tasks involve utilising previously learned facts or procedures, often committing such facts to memory, and have no connection to the underlying concepts (1998).

4. All three authors analysed the tasks in each lesson and resolved any disagreement through discussion. Inter-rater reliability was 90% for all tasks across all lessons analysed based on percentage of agreement.

5. There is of course the possibility that, no matter how vague or directive the lesson directions may be, teachers may not follow the literal curriculum.

Additional information

Funding

This work was supported by the National Science Foundation [grant number 0242704].

Notes on contributors

Alison Castro Superfine

Cathy Kelso was an author on the Brown et al. (2009) paper, is one of the primary developers of the Math Trailblazers curriculum and was Principal Investigator of the Math Trailblazers Research and Revisions (MTBRR) Study.

Anne Marie Marshall

Alison Castro Superfine was Co-Principal Investigator of the MTBRR Study.

Cathy Kelso

Anne Marie Marshall was a Visiting Research Associate on the MTBRR Study.