Educative Curriculum Materials, Part 1

For more than 20 years now, educative curriculum materials have been a popular focus for mathematics education research, development, and theorizing. When the 1989 NCTM Standards laid out new and ambitious ways of teaching mathematics, curriculum materials were seen as a potentially powerful mechanism for supporting teachers in making the needed changes to their practice (Ball & Cohen, 1996). Because they were (and still are) so widely used, and fit into the day-to-day work of teachers, they seemed (and still do seem!) like a fruitful avenue for teacher learning. Several development groups received NSF funds to create educative curriculum materials, so called because they were intended to support both student and teacher learning.

The logic in this argument makes sense to me, and I spent a large chunk of my career working on a couple of sets of these educative curriculum materials. I truly, sincerely loved my work. I never believed I had it in me to be a teacher. I was too anxiety-ridden to handle all the on-demand thinking and decision making, and I was never very good at developing rapport with kids. But I did (do) admire teachers and think their work is both challenging and important. When I stumbled into a career in educative curriculum materials development, I was really happy to have found a way to support educators.

I’m still proud of that work, and respect the colleagues I worked with. But graduate school has given me some time for thoughtful reflection on our efforts, and has me wondering if we’ve gone a bit astray on our efforts to make curriculum materials educative.

The problem is this: For the most part, our methods for making materials educative is simply to provide more and more information. To help teachers anticipate student thinking, we supply sample student work. To deepen teachers’ mathematical content knowledge, we provide mathematical background that goes into greater depths than we expect students to reach. To give teachers a model of how a discussion might play out, we script questions and sample student dialogue. To help teachers discern the intended takeaways from each activity, we provide the rationale for the activities and the reasons they are sequenced as they are.

It’s not that I think all this information should be concealed or ignored. I understand the purpose of providing it. Davis and Krajcik (2005) laid out five high-level guidelines for creating educative curriculum materials, and the first four have to do with providing the kinds of information described above. (It’s a great piece to read if you’re interested in this topic.)

My concern is that in the course of providing all this information, we’ve created materials that are wildly over-specified. With lessons scripted out and detailed rationales for why the lessons are as they are, the materials end up reading like an argument for why they should be implemented exactly as they are written — even if that’s not what was intended. And worse, oftentimes it’s even generous to call what we write an argument. Several researchers have analyzed existing educative materials and found that their voice and structure tends to talk through teachers, telling them exactly what to say to students, rather than to teachers (Stein & Kim, 2009; Herbel-Eisenmann, 2007). As educators ourselves, we know that telling a student what to do step by step isn’t particularly educative. Why do we think materials that tell teachers what to do step by step will be educative?

There are other issues with overspecification, too. For one thing, we know that teachers don’t read curriculum materials in their entirety, and not all teachers read them the same way (Remillard, 2012; Sherin & Drake, 2009). Overspecification also seems to translate to lack of flexibility in the opinion of some teachers and districts, who are abandoning structured curriculum materials to create their own from online resources (Choppin & Borys, 2017).

The biggest problem I see with overspecification, though, is that it doesn’t leave much room for teacher decision-making. In our eagerness to use educative curriculum materials to support teacher learning, I think we have lost sight of the fact that implementation is, in a sense, a second act of curriculum design. Adapting teaching practices to particular students and contexts is a critical part of education that lies solely in the hands of teachers, and curriculum materials that are too overly specified won’t support the development of this skill. In their fifth guideline for the development of educative curriculum materials, Davis and Krajcik (2005) described this skill as pedagogical design capacity and argued that educative curriculum materials should promote it: “Promoting a teacher’s pedagogical design capacity can help him participate in the discourse and practice of teaching; rather than merely implementing a given set of curriculum materials, the teacher becomes an agent in its design and enactment” (p. 6).

I just don’t think our overspecified materials are supporting the development of pedagogical design capacity. So what can we do better? If educative materials need to provide so much information, and providing that information tends to lead to overspecification, which in turn limits the development of pedagogical design capacity …. Are we stuck?

In a curriculum delivered in print, perhaps. In a curriculum delivered digitally, perhaps not. Several research teams have identified ways in which a digital medium could ease this tension between providing needed information and overspecifying. For example:

• In a digital space, information can be delivered via multiple media (Davis & Krajcik, 2005), which could help developers provide information in ways that don’t prescribe what teachers do.
• Provision of hyper-links between related material can increase teacher agency and metacognition while reviewing the materials (Shapiro & Niederhauser, 2004), and a digital medium allows developers to define multiple links between materials that provide multiple pathways through the curriculum.
• Integration of student-facing technology into the materials can stimulate teacher thinking and allow developers to shift from scripting to steering their planned activities (Hoyles, Noss, Vahey, & Roschelle, 2013).

I’ll be exploring these ideas about how a digital medium could help to develop curriculum materials that are educative without being overspecified over the next two weeks.

References

Ball, D. L., & Cohen, D. K. (1996). Reform by the book: What is — or might be — the role of curriculum materials in teacher learning and instructional reform? Educational Researcher, 25(9), 6–8, 14.

Choppin, J., & Borys, Z. (2017). Trends in the design, development, and use of digital curriculum materials. ZDM – International Journal on Mathematics Education, 49(5), 663–674.

Davis, E. A., & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning. Educational Researcher, 34(3), 3–14.

Herbel-Eisenmann, B. A. (2007). From intended curriculum to written curriculum: Examining the “voice” of a mathematics textbook. Journal for Research in Mathematics Education, 38(4), 344–369.

Hoyles, C., Noss, R., Vahey, P., & Roschelle, J. (2013). Cornerstone Mathematics: Designing digital technology for teacher adaptation and scaling. ZDM – International Journal on Mathematics Education, 45(7), 1057–1070.

Remillard, J. T. (2012). Modes of engagement: Understanding teachers’ transactions with mathematics curriculum resources. In G. Gueudet, B. Pepin, & L. Trouche (Eds.), From Text to “Lived” Resources: Mathematics Curriculum Materials and Teacher Development (pp. 105–122). Springer Netherlands.

Shapiro, A., & Niederhauser, D. (2004). Learning from hypertext: Research issues and findings. In Handbook of Research on Educational Communications and Technology (pp. 605–620).

Sherin, M. G., & Drake, C. (2009). Curriculum strategy framework: Investigating patterns in teachers’ use of a reform-based elementary mathematics curriculum. Journal of Curriculum Studies, 41(4), 467–500.

Stein, M. K., & Kim, G. (2009). The role of mathematics curriculum materials in large-scale urban reform: An analysis of demands and opportunities for teacher learning. In J. T. Remillard, B. A. Herbel-Eisenmann, & G. M. Lloyd (Eds.), Mathematics Teachers at Work: Connecting Curriculum Materials and Classroom Instruction (pp. 37–55). New York: Routledge.