A few weeks ago, I wrote about my quest to understand the essential features of curriculum, with the hope of eventually creating a framework for the design of digital curriculum materials that both allow for teachers to make adaptations to their contexts and maintain curriculum coherence. In the many years I’ve been thinking about how to design flexible curricula, I have always approached it from this angle: Figure out the essence of the current version of a curriculum (in my head, this is generally a textbook, although I acknowledge there are other forms), and build those essential features into a digital platform.
One of my projects for this first semester of graduate school is a targeted effort to understand and better articulate my research interests, and so I’ve spent some time thinking about why this question and this particular approach is of such interest to me.
My interest in the question is easy to trace. Over the years of my career as a developer of textbooks, increasing numbers of schools and districts have begun abandoning textbooks as a source of curriculum in favor of putting together their own collections Open Educational Resources (OERs) (Gueudet, Pepin, Sabra, & Trouche, 2016; Ruthven, 2016). Although I recognize that there are likely a set of complex interconnected reasons for this trend, I believe that one of them is the lack of adaptability of traditional printed curricula. Static delivery simply isn’t meeting teachers’ needs, so I want to figure out how to design something that will.
The reasons I’m drawn to the first step of my general approach, figuring out a curriculum’s essential features, probably stem from a number of things. First, there’s the mathematician in me who loves to strip things down to their essence. There is also a pragmatic appeal to this step. This problem is one of navigating the tension between some things needing to change and some things needing to stay put. It just makes sense to me to start by figuring out which is which. Finally, there’s the level of personal intrigue in this question. Despite being a curriculum developer for ten years, I don’t think I can articulate the essential features of the programs I worked on. This question is thus a sort of personalized puzzle for me. (And I love puzzles!)
I can explain the rationale for designing flexible curricula and the reasons for attention to essential features, then. What I’ve been having more of a problem with is explaining the final piece: why I think delivery of curriculum through digital means is the way to go.
I did come up with a few reasons. The industry is going digital, so we should figure out the best ways to take advantage of that. Digital versions allow for easier updates. And so on. But I wasn’t satisfied. None of these seemed to justify the use of digital platforms for this purpose specifically. Why is technology important to the issue of helping teachers made adaptations to curriculum? Why not instead focus on finding better ways to communicate the essential features to teachers directly, instead of embedding them into a digital tool?
This week I read a handbook chapter by Cecilia Hoyles and Richard Noss, two mathematics education scholars at the University of London, that helped me articulate why I’m partial to the idea of a digitally-based curriculum. The chapter is, in part, a review of research on use of digital tools in mathematics education. Hoyles and Noss (2003) organized the discussion around two categories of tools: programmable microworlds, like Logo, and expressive tools, like the draggable objects in dynamic geometry systems. The latter group was characterized (at first) as a set of black boxes; the end user does not see the tool’s inner workings. The former, by contrast, were characterized as open; the end user creates tools for their own use.
Toward the end of their review, Hoyles and Noss (2003) pointed out that the lines between the two categories were becoming blurred: microworlds were being developed with more pedagogic constraints on users’ constructions, and tools were becoming more programmable. They expressed support for the programmable tools, in particular, noting the following:
The tools of an environment encapsulate mathematical relationships in some sense: but these relationships lie dormant until they are mobilised, and it is in their mobilisation that meanings are created. The individual steps onto an already-built structure: and what is seen – and taken – from that structure is mediated by the activity structures, intentions and pedagogical goals of the setting. This phenomenon is both more explicit and more visible when learners are (re-)constructing tools for themselves[.] (Hoyles & Noss, 2003, pp. 339-340)
In short, they argued that when tools are programmable, the intentions of the tool designer are made more explicit to the user. By engaging in a process of construction, the limitations placed on that construction are made clear and a user can better see and understand them.
I was struck by this argument, because it seemed to translate directly from tools to curriculum materials. I’m drawn to the idea of a digital curriculum that supports adaptation because a digital medium, as opposed to a print one, would allow teachers to interact with the curriculum. Teachers would be able to do more than plan an adaptation. They’d be able to actually adapt the materials to reflect their plans — to construct their own versions of the curriculum. As they did so, a system that embeds the essential features could both constrain those adaptations and provide feedback to teachers about the reasons for those constraints. Through this interaction, I believe teachers would better understand the reasons curricula are designed as they are than they would otherwise.
This, in my opinion, would be a new class of educative curricular materials (Davis & Krajcik, 2005) designed specifically for managing the tension between allowing for flexibility and maintaining curriculum developers’ often meticulous but under-communicated attention to designing coherent sequences of activities. Moreover, it would be one intentionally designed to accommodate both stages of curriculum design described by Remillard (2005): the design and population of the digital platform by curriculum developers is stage one, and the planning and enactment of curriculum materials by teachers is stage two.
Here’s the essence (as stated above, I do love articulating essence): I’m drawn to the idea of digital delivery of adaptable curriculum because it supports active adaptation of the curriculum materials by teachers, thereby respecting their roles in the development of curriculum. It positions them to be in dialogue with the curriculum developers and co-construct the curriculum.
This new understanding of how I think about the creation of flexible digital curriculum doesn’t make the task any easier to accomplish. As I said above, I still don’t know what the essential features of curriculum are, either in general or for specific programs I’ve helped to develop. And I definitely don’t know how to express those features via design principles. But it has given me a new frame to think about the problem. I’m excited to see where it leads me.
Davis, E. A., & Krajcik, J. S. (2005). Designing educative curriculum materials to promote teacher learning. Educational researcher, 34(3), 3-14.
Gueudet, G., Pepin, B., Sabra, H., & Trouche, L. (2016). Collective design of an e-textbook: teachers’ collective documentation. Journal of Mathematics Teacher Education, 19(2-3), 187-203.
Hoyles, C., & Noss, R. (2003). What can digital technologies take from and bring to research in mathematics education?. In Second international handbook of mathematics education (pp. 323-349). Springer Netherlands.
Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of educational research, 75(2), 211-246.
Ruthven, K. (2016). The Re-Sourcing Movement in Mathematics Teaching: Some European Initiatives. In M. Bates & Z. Usiskin (Eds.). Digital Curricula in School Mathematics (pp. 75-86). Charlotte, NC: Information Age Publishing.