This article describes a mathematics curriculum design heuristic that was developed and used in the design of CPM Educational Program textbooks. It introduces a metaphor of mathematics curriculum as a narrative story, which allows for the design of mathematical experiences that emotionally moves students and teachers and compels them to engage. Specifically, it explains how curiosity and surprise can be intentionally designed within a mathematical sequence of curricular elements, such as tasks. Background that spurred the development of the mathematical story framework is offered and examples from designing lessons for Algebra and middle school are provided.
Issue 8 – October 2015
Welcome to Educational Designer #8
Educational Designer is a key vehicle for attaining ISDDE’s goals. First, it provides stimulation for our core members (designers, design group leaders, and those who commission work from them). Second, the journal contributes to garnering wider recognition of the critical importance and extreme challenge of excellence in design. Third, the thought-provoking contributions from existing members as well as newcomers seed discussions that help build the ISDDE community. The varied content of each issue assures that Educational Designer continuously contributes to these goals in different ways.
The three articles in this issue feature designers’ own stories, thoughtful reflections and craft wisdom. Leslie Dietiker describes how she works to increase student engagement in mathematics and shares heuristics for designing mathematical sequences which, like narratives, trigger curiosity and surprise. Colin Foster shares his convergent-divergent model for the design of mathematical tasks, the execution of which are educative for both teachers and learners. And Jacqueline Barber describes the trans-disciplinary collaboration that yielded a breakthrough curriculum, for which she received the 2012 ISDDE prize for excellence in design. As always, response pieces to any of the above would be most welcomed by the editors.
With this issue, my term as editor draws to a close. It has been an honor and a privilege to serve on the Educational Designer team. I’d like to express my gratitude to Hugh Burkhardt and Daniel Pead. In the last 8 years, they have led by example, exemplified the collaborative spirit and put smiles on my face. Appreciation also goes to the ISDDE executive, which has served as the editorial review board since the journal’s inception, as well as the authors with whom I have had the pleasure of working. I thank the ISDDE community, for their interest, feedback and creative ideas. Finally, the energy and competence of the new editorial team makes this transition both easy and exciting for me, for which I am extremely grateful.
Happy reading!
Susan McKenney
Editor of this issue
Shaping Mathematics into Compelling Stories:
A Curriculum Design Heuristic
Leslie Dietiker
Dietiker, L. (2015) Shaping Mathematics into Compelling Stories. Educational Designer, 2(8).
Retrieved from: http://www.educationaldesigner.org/ed/volume2/issue8/article27/
Retrieved from: http://www.educationaldesigner.org/ed/volume2/issue8/article27/
The Convergent–Divergent Model: An opportunity for teacher–learner development through principled task design
Colin Foster
The tasks that mathematics teachers are invited to use in their classrooms have profound effects not just on the learners who do them but also on the teachers themselves. This paper introduces the Convergent–Divergent Model (CDM) for the design of mathematical tasks. The CDM consists of two distinct phases: the first, a convergent problem-solving episode, and the second, a more divergent, open-ended, exploratory part. The two-phase design is built on twin intentions both for the mathematical growth of the learner and for the pedagogical development of the teacher. The principles of design employed in this model are elucidated through descriptions of the construction of several examples of such tasks in published mathematics teacher resource books written by the author.
Foster, C. (2015) The Convergent–Divergent Model. Educational Designer, 2(8).
Retrieved from: http://www.educationaldesigner.org/ed/volume2/issue8/article28/
Retrieved from: http://www.educationaldesigner.org/ed/volume2/issue8/article28/
How to Design for Breakthrough:
A story of Collaborative Design across Disciplines
Jacqueline Barber
How does one design for breakthrough? The goal of this paper is to communicate the potential for working across disciplines and domains in order to design breakthrough approaches and solutions to persistent problems in education. By breakthrough I mean a discovery that leads to new understanding and removal of barriers to progress. I reflect on a particular design experience that brought together players with different expertise; specifically, I describe the challenges we faced, and share the discoveries we made about how to take best advantage of what the diverse set of individuals brought to the table.
Barber, J. (2015) How to Design for Breakthrough. Educational Designer, 2(8).
Retrieved from: http://www.educationaldesigner.org/ed/volume2/issue8/article29/
Retrieved from: http://www.educationaldesigner.org/ed/volume2/issue8/article29/