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Tuesday, July 2 • 3:30pm - 4:10pm
How educative is educative? Examining mathematics curriculum materials

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All too often, curriculum materials developed to support school mathematics gain short-term acceptance, but soon become little more than a set of good ideas or tasks to be used on an ad hoc basis if there is time. As such they fail to fulfil their goal of promoting sustainable reform in school mathematics. I argue that in order to promote sustainable change curriculum materials ought to be educative (Davis & Krajcik, 2005) in the sense that they enable teachers to understand the intent of the designer, and to engage with the resources in ways that are powerful for both teacher and students. Ideally educative curriculum materials:
• help teachers anticipate what learners may think about or do;
• support teachers in their own learning of the subject matter;
• describe ways in which the separate resources relate to each other and build progressive understanding;
• make visible the designers’ pedagogical decisions; and
• promote teachers’ pedagogical design capacity.

But how educative is educative? How do we decide whether or not, or to what extent, or how, curriculum materials actually enact and embed the principles described in the literature?
Legitimation Code Theory provides a framework that enables us to examine curriculum materials to determine the extent to which they promote the knowledge building ideals that the designers seek to embed, as well as the effectiveness with which these ideals are communicated to teachers. This paper will use the Semantics dimensions of LCT to examine school mathematics curriculum materials.

I use textual analysis of two sets of curriculum materials with the same focus and intent, but different design features. One set of materials comes from a mathematics textbook, in which students are provided with principles and techniques, which they then apply in a carefully graded set of exercises. They may then apply these to problems that have a supposed real-world connection. By contrast the other set of materials comes from an Australian mathematics curriculum project, reSolve: Mathematics by Inquiry, in which students first encounter a situation that may be puzzling or challenging, then explore the situation, unfold the mathematics and seek meaning, and ultimately build conclusions that apply more generally.

As with all resources, however, it is eminently possible that teachers may fail to see the principles embedded in the materials no matter how well designed they may be. As Schoenfeld (2006, p. 17) says: “one can imagine curricular materials that, when used in the way intended by the designers, result in significant increases in student performance, but, when used by teachers not invested or trained in the curriculum, result in significant decreases in student performance.”

Hence, the paper examines both the extent to which the two contrasting resources build deep student knowledge, and also the extent to which they let teachers “in on the secret”.
Specifically, the paper asks:
1) What semantic codes are evident in the curriculum materials?
2) How do the materials suggest variation in terms of semantic gravity and semantic density?
3) How are these organizing principles of knowledge-building communicated to the teacher through the curriculum materials? That is, how educative is educative?

The study simultaneously informs both the mathematics education research and design community and the LCT community. It provides a new perspective on mathematics curriculum and knowledge-building that remains unexplored but offers much potential in mathematics education research. At the same time, it adds to the body of work currently examined using LCT. The study sheds light on how LCT can be used to examine written curriculum materials that are designed to be educative for teachers and leads to practical recommendations and strategies for enhancing the educative quality of such resources.


Tuesday July 2, 2019 3:30pm - 4:10pm SAST
Room B46

Attendees (2)