The challenges and possibilities of aligning large‐scale testing with mathematical reform: the case of Ontario

Abstract

In 1997, the Ontario government, like many other jurisdictions, undertook systemic reform of their elementary school mathematics programme, developing a new mathematics curriculum, report card, and province‐wide assessment. The curricular reform embodied a new vision of mathematics learning and instruction that emphasized instruction using challenging problems, the student construction of multiple solution methods, and mathematical communication and defence of ideas. While the design of the original large‐scale assessment incorporated much of the latest research and theory on effective practices at that time, these traditional item development and scoring practices no longer adequately assess mathematics achievement in reform‐inspired classrooms. The difficulties of marrying traditional assessment practices with a reform‐inspired curriculum could be addressed by creating a construct definition from the recent research findings on students’ mathematical development in reform‐inspired classrooms. The importance, challenges and implications of redefining the construct on the basis of existing research on students’ mathematical development, as well as collapsing the traditional content‐by‐process matrix for item development, are explored.

Notes

1. The second author was Co‐Chair of the panel.

2. The term Big Idea is used in a variety of ways in the recent literature on children’s mathematical development. We use Fosnot and Dolks, (2001b) notion; that is, when students construct a Big Idea, it is big because they make connections that allow them to use mathematics more effectively and powerfully. These are mathematical connections; for example, the construction of the commutative property (a × b = b × a) when learning multiplication.

3. The three types of equal grouping and partitioning problems (no remainders), can be illustrated from the following example. There are 42 frogs altogether. There are 7 frogs sitting on each lily pad. There are 6 lily pads. When the total number of frogs is unknown then it is a multiplication problem, when the number of groups of frogs (lily pads) is unknown then it is a measurement problem, and when the number of frogs in a group (on a lily pad) is unknown then it is a partitive (fair shares) problem (adapted from Carpenter et al., 1999, pp. 33–34).