Educative curriculum materials
Educative curriculum materials refer to textbooks, workbooks, planning guides, and other curriculum materials designed to support teacher learning as well as student learning.
Origins and Perspectives
The idea that curriculum materials in mathematics should support teacher learning is a relatively new concept. The "new math" reforms of the 1960s and early 1970s, most prominently that of the School Mathematics Study Group (SMSG), became well-known for representing a departure from traditional mathematics curriculum. These reforms failed to take hold, in part, because teachers did not receive adequate support to teach the new mathematics. The director of SMSG, Edward Begle, admitted that "in our work on curriculum we did not consider the pedagogy" (Kline, 1973, p. 110).
Following the 1989 publication of the Curriculum and Evaluation Standards for School Mathematics, a second wave of mathematics curriculum reform began, largely enabled by funding from the National Science Foundation. Ball and Cohen (1996) recognized that without support, teachers might resist or struggle to use the new materials as their authors intended. Ball and Cohen suggested that curriculum materials could influence teacher practice in the following ways:
- Crossing Boundaries: If the goals and rationales of the curriculum developer were made explicit in teacher support materials, teachers could better understand the content, how it was intended to be taught, be prepared for issues that might arise upon enactment, and better understand how the learning of current content influences the learning of future content.
- Improved Instruction: Instead of focusing on fidelity of implementation, curriculum adoption should be seen as an opportunity for professional development and teacher cooperation targeted at increasing teacher learning and effectiveness.
- Partners in Practice: For curriculum of this quality to be developed, more research is required on teacher learning and curriculum use, instead of viewing curriculum simply as something for student use.
Teachers' Curricular Knowledge
Shulman (1986) recognized a need for a new conceptualization of teacher knowledge that was not solely about content, nor solely about teaching, but rather specialized knowledge for teaching specific content. While Shulman's 1985 AERA presidential address and 1986 article is best known for pedagogical content knowledge (PCK), he also described a specialized knowledge he termed curricular knowledge, which he likened to an expert physician's knowledge of available treatments, their effectiveness, costs, side effects, and interactions with other treatments. For teachers, curricular knowledge means knowledge of available textbooks, software, manipulatives, videos, activities, demonstrations, and the likelihood that each will be effective with their students. Shulman also included in curricular knowledge a horizontal knowledge of the curriculum in students' other subjects, as to encourage multi-disciplinary learning, and a vertical knowledge of the curriculum in other grades.
In mathematics education, Shulman's conceptions of specialized teacher knowledge have been further developed by Ball, Thames, and Phelps (2008). Referring to "domains of mathematical knowledge for teaching" (MKT), Ball et al. describe "knowledge of content and curriculum" as a particular domain of pedagogical content knowledge but provide few other details. Unlike Shulman (1986), Ball et al. separate knowledge of curriculum outside a teacher's grade and subject, preferring to categorize "horizon content knowledge" as a special kind of content knowledge.
Aims of Educative Curriculum Materials
- Address each area of knowledge necessary for exemplary practices — content knowledge, pedagogical knowledge, and PCK
- Situate teacher learning by meshing the content of the support to lessons for students
- Link different knowledge areas within lessons
- Make knowledge accessible to teachers through short scenarios or models of actual practice
- Address immediate needs for understanding as teachers plan for lessons soon to be enacted
These principles were further refined by Davis and Krajcik (2005) into a set of five guidelines for educative curricula (pp. 5-6):
- Materials could help teachers learn to anticipate and interpret student thinking or responses to instructional activities (Ball & Cohen, 1996; see also Collopy, 2003; Heaton, 2000; Remillard, 2000)
- Materials could support teachers' learning of subject matter (Ball & Cohen, 1996; see also Heaton, 2000; Schneider & Krajcik, 2002; Wang & Paine, 2003)
- Materials could help teachers consider ways to relate units during the year (Ball & Cohen, 1996; Wang & Paine, 2003)
- Materials could make visible the developers' pedagogical judgments (Ball & Cohen, 1996; see also Heaton, 2000; Petish, 2004; Remillard, 2000; Shkedi, 1998)
- Materials could promote a teachers' pedagogical design capacity, referring to the ability to use personal and curricular resources to achieve productive instructional ends (Brown & Edelson, 2003)
Brown & Edelson's (2003) pedagogical design capacity refers to a type of teacher knowledge that prevents the making of "lethal mutations" (Brown & Campione, 1996, p. 291) to their curriculum. This is important in light of the generally low quality of many curricular resources (Hubisz, 2003; Kesidou & Roseman, 2002) and teachers' need to make adaptations (Barab & Luehmann, 2003).
Research on Educative Curriculum Materials
To date there are few curricula designed with the above principles and guidelines in mind. One elementary mathematics curriculum, TERC Investigations, has been studied as a potential educative curricula. Results of these studies have been mixed. In science, some curriculum materials developed as part of a research project also included educative features.
Collopy (2003) studied two upper-elementary teachers use of educative curriculum materials in the absence of ongoing professional development. Both were veteran teachers, with Ms. Clark having 26 years of experience and Ms. Ross having 11 years of experience, 9 of which came after a 20-year absence from teaching. Both used Investigations in Number, Data, and Space, an elementary mathematics curriculum from TERC. Over the course of 41 observations and 28 interviews, Ms. Clark showed little change in her beliefs about curriculum and traditional approaches to teaching, and did not appear to be influenced by the educative features of the curriculum. Ms. Ross, however, showed a shift from traditional to reform-based practices and showed far greater evidence of being influenced by the educative features of the curriculum.
Remillard and Bryans (2004) studied eight elementary teachers using Investigations in Number, Data, and Space from TERC. Years of teaching experience ranged from 4 years to 30, with half of the teachers having 25 or more years of experience. As part of a 5-year study, data from the first two years informed these findings, with each teacher observed at least twice and interviewed at least twice in Year 1, followed by most teachers being observed 6-7 times and interviewed three times in Year 2. As with Collopy (2003), researchers focused on teachers' beliefs and classroom practice. Use of the curriculum varied, with some just using it as a resource to draw upon when needed and others following the curriculum closely. Researchers found a complex interaction of how teachers' beliefs about both mathematics teaching and learning and the role of curriculum and how teachers engage with and use new materials. Orientation towards curriculum had a greater influence on Investigations use than beliefs' about teaching and learning. Of those teachers most open to the curriculum, many were amongst the newest teachers, those without established repertoires of curriculum use.
As part of a larger study to reform science and mathematics learning in urban schools Schneider and Krajcik (2002) studied three teachers with 1, 4 and 16 years of experience. The curriculum materials were designed to be educative and teachers spent about 30 hours with the materials in a summer workshop before getting another 30 hours of professional development during the school year. Schneider & Krajcik found that the most veteran teacher made the most use of the educative features, while the teacher with 4 years of experience tended to use only the student portions and not the teacher materials. The first-year teacher read the educative materials but generally focused on student behavior during class activities instead of student learning.
Educative curriculum materials show promise to help teachers at a large scale, but the limited research thus far shows mixed results. However, for teachers who attend to the educative features, outcomes are generally positive. For these materials to aid in developing curricular knowledge for all teachers, more needs to be understood about teachers' dispositions to curriculum as well as their beliefs about teaching and learning mathematics.