Chapter 1 - Teachers' learning need for implementing school mathematics reform

Teachers’ learning needs for implementing school mathematics reform

The previous vignette shows that the kind of school mathematics reform currently promoted by many constituencies involves much more than “superficial features” such as using manipulatives or introducing computers in the classroom. Rather, whenever we speak of “reform-oriented” practices in this monograph, we refer to a comprehensive approach to mathematics instruction that is centered on teaching for understanding and enabling students to engage with meaningful problems and “big ideas” in mathematics. This approach is characterized by a set of beliefs and theories about what counts as significant mathematics, how students learn and what conditions call such learning in a classroom environment, as articulated in the NCTM Standards (1989, 1991, 1995, 2000) and much of the current literature in mathematics education. At the same time, this does not mean that the most recent wave of school mathematics reform can be reduced to a prescriptive set of teaching strategies or “exemplary lessons.” As argued throughout this monograph in the case of professional development, no single model of reform-oriented mathematics teaching will work for all, and all teachers will need to make decisions about what will be most appropriate and effective for their students.

Regardless of these differences, our vignette suggests that teaching mathematics in a reform-oriented way demands a lot more from teachers – even experienced teachers – than teaching a traditional mathematics lesson. However, teachers interested in reform should not be given the message that anything “traditional” is necessarily “bad” nor that they have done everything wrong so far and should abandon all their current practices. Teachers indeed bring valuable experience to reform, although they are asked to review their beliefs and practices critically in light of new instructional goals and pedagogical approaches. Identifying what teachers need to meet this enormous challenge, therefore, is a critical prerequisite to establishing worthwhile professional development goals and evaluating how specific professional development practices may contribute to achieving such goals.

Drawing from the literature on teacher development and reform (e.g., Friel & Bright, 1997; Fennema & Nelson, 1997; Darling-Hammond, 1997; Wilson & Berne, 1999), we grouped the main learning needs of teachers engaging in school mathematics reform into nine categories (see Figure 6), which we will examine in more depth in the rest of this chapter.

Figure 6

Main categories of teacher learning needs

1. Developing a vision and commitment to school mathematics reform.

2. Strengthening one’s knowledge of mathematics.

3. Understanding the pedagogical theories that underlie school mathematics reform.

4. Understanding students’ mathematical thinking.

5. Learning to use effective teaching and assessment strategies.

6. Becoming familiar with exemplary instructional materials and resources.

7. Understanding equity issues and their implications for the classroom.

8. Coping with the emotional aspects of engaging in reform.

9. Developing an attitude of inquiry toward one’s practice.

Before engaging in this analysis, a few words about possible differences between elementary and secondary teachers of mathematics are warranted. Indeed, elementary and secondary teachers come to professional development experience with quite different preparation, background in mathematics and teaching experiences. Secondary teachers are usually specialists in their subject matter; most have completed the equivalent of a major in mathematics and teach only mathematics courses (often multiple sessions of the same two or three courses) to a total of 100 to 150 different students each year. Elementary teachers, instead, have been trained as generalists and usually teach all subjects to a class of 20 to 30 students; many of them have taken only one college-level mathematics course, although they may have had a wider exposure than their secondary colleagues to learning theories and innovative teaching practice as part of their training. It is also not uncommon for elementary teachers to express a greater interest and confidence in teaching language arts or almost any other subject matter! – than mathematics. These differences will undoubtedly play an important role in elementary and secondary teachers’ expectations, responses and even attitudes toward professional development in mathematics, and it will be critical for every professional development provider to take them into serious consideration in their planning. At the same time, we believe that elementary and secondary teachers alike experience all of the learning needs identified in this chapter, although they may do so differently.

Developing a vision and commitment to school mathematics reform

Mathematical experiences such as the one described in the above vignette are not likely to happen unless teachers believe reform is important and understand what school mathematics reform calls for. Teachers interested in reform must thus become familiar with the new instructional goals and teaching practices proposed and understand their rationales.

Teachers need to develop a personal understanding of the reform recommendations articulated in the NCTM Standards (1989, 1991, 1995, and 2000) and other documents. Teachers also need “images” of reform classrooms in action, such as that offered in our vignette, because reform-oriented instruction is so different from the experiences of most teachers and students. By reading scenarios from actual mathematics classrooms, teachers can observe, in their mind’s eye, the learning environment, typical activities and tasks that are taking place, and students’ reactions. Several professional development projects have recently recognized this important need and responded to it by creating written and/or video images of reform-oriented mathematics lessons (e.g., Borasi, Fonzi, Smith & Rose, 1999; Ferrini-Mundy, 1997).

Because changing practices is not easy, teachers also need to be convinced that their students will benefit. Indeed, research on professional development efforts has shown that program outcomes, and teacher change in particular, correlate with the level of individual teachers’ participation, effort and identification with reform goals and agendas (e.g., Clarke, 1994; Loucks-Horsley, 1997). At the same time, participating teachers initially may have only a limited vision of their needs and goals in terms of instructional innovation (Ferrini-Mundy, 1997). Thus, a professional development program should strive to create a felt need for reform while also taking into consideration the participants’ perceived needs and actual constraints.

For some teachers, just witnessing students’ active engagement and enjoyment of reform activities and seeing the depth of the mathematics learned in those lessons may be reason enough to want to offer similar opportunities to their own students (Fennema, Carpenter & Franke, 1997). Others, however, may need further evidence of the need for change, such as data on student achievement in comparative studies.

Developing a vision and commitment to reform among mathematics teachers is an ongoing and long-term goal for any professional development project. It is clearly the most critical element of any professional development program aimed at initiating the process of reform, although it should also continue to be an ongoing goal for any professional development project.

Strengthening one’s knowledge of mathematics

Shulman’s research identified subject matter knowledge and pedagogical content knowledge as key variables influencing teachers’ decisions in the classroom:

Prior subject matter and background in a content area affect the ways in which teachers select and structure content for teaching, choose activities and assignments for students, and use textbook and other curriculum materials. (Shulman & Grossman, 1988, p.12).

While developing teachers’ knowledge of mathematics has always been considered a desirable goal of professional development, what counts as desirable mathematical knowledge has changed with the reform agenda. Reform-based curricula are informed by a different set of instructional goals. These include areas of mathematics that have been neglected in the traditional K-12 curriculum, such as probability and statistics. Even more importantly, there is a new emphasis on understanding “big ideas” in mathematics and on apprenticing students to the ways of thinking practiced by mathematics professionals.

Given their limited preparation in mathematics, elementary teachers are the ones often feeling the greatest need for learning more mathematics and deepening their own understanding of and confidence in the subject. However, despite their more extensive preparation in mathematics, secondary teachers also experience this need, as illustrated in our classroom vignette. In order to conduct the lessons on area formulas reported in the vignette, Mrs. Callard needed to know a variety of strategies for computing the area of complex figures, not just how to apply known formulas. She had to know how to develop area formulas, when to apply them and where mathematical definitions come from. These are aspects of mathematics that even teachers certified to teach secondary mathematics have not learned in their previous training (Fennema & Franke, 1992; Sowder, Philipp, Armstrong & Schappelle, 1998).

Furthermore, research on teachers’ beliefs about mathematics (Thompson, 1992) documents the impact on curricular decisions and instructional practices of teachers’ views on the following key topics: the nature of mathematics as a discipline; what constitutes legitimate mathematical procedures, results and justifications; and what constitutes desirable goals and acceptable outcomes for school mathematics instruction. Most teachers, regardless of whether they are generalists or specialists, never had the opportunity to make their beliefs explicit in traditional teacher preparation. Readings and discussions about the discipline of mathematics are notably absent from school mathematics and even college-level mathematics courses. Nevertheless, because they studied in traditional mathematics classes, most teachers hold deep-seated beliefs that mathematics is a body of absolute truths with little room for creativity or personal judgment. This means that, as teachers, they are likely to value correct answers over tentative conjectures, standard procedures over personal approaches to solutions, and facts and algorithms over inductive problem solving and reasoning skills.

Since these views conflict with the most recent calls for school mathematics reform (Borasi, 1996; NCTM, 2000), professional development programs designed to promote reform must provide opportunities for participants to critically examine their views of mathematics as a discipline and offer alternative perspectives grounded in reform.

Continued