 
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
“reformoriented” 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 reformoriented 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
reformoriented 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.
Regardless of these differences, our
vignette suggests that teaching mathematics in a
reformoriented 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; DarlingHammond, 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
collegelevel 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 reformoriented 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 reformoriented
mathematics lessons (e.g., Borasi, Fonzi, Smith & Rose,
1999; FerriniMundy, 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; LoucksHorsley,
1997). At the same time, participating teachers initially may
have only a limited vision of their needs and goals in terms of
instructional innovation (FerriniMundy, 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 longterm
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.
Reformbased curricula are informed by a different set of
instructional goals. These include areas of mathematics that
have been neglected in the traditional K12 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
collegelevel mathematics courses. Nevertheless, because they
studied in traditional mathematics classes, most teachers hold
deepseated 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


 