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Figure 7
NSF-funded exemplary comprehensive
mathematics curricula
Elementary school (K-5):
• Everyday Mathematics
• Investigations in Number,
Data and Space
• Math Trailblazers
Middle school (5-8):
• Connected Mathematics Project
(CMP)
• Mathematics in Context (MiC)
• MathScape
• Middle Grades Math Thematics
• Middle School Mathematics
through Applications Project (MMAP)
High school (9-12):
• Contemporary Mathematics in
Context (CORE-Plus)
• Interactive Mathematics
Program (IMP)
• Math Connections
• Mathematics: Modeling our
World (ARISE)
• SIMMS Integrated Mathematics
* web addresses are current at time of
publication
In order to be considered
“exemplary,” a unit or comprehensive curriculum
must be consistent with the NCTM Standards, designed by groups
of specialists in mathematical content and pedagogy, and
revised based on field tests in various instructional settings.
Exemplary instructional materials are
much more than a textbook for students. They usually include a
rich collection of documents to support learning experiences.
The documents may include suggestions for planning lessons and
orchestrating class discussions, examples of student work,
tools and rubrics for assessment, and opportunities for
teachers to learn more about the mathematical concepts to be
taught.
While there is certainly a value for
teachers to create their own innovative lessons and units, the
results of the multitude of Teacher Enhancement and Local
Systemic Change projects supported by the NSF in the last two
decades suggest that the use of exemplary comprehensive
mathematics curricula is critical to the success of systemic
reform. That is, if the goal is to reform the entire
mathematics program within a given school or district, not just
to improve the practices of a few committed teachers, it is
very difficult to achieve significant success unless the system
adopts a coherent curriculum that ensures that students engage
in a well-constructed sequence of worthwhile mathematics
experiences, and frees teachers to focus their energy on
improving their instructional practices and evaluating their
students’ learning.
While exemplary instructional materials
can revolutionize the way we approach school mathematics reform
(Ball & Cohen, 1996; Russell, 1997), they also require
considerable time (and, in some cases, special expertise) to be
used efficiently. Therefore, professional development programs
should include opportunities for teachers to become familiar
with at least some exemplary instructional materials, selected
so as to maximize the participants’ opportunities to
implement reform in their classes.
Teachers also need to learn about high
quality software and other technological tools if they are to
implement mathematical learning experiences consistent with the
most recent calls for reform. Indeed, new technologies such as
graphing calculators, spreadsheets, and programs like the
“Geometer’s Sketchpad” and statistical
packages like “Fathom,” have radically changed the
way certain mathematical topics can be taught in school (e.g.,
Dunham & Dick, 1994; Rojano, 1996). Teachers need to become
proficient users of these technologies and to learn to consider
how using these tools could affect not only their teaching
practices but also their instructional goals.
Understanding equity issues and their
implications for the classroom
At the forefront of the current call for
school mathematics reform is the directive that all students
should have opportunities to learn mathematics (NCTM, 1989,
2000; Secada, Fennema & Adajian, 1995). The
underachievement of some ethnic minorities and women has been
the cause of serious concern and one of the reasons that led to
the recent critical scrutiny of curricula and teaching
practices (Chipman & Thomas, 1987; National Science
Foundation, 1986; Oakes, 1990; Secada, 1992). Students with
disabilities may also perform much better in mathematics if
they have appropriate learning opportunities and support
(Silver, Smith & Nelson, 1995; Thornton & Langrall,
1997).
Because the new instructional goals and
teaching practices articulated in the NCTM (2000) Standards are
meant to recognize and respond to student diversity,
researchers and policy makers are confident they will help
bridge the achievement gap. Our vignette is evidence of how
mathematical tasks can be designed to provide access to
students with diverse learning styles, strengths and background
experiences. An open-ended task, such as finding the area of a
“fish,” offers many more opportunities for success
for all students than traditional tasks that recognize only one
correct solution and one way to achieve it. Multiple forms of
assessment, as exemplified in our vignette by the combination
of a group performance assessment and more traditional
paper-and-pencil tests, may also help students with different
strengths and learning styles to show more easily what they
know.
However, taking on new instructional
goals and teaching practices will not be enough for teachers to
fully address equity issues in school mathematics. Each teacher
must first gain a good understanding of the many issues related
to equity and diversity and their implications for mathematics
instruction (Darling-Hammond, 1998). Teachers must also become
aware of their own biases and privileges and learn how these
may affect their relationship with students who are different
with respect to race, class, gender, primary language, sexual
orientation, etc. (Weissglass, 1996). Teachers must also
believe that all students can learn mathematics when they are
provided with ample opportunities, conditions conducive to
learning and high teacher expectations.
Teachers also need to know how to
identify their students’ unique needs and how to
differentiate instruction to address those needs. For example,
it was important for the teacher in our vignette to recognize
the different strengths and abilities of her students in order
to place them with an appropriate partner for the final
project; the same knowledge enabled her to offer additional
scaffolding for some students who needed it. To respond to
students with specific learning disabilities, teachers may need
knowledge that is even more specialized.
Coping with the emotional aspects of
engaging in reform
Several reform projects have noted that
emotions, both positive and negative, inevitably accompany
efforts to change one’s teaching practices (Clarke, 1994;
Ferrini-Mundy, 1997). A participant in one of our professional
development projects aptly described her initial experiences in
instructional innovation as an “emotional
roller-coaster”; at times she felt elated by her
students’ success and the depth of their mathematical
thinking, but she could also sink into dejection from an
unsuccessful instructional experience she had spent hours
putting together or from the opposition presented by a parent
or administrator. Some teachers may suddenly feel inadequate
after years of perceiving themselves as successful teachers and
may even blame themselves for “doing it wrong.”
Studies of learning and problem solving
show that behavioral changes often engender strong feelings of
anxiety, frustration and elation (McLeod, 1992). Teachers need
to know that conflicting feelings will inevitably arise and
they need to find ways to cope with these feelings. If
emotional needs are not directly addressed, teachers may even
drop out of professional development programs and reform
efforts. Weissglass (1993) has suggested that “any reform
that does not provide methods for people to systematically and
profoundly address their feelings, emotions and values related
to reform will be inadequate.” (p. 3)
For teachers to recognize and deal
constructively with feelings, they need, among other things, to
break the isolation that so often characterizes teachers’
work. The need for teachers to share ideas and feelings with
other teachers involved in research and reform has been long
recognized in the teacher education literature (e.g., Clark,
1994). Quality professional development programs should strive
to meet this need by creating opportunities for teacher
collaboration.
Continued
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CHAPTER 1 continued