## Philosophy of MiC |

*Mathematics in Context* represents a comprehensive mathematics curriculum for the middle
grades consistent with the content and pedagogy suggested by the
NCTM *Curriculum and Evaluation Standards for School Mathematics*, and *Professional Standards for Teaching Mathematics*. The development of the curriculum units reflects a collaboration
between research and development teams at the Freudenthal Institute
at the University of Utrecht, The Netherlands, research teams
at the University of Wisconsin, and a group of middle school teachers.

A total of 40 units have been developed for Grades 5 through 8.
These units are unique in that they make extensive use of realistic
contexts. From the context of tiling a floor, for example, flow
a wealth of mathematical application; such as similarity, ratio
and proportion, and scaling. Units emphasize the inter-relationships
between mathematical domains; such as number, algebra, geometry
and statistics. As the project title suggests, the purpose of
the units is to *connect* mathematical content both across mathematical domains and to
the real world. Dutch researchers, responsible for initial drafts
of the units, have 20 years of experience in the development of
materials situated in the real world. These units were then modified
by staff members at the University of Wisconsin to make them appropriate
for U.S. students and teachers.

Because the philosophy underscoring the units is that of teaching
mathematics for understanding, the curriculum will have tangible
benefits for both students and teachers. For students, mathematics
should cease to be seen as a set of disjointed facts and rules.
Rather, students should come to view mathematics as an interesting,
powerful tool that enables them to better understand their world.
All students should be able to reason mathematically; thus, activities
will have multiple levels so that the able student can go into
more depth while a student having trouble can still make sense
out of the activity. For teachers, the reward of seeing students
excited by mathematical inquiry, a redefined role as guide and
facilitator of inquiry, and collaboration with other teachers
should result in innovative approaches to instruction, increased
enthusiasm for teaching, and a more positive image with students
and society.

Each of the units uses a theme that is based on a problem situation
that should be of interest to students. These themes are the "living
contexts" from which negotiated meanings can be developed and
sense-making can be demonstrated. Over the course of the four-year
curriculum, students will explore in-depth the mathematical themes
of number, common fractions, ratio, decimal fractions, integers,
measurement, synthetic geometry, coordinate and transformation
geometry, statistics, probability, algebra, and patterns and functions.
Although many units may emphasize the principles within a particular
mathematical domain, most will involve ideas from several domains,
emphasizing the interconnectedness of mathematical ideas. These
units are designed to be a set of materials that can be used flexibly
by teachers, who tailor activities to fit the individual needs
of their classes.

Students working individually and in flexible group situations,
which include paired work and cooperative groups. We believe that
the shared reality of doing mathematics in cooperation with others
develops a richer set of experiences than students working in
isolation.

Students exiting *Mathematics in Context* (MiC) will understand and be able to solve non-routine problems
in nearly any mathematical situation they might encounter in their
daily lives. In addition, they will have gained powerful heuristics,
vis-à-vis the interconnectedness of mathematical ideas, that they
can apply to most new problems typically requiring multiple modes
of representation, abstraction, and communication. This knowledge
base will serve as a springboard for students to continue in any
endeavor they choose, whether it be further mathematical study
in high school and college, technical training in some vocation,
or the mere appreciation of mathematical patterns they encounter
in their future lives.