With the goals, aspirations, and background experiences of today's
students so diverse and eclectic, the secondary school mathematics
curriculum must not only prepare students for formal advanced study
in the subject, but must also develop students' problem solving and
communication skills as well. Mathematical numeracy is formulated through
a three-pronged approach which stresses the acquisition of fundamental
skills, the application of these skills in sophisticated and realistic
situations, and the exposition of the problem solving process and its
results using concise and coherent language.
Fundamental Skills
Most strongly associated with the traditional study of mathematics,
the mastery of fundamental skills is an essential aspect of mathematical
and scientific
literacy. Students must be familiar with the formal notation, operations,
procedures, and rules of mathematics as with any other foreign
language or logical system,
and they will receive ample instruction and practice in the same.
Typical assignments that emphasize the acquisition of basic skills
include daily warm-up problems, classwork, and homework assignments
Applications and Problem Solving
Just as a pile of bricks and a trowel full of mortar are nothing
until they are assembled by a skilled and experienced craftsperson
into a sturdy and beautiful
structure, a student with a hodgepodge of formulas and theorems is not fully
educated until he or she can use these skills to solve complex and non-trivial
problems. Unlike basic skills, however, problem solving acumen cannot be
acquired by dutifully aping the actions of the instructor, but
requires a measure of
creativity and intellectual risk-taking. Many aspects of the process, nevertheless,
can be formalized, and with sustained practice and exposure to models of
effective problem solving, students will have ample opportunities
to develop their analytical
reasoning abilities.
Typical assignments that emphasize problem solving include POWs, projects,
and in-class experiments
Communication
Albert Einstein and Steven Hawking would not be the household names
that they are unless, in addition to their first-rate intellects,
they possessed the
ability to communicate their findings in language accessible to a wide and
varied audience. Scientific and thechnological breakthroughs are useless
unless they can be shared with others, and thus, the ability to
communicate one's
thought processes and results is as important as having the ability to obtain
those results in the first place. Reading, writing, and speaking are not
the sole responsibility of departments of English, and are, by
necessity, integrated
through the mathematics curriculum.
Typical assignments that emphasize communication skills include journal
entries and POWs
Assessments and Evaluations
An integral aspect of the instructional process, assessment and evaluation
provide teachers with tangible evidence of student achievement, as well as
feedback for future modification and adjustment. Most often associated with
in-class individual tests and quizzes, assessments can also take the form
of projects, individual, small-group, and whole-class discussions,
teacher observations,
journal responses, and oral presentations. Opportunities for students to
demonstrate their knowledge and achievement are frequent and varied.
Standards Alignment
In order to ensure that all students have access to a challenging
and rigorous course of mathematical study, standards and benchmarks
for student achievement
have been established at both the state and national levels.
Instructional activities are geared towards the acquisition of these standards,
and assessments are tailored towards the demonstration of attainment of these
standards.
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