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MATHEMATICS
Position Statement
Secondary mathematics textbooks have been carefully reviewed by the State Textbook and Improvement of Instruction Committee and adopted by the State Board of Education. The trends in mathematics education were reviewed, major factors were discussed, and are listed on page three as the "Ten Basic Skill Areas." A district selecting new mathematics books should consider these in selecting textbooks.
COMPUTERS AND CALCULATORS
Both the NCSM and the NCTM have goals for both computer literacy and calculator/computer use for all students. Both the computer and the calculator should be available, if at all possible, and allowed for use in the secondary mathematics classes.
Problem Solving
Two national groups, the National Council of Teachers of Mathematics (NCTM) and the National Council of Supervisors of Mathematics (NCSM) have both listed Problem Solving as the first and primary goal for the mathematics programs in the decade ahead. (See lists of recommendations below:)
AN AGENDA FOR ACTION
RECOMMENDATIONS FOR
SCHOOL MATHEMATICS OF THE 1990'S
The National Council of Teachers of Mathematics recommends that --Problem solving continue to be a focus of school mathematics in the 1990's.
· Basic skills in mathematics be defined to encompass more than computational facility.
· Mathematics programs take full advantage of the power of calculators and computers at all grade levels.
· Stringent standards of both effectiveness and efficiency be applied to the teaching of mathematics.
· The success of mathematics programs and student learning be evaluated by a wider range of measures than conventional testing.
· More mathematics study be required for all students and flexible curriculum with a greater range of options be designed to accommodate the diverse needs of the students population.
· Mathematics teachers demand of themselves and their colleagues a high level of professionalism.
· Public support for mathematics instruction be raised to a level commensurate with the importance of mathematical understanding to individuals and society.
NATIONAL COUNCIL OF SUPERVISORS OF MATHEMATICS
Ten Basic Skill Areas
PROBLEM SOLVING
Students should learn specific strategies for problem solving since learning to solve problems is the principal reason for studying mathematics.
APPLYING MATHEMATICS TO EVERYDAY SITUATIONS
Students would learn to inspect all results and to check for reasonableness in terms of the original problem.
ALERTNESS TO THE REASONABLENESS OF RESULTS
Students should learn to inspect all results and to check for reasonableness in terms of the original problem.
ESTIMATION AND APPROXIMATION
Students should be able to carry out rapid approximate calculations by first rounding off numbers and having some sense of what the result should be.
APPROPRIATE COMPUTATIONAL SKILLS
Students should gain facility with addition, subtraction, multiplication, and division with whole numbers and decimals and simple computation with common fractions and percentages.
GEOMETRY
Students should have knowledge of concepts such as point' line, plane, parallel, perpendicular, simple geometric figures, both plane and solid, and measurement and problem solving skills.
MEASUREMENT
Students should be able to measure distance, weight' time, capacity, temperature, both in the metric and customary systems.
READING, INTERPRETING, AND CONSTRUCTING TABLES
Students should know how to read and draw conclusions from simple tables, maps, charts, and graphs and also make charts, maps, tables and graphs from data.
USING MATHEMATICS TO PREDICT
Students should learn how elementary notions of probability are used to determine the likelihood of future events.
COMPUTER LITERACY
Students should be aware of the many uses of computers in society, such as their use in teaching/learning, financial transactions and information storage and retrieval.
MATHEMATICS
Philosophy
Mathematics is the language of the scientific, business, and commercial worlds. It is reflected in most other facets of our lives to some degree. There are two major aspects of mathematics, (1) use and/or application and (2) beauty, symmetry and appreciation. In the area of application, mathematics is used to count, model or predict. In the area of appreciation are recurring patterns, symmetry, predictability and the excitement of discovery that is inherent in the study of mathematics itself.
Learning to solve problems is the principal reason for studying mathematics. In general, two main efforts must be made in order to accomplish this:
1. Good computational skills must be taught and maintained in addition, subtraction, multiplication and division using whole numbers, decimals and fractions.
2. Problem solving skills and strategies must be taught and reinforced by using meaningful problems.
Most textbooks provide for computational skill teaching but supplementary material is generally needed for the teaching of problem solving.
"A problem is a situation either quantitative or verbal that requires a solution for which the individual sees no apparent or obvious means or path to obtain the solution."
Obviously, thinking skills and understanding must be employed and will be enhanced by purposeful use of problems keyed to the basic concepts to be taught.
Other key elements in the philosophical framework for the mathematics curriculum must include the goal of mathematical literacy for all students. Literacy implies that the individual can apply mathematical knowledge and skills to satisfy common, personal, vocational and citizenship needs. Applying mathematics must not be left to artificial or trivial situations, but must be meaningful and motivating. Mathematics must also be taught as a way of thinking.
The use of technology must be incorporated where appropriate. Computer and calculator applications to mathematics, logic, statistics, graphing, probability and consumer mathematics must be made. It must be clear that pencil and paper computation is not prerequisite to the mathematics that adults do by estimation or approximation and use of calculators or computers. Adults do a great deal of the mathematics applied to the working world using technology and test the reasonableness of the results using that same technology.
There are major goals and critical components that must be present to have a useful and meaningful mathematics curriculum at all levels. The critical components of any curriculum or program are those basic elements that lie within the content of that curriculum. In general, the critical components of mathematics are number and operations, sets, functions, relations, systems and statistics, graphing and problem solving strategies. The critical components should not be confused with the important outcomes of mathematics. These are:
For all mathematics curriculum some or most of the above critical components must be a part of the course and all of the listed outcomes should be the goal for the course.
This course of study covers the following topics:
Two years of mathematics are required for graduation. A student can satisfy the requirement with any combination of two of the above listed courses.
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