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ED295827.Pdf DOCUMENT RESUME ED 295 827 SE 049 208 TITLE Michigan Essential Goals and Objectives for Mathematics Education. INSTITUTION Michigan State Board of Education, Lansing. PUB DATE Mar 88 NOTE 44p.; Graphs and pages with gray shaded areas may not reproduce well. PUB TYPE Guides - Classroom Use - Guides (For Teachers) (052) EDRS PRICE MF01/PCO2 Plus Postage. DESCRIPTORS Algebra; Calculators; *Curriculum Development; *Elementary School Mathematics; Elementary Secondary Education; Geometry; *Mathematics Education; *Mathematics Instruction; Measurement; Number Concepts; Problem Solving; *Secondary School Mathematics; State Curriculum Guides; State Programs IDENTIFIERS *Michigan ABSTRACT This document is designed to assist administrators and teachers in planning, developing, and implementing grades K-9 mathematics programs and to provide some guidelines for grades 10-12 instruction. It is intended to provide a philosophical foundation and curricular framework from which educators may construct a comprehensive local program t...$ meet the instructional needs of students. The document illustrates the integration of mathematical content with process skills. The mathematical content strand, are: (1) whole numbers and numeration; (2) fractions, decimals, ratio, and percent; (3) measurement; (4) geometry;(5) statistics and probability; (6) algebraic ideas; (7) problem solving and logical reasoning; and (8) calculators. (PK) ****************************4****************************************** * Reproductions supplied by EDRS are the best that can be made * * from the original document. * **************,t************* **************************************** Michigan State Board of Education Barbara Roberts Mason Dorothy Beardmore President Woe President la Cherry Jacobus Dr Gumeando Sales Secretary Treasurer Dr Edmund F Vendetta Canal M Hutton NASBE Delegate Annetta Miler Norman Otto Stockmeyer, Sr Ex-Offimo Members III James J Bia3chard Gary 0 Hawks Governor Interim Superintendent of Public Instruction FOREWORD The Michigan Department of Education is pleased to present the revised "Michigan Essential Goals and Objectives for Mathematics Education." This document sets forth the essential mathematical learning for elementary and middle schools. The "Michigan Essential Goals and Objectives for Mathematics Education" outlines the curriculum content necessary to foster understanding and promote reasoning, thinking, problem-soMng, and application skills. Individual schools may modify and expand the content, as appropriate, for their particular student populations. This document outlines those essential concepts and skills appropriate for learners in kindergarten through grade nine. While sequences are suggested, teachers' judg- ment about a particular student's readiness for more advanced Instruction will ultimately determine when new concepts and skills are introduced. The organiza- tion of contents and processes in this document is intended to help educators move each student from skill acquisition to higher-order learning while, at all times, fully engaging the students in rigorous academic study. The "Michigan Essential Goals and Objectives for Mathematics Education" should help elementary and middle/junior high school educators shape a mathematics curriculum that prepares students for the challenges of secondary school and beyond. The building blocks of an academic foundation are important not only to children and their family but also to the future of our communities and the nation as a whole. It is fitting to thank the many individuals, associations, and agenci3s who have provided assistance and support in the development and review of this document. Gary D. Hawks Interim Superintendent of Public Instruction March, 1988 4 I STATEMENT OF PURPOSE These essential goals and objectives are designed to assist administrators an, each - ers in planning, developing and implementing grades K-9 mathematics programs and to provide some guidelines for grades 10-12 instruction. They provide a philosophical fcJndation and curricular framework from which educators may construct a compre- hensive local program to meet the instructional needs of their students. This document illustrates the integration of mathematical content with process skills. In addition, It upgrades the bench mark expectations for achievement to be corn, nen- surate with the demands of a technological society. 5 ii 6 Table of Contents Page Introduction 2 Framework 4 New Directions 5 Mathematics Content Strands 1. Whole Numbers and Numeration 7 2. Fractions, Decimals, Ratio and Percent 12 3. Measurement 20 4. Geometry 23 5. Statistics and Probability 26 6. Algebraic Ideas 29 7. Problem Solving and Logical Reasoning 33 8. Calculators 35 6 1 Michigan Essential Goals and Objectives for Mathematics Education Introduction Quantitative thought and understanding form the keystone for the new mathematics objectives for Michigan. Support for this comes from a National Science Foundation report which stated that "...quantitative thought and understanding continue to become more important for more people..." This keystone is used insetting a new direction for curriculum and teaching that will help students learn to think, reason, solve problems and apply mathematics in real life situations. The objectives reflect mathematical knowledge that Is essential for all students' educational development and employment. Rote skills learned in a mean- ingless way do not prepar-3 students for the future. The view of computation is broadened to Include basic facts, mental arithmetic, estimation ano calculators. With the availability of calculators and computers in the workplace, the emphasis must be on conceptual development and problem solving. The use of calculato,s and computers to achieve the important mathematics objec- tives is suggested in Educating Americans for the 21st Century.' In Its Agenda for Action: Recommendations for School Mathematics of the 19806 2, the National Council of Teachers of Mathematics recommended that problem solving be the focus of school mathematics, that basic skills be defined to encompass more tnan computational facility and that mathematics programs take fun advantage of the power of calculators and computers at all grade levels. A liter report from the National Science Foundation, The Mathematical Sciences CurrlculumX-12: What is Still Fundamental and What is Not. 3 in asking recommenda- tions for elementary and middle school mathematics, stated 'A principal theme of K- 8 mathematics should be the development of number sense, including the effective use and understanding of numbers in applications as well in other mathematical contexts." 3 The changes suggested in the NSF report would 'replace excess drill in formal paper- and-pencil computations with various procedures to develop better number sense on the part of the student.' Substantially less emphasis was to be placed on paper and pencil execution of the arithmetic operations and de-emphasis was suggested for drill with larger numbers and fractions with larger denominators. The following content recommendations were included in the NSF report: 1) Mastery of 'xisic number facts 2) Selective use of calculators and computers 3i Mental arithmetic, estimation and approximation 4) Problem solving, including the use of calculates and computers as tools 5) Elementary data analysis, statistics and probability 7 2 6) Place value, decimals, percent and scientific notation 7; Intuitive geometry, including formulas for perimeter, area and volume 8) Algebraic symbolism and techniques, particularly in gradesseven and eight. Over the post two decodes there has been an explosion of researchon mathemat- ics learning and teaching. Syntheses of some of the iesearchcan be found in companion publications. ReseachwithicReactuSISCOffkleaLtVatititfiraatti and Research within Reach: Secondary School Mathematics.' Amongthe major national data sources on mathematics learning and mathematics teachingare those reported in the National Assessment of Education Progress5 and the Secondinterna- tional Mathematics Study." There Is unanimity from all reports and research results thatconceptualization of mathematics and understanding of problems should be valuedmore highly than just correct solutions to routine exercises.Yet there is extensive documentation that students ore now locking both conceptual understanding and problemsolving skill. For example, only half of the students finishing eighth grade could givethe meaning of the decimal 0.52 and only 20% of them could estimate theanswer to 3.04 X 5.3 as 16 given the choices of 1.6, 16, 160 and 1600. Fortoo long, mathematicsinstruction has been thought of as presenting rules and providing enough drill for studentsto master the sk1;1. As Simon pointed out, to survive in mathematicscourses, many students attempt to compensate for their lack of understanding by memorizingmathematical procedures and formulas. The mathematics objectives have been written toc framework of eight content strands and six process strands. The content strands are (1) whole numbersand numeration, (2) fractions, decimals, ratio and percent, (3) measurement, (4)geome- try, (5) statistics and probability, (6) algebraic ideas, (7) problem solvingand logical reasoning, and (8) calculators. The process strands are (1)conceptualization. (2) mental arithmetic. (3) estimation. (4) computation. (5) problemsolving, and (6) calculators and computers. Many of the objectives from previousdocuments have been retained but enhanced with
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