Teaching secondary mathematics : techniques and enrichment units

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書誌事項

Teaching secondary mathematics : techniques and enrichment units

Pearson/Merrill Prentice Hall, c2006

7th ed. / Alfred S. Posamentier, Beverly S. Smith, Jay Stepelman

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注記

Includes bibliographical references (p. 496-515) and index

HTTP:URL=http://www.loc.gov/catdir/toc/fy0604/2005045874.html Information=Table of contents

内容説明・目次

内容説明

For courses in Secondary Mathematics Methods. Teaching Secondary Mathematics: Techniques and Enrichment Units, 7th edition has been thoroughly revised to discuss current methods of teaching mathematics, considering all aspects and responsibilities of the job, beginning with a brief overview of the history of mathematics education and how it has evolved over time to include standards for teaching and assessment. The authors address how to craft rich and effective daily lesson plans, and how to use a variety of instructional tools and strategies to reach all students in a classroom. Problem solving is a key focus from its instructional underpinnings to its recreational and motivational aspects. The second part of the text provides mathematics teachers with a collection of enrichment units appropriate for the entire secondary school curriculum spectrum.

目次

-PART I METHODS OF TEACHING SECONDARY MATHEMATICS Chapter 1 The Challenge of Teaching Today's Students, Mathematics, and Society's Need Chapter 2 Planning for Instruction Long-Range Planning of the Curriculum Unit Plans Short-Range Planning Differentiated Instruction Cooperative Learning Mathematical Tasks Final Thoughts on Lesson Planning Chapter 3 Teaching More Effective Lessons Motivational Techniques Classroom Questioning Strategies for Teaching More Effective Lessons Literacy in Mathematics Writing Chapter 4 The Role of Problem-Solving A Psychnological View of Problem Solving Problem-Solving Preliminaries An Introduction to Problem Solving The Ten Problem-Solving Strategies Creating Mathematical Problems Creativity in Problem Solving Chapter 5 Using Technology to Enhance Mathematics Instruction Calculators Computers Chapter 6 Assessment Assessment for Monitoring Student Progress Assessment for Making Instructional Decisions Evaluating Student Achievement Chapter 7 Enriching Mathematics Instruction Enriching Mathematics Instruction with a Historical Approach Enrichment Techniques for All Levels The Gifted Student Using Calculators to Enrich Instruction Models and Manipulatives That Enrich Instruction Chapter 8 Extracurricular Activities in Mathematics The Mathematics Club Mathematics Teams Mathematics Contests Mathematics Projects The Mathematics Fair Cooperation with a University The School Mathematics Magazine The Mathematics Assembly Program Guest Speakers Program Class Trips of Mathematical Significance Peer Teaching Program The Computer The Bulletin Board PART II ENRICHMENT UNITS FOR THE SECONDARY SCHOOL CLASSROOM Cross-Catalogue of Enrichment Units Constructing Odd-Order Magic Squares Constructing Even-Order Magic Squares Introduction to Alphametics A Checkerboard Calculator The Game of Nim The Tower of Hanoi What Day of the Week Was It? Palindromic Numbers The Fascinating Number Nine Unusual Number Properties Enrichment with a Handheld Calculator Symmetric Multiplication Variations on a Theme-Multiplication Ancient Egyptian Arithmetic Napier's Rods Unit Pricing Successive Discounts and Increases Prime and Composite Factors of a Whole Number Prime Numeration System Repeating Decimal Expansions Peculiarities of Perfect Repeating Decimals Patterns in Mathematics Googol and Googolplex Mathematics of Life Insurance Geometric Dissections The Klein Bottle The Four-Color Map Problem Mathematics on a Bicycle Mathematics and Music Mathematics in Nature The Birthday Problem The Structure of the Number System Excursions in Number Bases Raising Interest Reflexive, Symmetric, and Transitive Relations Bypassing an Inaccessible Region The Inaccessible Angle Triangle Constructions The Criterion of Constructibility Constructing Radical Lengths Constructing a Pentagon Investigating the Isosceles Triangle Fallacy The Equiangular Point The Minimum-Distance Point of a Triangle The Isosceles Triangle Revisited Reflective Properties of the Plane Finding the Length of a Cevian of a Triangle A Surprising Challenge Making Discoveries in Mathematics Tessellations Introducing the Pythagorean Theorem Trisection Revisited Proving Lines Concurrent Squares Proving Points Collinear Angle Measurement with a Circle Trisecting a Circle Ptolemy's Theorem Constructing The Arbelos The Nine-Point Circle The Euler Line The Simson Line The Butterfly Problem Equicircles The Inscribed Circle and the Right Triangle The Golden Rectangle The Golden Triangle Geometric Fallacies Regular Polyhedra An Introduction to Topology Angles on a Clock Averaging Rates-The Harmonic Mean Howlers Digit Problems Revisited Algebraic Identities A Method for Factoring Trinomials of the Form: ax2 + bx + c Solving Quadratic Equations The Euclidean Algorithm Prime Numbers Algebraic Fallacies Sum Derivations With Arrays Pythagorean Triples Divisibility Fibonacci Sequence Diophantine Equations Continued Fractions and Diophantine Equations Simplifying Expressions Involving Infinity Continued Fraction Expansion of Irrational Numbers The Farey Sequence The Parabolic Envelope Application of Congruence to Divisibility Problem Solving-A Reverse Strategy Decimals and Fractions in Other Bases Polygonal Numbers Networks Angle Trisection-Possible or Impossible? Comparing Means Pascal's Pyramid The Multinomial Theorem Algebraic Solution of Cubic Equations Solving Cubic Equations Calculating Sums of Finite Series A General Formula for the Sum of Series of the Form tr A Parabolic Calculator Constructing Ellipses Constructing the Parabola Using Higher Plane Curves to Trisect an Angle Constructing Hypocycloid and Epicycloid Circular Envelopes The Harmonic Sequence Transformations and Matrices The Method of Differences Probability Applied to Baseball Introduction to Geometric Transformations The Circle and the Cardioid Complex-Number Applications Hindu Arithmetic Proving Numbers Irrational How to Use a Computer Spreadsheet to Generate Solutions to Certain Mathematics Problems The Three Worlds of Geometry ie Mix Graphical Iteration The Feigenbaum Plot The Sierpinski Triangle Fractals Appendix Additional Exercises Index About the Authors

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