Pedagogy and Content in Middle and High School Mathematics 1st Edition by Donald 9463511377 9789463511377

Pedagogy and Content in Middle and High School Mathematics 1st Edition by G. Donald Allen – Ebook Instant Download/Delivery ISBN(s): 9463511377, 9789463511377

Product details:

• ISBN 10:  9463511377
• ISBN 13:  9789463511377
• Author: Donald

The book provides an accumulation of articles, included in Focus on Mathematics Pedagogy and Content, a newsletter for teachers, published by Texas A&M University. Each article presents a discussion of a middle or high school mathematics topic. Many of the articles are written by professors at Texas A&M University. The book is broken into three parts, with the first part focusing on content and pedagogy, related to the NCTM content strands of Number, Algebra, Geometry, Measurement, and Statistics and Probability. Articles include an in-depth presentation of mathematical content, as well as suggested instructional strategies. Thus, the integration of content knowledge and pedagogical knowledge is emphasized. The second and third parts apply to assessments, mathematical games, teaching tips, and technological applications. While other pedagogical reference books may provide an in-depth look at how to teach a topic, this book includes articles that also explain a topic, in great length. Thus, teachers may develop content knowledge first and then re-read each article, in order to learn appropriate instructional strategies to use. Many articles include technological applications, which are interspersed throughout the book. In addition, a special section, which includes helpful information, available tools, training sessions, and other references, for using technology in mathematics, is also presented.

Table of contents:

PART I: CONTENT AND PEDAGOGY

SECTION 1: NUMBER

1. A BRIEF HISTORY OF ZERO

2. APPROXIMATING PI

ANCIENT EGYPTIANS

ANCIENT GREEKS

ANCIENT CHINESE

MODERN TIMES

ACTIVITIES

READINGS

3. THE CAESAR CYPHER

4. HOW BIG IS INFINITY?

ARITHMETIC

MAGNITUDE

HIGHER ORDERS OF INFINITY

REFERENCE

5. MAKING COMPLEX ARITHMETIC REAL!

6. EARLY PI

7. PRIMES, PERFECT NUMBERS AND MAGIC NUMBERS (JUST FOR FUN)

MAGIC NUMBERS

PERFECT NUMBERS

PROBLEMS

8. HOW DO WE DEFINE THE NUMBER “1?”

9. PERCENTAGE PROBLEMS

10. MICROWAVE MATH

11. FANTASY PROBLEMS AND FLYING CARPET SOLUTIONS

FANTASY PROBLEMS

EXAMPLES

FLYING CARPET SOLUTIONS

EXAMPLES

REFERENCES

SECTION 2: ALGEBRA

12. THE MYSTERY OF THE NEW “PLANET” (OR HOW REGRESSION SAVED THE DAY)

ECCENTRICITY

REFERENCES

13. GEOGEBRA IN THE CLASSROOM

REFERENCES

14. WORKING TOGETHER: The Math Part

15. A BRIEF LOOK AT CIRCLES

HOW TO CONSTRUCT A CIRCLE

HOW TO CREATE A CIRCLE WITH A CENTER AT THE ORIGIN

HOW TO CREATE A TRANSLATED CIRCLE

HOW TO CREATE A CIRCLE USING A GRAPHING CALCULATOR

EXPLAINING WHY A CIRCLE IS NOT A FUNCTION

16. OPTIMIZATION – WITH AND WITHOUT CALCULUS

1. DISTANCES BETWEEN POINTS IN THE PLANE

REMARKS

17. PYTHAGOREAN TRIPLES PLUS ONE

EXERCISES

REFERENCES

18. A BRIEF LOOK AT DERIVATIVES

19. A BRIEF LOOK AT ARITHMETIC AND GEOMETRIC SEQUENCES

ARITHMETIC SEQUENCES

GEOMETRIC SEQUENCES

FINDING THE NTH TERM

SERIES

20. A BRIEF LOOK AT SIGMA NOTATION

21. COMMUNICATING WITH LIFE IN THE UNIVERSE

THE DRAKE EQUATION

Number of planets with intelligent life = Number of possible planets × various probabilities

SETI (SEARCH FOR EXTRA-TERRESTRIAL INTELLIGENCE)

CURRENT PROJECTS BY THE CENTER FOR SETI INCLUDE

SETI@HOME

SPONSORS

NOTE

WEBSITES

REFERENCES

SECTION 3: GEOMETRY AND MEASUREMENT

22. THE MATHEMATICAL MYSTERY OF THE PYRAMID

23. THE SPHERE PACKING PROBLEM

LINKS

24. BIG, BUT NOT REALLY BIG NUMBERS

ACTIVITIES

25. THE NET OF A CONE

TRIANGLE EXPLORATION

THE TRIANGLE AND THE SECTOR

26. AREA OF A CIRCLE

27. GEOMETRY MEETS ALGEBRA – SUPER-CONIC CONSTRUCTIONS, PART I

INTRODUCTION

BASIC ARITHMETIC

FINDING ROOTS

SOLVING QUADRATICS

28. GEOMETRY MEETS ALGEBRA – SUPER-CONIC CONSTRUCTIONS, PART II

INTRODUCTION

SOLVING CUBICS

SOLVING QUARTICS

SECTION 4: STATISTICS AND PROBABILITY

29. LET’S MAKE WAR—JUST FOR FUN

REFERENCES

30. A BRIEF LOOK AT PROBABILITY

DEFINITION OF PROBABILITY

SIMPLE PROBABILITY

COMPOUND PROBABILITY

MUTUALLY EXCLUSIVE AND NON-MUTUALLY EXCLUSIVE EVENTS

INDEPENDENT AND DEPENDENT EVENTS

SAMPLE PROBLEMS

CONCLUSION

31. AREA UNDER THE NORMAL CURVE

A NORMAL DISTRIBUTION

STANDARD NORMAL CURVE

CALCULATING A Z-SCORE

USING THE Z-TABLE

EXAMPLES

Example 1

Example 2

Example 3

32. FINDING THE AREA UNDER THE NORMAL CURVE USING THE GRAPHING CALCULATOR

USING THE GRAPHING CALCULATOR

Example 1

Example 2

Example 3

33. HYPOTHESIS TESTING

T-TEST

Example

ONE-WAY ANOVA

Example

TWO-SAMPLE T-TEST

Example

ONE-PROPORTION Z-TEST

Example

Z-INTERVAL

Example

CHI-SQUARE TEST

Example

34. A BRIEF LOOK AT EXPECTED VALUE

FOR ONE TRIAL

FOR X TRIALS

PART II: ASSESSMENT

SECTION 5: CLASSROOM FORMATIVE AND SUMMATIVE ASSESSMENTS

35. THE EVIL TWINS – TESTING AND STRESS

36. UNFAIRNESS IN TESTING – MATHEMATICS AND SIMULATIONS

MATH EXAMPLES

NOTES

REFERENCES

37. ONLINE ASSESSMENTS IN MATH

Course Management Systems

Quiz/Test Creation Websites

Classroom Response Systems

Online Math Practice, Games, and Applets

Online Practice Tests

Online Portfolios

Online Surveys

Types of Online Assessment Items

Advantages of Online Assessments

Disadvantages of Online Assessments

Summary

38. WHEN IT COMES TO MATH, WHATEXACTLY ARE WE TESTING FOR?

SCOPE FOR TESTING

DOMAIN OF TESTING

TESTING SPECIFICS

NOTES

SECTION 6: LOW-STAKES AND HIGH-STAKES TESTING

39. ASSESSMENT VIA HIGH-STAKES TESTING

DEFINING ASSESSMENT

HIGH-STAKES TESTING

ADEQUATE YEARLY PROGRESS STATUS

ORIGINS OF HIGH-STAKES TESTING

CRITICISMS OF HIGH-STAKES TESTING

REFERENCES

40. HIGH-STAKES TESTING: Test Construction

A BRIEF GLANCE AT PROBLEMS WITH TEST CONSTRUCTION

GUIDELINES FOR IMPROVEMENT

REFERENCES

41. LOW-STAKES TESTS AND LABELS

PART III: TECHNOLOGY, GAMES, AND TIPS

SECTION 7: TECHNOLOGICAL APPLICATIONS

42. WHAT TECHNOLOGY WORKS FOR TEACHING MATHEMATICS AND WHY – A PERSPECTIVE, PART I

43. USING TECHNOLOGY IN TEACHING MATH

INVESTIGATION – CONVERTING A MIXED NUMBER INTO A FRACTION

PRESENTING SOME STEPS – RADIAL EXPRESSIONS ON A NUMBER LINE

NEGATIVE SQUARE ROOTS

REVISION – FRACTIONS

OTHER WAYS TO USE TECHNOLOGY IN MATH TEACHING

44. WHAT TECHNOLOGY WORKS FOR TEACHING MATHEMATICS AND WHY – A PERSPECTIVE, PART II

GENERAL PRINCIPLES ON TEACHING WITH TECHNOLOGY

45.THE GRAPHING CALCULATOR: A Brief Look at What It Can Do

MINIMUM OR MAXIMUM

INTERCEPTS

DERIVATIVE

CALCULATE COMBINATIONS AND PERMUTATIONS

CALCULATE THE AREA UNDER THE NORMAL CURVE

SECTION 8: MATHEMATICAL GAMES OR “RECREATIONAL GENRE PROBLEMS”

46. PROBLEMS IN MATHEMATICAL RECREATION

POSITIVE CLASSROOM PRACTICES

47. A MILE OF PENNIES

48. EASY PROBLEMS

AN EQUATION FOR LIFE

49. MATHEMATICAL GAMES AND LEARNING

IMPACT ON LEARNING

CHARACTERISTICS OF GOOD MATHEMATICAL GAMES

IMPACT ON LEVEL OF ENGAGEMENT

ONLINE GAMES VS TACTILE GAMES

THE MATTER OF TIME

INTEGRATION INTO THE CLASSROOM

FOLLOW-UP ACTIVITIES

TECHNOLOGICAL DEVICES

SECTION 9: TEACHING TIPS AND RESOURCES

50. TWO GREAT SOFTWARE TOOLS (WINPLOT AND MATHTRAX)

51. USING POLYA’S PROBLEM SOLVING PROCESS IN THE MATHEMATICS CLASSROOM TO PREPARE FOR TAKS

52. PROBLEM-SOLVING STRATEGIES – A QUICK CHECKLIST

STRATEGIES TO UNDERSTAND THE PROBLEM

STRATEGIES TO SIMPLIFY THE PROBLEM

STRATEGIES TO SOLVE A PROBLEM

STRATEGIES TO YOUR PEAK PERFORMANCE

53. WHAT IS MENTAL MATH?

WHAT DO STUDENTS NEED IN ORDER TO PERFORM MENTAL MATHEMATICS?

WHAT ARE SOME EXAMPLES OF “MENTAL MATH” PROBLEMS?

WANT TO TRY A FEW MENTAL MATH PROBLEMS?

54. A DIGITAL SIMULATION FOR PROSPECTIVE TEACHERS TO TEACH ALGEBRA CONCEPTS FOR EQUITY

INTRODUCTION

THE SETTINGS: WHEN, WHERE AND WHO

PREPARATION AND DESIGN FOR TEACHING ENVIRONMENT SIMULATION IN SECOND LIFE

REFERENCES

55. TEACHING IS A BALANCING ACT

NOTES

56. TAMU’S PEER PROGRAM PROMOTES STEM THE WORLD OVER

57. ENERGY MATH LESSONS FOR MATH CLASSES

58. MULTIPLE REPRESENTATIONS, I

DEFINING MULTIPLE REPRESENTATIONS – THE BASICS

WHAT ARE MULTIPLE REPRESENTATIONS?

MULTIPLE REPRESENTATIONS AND LEARNING TRANSFER

THREE DIMENSIONS OF FUNCTIONAL UNDERSTANDING

TWO LEARNING TRANSFER TRIADS

REFERENCES

59. MULTIPLE REPRESENTATIONS, II

1. INTRODUCTION

2. ALGEBRAIC TO GRAPHIC REPRESENTATIONS

3. ALGEBRAIC TO NUMERIC REPRESENTATIONS

4. NUMERIC TO GRAPHIC REPRESENTATIONS

DISCUSSION QUESTIONS AND ACTIVITIES

60. MULTIPLE REPRESENTATIONS, III

INTRODUCTION

EASY LEVEL QUESTIONS WITH ANALYSIS

MEDIUM LEVEL QUESTIONS WITH ANALYSIS

CONCLUSIONS

NOTE

61. MULTIPLE REPRESENTATIONS, IV

SUMMARY

NOTE

REFERENCES

62. THE TWO-MINUTE LESSON

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