The art of motivating students for mathematics instruction

Effective teaching is largely reliant on the teacher's ability to capture the genuine interest of the students for the material to be taught. This naturally rests on the planning that the teacher exerts in preparation for the lesson. Perhaps the single most important aspect of any lesson is the beginning of the lesson where the teacher must motivate the students for the ensuing lesson. This can be done in many ways and is also largely measure a function of the teacher's personality and voice. Studies have shown that what a teacher says accounts for 7% of the effectiveness package, the tone of the teacher's voice and the enthusiasm accounts for 38%, and the "body language" accounts for 55%. Teachers should be entertaining, without ever losing control of the lesson, and yet not be completely scripted to prevent accommodation to the quirks of any class.Yet even the finest style of presentation -- an important part of any teaching performance -- can only offer a portion of the overall effectiveness. The content of what is said is paramount! This then leads us into the theme of the book, namely, the techniques that can be used to motivate students in the first few minutes of almost any lesson in mathematics. This could be the most difficult part of a lesson to plan. It requires a modicum of creativity and yet it pays back by enabling a successful lesson. It is a very worthwhile investment of time.

Introduction	p. ix
Chapter 0 The Art of Motivating Students for Mathematics Instruction	p. 1
What Is Motivation	p. 2
Chapter 1 Indicate a Void in Students' Knowledge	p. 7
Topic: The Introductory Lesson on the Tangent Ratio	p. 8
Topic: Special Quadrilaterals	p. 9
Topic: Determining the Measure of an Angle Formed by Two Secants to a Circle	p. 10
Topic: Tangent Segments to the Same Circle	p. 12
Topic: Introducing Heron's Formula to Finding the Area of a Triangle	p. 12
Topic: Introducing the Quadratic Formula	p. 14
Topic: The Introductory Lesson on Imaginary Numbers	p. 14
Topic: Finding the Sum and Product of the Roots of a Quadratic Equation	p. 15
Topic: The Introduction to Exponential Equations	p. 16
Chapter 2 Discover a Pattern	p. 18
Topic: Counting Techniques	p. 19
Topic: Introducing Non-Positive Integer Exponents	p. 20
Topic: Caution with Patterns	p. 22
Topic: The sum of the Measure of the Interior Angles of a Polygon	p. 24
Topic: Introduction to Counting Combinations	p. 25
Chapter 3 Present a Challenge	p. 27
Topic: Introducing the Order of Operations	p. 27
Topic: Determining Prime Numbers	p. 29
Topic: Algebraic Applications	p. 31
Topic: Introducing the Concept of ¿	p. 32
Topic: Understanding the Value of ¿	p. 33
Topic: Introducing the Circumference of a Circle	p. 34
Topic: Finding the Sum of the Interior Angles of a Polygon	p. 35
Topic: Proving Triangles Congruent	p. 36
Topic: Introducing Geometric Series	p. 38
Chapter 4 Entice the Class with a "Gee-whiz" Amazing Mathematical Result	p. 39
Topic: Introducing the Nature of Proof	p. 40
Topic: Thales' Theorem	p. 41
Topic: Introducing the Nature (or Importance) of Proof	p. 42
Topic: Considering Division by Zero	p. 44
Topic: The Introductory Lesson on Sample Space in Preparation for Probability	p. 45
Topic: Introduction to the Concept of Area, or Looking Beyond the Expected	p. 46
Topic: Introduction to the Area of a Circle or to Finding Areas of Similar Figures	p. 48
Topic: Infinite Geometric Series	p. 48
Chapter 5 Indicate the Usefulness of a Topic	p. 50
Topic: Introduction to Proportions	p. 50
Topic: Applying Algebra	p. 51
Topic: Introduction to Similar Triangles	p. 52
Topic: Introducing Modular Arithmetic	p. 53
Topic: Introduction to the Concurrency of the Angle Bisectors of a Triangle	p. 53
Topic: Determining the Volume of a Right Circular Cylinder	p. 55
Topic: Introduction to Probability-Expected Outcomes	p. 56
Topic: Introducing the Product of the Segments of Two Intersecting Chords of a Circle	p. 57
Topic: Introduction to the Concurrency of the Altitudes of a Triangle	p. 58
Chapter 6 Use Recreational Mathematics	p. 60
Topic: Identifying Factors of Numbers	p. 61
Topic: Understanding Percents	p. 62
Topic: Reinforce Some Logical Thought in Mathematical Work	p. 63
Topic: Rationalize the Denominator of a Fraction	p. 64
Topic: Applications of Algebra Explaining Arithmetic Peculiarities	p. 65
Topic: Applications of Algebraic Counterintuitive Peculiarities	p. 67
Topic: Introduction to Divisibility Rules, Especially Divisibility by 11	p. 68
Topic: Application of Algebraic Solutions to Digit Problems	p. 70
Chapter 7 Tell a Pertinent Story	p. 72
Topic: Introducing Divisibility Rules	p. 73
Topic: Introduction to the Value of ¿	p. 73
Topic: Introduction to Prime Numbers	p. 75
Topic: Finding the Sum of an Arithmetic Series	p. 76
Topic: Introduction to the Pythagorean Theorem	p. 77
Topic: Introduction to the Centroid of a Triangle	p. 78
Topic: Introducing the Law of Sines	p. 80
Topic: Volume and Surface Area of a Sphere	p. 81
Topic: Discovering a Prime Producing Function	p. 83
Chapter 8 Get Students Actively Involved in Justifying Mathematical Curiosities	p. 85
Topic: Introducing Probability	p. 85
Topic: A Lesson on Digit Problems and Place Value	p. 87
Topic: Application of Digit Problems in Algebra	p. 88
Topic: Introducing Base-2 Number System	p. 90
Topic: Application of Digit Problems in Algebra, or Using Algebra to Justify an Arithmetic Peculiarity	p. 91
Topic: Introducing the Properties of the Midline of a Triangle	p. 92
Topic: Applying the Trigonometric Angle Sum Function	p. 94
Chapter 9 Employ Teacher-Made or Commercially Prepared Materials	p. 96
Topic: Introducing the Concept of a Function	p. 97
Topic: Developing the Formula for the Area of a Circle	p. 98
Topic: Developing the Sum of the Angles of a Triangle	p. 99
Topic: Introducing the Triangle Inequality	p. 100
Topic: Introducing the Pythagorean Theorem	p. 101
Topic: Extending the Pythagorean Theorem	p. 103
Topic: Introduction to Angle Measurement with a Circle: by Moving the Circle	p. 104
Topic: Concept of Similar Triangles	p. 107
Topic: Introducing Regular Polygons	p. 108
Topic: Introducing the Parabola	p. 110
Index	p. 112

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