Pedagogy and Content in Middle and High School Mathematics

Description

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. Front Matter ....Pages i-xi Front Matter ....Pages 1-1 A Brief History of Zero (G. Donald Allen)....Pages 3-6 Approximating PI (G. Donald Allen)....Pages 7-10 The Caesar Cypher (G. Donald Allen)....Pages 11-12 How Big is Infinity? (G. Donald Allen)....Pages 13-15 Making Complex Arithmetic Real! (George Tintera)....Pages 17-19 Early PI (G. Donald Allen)....Pages 21-23 Primes, Perfect Numbers and Magic Numbers (Just for Fun) (G. Donald Allen)....Pages 25-28 How do we define the Number “1?” (G. Donald Allen)....Pages 29-30 Percentage Problems (G. Donald Allen)....Pages 31-32 Microwave Math (G. Donald Allen)....Pages 33-35 Fantasy Problems and Flying Carpet Solutions (G. Donald Allen)....Pages 37-40 The Mystery of the New “Planet” (Or How Regression Saved the Day) (G. Donald Allen)....Pages 43-46 Geogebra in the Classroom (Diem M. Allen)....Pages 47-48 Working Together (G. Donald Allen)....Pages 49-52 A Brief Look at Circles (Amanda Ross)....Pages 53-56 Optimization – with and Without Calculus (G. Donald Allen)....Pages 57-66 Pythagorean Triples Plus One (G. Donald Allen)....Pages 67-71 A Brief Look at Derivatives (Amanda Ross)....Pages 73-76 A Brief Look at Arithmetic and Geometric Sequences (Amanda Ross)....Pages 77-80 A Brief Look at Sigma Notation (Amanda Ross)....Pages 81-82 Communicating with Life in the Universe (G. Donald Allen)....Pages 83-88 The Mathematical Mystery of the Pyramid (G. Donald Allen)....Pages 89-91 The Sphere Packing Problem (G. Donald Allen)....Pages 93-93 Big, But Not Really Big Numbers (G. Donald Allen)....Pages 95-96 The Net of a Cone (Sandra Nite)....Pages 97-98 Area of a Circle (Dianne Goldsby)....Pages 99-100 Geometry Meets Algebra – Super-Conic Constructions, Part I (G. Donald Allen)....Pages 101-106 Geometry Meets Algebra – Super-Conic Constructions, Part II (G. Donald Allen)....Pages 107-111 Let’s Make War—Just for Fun (G. Donald Allen)....Pages 113-123 A Brief Look at Probability (Amanda Ross)....Pages 125-130 Area Under the Normal Curve (Amanda Ross)....Pages 131-140 Finding the Area Under the Normal Curve Using the Graphing Calculator (Amanda Ross)....Pages 141-143 Hypothesis Testing (Amanda Ross)....Pages 145-150 A Brief Look at Expected Value (Amanda Ross)....Pages 151-154 Front Matter ....Pages 155-155 The Evil Twins – Testing and Stress (G. Donald Allen)....Pages 158-160 Unfairness in Testing – Mathematics and Simulations (G. Donald Allen)....Pages 161-164 Online Assessments in Math (Amanda Ross)....Pages 165-168 When It Comes To Math, What Exactly are We Testing For? (G. Donald Allen, Sandra Nite)....Pages 169-175 Assessment via High-Stakes Testing (Amanda Ross)....Pages 178-183 High-Stakes Testing (Amanda Ross)....Pages 185-186 Low-Stakes Tests and Labels (Amanda Ross)....Pages 187-188 Front Matter ....Pages 189-189 What Technology Works for Teaching Mathematics and Why – A Perspective, Part I (G. Donald Allen)....Pages 192-195 Using Technology In Teaching Math (Antonija Horvatek)....Pages 197-204 What Technology Works for Teaching Mathematics and Why – A Perspective, Part II (G. Donald Allen)....Pages 205-207 The Graphing Calculator (Amanda Ross)....Pages 209-213 Problems In Mathematical Recreation (G. Donald Allen)....Pages 216-219 A Mile of Pennies (Dianne Goldsby)....Pages 221-222 Easy Problems (G. Donald Allen)....Pages 223-224 Mathematical Games and Learning (Amanda Ross)....Pages 225-228 Two Great Software Tools (Winplot and Mathtrax) (G. Donald Allen)....Pages 231-232 Using Polya’s Problem Solving Process in the Mathematics Classroom to Prepare for Taks (Sandra Nite)....Pages 233-235 Problem-Solving Strategies – A Quick Checklist (G. Donald Allen)....Pages 237-239 What is Mental Math? (Donna Lackey)....Pages 241-243 A Digital Simulation for Prospective Teachers to Teach Algebra Concepts for Equity (Tingting Ma)....Pages 245-248 Teaching is a Balancing Act (G. Donald Allen)....Pages 249-252 Tamu’s Peer Program Promotes Stem the World Over (Jennifer Graham, Michele Ward, Larry Johnson)....Pages 253-254 Energy Math Lessons for Math Classes (Sandra Nite)....Pages 255-256 Multiple Representations, I (G. Donald Allen)....Pages 257-262 Multiple Representations, II (G. Donald Allen)....Pages 263-276 Multiple Representations, III (G. Donald Allen)....Pages 277-287 Multiple Representations, IV (G. Donald Allen)....Pages 289-294 The Two-Minute Lesson (G. Donald Allen, Dianne Goldsby)....Pages 295-297