Muutke küpsiste eelistusi

Tactile Learning Activities in Mathematics: A Recipe Book for the Undergraduate Classroom [Pehme köide]

  • Formaat: Paperback / softback, 314 pages, kõrgus x laius: 254x178 mm, kaal: 572 g
  • Sari: Classroom Resource Materials
  • Ilmumisaeg: 01-May-2018
  • Kirjastus: American Mathematical Society
  • ISBN-10: 1470443511
  • ISBN-13: 9781470443511
Teised raamatud teemal:
  • Formaat: Paperback / softback, 314 pages, kõrgus x laius: 254x178 mm, kaal: 572 g
  • Sari: Classroom Resource Materials
  • Ilmumisaeg: 01-May-2018
  • Kirjastus: American Mathematical Society
  • ISBN-10: 1470443511
  • ISBN-13: 9781470443511
Teised raamatud teemal:
Q: What do feather boas, cookies, and paper shredders have in common? A: They are all ingredients that have the potential to help your undergraduate students understand a variety of mathematical concepts. In this book, 43 faculty from a wide range of institutional settings share a total of 64 hands-on activities that allow students to physically engage with mathematical ideas ranging from the basics of precalculus to special topics appropriate for upper-level courses. Each learning activity is presented in an easy-to-read recipe format that includes a list of supplies; a narrative briefly describing the reasons, logistics, and helpful hints for running the activity; and a page that can be used as a handout in class. Purchase of the book also includes access to electronic printable versions of the handouts.

With so many activities, it might be hard to decide where to start. For that reason, there are four indices to help the reader navigate this book: a concept index, a course index, an author index, and a main ingredient index. In addition to providing activities for precalculus, calculus, commonly required mathematics courses for majors, and more specialized upper-level electives, there is also a section describing how to modify many of the activities to fit into a liberal arts mathematics class.

Whether you are new to using hands-on activities in class or are more experienced, the authors hope that this book will encourage and inspire you to explore the possibilities of using more hands-on activities in your classes.

Bon appetit!
Acknowledgments ix
Preface xi
How to Use This Book xv
Modifications for Liberal Arts and Topics Courses xvi
I Appetizers (Before Calculus)
1(38)
1 Precalculus
3(36)
1.1 Using Parentheses with the Game of Telephone
5(5)
1.2 Function Ball Toss
10(4)
1.3 Mathematical Modeling Using Long-Exposure Photography
14(4)
1.4 Function Composition Using Crackers and Cheese
18(4)
1.5 Walking Function Transformations
22(5)
1.6 Graphing Piecewise Functions with Feather Boas
27(4)
1.7 Trigonometry Parameter Comparisons
31(8)
II Main Courses (Calculus)
39(122)
2 Differential Calculus
41(34)
2.1 Adding Movement to Velocity Explorations with Ziplines
43(5)
2.2 Creating Limit Windows with Index Cards
48(3)
2.3 Extreme Values with Pipe Cleaners
51(3)
2.4 Graphing Puzzles Using the First and Second Derivatives
54(4)
2.5 Graphing Functions from Derivative Information Using Bendable Sticks
58(4)
2.6 Spread the Word: Modeling Logistic Growth
62(5)
2.7 Maximizing the Area of a Fenced in Region Using Bendable Sticks for Constraints
67(3)
2.8 The Optimal Origami Box
70(5)
3 Integral Calculus
75(34)
3.1 Chewing Gum Riemann Sums
77(4)
3.2 Paper Shredder Riemann Sums or Cut the Bunny
81(4)
3.3 Estimating Calories in a Cookie with Riemann Sums
85(4)
3.4 So Many Integration Techniques Which to Use?
89(4)
3.5 Centers of Mass of Candy Point Masses on a Plane
93(4)
3.6 Volume Estimations with Fruit Cross Sections
97(4)
3.7 Fun with Infinite Series
101(8)
4 Multivariable Calculus
109(52)
4.1 Physically Creating Three Dimensional Graphs
110(5)
4.2 Building Functions of Two Variables with Cookies
115(5)
4.3 Exploring Contours in the Physical World
120(4)
4.4 Matching Photographs with Contour Lines
124(4)
4.5 The Gold Mine: Tangent Plane Approximation Using Tangible Surfaces
128(4)
4.6 Visualizing Second Order Partials on a Football
132(4)
4.7 Partials, Gradients, and Lagrange Multipliers on a Pringles® Chip
136(4)
4.8 Volume Estimation Using a Sheet Surface
140(3)
4.9 Visualizing and Estimating the Mass of a Solid Using Multi-Colored Blocks
143(5)
4.10 Using a Jack to Visualize the Right Hand Rule for Cross Products
148(3)
4.11 Properties of Flux Using an Overhead Projector
151(4)
4.12 Vector Analysis of a Pop-Up Page
155(6)
III Desserts (Upper Level Courses)
161(136)
5 Sophomore / Junior Courses
163(66)
5.1 Crowdsourcing to Create Slope Fields
165(4)
5.2 Who's in My Differential Equations Club?
169(4)
5.3 Population Modeling Using M&M's®
173(5)
5.4 Modeling of Fishing and Restocking with Pennies
178(5)
5.5 Modeling a Falling Column of Water
183(4)
5.6 Using Linear Algebra Definitions to Find Your Team
187(3)
5.7 Picturing Prime Factorization
190(4)
5.8 Traffic Jam: A Lifesize Logic Puzzle
194(4)
5.9 Living De Morgan's Laws
198(4)
5.10 Using Circuits to Teach Truth Tables
202(5)
5.11 Determining the Validity of an Argument Using True/False Cards
207(4)
5.12 Proof Rearrangements
211(4)
5.13 Properties of Functions on Finite Sets Using Candy
215(4)
5.14 SET® in Combinatorics/Discrete Math
219(5)
5.15 Human-Powered Computing
224(5)
6 Junior / Senior Courses
229(68)
6.1 Using Candy to Represent Equivalence Relations
231(4)
6.2 Finding the GCD: Euclidean Disc Toss
235(5)
6.3 Symmetry and Group Theory with Plastic Triangles
240(5)
6.4 Finding Groups in a (New) Color Cube Puzzle
245(5)
6.5 Acting Permutations
250(4)
6.6 Nametags and Derangements: A Class Permutation
254(4)
6.7 Discovering Catalan Numbers Using M&M's®
258(4)
6.8 Walking the Seven Bridges of Konigsberg
262(4)
6.9 Designing Round-Robin Tournaments Using Yarn
266(6)
6.10 Constructing Disjoint Hamiltonian Cycles of Complete Graphs Using Yarn
272(5)
6.11 Exploring the e-N Definition of Sequence Convergence with Yarn
277(4)
6.12 Exploring the e-6 Definition of Continuity
281(4)
6.13 Walking Complex Functions
285(4)
6.14 Graphing Complex Functions with Feather Boas
289(4)
6.15 Exploring Knots
293(4)
Indexes 297(1)
Concept Index 297(2)
Author Index 299(2)
Main Ingredient Index 301(2)
Course Index 303
Julie Barnes, Western Carolina University, Cullowhee, NC.

Jessica M. Libertini, Virginia Military Institute, Lexington, VA.