2007360250_McGinnis_TP
3/22/07
4:40 PM
Page 1
Professor C.L. McGinnis Okaloosa Walton College
The Art and Mystery of Mathematics Professor C.L. McGinnis Okaloosa Walton College 100 College Boulevard, Niceville, Florida 850-729-6028
7360250_CH00_FM_pi-vi.pdf
3/28/07
2:38 PM
Page ii
Cover image: Ball, by Jason A. Miller. Copyright © 2007 by Pearson Custom Publishing All rights reserved. Permission in writing must be obtained from the publisher before any part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system. All trademarks, service marks, registered trademarks, and registered service marks are the property of their respective owners and are used herein for identification purposes only.
Printed in the United States of America 10 9 8 7 6 5 4 3 2 1
ISBN 0-536-38629-3 2007360250 KC Please visit our web site at www.pearsoncustom.com
PEARSON CUSTOM PUBLISHING 75 Arlington Street, Suite 300, Boston, MA 02116 A Pearson Education Company
7360250_CH00_FM_pi-vi.pdf
3/28/07
10:59 AM
Page iii
Motivation for “The Art and Mystery of Mathematics” “The Art and Mystery of Mathematics” is a workbook designed to teach through the AMATYC standards. The activities are investigations of mathematical topics allowing students the opportunity to experience mathematics, develop mathematical power, communicate mathematically, and connect mathematics with personal interests and experiences, as well as, present problems and solutions in a professional manner. The following assignments provide mathematical collaborations, investigations and problem solving addressing the AMATYC standards for Intellectual Development, Content and Pedagogy.
Intellectual Development Problem Solving Liberal Arts I Four Steps to Problem Solving Venn Diagram Investigations Pythagorean Theorem Composite Shapes Shapes of Nature Liberal Arts II Number Patterns Linear Equations The Box Problem Exponential Function Saving for Retirement Buying a House Modeling Liberal Arts II Linear Equations The Box Problem Exponential Functions Reasoning Liberal Arts I Venn Diagrams Venn Diagram Investigations Using Logic Gates to Solve Arguments Shapes of Nature Liberal Arts II Triangles Communicating All assignments and group activities are presented as formal written papers or as classroom presentations. The assignments are designed to give students the opportunity to read, write, listen to and speak mathematics.
iii
7360250_CH00_FM_pi-vi.pdf
3/28/07
10:59 AM
Page iv
Content Number Sense Liberal Arts II Number Base Assignment Number Patterns Symbolism & Algebra Liberal Arts II Fibonacci Numbers Lucas Numbers Geometry Liberal Arts I Pythagorean Theorem Composite Shapes Shapes of Nature Liberal Arts II Modulo Design Topology and the Mobius Strip Function Liberal Arts II Fibonacci Numbers Lucas Numbers Linear Equations The Box Problem Exponential Functions Saving for Retirement Buying a House Discrete Mathematics Liberal Arts II Fibonacci Numbers Lucas Numbers Probability & Statistics Liberal Arts I Give examples where you have used statistics in your life. Find an article that contains the results of a statistical study. Describe the results.
iv
7360250_CH00_FM_pi-vi.pdf
3/28/07
10:59 AM
Page v
Pedagogy Teaching with Technology—Technology can be used in finding number patterns, as well as, in topics that require graphing or computation. Interactive & Collaborative Learning—The assignments may be completed in groups. Group projects are designed to give students the opportunity for exchanging ideas and learning from group discussions. Connecting with Other Experiences—Students in the Liberal Arts Mathematics course tend to have broad backgrounds; however, many are education majors and fine arts majors. Both these types of students do well with creative group assignments. For example: Liberal Arts II—Group Assignment One: “Create a Number Base Design,” and Individual Assignment Two: “Modulo Design.” Multiple Approaches—The activities allow students to view mathematics from multiple approaches—numerical, graphical, symbolic and verbal giving students a broader understanding of mathematical reasoning. Experiencing Mathematics—Each activity is designed to provide students with non-traditional learning activities that promote independent thinking, independent learning and problem solving. Interactive Lecturing—The activities in “The Art and Mystery of Mathematics” are completed through guided instruction in the classroom. Students are engaged as active listeners and participants.
v
7360250_CH00_FM_pi-vi.pdf
3/28/07
10:59 AM
Page vi
Liberal Arts I Assignments
Page Assignment
Four Steps to Problem Solving
Classroom Activity
Venn Diagrams
Assignment
Venn Diagram Investigations
Classroom Activity
Building Logic Gates
Classroom Activity
Logic Gate Practice
Classroom Activity
Using Logic Gates to Solve Arguments
Assignment
Finding Logical Arguments in the Newspaper
Writing Assignment
Lewis Carroll
Assignment
Pythagorean Theorem
Assignment
Composite Shapes
Assignment
Shapes of Nature
Writing Assignment
Probability and Statistics
vi
Due Date
Grade