Math, Logic and Critical Thinking Resources

Mathematics Resources: An Incomplete Guide
Math Olympiads
Review: Jacob’s Algebra and Geometry books
SET: The Family Game of Visual Perception
Logic Problems for elementary and up
The world-famous Math.doc by Dale Reed (lots of math links compiled by and for homeschoolers)
Online Maze Applet
Who Owns the Zebra?
Trivia Planet (logic games, puzzles, science)
Hoagies Gifted Math and Science Links
Triangular Math Facts Cards
Math Drill Sheets
Logic Puzzles
Chess Game Strategy
Student contests across the nation: how you can host a local group
Economics Study Resources

Math Recommendations

The Open Court Real Math books have been reprinted by SRA under the name Explorations and Applications. This math series is highly recommended. They are still available in their previous printing as Open Court books, in some places. They contain the same problem sets as the Explorations and Applications series. Differences include a greater use of color and graphics in the current edition, and more manipulative-based games. See the SRA website for more information.

Don’t miss the excellent review of Open Court by Mathematically Correct. Explorations and Applications was one of the few programs to receive an “A” grade.

Recommended books:

Creative Problem Solving in School Mathematics by Dr. George Lenchner. Teaching Problem-Solving? This textbook for teachers can help you. It uses about 400 challenging nonroutine problems to extend elementary and middle school mathematics into such topics as sequences, series, principles of divisibility, geometric configurations, and logic. It is the foundation of the Math Olympiad program, and is based upon the author’s popular inservice course, The Art of Problem-Solving. The book is organized into 4 sections: Teaching Problem Solving; Some Problem Solving Strategies; Some Topics in Problem Solving; Resource Problems. Both The Arithmetic Teacher (NCTM, 1984) and Curriculum Review (1984) reviewed the book quite favorably. Each called it “an excellent resource”.

Math Olympiad Contest Problems for Elementary and Middle Schools by Dr. G. Lenchner. The Math Olympiad contests presented these 400 challenging problems and ingenious solutions over a period of 16 years. Aimed at young students, their teachers and parents, the book contains an unusual variety of problems, a section of hints to help the reader get started, and seven unique appendices that inform and enrich, among other features. Mathematics Teaching in the Middle Schools (NCTM, May 1997) said that the book “is so complete, concise, and well done that it really should be part of your professional library”.

One Equals Zero and Other Mathematical Surprises: Paradoxes, Fallacies, and Mind Bogglers by Nitsa Movshovitz-Hadar and John Webb. Grades 9–12. One equals zero! Every number is greater than itself! All triangles are isosceles! Surprised? Welcome to the world of One Equals Zero and Other Mathematical Surprises. In this book of blackline activity masters, all men are bald, mistakes are lucky, and teachers can never spring surprise tests on their students!

The paradoxes and problems in each One Equals Zero activity will perplex your students, arouse their curiosity, and challenge their intellect. Each counterintuitive result, false analogy, and answer that defies expectation will encourage students to look at familiar mathematical situations in a new light. By solving the paradoxes, your students will come to better understand both the possibilities and the limitations of mathematics.

Many of the paradoxes, fallacies, and mind bogglers in One Equals Zero are based on classic paradoxes and can be used in algebra, geometry, trigonometry, statistics, or calculus classes. What makes this book unique are the detailed teacher’s notes that accompany each activity and that provide a thorough explanation of the paradox or problem; in-depth pedagogical and mathematical comments; suggestions for extensions; and for many activities, related historical material. Also included in each set of teacher’s notes is a list of the activity’s key concepts. A matrix of these concepts at the beginning of the book allows you to place each activity in a suitable context. And a list of recommended readings guides you and your students to a wealth of related material.

Each of the activities in One Equals Zero can be completed in less than one class period and requires no additional materials, although several of the book’s geometry activities can be enhanced by the use of The Geometer’s Sketchpad® software. With One Equals Zero, you can transform mathematical errors and quandaries into positive learning experiences. Along the way, you’ll encourage your students to see that the development of mathematical skill is a process of creative struggle and spirited debate.