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Math Made Visual: Creating Images for Understanding Mathematics (Classroom Resource Material) Hardcover – April 10, 2006

ISBN-13: 978-0883857465 ISBN-10: 0883857464

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Product Details

  • Series: Classroom Resource Materials
  • Hardcover: 172 pages
  • Publisher: The Mathematical Association of America (April 10, 2006)
  • Language: English
  • ISBN-10: 0883857464
  • ISBN-13: 978-0883857465
  • Product Dimensions: 7.3 x 10.4 inches
  • Shipping Weight: 1 pounds
  • Average Customer Review: 4.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #2,136,550 in Books (See Top 100 in Books)

Editorial Reviews

Review

This is a superb book. If you only buy one book for your own or your departmental library this year, this would be an excellent choice...I thoroughly recommend this book to teachers, mathematics educators, students and anyone interested in the visual side of mathematics. --Mary Coupland, Australian Mathematics Teacher

This wonderful book is a fitting edition to the Classroom Resource Materials series. Indeed any teacher of mathematics at the high school level or above should have a copy. Let me take that a bit further: anyone with an interest in mathematics should have a copy! While I ended up reading it pretty much straight through, this is a wonderful reference book which can be consulted whenever one is stuck for a way to make a concept come to life or for an activity to get students involved in mathematics.

The first two-thirds of the text consists of a wonderful set of examples of how visualization can aid understanding and inspire exploration. Each section ends with a set of challenges for the reader. These problems would make wonderful projects for pre-service high school teachers -- many of them can be implemented in Geometer's Sketchpad. The final section of the book consists of hints for solving these challenges. Sandwiched between these two sections is a short section providing suggestions as to how these ideas can be used in a classroom. While technology would certainly help, many of the hints involve simple paper folding and cutting. Geometer's Sketchpad would certainly suffice to create most all of the 2-dimensional figures.

Part I consists of 20 short chapters each with several related concepts. These chapters are only loosely related to one another and assume minimal mathematical background on the part of the reader. They seem designed with browsing in mind. If you are stuck for a way to explain a concept or for nice examples spend a few minutes with Math Made Visual. Here are a few samples. I am not going to attempt a summary as the book has no 'plot' -- just a wonderful collection of short stories!

Chapters 1 through 4 demonstrate ways to represent numbers (and their sums and products) using geometric elements (triangular numbers), line segments, areas, and finally volumes. The formula 1 + 2 + ... + n = n(n + 1)/2 is derived in several interesting ways, all of them, I suspect, more convincing to students than the standard proof by induction. This formula and others (sum of the odd numbers, sum of the first in squares, etc) are then illustrated using line segments, areas, and volumes in subsequent chapters.

As one might expect, the Pythagorean Theorem shows up early and often. There is also a very nice proof of Herron's formula for the area of a triangle. We also encounter proofs of several of the standard trigonometric identities including Ptolemy's Theorem.

...A review of this sort can't do this book justice. To appreciate it you have to see it. The visuals (and the wonderfully clear text which accompanies them) are wonderfully conceived and masterfully executed. This is a book you will find yourself picking up again and again. --Richard Wilders, MAA Reviews

Book Description

The object of this book is to show how visualization techniques may be employed to produce pictures that have interest for the creation, communication and teaching of mathematics. The authors describe methods to visualize mathematical ideas, with applications to concrete cases, and practical approaches for making visualizations in the classroom.

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19 of 21 people found the following review helpful By Charles Ashbacher HALL OF FAMETOP 500 REVIEWERVINE VOICE on January 13, 2007
Format: Hardcover
Often, the best way to teach a proof is by drawing an image that illustrates the ideas. While mathematics is based on abstract concepts, humans are creatures whose intuition is largely based on images. This book describes many ways in which concepts can be visually represented and these images truly are worth a thousand symbols. Part I consists of twenty chapters, which are called:

*) Representing numbers by graphical elements
*) Representing numbers by lengths of segments
*) Representing numbers by areas of plane figures
*) Representing numbers by volumes of objects
*) Identifying key elements
*) Employing isometry
*) Employing similarity
*) Area-preserving transformations
*) Escaping from the plane
*) Overlaying tiles
*) Playing with several copies
*) Sequential frames
*) Geometric dissections
*) Moving frames
*) Iterative procedures
*) Introducing colors
*) Visualization by inclusion
*) Ingenuity in 3D
*) Using 3D models
*) Combining techniques

Each chapter has several sections where a specific type of problem is examined in each section. For example, the three sections of chapter 1 are:

*) Sums of odd integers
*) Sums of integers
*) Alternating sums of squares

Each chapter terminates with a section called "challenges", which is a set of problems that are to be solved by creating images similar to those demonstrated in the chapter. Hints and solutions to these problems are provided in an appendix. Part II of the book is called "Visualization in the classroom" and is a short history of visualization and a demonstration of how physical objects can be used to illustrate the concepts.
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5 of 6 people found the following review helpful By Eskychesser on July 17, 2011
Format: Hardcover Verified Purchase
I purchased this book for my MA501 class at Northern Michigan University. This was a summer class - 4 weeks long and this book was the required text.

I was very disappointed in the number of typos in this book. The authors should be rather embarrassed by this. I know, usually no book is exempt from some sort of mistake, but this book is littered with them! Then to make matters worse, there are some problems that are just flat incorrect. One good point is, the authors do attempt to give answers to every question in the book - but even those were wrong on occasion! There is NOT a lot of substance to this book in terms of explanation either. It's almost like this is a hodgepodge of work slammed together to make a text. I did enjoy part two - which was a bit more written.

The math in this book is very well. The authors DID get this right. They show many different ways proofs can occur without long written statements and rather by simple pictures. The topic in math is an upcoming theme and I think will be integrated more and more into future mathematics of education.

Although I DO recommend this book - It's a shame the authors didn't put a little more time into the mechanics part of their work. When one pays $50 for a book - errors should be scarce if not nonexistent.
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Format: Hardcover
I animate math for educators at Shader Joes dot com animation studio so I love the VERY FEW books out today that promote visual math education. The best of the best I've ever found (at a reasonable price) is Kiran Desai's: Mathematical Recurrence Relations: Visual Mathematics Series. It even shows visual and tabular solutions for linear equations and degree 5 polynomials!

The demand for Math Made Visual is high, and it comes and goes on Amazon. When supply is down, it's been as high as $400, so if you can get it reasonably, do so! Abe books (Amazon's partner) often has it good condition used for about $60 and the original publisher (Math Assn of America) has it as PDF or print on demand (ie new) for about $50 as another reviewer said, with high shipping (min $12) included in that number. They distribute though Cadmus Journal Services, which I wish Amazon would buy, because they offer many expensive items at great prices like Abe.

There are typos and errors, but as with many on demand books, this is the luck of the draw on which file the printer uses. I've seen four so far which vary greatly on typos. That said, to be fair, they are mostly in rush to press descriptions which don't really take away from the value of the book. If you get all emotional or huffy about mistakes, don't get this, but if you really are more interested in content, don't sweat it. The PDF is uniformly better, but then you have the LaTex symbology trade off issue, as with much math on Kindle.

The coverage is basically advanced High School and is excellent.
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