After 30 years of software development, David McAdams was looking for something new to do. He turned his attention to math instruction. Through his coursework at Utah Valley University, he learned how critical vocabulary acquisition is to all learning, and especially to math. Math has long been regarded as its having its own language, with its own syntax and symbols. The acquisition of this language has been found to be a barrier to many students.
When approaching his teaching internship, Mr. McAdams started to extend the existing course of instruction with activities designed to help student learn the language of math. However, as he looked for resources to which he could refer his students, he found that there was certainly no single resource, and in fact no combination of resources that students at the intermediate algebra level could use to find all the definitions they might need during coursework. While still working as a teaching intern, Mr. McAdams started to collect a list of words along with definitions useful to his students.
After the completion of his internship, Mr. McAdams continued to develop this list into a comprehensive dictionary, written for middle school and high school students. "All Math Words Dictionary" is the culmination of ten years work collecting, classifying and describing all of the words a student might encounter in their studies of pre-algebra, algebra, geometry and calculus. This dictionary was developed using the four 'C's of math writing:
- Concise: Definitions are compact, yet understandable.
- Complete: All words and phrases of interest to targeted students are included, plus a few just beyond the scope of the target classes. Tables of symbols and notation, formulas, and units of measurement, plus lists of properties of objects give the student all the information needed to weld their understanding of the concepts and decipher many problems.
- Correct: The definitions have been thoroughly reviewed for mathematical and literary correctness.
- Comprehensible: The definitions are written to be understood by targeted students. Abundant illustrations aid in understanding.
This book has over 3000 entries; more than 140 notations defined; in excess of 790 illustrations; an IPA pronunciation guide; and greater than 1400 formulas and equations. It is available in several editions:
- Color Classroom Edition: Uses a larger font, and larger, color illustrations. The color in the illustrations helps in understanding by separating the various elements by color. Also, most of the illustrations are color coded: red for the object being defined, green for the most closely related object, and blue for a tertiary object.
- Home Edition: Uses a smaller font and smaller illustrations for individual study. Images are in gray scale.
- Home Color Edition: Uses a smaller font and smaller illustrations for individual study. Images are in color.
- Large print: Printed using a 16 point Tiresias LP font with much larger illustrations. Images are in gray scale.
- Dyslexic's: Printed using OpenDyslexic and Eulexia fonts for dyslexic learners. Images are in gray scale.
While working on the dictionary, between playing with his grandchildren, Mr. McAdams started developing other ideas for math literacy. He noticed his preschool grandchildrens' natural interest in and ability with numbers. He wondered, how much of number theory can preschoolers understand and articulate? "Numbers", written for first and second graders began exploring these possibilities. "Numbers":
- Delves into the concept that numbers describe quantity: How many; How much; How long; How far.
- Describes the use of counting (the basic principle of number theory) to arrive at a quantity.
- Discusses that numbers can be large and small.
- Introduces the concept of zero.
- Tells how numbers can be written with digits or letters.
His own childrens' encounters with the concept of infinity not only let him know that the concept of infinity is within the reach of grade-school children, but excites their minds as they wrap their thoughts around it. Mr. McAdams wrote "What is Bigger than Anything?" (originally called "Bigger than Biggest") to bring this unbridled fun into book form. This book:
Reveals that big is relative, there is almost always something bigger.
Asks the question, "What is bigger than anything?"
Introduces infinity as meaning bigger that anything.
Brings to life Archimedes axiom stating that there is always at least one more number.
Teaches that since there is no last number, numbers are infinite.
Noticing that children are naturals at grouping into common groups, Mr. McAdams decided to see if the basic principles of set theory could be taught to children. He quickly realized that children inherently knew the basic concepts of set theory, only lacking the standard vocabulary. He is pleased with the success of "Swing Sets" in teaching first through third graders the basic vocabulary of sets. This book uses objects familiar to children, namely swing sets to introduce:
- The definition of a set: a group of objects such that it is know if a object belongs.
- The process of deciding if an object is part of a particular set.
- The beginnings of set notation (italicized capital letters for sets, italicized lower case letters for elements of a set).
- What it means to be an element of a set, and the notation for elements of a set.
- What it means to not be an element of a set and the notation for not-elements of a set.
At this point, Mr. McAdams took a departure from teaching tools into the arena of pure mathematical delight. While working with Fractal Forge he came up with 123 fractal images that delighted himself and many people around him, particularly children. Published under the name "My Favorite Fractals", this book is available to delight eyes young and old everywhere. The ISBNs are 978-1518876264 and 978-1632700537.
While reading a book on colors to his grandson Sawyer, got to thinking how boring books are colors are for adults. Returning to teacher mode, but not math mode, Mr. McAdams, he put his mind to improving on the traditional color concept book for toddlers. "What in the natural world," he mused, "has enough of the primary and secondary colors to teach colors to children?" His answer was either frogs or parrots. Then on archive.org, he found "Histoire Naturelle des Perroquets", published in 1805 with amazing color plates of parrots. Recognizing the interest parrots would have for children, not to mention their oft-patient parents, Mr. McAdams downloaded the images, restored them, then added them to his book "Parrot Colors". Recognizing that the simplicity of the text lent itself to automatic translation, he translated the book into 79 languages so far. Interestingly enough, the Bosnian edition has outsold the English edition.
Given the outstanding success of Parrot Colors, particularly among groups that are refugees, or were refugees a generation or so ago, Mr. McAdams decided to see what other subjects lent themselves to learning colors. He added Flower Colors, Space Colors.
Next, Mr. McAdams remembered how, in his youth, he found a few printouts of geometric nets and was fascinated how they folded together into complex, 3-dimensional objects. He gathered his resources and, using the free application GeoGebra, created 79 geometric nets to cut out and tape together. This book is called "Geometric Nets Project Book". It is a hands-on introduction to three dimensional geometry using geometric nets. Each net has, on its first page, instructions for putting the net together. This allows a parent or teacher to copy the net for one or more students. See the book for the full details of the copyright. Given the success of this book, Mr. McAdams has started on a version with tabs for easier construction. This book is expected to be finished about July 2016.
People, including Mr. McAdams, are fascintated by large numbers. Mr. McAdams has always wanted to have a book with the first million digits of pi. Checking online, he found that such books existed, but were way too expensive for the amount of work it takes to create. So he created his own book, unimaginatively call "The First Million Digits of Pi". This books is for the discerning math lover who thinks it is cool to have pi to on million digits on his table.
The understanding preschoolers and kindergartners pick up on in geometry is shape names. Shapes provides learning on shape names.
Mr. McAdams has thoroughly enjoyed the create process of writing, and plans to continue to write far into the future.
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