Fractonia by P.R. Lewis at“Fractonia” is now available for Kindle e-book readers. Unlike Google Play, Amazon is not offering a special introductory price for the ebook. However, Amazon has enabled the popular ” text-to-speech” option for this book. “Text-to-speech” is available on the following devices: Kindle Fire HDX, Kindle Fire HD, Kindle Touch, Kindle Keyboard, Kindle (2nd generation), and Kindle DX.

Amazon does offer a preview of the book, albeit disappointingly short. If you are interested in seeing a little more of the book before you decide to purchase, I recommend a visit to Lulu. Lulu is offering a more detailed, downloadable preview of the book in ePUB format. You can also purchase the ebook or the print version of “Fractonia” directly from the Lulu bookstore.

Purchase the Kindle-formatted version of “Fractonia” from


Graphing Can Be Fun

Desmos Free Graphing CalculatorIf mathematical graphs are generally not your cup of tea, perhaps you should try a cup of coffee instead? How about a cup of coffee that is sketched from a collection of equations your students might recognize? That’s not quite your textbook flavor of graphing mathematics, is it?

Desmos offers a remarkable and FREE online graphing calculator that allows you to visualize mathematical equations quickly and easily. Imagine turning equations into images everyone can identify and associate with? According to Desmos, “learning is a process of exploration and discovery, not a series of answers”.  The students who explore tend to be the students who learn, and they have fun doing it. The creators of this extraordinary online calculator believe that “everyone can learn and enjoy math, given the right environment.” The website creates just that environment. Using the available tools. you can upload your own graphs so they are displayed on the screen. The option to change colours aids students in relating the mathematical equations to what they see on the screen.

Why not make your next lesson about graphs an exercise in discovery learning for your homeschooled child or classroom students? If you believe that “math is beautiful and surprisingly fun”, you will enjoy playing with the free online graphing calculator that Desmos has made available. Give it a try and let me know how you experienced the calculator.


Learning Math the Natural Way

"Memory Tips for Math" by D. YatesLet’s be honest. Not every child is a natural mathematician. Encouragement and praise is great, but the help it provides can never substitute for real, hands-on, practical help that makes the mathematics learning experience effective. Many children try their best, yet their efforts leave them caught in a constant struggle to grasp the mathematical concepts. Their frustration is evident as they become tongue-tied with the heavy math jargon. How can a parent or teacher reach those children who are not natural logical or mathematical learners? How does one bring the best out of the kids who don’t naturally thrive on numbers and logic problems? In her book, “Memory Tips for Math, Memorization and Learning Styles: The Successful Way to Teach K-5 Math” Donnalyn Yates proposes a practical and creative solution that will take a lot of the “ouch” out of math class.

Memory Tips for Math, Memorization and Learning Styles” recognizes that the three most common perceptual learning styles are visual, auditory and tactile/kinesthetic. Learning activities in the book focus on providing these categories of learners with stimulation that leads to effective learning. Acronyms, pictures, rhymes, and stories help students to develop vocabulary and retain mathematical procedures. For example, think about how you learned the relationship between the gallon, quart, pint and cup. Now imagine if you had discovered this relationship through a story of fantasy. Imagine the Kingdom of Gallon in which lived three queens of the family of Quart. Each Queen Quart lived in a castle with a young prince and princess – they’re the Pints. Prince and Princess Pint don’t have children but each of the Pints has 2 cats – the cats are the Cups. Imagine how much fun you might have had in Math class if you learned using the tools provided in “Memory Tips for Math, Memorization and Learning Styles: The Successful Way to Teach K-5 Math”. As you read the creative examples, don’t be surprised to find yourself conjuring up a few inspired examples of your own to help your child or student learn more effectively.

This book can be purchased at a discount of 30% for a limited period. Use coupon code FEBRUARYCART305USD at check out. The coupon expires on 19 February 2012.



Questions and answers are simply mathematics

If you find the study of mathematics dreadfully boring, it is time to play a little. In “Amusements in Mathematics” by Henry Ernest Dudeney (published by David Gaddy, Nov 2011),  plenty of mathematical fun is crammed into 640 pages. According to the author, this collection of puzzles and mathematical problems was created so that the user of the book could tap into the pleasure of “doing math”.

Henry Ernest Dudeney (1857-1930), an English mathematician, is best known as a master of logic puzzles. The author views mathematical puzzles as perplexing questions begging our answers. The reader is drawn into the hunt for solutions and answers to these questions. Asking and answering questions is a part of human life, and comes naturally to us all. When mathematics is viewed as the process of asking and answering questions, we allow ourselves to bypass any existing “number” prejudices and start to enjoy what comes naturally.

Amusements in Mathematics” also includes a discussion on the psychology of puzzles and the application of math in our daily lives.  It is an excellent resource for mathematics teachers seeking a readily accessible collection of “questions” that will spice up a lesson. However, this puzzle book is just as useful to anyone seeking a little mental stimulation – after all, we can all answer questions and should not shy away from the challenge of doing so often. This extensive collection of puzzles and problem-solving exercises is now available from  The book can be purchased at a saving of 20% until the end of February 2012 using the following coupon code: 20% off books – Enter code FEBBOOKS12 – Save up to $25 – Offer ends 2/29/12


Can I make my own linear equation jigsaw puzzle?

Converting your “less than exciting” linear equation worksheet activities to puzzles is possible with a small investment in some supplies and a slightly larger investment in time. To get started, find some sturdy, colorful cardboard, a ruler, black marker, a pair of scissors, self-adhesive lamination plastic, an elastic band, and a set of solved linear equations. Dark colored card tends to be difficult to read equations from, so avoid dark colors unless you are working with white or silver metallic markers. While I prefer working with black markers, any colored pens that create contrast with the background card color will work.

Your puzzle can take any form, but simple shapes are the easiest to work with. For beginners, I recommend a square puzzle with no more than 9 pieces. Use the ruler to mark out a square on the card, and divide the square into a table with 3 equally spaced columns and 3 equally spaced rows. If you are feeling less ambitious, start with a 2×2 table. Make sure the lines and boundaries of the puzzle are drawn in bold ink. Neatly insert an equation along a side of a cell that has an adjacent cell. The solution to this equation is filled in across the boundary line in the neighboring cell. Try not to choose equations that will generate the same solution as this may cause confusion for learners who are new to this type of puzzle building. Duplicate solutions can be intentionally incorporated into more challenging puzzles, but should be avoided when first introducing these puzzles to a class or student. Complete the puzzle with equations and solutions, laminate the card for durability, and cut the puzzle into its individual pieces. Use the elastic band to keep the puzzle pieces together.

If you are new to putting the pieces back together, or want to know how to explain the process to your students, read “How to Solve a Linear Equation Jigsaw Puzzle“.


How do I build a linear equation jigsaw puzzle?

Unlike traditional “picture” jigsaw puzzles, linear equation jigsaw puzzles are largely blank. There are seldom patterns or background images to guide you as you put the pieces together. Although traditionally rectangular, some puzzles are designed to take on unexpected shapes when completed. However, these “shaped” puzzles are not usually sold with obvious clues that will allow the puzzle builder to construct the puzzle using only the goal of a particular shape. There are no short-cuts, cheat-sheets, or ways to avoid solving the equations. If you want to build the puzzle, you must first solve the equations printed on the puzzle pieces – they alone hold the keys to putting the puzzle together. If you are new to linear equation jigsaw puzzles, and need some help getting starting, read “How to Solve a Linear Equation Jigsaw Puzzle“.


Are linear equation jigsaw puzzles only for classroom use?

Puzzles are enjoyed by everyone from grandma to your toddler. Classrooms certainly don’t have exclusive rights over them. While perfect for building class spirit and developing team work skills within the classroom environment, linear equation jigsaw puzzles are even more useful at home.

If you home school your children, integrate the puzzles in your home school lesson plan to spice up traditional algebra lessons. Parents with children who show reluctance to do their algebra homework can encourage an interest in the subject by introducing these puzzles as part of a reward system. For example, for every 3 traditional equation worksheets completed, the child could earn the opportunity to complete a linear equation jigsaw puzzle instead of a worksheet.

Does your family enjoy building puzzles together? Take it to the next level by completing a linear equation jigsaw puzzle as a family. This type of family activity helps encourage an appreciation for mathematics, and teaches children that the topics they deal with “in school” are not for exclusive use in school.


Mathematics as a Family Activity

Mathematics doesn’t belong exclusively in the maths classroom. Parents can, and should, integrate it in a number of enjoyable family activities. In most cases, when they are enjoying themselves, children will not even be aware that they are developing their mathematical skills as they play. Do parents require special skills or need to take some course to encourage their children to develop basic mathematical skills early? Fortunately not. In fact, you don’t even need to be “good at Mathematics” to have fun with your kids. And that is the key: fun. Children need to learn that addition, subtraction, multiplication, and division (and later calculus and trigonometry) are not just useless, intimidating procedures weighing down their homework. The best way for children to learn this, is to learn it without directly associating the learning with formal Mathematics.

As part of this blog, I will share some of the mathematics-oriented family activities that I enjoy, and which don’t require special training. Some of these ideas will be so obvious and “everyday” that you will wonder why you haven’t been “playing” all along. Join me as we explore these ideas and develop them into games for the whole family.


Where it all begins…

Welcome to my blog.  You are invited to journey with me as we explore learning.  Before you decide that this topic has no relevance to you, let me present evidence to the contrary.  You are, after all, able to read this paragraph right now because you learned to read at some earlier time.  You can also tell me how many letters are in the first word of this paragraph, because once upon a time you learned to count.  Just like me, you are an experienced learner.  Learning is something we all do, and have done since we were infants.  As both a scientist and an educator, I derive great pleasure from seeking truth, acquiring knowledge, experimenting with it, and then sharing that knowledge and experience with others. This blog is my way to share what I have learned, and am still learning, with you. Join me as we ask questions, seek answers, digest old angles to the learning debate, explore new ideas that make learning exciting for children and adults alike, and take down the intimidating monsters that have guarded the gates to learning for too long.