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



Fractonia by Pearl R. Lewis“Fractonia” has been available for some time from e-book stores around the world. You can read the book on your computer, your tablet, or your phone. But if you are not a fan of virtual books, then this post brings you good news. Paper rules! “Fractonia” is a available as a REAL, tree-based book. You can now purchase your PRINT (paperback) copy of the book, and turn those pages the old fashioned (best) way.

The 116-page illustrated paperback is printed in the easy-to-handle (and slip into your bag) 6″x9″ format.

If you are new to the title and have not been following the development of this project, you can read more about Fractonia in the book section of my website. The book is suitable for middle school (advanced) readers, high school students, and adults. While prior knowledge of very simple fraction algebra is a plus, it is not essential. If you previously avoided mathematics as if it was the enemy, and have little to no recall of algebra, you are the perfect reader for this book. 

“Fractonia” is an adventure story that demonstrates that mathematics can be visualized as something quite different from a stack of numbers and equations. While not all students think “in pictures”, many who are turned off from more traditional ways of approaching mathematics can benefit from exploring topics in an image-centered way. Even though this book is advertised as a children/teen book in many places, this book is a good way for parents and teachers to explore the concept of visualization in mathematics.

Go on – give it a try. If you discover that you cannot connect with the strange characters or that the odd reference to a mathematical term is frying your brain, you can always donate the book to your local school library. Take a break from whatever you have planned this weekend, and go on a mind adventure – you know you want to do it.



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


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.


Stop blaming the parents and teachers for students’ choices.

Peter Hilts, in his article  “Is it time to blame the students?”  addresses an issue that many educators feel uncomfortable expressing opinions on.  In this “politically correct” time that we live in, everyone is afraid to step on toes.  Responsibility is commonly shifted from one person to the next, so no-one has to feel too bad for too long.  Hilts boldly looks at that the statement “all students are all good all the time” and critically evaluates it from the perspective of the teacher.  If students are not just to acquire knowledge as they grow in years, but are also expected to “grow up“, shouldn’t they be taught to shoulder some responsibility for their learning?

If attendance, effort, and integrity are part of the problem in education, it isn’t fair to hold teachers, parents, reformers, unions, politicians, or the tooth fairy responsible,” says Hilts.  He is to be commended for making such a bold stand on a sensitive educational issue.   “Students who give partial or no effort to classwork, exams and standardized tests are mostly or exclusively responsible for their behavior.  When a student who can attend skips instead, that student is responsible.”  Certainly any education system has some disinterested teachers, or teachers who simply hate the work they do but refuse to leave it.  Every society has some parents who actively discourage the educational growth of their children, or who simply don’t care enough to encourage it.  But is it always the teachers and the parents fault when children don’t succeed at school?

As Hilts so insightfully points out, “responsibility has two faces”, and this is as true in the classroom as it is anywhere else.  When a teenage student is offered the opportunity to learn and CHOOSES not to, shouldn’t they be the ones to accept responsibility for that choice?


Is kindergarten too young to study Physics?

Studying Physics in a kindergarten classMany parents of young children have vague (and sometimes not so pleasant) memories of studying Physics during their high school years.  These same parents with their somewhat patchy memories of what matter and energy are, and how these “Physics things” interact, would be astounded to learn that their kindergarten-age children are in fact ready to study Physics.  But isn’t Physics terribly complex with lots of formulae, obscure calculations, and plenty of abstract concepts to glue it all together?  How can a kindergarten-age child possibly study Physics?

 [1]Marxen in her article “Push, Pull, Toss, Tilt, Swing: Physics for Young Children”, explores the role of Physics in the learning process and problem-solving skill development of young children.  Marxen comments that there are “similarities between how children think and learn and how scientists work. Children, like scientists, are theory builders. When children are allowed to construct knowledge by acting on their environment, they expand their understanding, which in turn contributes to their intellectual development.”  So your children are little rocket scientists in disguise, how exactly are they learning and building these theories?

Marxen explains that young children’s Physics experiences usually involve the movement of objects.  For most parents and teachers, “movement of objects” is synonymous with play.  The action is primary and the observation is secondary. Children typically make discoveries about matter and energy through creative play and simple discovery activities in the classroom and at home. For example, something as simple and inexpensive as some small balls and a few sheets of cardboard (that can be folded into ramp-like structures of varying steepness) can invite children to explore concepts that will only be translated into detailed formulae and complex concepts many years down the road for them.  Playing and learning to ask the question “why does that happen” gives these children the opportunity to acquire valuable learning experience.  This experience can be built upon to create a practical knowledge base which will later provide a sturdy foundation to which more complex, abstract Physics knowledge can easily be added.

Are kindergarten children too young to study Physics?  Absolutely not!  Teachers and parents alike can introduce young children to Physics discovery and learning with play-based activities without fear that the children may be overwhelmed or turned off Physics.  Plan playtime or classroom activities that focus on getting the children to experiment and make observations about the world they live in, and you will be well on your way to stimulating a life-long interest in, and appreciation for Physics.

[1]        Carol E. Marxen; Childhood Education, Vol. 71, 1995.


Common sense – the stepping stone to successful problem solving

“My kids seem to have no common sense.  What do I do?”

 Before we consider whether common sense is something that can be acquired through exercise or practice, a curious reader may well ask, “But how do we know if we (or our children or students) have enough common sense?”  How much is enough?  Was I born to struggle with issues that require common sense?  Is my lack of common sense just the result of my genetic coding?  And why is problem solving hampered by the absence of common sense?  Can’t I find a way to become good at problem solving without growing my common sense?

These questions introduce complex topics that promise to weigh down the most athletic mind.  It’s easy (and extremely informative) to get caught up in the theories and debates that psychologists and educators invest themselves in.  My experience, however, is that most parents and teachers need practical solutions that will make learning easier for the children, and not a bunch of theoretical textbook quotations.  So here, we will rather focus on the practical issues, and how to overcome real-life hurdles that keep students from succeeding.  Parents and teachers may find they identify a little better with their children and students if they first challenge themselves to a fun, common sense test (an example is found at  The score doesn’t matter nearly as much as the insight this test will offer us into recognizing why common sense is so very important in the problem solving process.


How do we challenge and motivate students?

Every teacher knows that getting our students excited about learning is not always easy.  There are, however, some successful ways to engage learners and raise their excitement levels.  Elena Aguilar describes one such approach in the article, Do Your Final Projects Challenge and Motivate Students? | Edutopia.  Give students a clear goal, a practical way to express what they have learned, and you will encourage learning.  Aguilar describes how “dangling” the final project in front of the students actually lures them into the learning process.  For the students, “the purpose of learning discrete skills” becomes apparent.  “They see how the learning will be applied, they know that there’ll be an audience at the end, and they anticipate the fun.”


Taking arithmetic exercises out of the classroom

Most kids dread mathematics homework, but won’t mind playing a game.  The LPN Game is a very simple, fun, number-based activity suitable for the whole family.  The game, which is customizable in difficulty, can be played by all the members of the family, play group, or students in the classroom, and is a great way to introduce very young family members  or students to the process of combining numbers in a fun, non-threatening environment.  Without realizing it, your children or students will soon be “doing arithmetic” exercises outside of the classroom without the need for books or pencils.

The LPN Game (available in print format) will soon be available as an affordable download from  The low-cost download version is ideal for teachers and parents on a tight budget.


Expecting too much of the teacher?

By the time a young person enters a high school science class, they should be brimming over with curiosity and a desire to learn. Does that describe the average student? No. Most drag themselves to class, disinterested and intimidated by the material they encounter. The teacher is left with immense task of not only communicating the facts, but also trying to stir up some curiosity and instill and develop some basic skills (such as observation of the environment). Is this really the responsibility of the teacher, or are we expecting them to do the very things that should be part of family life?

I believe that education begins at home. I also believe that it should begin early. Developing the natural curiosity of a child is part of the role of the parent. Unfortunately, many parents sit their little ones down in front of the TV, pop in an “educational” dvd, and hope the edutainment on the screen will do their work for them.