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.



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?


Parents are the reason that students cannot hack the Math in Physics?

High school kids cannot use fractions.Another physics teacher told me that students cannot hack the math in physics,” says Stewart Brekke in his article entitled, “Urgent Math Crisis in our Nation: Basic Math Deficits Affect Student Performance in High School Physics and Chemistry“.  Is this an unusual observation for a Physics teacher?  Brekke estimates that the USA “may now have over 100,000 high-school students who do not know fractions and decimals well enough to do high-school physics and chemistry successfully, let alone go on to college and pass a physics or chemistry course.”

There is clearly a problem on our hands – many teens cannot do basic mathematics.  Where do we find the source of this problem?

Stewart Brekke speculates that part of the problem may be attributed to the elementary schools placing too much emphasis on reading skills and not nearly enough on basic arithmetic skills. Japanese elementary school students typically spend two to three times as much time on developing mathematical skills as their American counterparts. The result of this shift in priorities is evident.  Stewart also believes that the “lack of a proper foundation at home” is also a significant contributor to the poor arithmetic skills observed in high school students. Sadly, many children enter first grade without being able to count to ten, and their progress in arithmetic skill development is severely hampered.

It is not that parents do not care, for, on the whole, I have seen them show deep concern about their children’s education, but that many of these parents do not take the time to teach their children number facts nor reading skills. These parents must be informed early that their child’s success in school means that they must start educating their children before they enter kindergarten,” says Brekke.

Education systems all over the world invest vast sums of money into remediation of high school students struggling with poor basic skills. Yet high school Physics and Chemistry classes continue to shrink in size as teenagers avoid confronting the issues that stand in their way of understanding these subjects.  Are we trying to solve a problem instead of preventing it?  What would happen if more of the national or state education investment was used for programs aimed at educating the PARENTS of pre-school children, thus effectively equipping them to help their children develop the basic skills needed for future success at school? 

 Can parents make a difference at home?  All indications are that if parents do not participate in the education process BEFORE their child enters the school system, they may in fact be contributing to their child’s future scholastic failure.


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.


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.


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.