## Math Can Take You Places – #Fractonia Included

FRACTONIA is a short novel for young readers that was intentionally created as an informal learning experience. This story takes a topic from mathematics (fractions, in this case) out of the classroom and into an imaginary world of exploration and discovery. The reader is encouraged to leave behind his or her mental image of what a fraction is, in order to consider a completely different image of what a fraction could be. Changing the way a student imagines a concept or topic can open the door to a “clean slate” relearning experience. When preconceived ideas are no longer posing as formidable obstacles to learning, the educator is given a second chance to lay a solid foundation in the fundamentals.

I wrote FRACTONIA in response to how some young students I know were experiencing fractions. In battling the fraction monster, some students had sadly come to believe that they were simply incapable of understanding fractions or how to work with them. Once a student is convinced they cannot have victory over the monster, there is little teachers and parents can do to change the student’s mind. Young learners with this view grow into older students that fear and hate mathematics. I set out to write a story that would help the readers repaint their mental image of the fraction monster. Fractions should not make anyone feel stupid. Most people have the capacity to understand and work with basic fractions.  I wanted to share a story that would get the reader to be able to look past the intimidating numbers and mathematical operators, and allow them to see that mathematics is a language communicating ideas and describing images of the world we live in.

A short except from FRACTONIA (Chapter 4):

“Where is Miss Brady and the rest of my class?” Matthew decided it was time to outsmart Miss Brady’s hypnotist. Matthew was determined to show the crafty man that he was not entirely under his spell. Yes, he couldn’t explain why the man looked more like a giant mosquito than a man, but that didn’t mean he had to pretend that he had lost the ability to think.

“Miss Brady?” A small, silver plate about the size of a credit card suddenly appeared in the hand (or would it be the paw or the claw?) of Merc. The plate vibrated, buzzed a little, and then vanished. Merc looked up and confidently announced, “No “Brady” in the Royal Service Extraordinaire, and no “Miss” amongst the Numo Regulars, either.”

Matthew’s look of bewilderment elicited another hearty laugh from Merc. “This must be your first time in Fractonia. You don’t know what I am talking about, do you?” Merc asked.

Matthew sighed deeply, suddenly feeling overwhelmed and unsure of himself. He shook his head vigorously as he sensed the threat of tears. “No. No, I don’t have any idea what is happening to me. Are you a hypnotist? Am I dreaming or hallucinating?” Matthew felt torn between his mind’s interpretation of his experience and what his physical senses were telling him was real. What was Merc? Could someone make him imagine something as sophisticated and extraordinary as Merc?

“No, Math, you are not dreaming. You did not imagine me. I am not a hypnotist, although I did once give a speech that put a bunch of entities to sleep. You are not hallucinating. You have simply been translated.” Merc stopped for a moment to let his words sink in.

“Right now, you are in Fractonia. Judging by your appearance, I can guess that you are a human male from the Earth world. Juvenile. Perhaps somewhere between ten and fifteen Earth years in age. Am I right? I am quite the expert, you know. I can identify over fourteen trillion species from over eight million realms. By the way, I am the Communications Officer with the Inter-Realm Royal Service Extraordinaire. I have been working at the Fractonia Outpost for the past seven million three hundred and forty-nine thousand two hundred and fifteen yonkinots.” Merc smiled reassuringly. “Do you still feel as if you are dreaming?”

FRACTONIA is available in print and digital format. (Use the links on “print” or “digital” to buy the book directly from Lulu, or google the title to find it at your favorite online booksellers.) To create a special Fractonia gift set for a young reader, I recommend combining FRACTONIA with the accompanying paperback coloring book: COLOR the REALM of FRACTONIA. The coloring book includes many of the illustrations that you will see in the novel, plus some extra characters that are mentioned, but not illustrated, in FRACTONIA. Additional FRACTONIA goodies, such as t-shirts, hoodies, water bottles, stickers, stationery, and pillows (which are ideal as gifts or classroom prizes) are available from Café Press.

## #ScienceMustFall

Science and mathematics are objective, genderless, race-blind subjects that can effortlessly bridge language and cultural differences. But is that really true? This week saw online outcry to the #sciencemustfall proposal, an unexpected sidebar to the decolonization and #feesmustfall campaign currently raging on university campuses throughout South Africa. In a seemingly spontaneous statement (you can watch the video here), a “fallist” addresses the science faculty of the University of Cape Town, and calls for “western” science to be banished from African education.

This begs the question: “Why would this student (or anyone else) feel that something as universal as “western” science has no place in the culture they best identify with?

## Can Mathematics be Decolonized?

Karin Brodie, professor of Education and Mathematics Education at South Africa’s University of the Witwatersrand, in her article “Yes, mathematics can be decolonized. Here is how to begin“, hints at a possible reason. Mathematics apparently presents itself as a subject that is not, or should not be, accessible to all people (at least at higher education level). The perception is that, even with significant effort, if you lack the right kind or level of intelligence, you are doomed to be a mathematics outsider. Not everyone believes this, but the perception remains, and has done much to scare the less obviously gifted away from the subject. Possibly the sciences suffer from a similar “elitist” reputation. Professor Brodie says that “as teachers, my colleagues and I need to believe – to know – that all students can do mathematics. This knowledge must be transmitted to them. They must be shown that mathematics is a human enterprise: it belongs to all, and it can be taken forward to transform society.”

## THE UNIVERSAL VALUE OF SCIENCE AND MATHEMATICS

If students are to come to understand the universal value of subjects such as science and mathematics, they must come to believe they can own these subjects. They must believe they can be part of the process of generating new knowledge to build on what already exists (and has been gathered by people of all cultures and races). If students view these subjects from a distance, they are more likely to associate them with something foreign and threatening. Reduce the distance and the image viewed will not be so distorted.

Should science (and mathematics) “fall” or be removed from a particular cultural group’s education system, because students see these subjects as discriminatory? Surely a better approach is to change the attitude and perception that people have of the subjects instead of the content of the subjects? Why reinvent the wheel when the wheel doesn’t judge and doesn’t mind who owns it?

## FRACTONIA at Amazon

“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 Amazon.com.

Android loyalists can relax. It is your turn. Apple Stores are not the only device stores to stock Fractonia . If you own an Android device and usually shop at the Google Play Store, you can now purchase a copy of “Fractonia” at Google Play. Google is currently offering a new release price, so you can add the book to your e-library at a significant discount.

Books purchased from the Google Play Store are not only readable on tablets and phones. You can settle back and read these books on your computer using your computer’s web browser.

Join the Fractonian adventure. Take the journey with the lead character, Matthew Roberts. Explore a new world. From silent beasts to the talkative representative of the Royal Service Extraordinaire, there is no shortage of the bizarre and the wonderful in the world of Fractonia. There is much to distract a curious mind in Fractonia and it is easy to fall prey to the passing of the yonkinots. Will Matthew be distracted from discovering the real reason that he was invited to this world? Are you willing to find the answer? The clock is ticking, and time is running out – for Matthew and for Fractonia.

## FRACTONIA in Print

“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.

## FRACTONIA at iTunes and iBooks

“Fractonia”, the math-centric adventure for curious minds by Pearl R. Lewis, has found its way into the iWorld. If you use a Mac computer or your Mac or iOS device to read e-books, you can now purchase a copy of “Fractonia” directly from iBooks or iTunes.

• You will find “Fractonia” listed is the Sci-Fi and Fantasy category of the iStores, in the English language division.
• To view this book, you must have an iOS device with iBooks 1.3.1 or later and iOS 4.3.3 or later, or a Mac with iBooks 1.0 or later and OS X 10.9 or later.

## What Sane Person Writes a Novel about Fractions?

“Mathematics is boring. Why do we have to study it anyway?”

“Do I REALLY have to finish all my Math homework? It’s just the same stuff over and over, and it makes no sense to me.”

“I hate doing these algebra exercises. They are SOOOOO boring.”

“I don’t understand this. It’s stupid. Why can’t I do something useful with my time?”

If you are a parent or teacher, then you have probably heard it all. The whining. The complaining. The angry outbursts. For a logical and emotionless subject, Mathematics has an uncanny ability to draw passionate responses from young people. It’s seldom a “YAY, I have Math homework” kind of response. No, it’s more like “ARGHHHH, I HATE Math!”

So why would anyone choose Mathematics as a starting point for a youth novel? And note that we are not talking about some mystical and captivating mathematical subject like String Theory or Equations of Relativity. No, sirree! We like a challenge, don’t we? Out with the exciting stuff, so we can sink our teeth into a common, garden-variety subject: fractions. Yes, you read that correctly. FRACTIONS. Not eye-popping fractal mathematics, mind you. Just regular fractions with numerators and denominators: those little number beasts you encountered way back in grade three of four.

Fractions in all their simple glory were the starting point for “Fractonia”. So is this a story about fractions? (Are you yawning and shaking your head in disbelief?) Yes, but probably not in the way you think. When I was at school and fractions were introduced to the class, the teacher talked about picking apples from a tree. (That was in the days when children actually went outside and climbed trees, so students could relate to the image of apples hanging from a tree.) More recently, while doing research for a new project, I took a look at some junior school materials focused on fractions. The apples were gone from the chapters about fractions. In their place, the reference to pizza slices appeared more often than anything else. (It seems the “an apple a day” phrase has been replaced with “a slice of pizza a day“.) Imagine this pizza being cut into pieces. Your friend eats one slice. You eat five slices. What percentage of the pizza is left? Is this stimulating your imagination and encouraging learning, or is it just making you think that you are hungry? Is there a different way to visualize fractions?

I set out to create a story that would give readers an entirely new perspective on fractions. Why? So they could better understand fractions? No – so they could know it is possible for something as “boring” as fractions to become interesting just by changing our perspective. I wanted to paint an imaginative picture over those sad pizza slices with no story to tell – a picture so unexpected that it would encourage readers to create their own imaginative ways to view subjects they found “boring”. In my experience, an interested student is more likely to learn and overcome learning difficulties than a student who is bored with the topic they are studying. In her article entitled, “How the Power of Interest Drives Learning“, Annie Murphy Paul says the following: “When we’re interested in what we’re learning, we pay closer attention; we process the information more efficiently; we employ more effective learning strategies, such as engaging in critical thinking, making connections between old and new knowledge, and attending to deep structure instead of surface features. When we’re interested in a task, we work harder and persist longer, bringing more of our self-regulatory skills into play.” If we learn better when we are interested, why not find a way to make what we have to learn interesting and engaging? It seems like a simple, common-sense way to ensure we learn more and enjoy doing it.

At its core, “Fractonia” is less about Mathematics and more about attitude. Yes, fractions are part of the story, but no, the story is about exploration, discovery, and possibility. It’s about taking responsibility for our own learning. Our learning is not our parents’ or our teachers’ responsibility – it is OURS: yours and mine. We don’t have to wait for our teacher to make the subject exciting or justify why we should study it. We don’t need to be entertained before we can learn something. No, the process of learning is an adventure that can be created and hosted inside your very own imagination. Go on the adventure, or stay home and mope about how boring everything is.

## FRACTONIA Book Release

“Fractonia” is uncloaked! The doors to the secretive Fractonian Realm have finally been opened to Earth dwellers. You (yes, YOU) are invited to go where few have gone before.  Are you ready to discover what lies on this side of the Beyond Realm?

## BEYOND REALM

All worlds this side of the Beyond Realm face challenges of galactic proportion, but only Fractonia is in a race against time. In an effort to find the elusive key to survival, Fractonia opens its doors to a select few outsiders: creatures believed to carry Fractonia’s solution.

## INVITATION TO VISIT FRACTONIA

To his surprise, Matthew Roberts receives an invitation from Fractonia. Perhaps you have met the freckle-faced young Roberts? Matthew is the well-adjusted youth who isn’t crippled by peer pressure or intimidated by homework on Fridays. He plays nicely with team mates, yet functions just as comfortably on his own. He is the nice guy everyone gets on well with, yet few remember to invite to their parties. So why did someone as average as Matthew get an invitation to visit a secretive realm?

Matthew may be unremarkable in most areas of his life, but he does possess a certain something that turns heads. Matthew Roberts has an insatiable appetite for adventure. And he knows exactly how to feed that appetite. In fact, he does it so well that it gets the attention of a world he did not even know existed.

## TRANSLATED into FRACTONIA

Adventure doesn’t follow playground rules or keep weekend hours. Sometimes it comes knocking when you least expect it. Matthew is grappling with the challenges of a mathematics class when a new adventure knocks him right off his chair. Matthew finds himself translated into the Fractonian Realm – the perfect destination for exploration and discovery. From the silent memory beasts to the talkative representative of the Royal Service Extraordinaire, there is no shortage of the bizarre and the wonderful in Fractonia.

## THE PASSING OF THE YONKINOTS

With so much to captivate one’s attention, it is tempting to fall prey to the passing of the yonkinots . Will Matthew become so distracted by what this new world has to offer that he fails to discover the real reason for his invitation? The clock is ticking, and time is running out – for Matthew and for Fractonia.

## MATHEMATICAL LOVE STORY

Love stories abound, even in the world of Mathematics. Mathematics may not be the first thing that springs to mind when you think of romance, but it does boast its fair share of romantic dramas. Norton Juster took the time to document one such love story in “The Dot and the Line: A Romance in Lower Mathematics“.

As in all love stories, there are well constructed characters, although these particular characters cannot claim to be multi-facetted. Meet the “him”: a boring, straight line. There is the “her”: a gorgeous dot. And then there is “the competition”: the bad-boy squiggle. Line falls for dot, but squiggle gets in the way. What is line to do when dot gets tangled up with squiggle? Mathematics holds the key, and line is determined to unlock the solution to his problem.

## OLD FASHIONED LOVE MOVIE

The Dot and the Line” was published in 1963, and turned into a short film (shown below) in 1965. Apparently, Norton Juster found inspiration in the mathematics fiction classic “Flatland: A Romance of Many Dimensions” (1884).

## FLATLAND and EINSTEIN

Flatland: A Romance of Many Dimensions” was written by an English school teacher named Dr Edwin Abbott. The story plays out in a two-dimensional world where women are simple line segments and men are the more complicated polygons. It may sound like the kind of geometry lesson that will put hairs on the chest of any women’s libber, but you won’t know for sure until you read it. “Flatland” is a lot more than mathematics in an easy-to-read, story format, yet it remains best known for how it opens up the concept of dimensions and challenges us to explore new perspectives.

Sadly, this quaint book went largely unnoticed until Albert Einstein’s general theory of relativity (in which the fourth dimension of time plays a significant role) was published in 1915. Thankfully, someone mentioned this extraordinary book in the same Nature article as Einstein was mentioned (1920), and “Flatland” rose to join other mathematical works of note. I discovered “Flatland” many years ago in the basement of a university library, and hope many more students had the curiosity to pull this book from the dusty shelf after me. If you have not read “Flatland: A Romance of Many Dimensions“, do yourself a favor and borrow or buy a copy.

## The Joy of Mathematics

That the mysteries of mathematics can put a smile on your face may seem far-fetched to some. It is not, however, a strange idea to  Professor Arthur T. Benjamin of Harvey Mudd College. He loves mathematics and is certainly the most enthusiastic mathematics teacher I have ever seen in action. I purchased “The Joy of Mathematics” for a family member, but ended up sitting down to watch the lectures with the gift recipient. I don’t recall ever seeing a maths teacher with so much energy and eagerness to share what he knows. If you are not terrified by numbers (and even if they do scare you a little), you are ready for the magic of mathematics presented in a way only a passionate and down-to-earth mathematician can do it.

The Joy of Mathematics” consists of 24 half-hour lectures that celebrate the sheer joy of mathematics. The lectures are taught by a mathematician who is also a magician, with numbers and the odd rabbit in the hat. Professor Benjamin is renowned for his feats of mental calculation performed before audiences at schools, theaters, museums, and conferences. Yes, you will be in awe of him as you watch him process numbers at speeds that will make you dizzy. But unlike many other magicians, the professor isn’t selfish with his mathematical magic tricks. In this course, Professor Benjamin lets you in on some of the secrets of his wizardry. You may be astounded to learn how easy it is to perform some calculations you once thought would need more than your pocket calculator. By the end of the course, you may decide your new bag of tricks has turned you into something of a minor maths wizard yourself.

Who can benefit from this course? This course is a great refresher course for those who have lost touch with their high school mathematics training and want to feel more comfortable around numbers. It’s also a great warm-up to college entry-level mathematics, and precursor to advanced algebra and basic calculus. For those high school students who feel threatened by mathematics, time spent working through the examples given during the lectures will deepen understanding and boost confidence. Even if you have a degree in mathematics, this course is sure to work out your mental muscles in a way that is both enjoyable and enlightening.

While the complexity of the material presented is not beyond the abilities of average high school students in beginner algebra courses, be warned that at times Professor Benjamin’s enthusiasm causes him to accelerate. If he starts presenting new concepts too quickly, don’t be afraid to reach for the remote and rewind… over and over again, until you feel comfortable enough to move on.  In fact, Professor Benjamin is well aware that his audience is not a university class and will remind you to use your remote from time to time. Take his advice to get the most out of these lectures. Take each lecture at your own pace. Repeat each lecture a few times to let the explanations sink in. I also recommend keeping a pen and the notes that accompany the DVDs handy. Add your own personal notes to those provided with the lectures. You will learn a lot during each short lecture, and personal notes will help you reflect better on what you have learned before you start a new topic. Don’t move on to a new lecture until you feel like you “got it”, or at least got most of it. If you progress too quickly without understanding and internalizing the material, the more advanced lectures may be lost on you.

The Joy of Mathematics” is currently available from The Great Courses, a company that strives to make high quality teaching and the skills of university professors accessible to the general public. (Photo credit: Richard Faverty)