Math Can Take You Places – #Fractonia Included

Merc, a character from FRACTONIA by Pearl R. Lewis #fractoniaFRACTONIA 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?”

Color the Realm of Fractonia by Pearl R. Lewis
Color the Realm of Fractonia
Fractonia by Pearl R. Lewis - a calculated adventure for inquisite minds
Fractonia

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.

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What Sane Person Writes a Novel about Fractions?

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.

If you have never had a teacher show you HOW to create your very own learning adventure, sit down and read. But don’t read to be entertained – read to discover. Read so the book can become your teacher and show you how to create your own learning adventure. “Fractonia” is my adventure with something as simple as fractions. Other authors will take you on different adventures. You may not be ready to write your adventure in a book, but you are ready to have an adventure. There are no age limits on learning – we never outgrow a good adventure. What will your next adventure be?

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The Dot and the Line: A Romance in Lower Mathematics

The Dot and the Line by Norton JusterMATHEMATICAL 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.

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