Education Has An Unhealthy Fixation With Fractions — And It’s Hurting Everyone.
The last time I wrote a blog immediately after knowing/coming across something was when Anthony Bourdain died. It hit me like the proverbial “ton of bricks”. The day after he died, I wrote a blog about his impact on my teaching mathematics.
This blog’s reaction time was even faster…
I wish I could take credit for the above picture. I can’t. But, I could have easily authored it. I think I have hated fractions my whole life — as a student, as a teacher, and now as author/speaker.
For me, fractions are more like answers to interesting probability questions or those wonderfully, whimsical geometry shading problems that I found in Geometry Snacks(Ed Southall and Vincent Pantaloni) — one of my favorite math problems book in the last few years!
Without an interesting context or problem, I care for fractions with the same desire of getting a root canal — with 17th century dentistry. The need for exaggeration/humor is a function of my disdain for how much fraction discussion dominates the landscape of math education. You would think students and teachers are getting honorary degrees from Fraction University!
I think the British have a phrase for this kind of attention — making a meal of it. The precise definition is rather bang on.
The tipping point of my frustration with the amount of hyperventilation there is about fractions — hence valuable uptake of mathematical oxygen — was coming across the video below. I came across it early this morning. Like a bakery, the blog you are reading will have come out by noon(I am also writing a blog about the The Global Math Project at the same time!)
Manjul Bhargava is a Canadian-American mathematician. He became a full-time tenured professor at Princeton before he turned 30. Andrew Wiles, of Fermat Last Theorem fame, supervised his doctorate. He won The Fields Medal in 2014.
Manjul Bhargava also hated math in schools.
In fact, he would skip school to avoid math classes. While you should know why, watch the video from the about the 4:30 mark to the 6:00 mark. In those short 90 seconds, Manjul, with his Indian modesty and humility, hits it out of the park.
Manjul hated math class. So have thousands before him. So will thousands after him. Things are finally changing for the good in math education, but a lot of work still has to be done.
For one, mathematics needs to be fun in the most unapologetic terms possible.
Sorry. Not going to get into a debate with traditionalists and others who will tether the learning of mathematics to required procedures/direct instruction and rail against fun and entertaining math. I am sorry if your experience sucked. Don’t download your misery onto children framed in the arid soil of math facts, memorization, and “robotic learning” that Bhargava makes reference to. Unless you have a Fields Medal in your cabinet drawer, I am unsure how much you can chime in against his humble call.
Bhargava’s specialty lies in Number Theory. He explains what that branch of mathematics is in the interview. Paraphrasing, number theory is the art of seeing the relationships of whole numbers. Yes. He used the word “art”. Bhargava also is student of Sanskrit poetry. He posed a brilliant question regarding short and long syllables towards the end of the interview.
If you have 8 stanzas left to finish a poem, and you have two kinds of syllables — short and long — how many different ways are there to finish the poem. He then translated it to simply mean if you just have “1's” and “2's”, how many ways can you add up to get 8?
Well, start small?:)
1 = 1 (1 way)
2 = 1 + 1, 2(2 ways)
3 = 1 +1 + 1, 2 + 1, 1 + 2(3 ways)
4 = 1 + 1 + 1 + 1, 1 + 1 + 2, 1 + 2 + 1, 2 + 1 + 1, 2 + 2(5 ways)
5 = ?
I won’t give away the answer. That would rob you of the delight that lies ahead.
Why don’t we spend more time with whole numbers? Why do we rush to fractions like its kobe beef being served at The Bellagio Buffet — when it’s 99 cents shrimp at Circus Circus.
One of the best articles I have come across which painfully articulates the intrusion/infection of fractions in math education is this one — Enough With Fraction, Already…
Fractions are a number on the number line. Can you locate them? Good. Do you know how to find 3/8 as a percentage in your head?(What number should you multiply 8 by to get to 100? Do that to the top. That’s your decimal equivalent) How do you add/subtract fractions that have different denominators? What does the multiplying symbol mean between fractions?(the word “of”). What is division of fractions? Our entire curriculum of fractions should be contained here and with fractions that have denominators that don’t go all Egyptian — unless you are teaching Egyptian Fractions(which most teachers are not).
Worksheets like the ones below are unfortunate staples in some classrooms. If this isn’t the buzzkill for wanting to learn mathematics, then I have no idea what is. Do students have any intuitive toehold to any of the questions below?? Are there students who answering question #2 going “hmmm…I think the answer is going to be just above 20%”
They are, like trained seals, going to flip and multiply, get the answer 11/48, spend a couple of nervous seconds to see if simplifies(why we do this is beyond me as well), and then wait for the green check mark to arrive.
Fractions in schools should be relegated around exploration and modeling. Technology can definitely help with that — especially in the play factor that Bhargava alludes to often in the interview.
Here is a video I made using an activity found in Buzzmath.
Mathematics needs to be fun. There I said it again. Imagine how many Manjul Bhargava’s lie in wait, but are turned off of mathematics — and don’t have a mother who is a supportive math professor?
At least be honest about our intentions. We live in a testing/performance culture. But, having such an unhealthy obsession with fractions not only turns off kids — it causes math anxiety. Fractions are hard, right James Tanton!
But even worse, fractions becomes some lauded Canon in learning mathematics. For the Back-To-Basics folks it becomes something like a dog on a bone. The ridiculous notion that fractions are critical gatekeepers for everything beyond only gets amplified — hence, distorted. Distorted by them, by media, by anyone who wants to distill math education issues into a sound bite.
Number theory and attention to whole numbers is the bloody rabbit hole to being mesmerized and amazed by mathematics. Fractions is the swamp that bogs down students — and teachers. Fractions, aided by the paranoia of society and displaced values by education, basically took a shovel and covered up that hole with dirt.
If the goal of fractions is to turn off as many students as possible as early as possible, then fractions have exceeded expectations.
In the end, it is quite simple. Do you agree or disagree with a Princeton professor of mathematics that won a prestigious Fields Medal on the state of math education being boring. It shouldn’t take a high profile mathematician to bring mathematics down to its most fundamental element — play — and convince you that is what we should be doing.
It should be a natural call. A human call.
Until we change what we do, the call will only be bureaucratic and political.