# ZeroSum Ruler (home)

## Blogging on math education and other related things

### Dirty Word of the Day: MemorizationOctober 21, 2012

As a high school Math teacher, I hear all the time, “I suck at Math!”, especially, considering that everything else in the world is found at the push of a button, when my students are faced with problems they can’t immediately solve.  I hear “I hate Math” when we’re solving equations, when we’re factoring, when we’re plugging x values back in to find angle sizes.   I hear it all the time.  but it’s when I hear it that got me thinking.

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Since 2003, I’ve been keeping a mental log of all the times I have heard “I hate Math” or “I suck at Math”, mainly because each one has left its own little crater on my Math soul.  I want – need, really - to figure out why kids feel this way.

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It took nearly 9 years, but yesterday I finally figured out why some kids hate Math with all of their being.  It’s because they can’t multiply.  This had been my suspicion for a few years, but yesterday it became clear that multiplication makes the difference.

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“But multiplying is easy, it’s not that.  Math is WAY harder than just multiplying!” you may say.  And I agree with you.  However, Math is 90% confidence, and when a kid loses this confidence because “multiplying is easy” and he can’t multiply, then he feels like a loser and closes off to the rest of his years of problem solving.

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The Conclusive Evidence

I had never seen a little kid do Math until yesterday when a former student of my husband came over with her Mother for lunch.  She’s in 4th grade now and has been having trouble with Math, so we sat down with her current homework: multi-digit multiplication problems.  The algorithm “multiply then carry, then multiply again and add what you carried” is a little weird, but she got that part.  Then all of a sudden out of nowhere, with fists slamming on homework…

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“I stink at Math!”

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“I hate Maaaaath!”

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Within the giant problem my husband gave her to do, she needed to multiply 8 x 5.  When it didn’t come immediately, she exploded.  And up went the walls.  Single-digit “multiplication is easy”, right?  Not if you don’t know it.  If you don’t know 8×5, then Math is the shittiest subject there ever was, ever is, or ever will be.  It totally blows.

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So what would help her?  Memorizing her multiplication tables.  Sounds simple and ridiculous, right?  Hold on a second.  Below are a few excerpts from an article, “Chess Experts Use Brains Differently Than Amateurs”:

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Experts use different parts of their brains than amateurs, maximizing intuition, goal-seeking and pattern-recognition, says a new study that examined players of shogi, or Japanese chess.

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Researchers believe that experts who train for years in shogi are actually perfecting a circuit between the two regions that helps them quickly recognize the state of the game and choose the next step.

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“Being ‘intuitive’ indicates that the idea for a move is generated quickly and automatically without conscious search, and the process is mostly implicit,” said the study.

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Math is a lot like chess: strategy, visualization of next moves, attack!  When a kid is a multiplication amateur, strategy can never develop, patterns will never be recognized, Math will always be counterintuitive.  Multiplication facts take a lot less time to master than chess.

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Memorization: Mathematicians’ Dirty Word

Memorizing sight words doesn’t make reading Harry Potter easy, but it does make it easier.  This is why we do it.  So why not memorize multiplication facts to make Math easier?  At some point between being a Math student and being a Math teacher, ”memorization” became a dirty word.  I agree that we shouldn’t force kids to memorize every Mathematical formula or the digits of pi, but I remember a deep sense of pride in having my multiplication facts memorized.  Maybe the way it was done – calling us up one by one to recite the facts to our 3rd grade teacher – was not the best method and probably contributed to my high-strung demeanor.  But when I got to pre-Algebra, I could cross-multiply; in Algebra I could quickly find factors; and in Geometry I could “plug it in” without a calculator.  All of these seemingly-unrelated abilities contributed to my feeling that Math wasn’t impossible.  I had confidence because I could multiply quickly.  I was fluent, solving came easy.  I could do more advanced problems because I had confidence.  I had confidence because I didn’t need to stop and think through every instance of multiplication.

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A recent brain study done by Dr. Carolyn McGettigan in the UK yielded unexpected results.  Contrary to hypothesis, the expert beatboxer uses less of his brain than the novice:

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The novice used many more brain areas, suggesting a need to plan each sound and a lack of automatic processing.

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Dr Carolyn McGettigan, a neuroscientist at University College London, compared magnetic resonance imaging (MRI) scans during two tasks – counting and beatboxing.

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Dr McGettigan says: “When you think about an expert you might think they activate extra bits of the brain – not just the bits you use to make sounds, but something exciting and different that you might not expect.”

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“What we have at the moment is a demonstration that being an expert doesn’t mean you activate more of your brain. The phrase ‘less is more’ is sort of appropriate here.”

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Thinking is Overrated

Thinking is important, but not that important.  When it comes to the building blocks of any language, a level of fluency is essential.  Without it, reading is exhausting, and things that are exhausting are avoided.  I doubt that my husband – a true bookworm - would have read the entire Harry Potter series [more than once] if he had to individually sound out each word.  It just wouldn’t have happened.  J.K. Rowling would have never earned the necessary funds to  go on to write The Casual Vacancy (is it any good?) if everyone struggled through her Harry Potter books.  Is it any mystery that kids hate solving equations or finding missing side lengths if they have to “sound out” each instance of multiplication?

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So what to do?

We have to stop making our kids think so much!  It’s exhausting them.  When I was a kid, my parents gave me this Math toy that tricked me into learning my multiplication facts.  Flashcards for facts up to 12×12 are also great.  It’s got to be fun, not forceful, of course, but it’s got to happen.  It will make all the difference later and is really that simple.

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### Wanna be a Math Hero? Answer these questions!September 17, 2012

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These Math students need YOUR help.

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If you’ve checked all recent posts on Facebook, refreshed your Twitter page until it can be refreshed no more, all of your Pinterest friends seem to be on vacation and your email is all read, why not answer some Math questions?

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I’ve been addicted to this site since last night, which in 2012 terms is an eternity.  All I can imagine are kids all over the US toiling away at their Math homework, one hand on head, one wrapped around a pencil, foregoing food, sleep, showering, just to get tomorrow’s math work complete in time for their teachers to put a small check in the corner.   Hey, maybe a few teachers are stickerers, I don’t know.  Personally, I’m a grape-flavored stamper.  So here I come to the rescue!  The THANK YOU! emails are cool to get; I do feel a bit like a hero today.

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Questions range from “Plz help me graph y = 45x + 40” to “What is the square root of 1 – i?  So try it out!  It’s a great way to put that advanced degree to good use!

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### 5 Principles of the Evil Teaching GuruAugust 13, 2012

Filed under: algebra,class,education — ZeroSum Ruler @ 11:29 pm
Tags: ,

People who don’t teach have no idea.  Even non-teachers who are all “ra-ra-teachers” have only a slightly better idea.  Broadway performers and circus sideshows have a clue.  Only a teacher can know what it’s like to be on 24/7 for 10 months a year.

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So as a teacher, I was curious about the auto-notification that popped into my inbox recently “Five Principles of the Evil Teaching Guru” by Maxwell’s Demon.  I mean, another person calling me evil?  Haven’t teachers been beaten down enough already?  But since it’s summer and teachers don’t work in the summer (right?) I had a few minutes to read.  At first I read just the five principles:-

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1: Know that teaching is impossible (wait, what?)

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2: Believe that it is important to impose yourself (be a [buzzword] bully?)

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3: Do less (um, fired?)

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4: Confuse and take risks (“I’m confused.” No, you just need to remember your pencil.)

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5: Learn (ok, this one is good already)

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I was more or less horrified by these five principles.  However, it was already a much different post than the title lead me to believe.  Since the last one was “Learn”, I thought that there may be more to the story so I decided to keep reading.  You know the old “Don’t judge a book by its cover”?  Well, this should be recrafted to something along the lines of “Don’t judge a blog post by its subtitles” or something.  You get the idea.

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1) Teaching is impossible

The idea of teaching implies that you can be the active party in someone else’s learning. This is not really the case if you want to go beyond a little rote recitation and rule following.

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2) Impose yourself

Once you have accepted that you are engaged in a fool’s errand get arrogant, unless you are confident that you can persuade, cajole and trick people into learning for themselves, you will not be able to. In order to do this you must be able to gain some control, getting a classroom or individuals to listen to you. Without some form of control you will be ignored or even humiliated. Once you can gain control, however, please do not stop there. Many do, and they become the legends people complain about for years to come. Instead…

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3) Do less

Remember that what you do really does not matter. It is what your students do that matters. If you have opened up a class discussion and it is going well and on topic, let it be. The best state for anyone learning is when they go for it on their own, the teacher silent.

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4) Confuse and take risks

Now we are into the essential, but dangerous skill. There is certainly bad confusion, but there are good forms too. Again this is about what the student does, more than about you. The simplest thing is to simple “be less helpful” but you can take it further and take a risk. Make your students confused, make them fail, it can really help their journey to learning independent of you.

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5) Learn

I have used the term students throughout this piece, but that is wrong, try to drop it from your thinking. Take every chance to learn from the people you work with, make it a two-way engagement. Also never forget to consciously hone your craft. You might have explained how to do a certain problem hundreds of times, is there a new way to try?”

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How great is this post?  I mean, I’m a bit hesitant to purposefully confuse my students as some find Math to be confusing enough, but this post reminds me that people appreciate more the things they find on their own and that it’s my job to make that happen.  It’s the difference between finding a dollar on the street and having Mom give you one.  The one from the street is way more awesome than the one Mom just hands over.  What can you buy with a dollar these days, anyway?

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### Crazy Things People Say to Teachers (and how to respond)June 28, 2012

Filed under: education,videos — ZeroSum Ruler @ 8:16 pm

“Must be nice having summers off.”  Have you heard this one?  Here’s a video from WeAreTeachers with ways to deal with this question as well as others we get as teachers.

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contact blog author Shana Donohue: shanadonohue@gmail.com

### “Gotta Be You” Official Music Video (by Secret Agent 23 Skidoo)May 27, 2012

Here’s a break from Math.  Ever feel like you’re just not good enough?  You’re appreciated somewhere.  Here’s a music video from Secret Agent 23 Skidoo, a musician from Asheville, NC whose friend Adam Strange is a super painter and whose art is hanging in my apartment.  Ok, enough of the run-on sentences… Chin up and Enjoy!

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Gotta Be You

### Top 10 Myths about Math EducationDecember 29, 2011

The following article and its 10 myths about Math education were posted on the Gideon Learning Blog.  From inquiry being the catch-all to memorization being a dirty word, this article hits all the kinks in the way we teach, or at least how we’re told to teach (see Myth #10), math today.  You can see the full article by clicking on the picture or by following the link underneath.  p.s. It’s not just the reps of the Boston Teacher’s Union who roll their eyes at the mere mention of TERC (see Myth #2)….

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### If Pigeons can do it, so can youDecember 24, 2011

Here is a fascinating article on the mathematical intelligence of…. pigeons