How and why to memorize multiplication facts

How and why to memorize multiplication facts

From Wikipedia:

In 1989, the National Council of Teachers of Mathematics (NCTM) developed new standards which were based on the belief that all students should learn higher-order thinking skills, and which recommended reduced emphasis on the teaching of traditional methods that relied on rote memorization, such as multiplication tables.


Yes, virtually all students can learn higher-order thinking skills. But automatic recall of multiplication facts is one of the ways that students can gain access to these higher-order skills. 

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How to get students to stop adding and subtracting on their fingers

How to get students to stop adding and subtracting on their fingers

If you want someone to stop doing something, it's helpful to train an incompatible behavior (this I learned from Karen Pryor). However, sometimes it's hard to know what that incompatible behavior should be.

Of course, you also have to see the existing behavior as a problem in the first place in order to want to change it. 

I've noticed that many students who struggle in math are finger-counters. In other words, they use their fingers to add and subtract numbers. This does not seem to me to be a coincidence. In order to figure out a solution, I had to delve into why the finger-counting was happening and why it was a problem.

Happily, as usually happens, the root of the problem was also the source of the solution. The incompatible behavior had the added benefit of being hands-on.

This post will explain my reasoning and help you take the first step to help someone overcome the habit of finger-counting when performing addition and subtraction tasks.

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Teaching fear

For so many of us, education boils down to fear.

First we have fear on behalf of our children, and then, at the appropriate time, we transfer the fear to them while still retaining a measure for ourselves.

We fear "not getting it." Not being good enough. We fear failing grades. We're afraid that we won't get into college, that we'll flunk out of college, that we'll choose the wrong major, that we won't get a job. 

We compete with other individuals, amassing AP classes and extracurricular activities in an academic arms race. And as a nation, we're worried that we'll be left behind as other countries train up generation after generation of highly skilled workers. 

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I believe in shortcuts.

I don't mean shortcuts that undermine what you're trying to do, like risking your life by rushing through a red light, or compromising your health by taking diet pills to lose weight, or never changing your strings so that your guitar sounds like broken windshield wipers. 

I like shortcuts that result from drilling down to the core essence of what you're trying to accomplish, allowing you to get maximum results from minimum effort and time.

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Common sense over Common Core

Béla Bartók, the celebrated twentieth century Hungarian composer, wrote playful and interesting piano music for children in addition to his larger works for advanced musicians. Some of these pieces were based on Eastern European folk melodies, and some were wholly original. There were several that I absolutely loved as a child, and I love teaching them to my piano students.

Mikrokosmos is a collection of études that progress from very simple to highly complex, which Bartók wrote to systematically address certain musical and technical challenges. While I love the concept, most of these (especially the ones for beginners) leave me cold musically. It strikes me as an attempt to reverse-engineer the process of becoming a musician - an idealized repertoire for an idealized student who will think like a professional musician from the first downbeat.

As I review the Georgia Performance Standards and the Common Core standards, I find myself thinking of Mikrokosmos. The standards are similarly comprehensive, cerebral, and virtually impenetrable unless you possess specialized skills. There is no recognizable equivalent to "Twinkle Twinkle Little Star" - the common-sense learning you remember from childhood.

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Learning is not linear

So, I'm now teaching middle school.

Following a calling is an incredible thing. I've found that it's best to not ask why I feel called to do something - I've just got to do it. Not that I'm impulsive, necessarily - I believe, as Rilke says in Letters to a Young Poet, that things grow within us without our awareness before they seem to spring up out of nowhere in our lives. The roots of this project go deep, even though a mere five months ago it was unknown even to me.

In order to best serve my students, I prepared. I researched curriculum. I reviewed the finer points of quadratics and quadrilaterals, colloids and covalents, appositives and apostrophes. I developed a daily schedule, put together a ton of IKEA furniture, and meditated on my vision for the school year.

Man, was I in for a surprise.

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How to get great results with anybody (including yourself)

I'll never forget the first Collegiate Chorale rehearsal I attended. Rob (or Berg, as he is affectionately known to his high school students) conducted the entire rehearsal in silence. He used gesticulations, exaggerated facial expressions, the piano, and the chalkboard to get his point across.

Since Rob, with his expressive features and tireless enthusiasm, gives the impression of a cartoon character come to life this was amusing, unsettling, and highly effective. And clearly memorable, since it's been well over a decade since that day and I can recall it in such detail.

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Guitar Technique Tips for Young Beginners (with video!)

If you're a parent or teacher working with a guitar student under the age of ten, this video is for you!

Here, I'll demonstrate some things to look out for in order to make sure that young guitarists are building the strongest possible technical foundation for their playing.

Older students can sometimes fudge technique, but getting anywhere on the guitar is pretty much impossible for little kids who don't have solid skills.

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How to be successful: self-talk lessons from a two-year-old

I am fortunate to be involved in the lives of many small people. Though I've never had a baby, I have friends, clients, and family members at every stage of the child-rearing game and am intimately familiar with its details.

In particular, I am lucky to know many excellent mamas who treat their very young children with respect and dignity, allowing them to make age-appropriate decisions as often as possible.

A mama of a little girl who has recently turned two shared a story that we can all learn from as we strive to accomplish great things in life. Great things such as weaning and potty-training.

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How to listen like a musician

When I was a kid, in those long moments when my mom would not! get off! the phone! to shower me with attention and answer whatever trivial and random question I had, I would lounge around and do the strange things kids do when they are bored. I developed a game in which I would lean my head upside down off the sofa or staircase and imagine an upside-down world where the ceiling was the floor and the floor was the ceiling. I visualized myself walking upon the sloping "floor" and passing by the chandeliers, floating upon their chains like strange metal trees.

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In defense of Taylor Swift

Photo by Jean-Baptiste Bellet.Yesterday I sat on a wooden stair on a seawall as the tide came in all around me. I thought about how easy it would be to accidentally drop my iPhone into the surf below - hundreds of dollars worth of magical technology and irreplaceable data gone in an instant.

It fascinates me that something that takes so much insight and sophistication to design and build can be destroyed in a flash. It takes far less effort to tear something down than to build it up.

Criticism is easy. Much easier than creating whatever it is that's being offered up to the critic.

It is with this in mind that I undertake a thoughtful criticism of Lizzie Widdicombe's profile of Taylor Swift in The New Yorker this week. My main issue? Ms. Widdicombe herself was too critical of her subject and missed the larger story of Taylor Swift's significance and influence.

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How to instantly make your piano playing sound more professional

The great thing about playing pop and rock songs by ear is that the sound and feel of your playing is up to you. I guess that's also the bad thing about it - there's no written score to guide you and infuse your playing with appealing licks and time-tested voicings. Here, I'd like to share a simple left-hand technique that will make you sound a lot better right away.

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The secret to coordinating your hands

Many would-be pianists have told me that they stalled out on the piano because they just couldn't get their two hands going at the same time. "First I learn one hand," the story goes, "and then I learn the other, but I can't stick them together!"

The thing is, that's not how pianists think. Flute, saxophone, trumpet - these are instruments that can only create monophonic (i.e., one note at a time) textures. The very nature of piano is polyphonic (many voices), and most of the music written for the instrument takes advantage of this.

But polyphonic does not equal "monophonic plus monophonic" - you can't just learn the parts separately and mash them together. You'll need a different strategy.

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Start at the end

Here we go! Another one of Casey's ridiculously counter-intuitive posts. Start at the end. It doesn't get more contrarian than that, does it?

This is the way I was taught to practice, and I continue to do it because it works. Time and time again I share this practice technique with my students, and I can always tell when they follow my directions because their playing sounds smoother and more confident. Learn how and why starting at the end works so well. Don't worry, we won't be going backwards.

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Turns out that thing only you can do is also the hardest thing you can do

"Find something you love and let it kill you." - Derek Sivers

Thoughts of inadequacy and self-doubt had better not get near my most important work. (Library of Congress photo)I've been hooked on House since 2007 when I crawled into bed exhausted in the middle of the afternoon after Eclectic Music's first-ever November recital. I decided to reward myself (for pulling off the recital, not for crawling into bed) with a TV episode downloaded from iTunes. I remembered seeing promos for the premiere of House during the legendary 2004 ALCS and it looked interesting, so I thought I'd give it a try. Seven seasons later, I am still along for every DDx and going-into-a-commercial panicked use of the crash cart.

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