Math Scales

Here's an idea to help musically inclined kids practice their basic arithmetic skills: Practice math sequences like you practice scales. This basic rebranding of "Counting By N" combines a clear metronomic pulse with a drive to perform faster and faster.

Just as we practice musical scales to expose where certain knots are in our fingers so that we can learn tunes more quickly, we can practice the Math Scales to get the basic arithmetic muscles smoothed out so that higher order problems can be solved more quickly.

Usually we practice in the car. While I bang out the pulse on the steering wheel they can run through a 6 scale or a 30 scale. Important variations include starting from non-zero values, as well as doing minus scales.

The grand challenge for the older child is to run through "all" the scales from 2 - 9 in a row for a record time. Actually even for me just the act of speaking out all those numbers is somewhat fatiguing so it takes some practice.

This is infinitely extendable and some ideas for variation that we've only begun to explore include:

• singing the scale
• trying them to different rhythms
• try making chords of the sequence, like what is the 7-scale major chord? Take the 1,3, and 5 note of the 7 sequence and add them together.
• Try different sequences like the squares, cubes, Fibonacci numbers.

Why do this:

• Identify weak spots. You'll quickly find out which steps in the sequence don't come out smoothly and naturally
• Gain fluency. If the child can bang out the N-scale quickly, they can do the arithmetic quickly.
• Helps them jump around the sequence correctly. Perhaps they forget 8 times 7 but remember 6 times 7 is 42 and can quickly fly two "notes" up their 7-scale to 56.
• Reinforce the idea of practice in math, as something that can be improved and not just "I'm good at math" or "I'm bad at math" (See Carol Dweck, Mindset).

Practice Ideas: Scales + Improv

My son loves to improvise but it is my job to also focus him on practicing his technique. Often between scales he launches into an improvisation within the key of the scale that we've just practiced. I don't want to suppress these creative outbursts, but I also want to move our practice along. One thing that works well is to suggest that he fit the next scale or arrepegio on my agenda into his improvisation when he gets a chance. This engages his creativity and gets the scale practiced at the same time.

In a twist on this game during piano practice, I told him that one hand was being well behaved but the other hand was totally wild. The left hand was dilligently practicing it's scale but the right hand was improvising. After doing that for a bit, of course, the right hand decided to behave but the left hand became unmanageable.

These games help me get through practice, and avoid the absurdity of chiding him to "stop improvising and practice your scales so you get used to the key so that one day you can, um...., [sheepishly], improvise."

Ball Practice

It has been very difficult to get my almost-4-year-old to concentrate in violin practice and lessons. Thanks to some clever treachery by our teacher though we are beginning to settle into a rhythm. Between every violin exercise that he does he gets to do something that is more immediately interesting to him. We have had success with 2 kinds of diversions: puzzles, and balls. For example, he gets to add one more piece to his puzzle every time he does, say, 10 ticki-ticki-pa-pas. Or he gets 10 "ball catches" after every 10 of some other violin exercise.

He has so much fun that all of a sudden he is asking to practice instead of resisting, and even making progress on the violin.

Felix Mendelssohn: Greatest Prodigy?

NPR has a great story on an Octet that Mendelssohn wrote at the age of 16.

Says Rob Capillow:

"And that was the greatest music, in my opinion, ever written at a young age," he says. "So I think in terms of sheer compositional quality, Mendelssohn — not Mozart — was the greatest child prodigy in the history of western music."

My favorite part of the piece is the analysis that starts at about 3:00.

Thanks to Luke for the pointer.

Calling in the Heavy Guns

Now and then when a practice session isn't going so well I need to call in the heavy guns. An occasionally call to Bach or Brahms can do wonders to get the focus back on practice.

Me, dialing: Hello, Johann?
Me, I mean, Bach: Yaaah, how's it going?
Me: Well we're having a little trouble focusing on your Gavotte here.
Bach: Well let me talk to him....

And I hand over the phone and let the old Master explain what needs to be done. If things really call for some ornery castigation I'll even call Beethoven himself to sputter out insults in a terrible faux-German accent. The mere threat of a call to Beethoven is often enough to get the focus back on correct bowings.

Once I even called Brahms on the phone and asked him to play along on a cello as we practiced his Waltz in Suzuki Violin Book 2. Afterward, I asked my son how he liked Brahms' improvised cello part. He liked it, so I asked him to play on his violin an octave higher, as I hadn't been able to hear Brahms play very well. It turned out to be true, Brahms' cello part was indeed quite nice.

Vitus

Vitus is a great movie about a prodigy who gets a bit overwhelmed by all the pressure his generally well meaning parents lay down upon him. It's an inspiring movie in it's own right, and it's a particularly good movie to watch for anyone who fears they may be putting a little too much pressure on their child.

I'm not going to recommend that actual young musical children watch it though. I don't think I'll show this to my kids.

Daniel Barenboim on Concentration in Practice

In his autobiography A Life In Music, conductor and pianist Daniel Barenboim says this about practicing (p9 in my copy):

"All individuals have different spans of concentration. I have no strict rule mself, such as playing eight hours a day or no more than forty-five minutes. Both extremes are equally counter-productive. I never play a single note when my concentration is no longer at its height, for to do so would be to fall into the trap of playing mechanically."

This sounds great in theory but some caveats may be in order in the case of small children. After all, they may still be learning the rudiments of how to focus on anything. Follow this guideline too strictly and your 5-year-old might never practice. You have to gently toe the line and work to extend and optimize their periods of concentration.

But it is a very important warning. You can usually bribe, threaten, or otherwise cajole a child to eventually get through practicing the days lesson but it truly could be counterproductive. I'll bet most kids could learn as much in 10 minutes of practicing where they choose to concentrate then they could in a week of being forced to while they're trying to weasel out of it.

You need to gently redirect the wandering mind and try a few times to get back on track. But I agree with not pushing too hard. The trick to finding the period of concentration in the young child might have more to do with finding the right time of day in the right part of eating and sleeping cycles. And if focus is not there sometimes you have to just let it go.

I've often struggled with the case where my child brings plenty of concentration to the table in a practice session, except it's all directed at music outside of our assigned lesson plan. I'm loathe to suppress his creative expression though I'm sympathetic to the view that he needs to keep building his technical proficiency to ultimately increase the range of what he is capable of expressing on the instrument. Our violin teacher introduced the idea of 2 different practices, so you keep a very structured frame of mind for the "official" practice and are more laissez-fair on the other one. That view has sometimes been useful but proven a little too structured for us. When an idea arises, you need to pursue it. But if you do nothing but chase ideas you might miss important elements of your training. Emphasis on 'might'. Improvisation fits more naturally into our piano practice; no surprise there since our teacher is a jazz man.

Professor Pocket

Parent Hacks has a lengthy review of a new "learn Spanish" CD. I followed their advice and got a copy on Itunes yesterday and it's a hit with the kids already. It sounds very interactive, almost like a TV show and cleverly overlays the Spanish and English. The music is definitely simplistic, repetitive "kids music" and is neither the most nor least annoying example of the genre.