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Friday, December 23, 2011

Quick Practice Tip: Factorial Repetitions

Here is a quick tip for assigning a student a certain number of repetitions for a tricky spot to be worked. It is called "factorials." Your students will enjoy this.

If you remember your math lessons from high school, you may remember the factorial expression "10!" and what it refers to. No? Well, many of us have stopped using those math lessons learned many years ago, and now that calculators are so prevalent, many of us may not even remember some of our basic math skills. One of my students did an internship with NASA this summer, and he found that he was rusty with his basic math skill of multiplication. Interesting. When we discussed how that could be, because he is a very, very bright student, he thought it was probably due to his not having to remember the multiplication tables because he used his calculator exclusively.

I digress. Back to the discussion about factorials. The expression "10!" means that you multiple 10 by each consecutive number lower:

10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1

Now in the math world, the expression 10! would equal 3,628,800. But for my teaching purposes, I use the factorial expression in a different way, because I doubt that my student (or his or her parent) would be willing to repeat something over 3.5 million times. Instead I ask my student to repeat a particular skill or passage 10!, which means:

day 1: play the passage 10 times
day 2: play the passage 9 times
day 3: play the passage 8 times
day 4: play the passage 7 times
et cetera until
day 10: play the passage 1 time

So in ten days the student will do a "factorial" of 10! and decrease the number of repetitions beginning with 10 times and ending with just one repetition. In sum total, the student will have done 55 repetitions. My student and his or her parent can handle that number.

If I asked my student to repeat something 55 times, I doubt that my student would have completed that assignment completely. By couching my instruction as a factorial, my student has a plan to follow. The assignment also gives motivation, because the incentive is that the practice assignment decreases with each day.


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