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June 25, 2009 | Math, eggs, and mandolins; higher level understanding
Eleven year-old Coco was survivng her Advanced Math class. Her instructor suggested in Parent/Teacher conferences that the pre-Algebra learning would come much easier if she were more flluent with her multiplication tables. In other words, the rote drilling of practicing and polishing single digit "times," 6 x 6, 7 x 9, 8 x 3, etc. was an activity that would bode well in developing a more intuitive sense of numbers that would become essential to higher level math.
Think about using numbers in real life. When a cook is serving omelets to 30 people, does he/she calculate exactly how many eggs he/she will need in planning the meal, or is there an intuitive sense based on culinary experience? Is it a matter of how many individual eggs, or cartons of eggs? You buy them in cartons after all (store generally don't sell individually) so thinking in dozens is actually a life skill; more likely to purchase four cartons of twelve eggs. Does one think the individual quantity of 48 as a function of 4 x 12, or does intuition kick in?
As youngsters, we practiced the times tables to understand the process of multiplication, but at some point we got beyond the process, and the results themselves became intuitive. We look at the number 64 as an instuitive product of the action of 8 x 8, without actually mentally calculating. At some point, we go from the primitive computation to instinct.
This is what drilling scale patterns and arpeggios is all about. In the beginning, we are looking at the components and make-up of an A scale, the C# in there, the G# that leads to the A, the E which is the 5th of the key, but eventually it becomes an intuitive entity unto itself. You come to an A chord in the song and you aren't thinking these elements, you're just thinking "World of A."
If you are new to the whole FFcP approach to learning the fretboard, be content that the early stages of understanding will start at this primitive level. You are developing a tactile memory, which over time will become something to build your intuition on. The cerebral part, the music theory might be overwhelming now, but over time it becomes subliminal recognition. The cognitive world of "hunch," "premonition," or even "feeling."
For now, just let your fingers enjoy the exercise.
Dr. Mao: Four Exercises to Sharpen Your Brain
Fingers, Ears, Brain
Osmosis and Effective Practicing
Posted by Ted at June 25, 2009 8:09 AM
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