DoodleMom has graciously turned over the keys to the blog to me today so that she can take a nap, help the children paint the dog or something. “Say something about logic or math and something,” were her instructions.
So Math.
I am an engineer. I receive requests from time to time to share my insights on topics mathematical. This is usually phrased as, “I really need help with algebra. Can you tutor me?” Being a soft touch, I often answer with the affirmative.
Have I learned anything yet from these trips with people down the rabbit hole?
Why yes, thank you for asking.
The fundamental obstacle most students need to overcome is that they do not know how to do basic arithmetic.
At this point you might be saying to yourself, “Self. We have calculators and computer spreadsheets and stuff. Why is this guy talking about basic arithmetic?”
Some people claim that algebra is the gateway to abstract math, or maths as they say in the mother country. Algebra and it’s hostile younger brother geometry are the simplest mathematical subjects which enable you to derive new facts.
My observations lead me to conclude that you cannot begin to understand algebra without having the following skills:
When you see a six you immediately think 6=(5+1, 4+2, 3+3, 2*3) as well as 6*6=36, 6*2+12, 6*3=18, 6*4=24 and so on.
And this all must happen without the student realizing that it is happening. It works best if this instantaneous recognition can happen with all numbers up to 20.
How can you gain this skill? Gym time and repetitions – Can you tell I used to play sports? Normal people say “practice, practice, practice.” And “Practice some more.”
Stay with me here, I’m about to sum things up.
DoodleMom tells me that the hierarchy of complexity in language and knowledge matters goes as:
- grammar
- logic
- rhetoric
I claim that for math the equivalent subjects are
- arithmetic
- algebra/geometry
- higher math
Now imagine that you are starting out to write, say, “The Hunger Games” while only sort of understanding the difference between nouns, verbs, and adjectives. Or maybe you only have the loosest understanding between cause and effect. Not very logical, even if that seems to be exactly what happened to the poor author of “Diary of a Wimpy Kid.”
This is exactly how math is taught to young students in schools today. And it is getting worse.
Spend any time with any elementary school teacher and you will quickly hear how forcing young students to memorize facts such as 4+2=6 is just “drill and kill” and that what we should be teaching instead is to allow the student to create new ways of exploring the answer to what is four plus two.
Much like asking a young student, who cannot spell, to sit down and write “Little Britches” or “Little House on the Prairie” or “If We Survive“.
Is this logical?
