Before you begin algebra
Posted 7/25/2020 by James
Great. First you have to understand that the site is very crude right now, so it’s not public until it is at least practical.
A bit about me: 67 years old, retired engineer. Florida teaching certifications (expired) in math, chemistry and physics grades 6-12. So I practice what I preach.
You can communicate with me via Google groups. My email is firstname.lastname@example.org.
There is one thing your son needs to do on his own is to be able to fill out the multiplications table without using a calculator. This has to be memorized.
The reasons are that (1) you need to be able to see combinations by looking at an expression or equation. If a calculator must be used, then you can’t see some of the properties of numbers. Reason (2) is that it trains the brain to see similar relationships when variables are used, such as
(3x^2 + 6x) factors into 3x(x + 2). I did that in my head on the fly.
Also know that 3x and x*3 are different things entirely.
x^2 mean x-squared or x*x and x^3 means x-cubed or x*x*x.
So, 2x = x+x does not equal x*x*x = x^3
After the multiplication table is memorized, I move into subjects that schools completely ignore:
1) The equals sign is used to mean five or six different things, depending on context. We discuss those.
2) Letters x,y,z usually mean something different than letters i,j,k which mean some different from a,b,c with agains are totally different from E, m and c used in E=mc^2, i used by itself, e used by itself, pi, r as in radian and r as in radius (similar but different).
So you see, there are a lot of prerequisites. We need to be 100% on the multiplication table. Make a blank table like the one shown (or print it).
Let me know when this has been done.
One last thing. Algebra is actually very easy; there aren’t that many rules, probably about 5% of the number of rules in English grammar. But, the rules are inflexible, so you have to know them rock solid. Recognizing this, I have devised a means for reconstructing each rule. Nothing is given as “This is the way. Do it.”
Now, many elementary teachers are lousy at math, so they insist that the students do things only one way without comprehension.
I often joke that I do not teach x but I do teach why.