Well...it may have taken nearly 30 years...but I get it....
I now understand why my elementary and middle school teachers drilled in the basics. I understand why I had to learn long division. Decimals. The rules for math. I see why my advanced math teachers in middle school (Kleppie and Brenstruhl) had me writing pages and pages and pages of equations the LONG WAY. Each and every step...over and over. (Even Miss Bommer had us doing the long way in high school before teaching any short cuts!)
Plug in the answer: 105-25=80...yes
I'm sure I could have done them in my head. But we were required to show the steps. SHOW the steps on paper...for each problem.
I did not understand why the advanced math teacher did not MAKE my son show his work last year. I kept hollering "SHOW YOUR WORK." And C's reply was, "Mr. Mick said I don't have to do that." And yes, when I talked to the teacher about this, I was told that C was bright and didn't need to show the work. Only the "hard for C" problems had to be written out. (Too bad C thought that they were all easy enough to do in his head.) I worried for him and those future "too hard to do in your head math classes." C* hasn't learned the habit of actually writing out the long problems. I'm sure it is going to hurt him one day.
B/c if you don't learn the basics and the long form, it is hard to learn the short cuts. Or have the insight on why the short cuts work.
Now I am teaching (not reteaching...teaching) my daughter who has the same math teacher this year. B/c she isn't being taught the long form. The formal form. Today, she was give the short cut for dividing decimals by 10, 100 or 1000...but she never learned the long form and rules for dividing decimals.
(And yohoo... y * .7 = .63 ... is not a multiplication problem. Essentially...it is a division problem.)
And yes, it is very confusing when you don't know the basics!
And yes, I was probably told that "students need to build on each step" as they learn more advanced math.
Today, I saw the confusion in a young mind... as I have seen several times this school year.
But...Knowing is half the battle. A* is learning. I just hope I am as good of a teacher as all those who helped me. Thanks. I see the big picture.
"I always explain every skill and concept thoroughly." Would you have a problem with that statement if it came home at the beginning of the year from your advanced math teacher? I see 3 mistakes: always, every and thoroughly.