On the back:
SAT scores on the Rise
Over the last three years, our students' SAT scores have been rising in all categories.
Do you wonder what happens when you back that up from 3 years to 5?
(properly formatted version)
They do what they do.
Thinking about schools and peers and parent-child attachments....I came across one of my favorite posts .
SAT scores on the Rise
Over the last three years, our students' SAT scores have been rising in all categories.
I remember being very discouraged (in the old traditional math days, no less) trying to understand mixture problems because the book we used approached it using tables and grids. When the problem changed a little bit, I couldn't figure out which numbers went into what boxes. I finally learned to approach the problems using governing equations and defining variables.
That understanding didn't come from solving one or two problems. I had to work at it. There were so many times when I thought I understood what I was doing only to feel completely lost when I tackled the homework set. That's when the real lightbulb goes on. Look at any proper math text book and you will see homework sets that give you all sorts of problem variations of the material in the section.
I also want to make a case for speed in helping understanding too. As you move along to more complex math, you need this speed or else you will be completely bogged down. In high school, I got really good at "seeing" right triangles in word problems, even if the triangles weren't explicitly drawn. I was very fast at finding any side or angle given "enough" information. I could state that a length was something like d*cos(theta) just by looking at it. I didn't have to draw a picture and stew over which leg is for sine and which leg is for cosine.
The mechanical monkey paradigm leads to all sorts of wrong conclusions. It also conveniently fits in with their predisposition to equate mastery with rote learning and drill and kill. When they talk of balance, they really don't mean it. They still think it's just for convenience rather than understanding.
This position might seem reasonable when it comes to the basic algorithms of arithmetic, but it falls completely apart as you head into algebra.
I think you are right, Paul. Learned disability - and it's almost impossible to correct in later years.
I see the same in my HS science classes. Elementary computations, numbers make them look like the deer in headlight...They ARE afraid. The ones that are not are either my ESL students who recently moved to the US or "math kids." And please, we don't do anything higher than what in Soviet schools would count as 6th grade... Maybe even 5th.
It's just that immediate "I don't get it" as soon as the numbers are involved.