Since retirement, I have been tutoring several students in a variety of grade levels from 1st through 7th. Each and every one of them required help in math. It seems that in math instruction, the focus is on concepts first and foremost. Now, I agree that understanding concepts behind learned responses creates deeper understanding and application. However, I also believe that for some students, the procedure needs to come before the concept is recognized. Math-minded students (and yes, I do believe some of us are math minded and some are not so much!) can learn concepts and hold onto them in order to apply them to appropriate problems. Students who are not so "math-savvy" need to have the concrete problems, and process to solve them, first, in order to have something to which the concept can connect. They need connections to previous learning that is concrete rather than conceptual.
Unfortunately, classroom teachers have limited hours/minutes in the day to address both kinds of learners. Needless to say, the math-minded students move more efficiently and successfully through the long list of objectives required, and the less-math-minded students, needing more time and effort, have hope the first week of school only to see it wear away steadily and quickly as the concepts pile up.
Fortunately for me, I get to take the time to fill in the gaps with the concrete strategies and watch the light come to their eyes when they"get it"!!
