As I have mentioned a couple of times, I am on a committee with both high school and higher education faculty that is working on lessening the number of students who require remediation when they enter college. We were talking about how students end up in the "remedial" mathematics classes and one of the college faculty made the remark that if a student couldn't multiply a 2-digit number by another 2-digit number by hand that he or she would automatically end up in the lowest class. In my mind, that seemed rather harsh, especially since calculator use is highly encouraged in our classrooms and have been since middle school. Why in the world would a 4th grade skill automatically preclude a student from progressing to a higher level math course when technology is so readily available and expected to be used? So, I asked. The college faculty member replied that it has to do with transferring from numeric to algebraic. If a student can multiply a 2-digit number by another 2-digit number, he or she can use the same process to multiply a binomial by a binomial - it is the same process. It has to do with number sense.
Later in the meeting, a different college faculty member made some of the same points. (He didn't come in until later in the day, so he had missed the earlier comments.) He mentioned fractions, signed numbers, and decimals as the basic skills that students should have and that students needed to understand the concepts behind them. Like with multiplying, these are concepts that resurface in mathematics. I have certainly seen this as we have worked with rational expressions. If students don't understand how to work with numeric fractions, how are they going to transfer that to algebraic fractions?
So now I am sitting here this evening starting to rethink calculators. On the one hand, I have students who have struggled with basic facts and are (mostly) able to work with algebraic concepts using the calculator to handle the computation. But am I doing my students a disservice by providing them the calculator? What if I didn't allow them calculators at all at the beginning of the year and tried to remedy the issues that came up? Would I even get anywhere? Maybe what makes more sense is as I am introducing the concepts that tie into those earlier concepts - introducing multiplying polynomials, for example, that I begin with the number sense concept that preceded it. It would take some research on my part - although with the Common Core State Standards, the progressions have been fairly well-documented. By taking the time to (briefly) review the numeric concept, maybe students would have a better handle on the algebraic concepts. It's a thought. I need to think a little more on this one.