Calculators

I have generally been a calculator proponent as long as I have been teaching. I have been hot and cold on graphing calculators - for a while, all of our Algebra 2 students had them but in the last few years, we have backed off and required only our Advanced Algebra 2 students to have them. Part of this is financial (remember - just over 50% free and reduced lunch)and part of it has been to have our Algebra 2 students concentrate more on learning the content rather than learning the technology and letting the technology do it for them. I want to make sure students understand what the technology is doing for them and over the years, I have watched students pretty much just let the technology do it and not really get what's going on. But as far as (scientific) calculators, I've pretty much given my students carte blanche. I guess that I've always felt that by the time they're in high school, they should be able to do the operations and letting them use the calculators expedites the process. And as far as fractions go, at this point, it's just easier to let them use the calculator so that we can move past that there are fractions in the problem and do the problem.

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.