## Monday, March 5, 2012

### Times Tables

So first the first time this semester, the community college where I work gave me a class in remedial prealgebra (fundamental operations on integers, fractions, decimals, percent, etc.) to teach. Thinking that the class would be largely review, and not knowing where a good starting point would be (you can't always tell if a textbook starting location is good or not for the students in your program), I decided on the first day of class to give a sample pretest of 20 questions to see what stuff was generally easy for the class, and what stuff hard. That turned out to be an excellent idea, and I got some good data I can use to structure the class going forward.

Here's one thing I noticed as the class took the pretest: At least one girl was doing counting on her fingers: like a lot of it, and pretty rapidly, too. So I started wondering about that, because while they were certainly add/subtract problems, that was maybe less than half the test, and I was a bit puzzled at what she could be doing with all that counting.

So later, I asked a more senior adjunct lecturer about it, and here was his claim: A lot of schools now don't bother to teach "times tables" anymore. I guess this would be in the context of the corrosive "concepts vs. operations" argument in basic arithmetic: someone decided that it's most important to know that multiplication is the same as repeated addition, and so the only way students from a program like that know how to simplify 7×3 is to perform 7+7+7 (or worse, 3+3+3+3+3+3+3). And I suppose that would also be consistent with only understanding addition as repeated counting (i.e., perhaps not even memorizing addition tables). So possibly that would explain in this case why so much finger-based adding/counting was going on.

True or False?

1. Not in this neck of the woods, but a lot of this stuff is regional.

There are also multiplication finger tricks that have nothing to do with repeated addition. For example, to multiply x by 9, lift finger x and then the number of fingers to the left of the raised finger is the first digit and the number of fingers to the right is your second digit.

2. ^ You might be right. A few days later, and it seems like the finger-counting student may be one of the sharper eggs in the class. So maybe she was doing something more sophisticated like that.

3. I would tentatively agree with your first impression: a worrying number of college-enrolled students are *hopeless* at recalling basic facts of all sorts. Many of my preservice teacher students need a serious wakeup call to realize that teaching K-7 students will require them to know these facts for immediate recall.

I do think that @Numberwarrior has a point - it can be regional. But in my recent experience, a "region" in which these things are still taught can be as small as one or two classrooms in a school, or one school in a district. And sadly, they seem to be in the minority nowadays. #feelingreallyoldrightnow

4. Update: A lot more finger-counting going on that I first thought. Now I don't think it's anything sophisticated, that's just how some students are still adding/multiplying.

5. ^ ClassProf: And I totally agree, among the fundamental issues here is an inability to remember just *anything at all* from one day to the next.