At the end of my afternoon's work, it occured to me that it is very important to me that my students do some meta-learning, that is, figure out how they learn best. I've often made reflection a formal part of my lesson-planning. Today, I made up a drill sheet of questions involving arithmetic operations with integers. They'll do two minutes with and two minutes without a calculator. They're easy questions. All answers are integer; every question has an operand between -4 and 4; and every operand is between -12 and 12. But I also made a pre- and post-drill reflection sheet. The true/false questions are about their results, areas for improvement, and most importantly their confidence. There is one open-ended question, i.e., what else did you learn about your skills?
The following are the my reasons for this exercise. I'm pretty much trying to convince them to put down the calculator - at least for the easy stuff. We'll work on recognising "easy stuff" later. I think that many students cling unnecessarily and counter-productively to the calculator. I think that the calculator gives them a false sense of security, because they are even more likely to make a mistake operating the calculator as to make a mistake with mental arithmetic. I think they work much faster with their brains than fingers. I expect that weak students will be somewhat better without the calculator but strong students will be vastly better without the calculator. Trust me, I will go over the numbers to see if my predictions are correct. OMG, this is action research. You can take the girl out of OISE.... I'm so ashamed.
My one data point so far is Dion. Of course, it is ridiculous to compare Grade 9's to a Descartes first runner-up but here it is anyway. With a calculator, 80 seconds gets him 16/16. Without a calculator, 80 seconds get him 58/60 and the sense that he's made a mistake somewhere.
BTW, until proficiency with mental arithmetic is in the secondary expectations, I will never deny a student a calculator or even deliberately make them feel badly about using one. Why shouldn't students have a security blanket? Don't students have too many insecurities about Mathematics already?
2 comments:
To this day, I still use my fingers to count time in hours. So afraid was I of the 12 to 1 transition that I never trusted my mental modulo. Even if I don't have do the mod I use my fingers. I think at the point it's more of an efficiency issue. The system works, and is faster than the other system, so why not use it? Irrefutable logic for an impatient person, and all done at the subconscious level.
As an experiment, I think I'll consciously try to remove this crutch. I'll keep you posted on my progress, missus lew. :)
I used to play a game called Krypto.
If you are not familiar with it, it goes like this. You get 5 numbers (cards numbered 0 - 25) and are allowed to manipulate the numbers with - + / or * to match a 6th number. In the classroom, the five numbers are put on the board, the the 6th is reveal to everyone at the same time. An other version of it is to take 5 numbers and try to construct the numbers 1 to 100. In all cases, all 5 numbers must be used.
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