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Re: ideal student
Posted:
Jul 29, 1995 8:04 PM


I teach high school math  algebra I and geometry. I have taught everything from seventh grade math through algebra II. At the junior high level we used to complain about the preparation the students had received at the elementary level and at the high school level we complain about the junior high level. When I read this list I see college teachers complaining  usually gently  about the high school level. After several years, I have come to the conclusion that all of us are trying hard and often feel that the students we are given are not prepared for the courses we teach. The result seems to be superficial learning with little real understanding  thus little retention.
The one thing that would make the most difference in my students would be the willingness to WORK for an answer. I find that students want to attack their paper with a pencil, do some quick arithmetic, and have an answer. (That is frequently what they have with this approach  an answer. Of course, it may have nothing to do with the problem.) Children seem to think that mathematics is just computation. They give up if a problem requires planning, testing, writing more than two lines, or thinking. They truly believe that if they can't solve a problem immediately, then I didn't teach them the correct procedure. They truly don't understand that, beyond drill and practice type exercises, A procedure can't be taught because you must plan your approach.
On the same line, a problem requiring much writing is greeted with, "All that for ONE problem?! That's too much WORK for one problem." I would really like it if all teachers outlawed "scratch" paper and insisted that all work be written on the hand in paper  including false starts and mistakes. So many students want to hand in "neat" papers, so they fastidiously erase work, do their henscratching on throw away paper, etc. Maybe a solution for this is for teachers, from K on, to appreciate the value of mistakes and corrections.
The last missing skill that I think is so important is the willingness to write down their procedure even when the computation is simple or a calculator is used. Here is a sill example: At 4:00 PM Jane bought 3 pens at $2.00 each. How much did she spend? Well 4+2=6 and 2*3=6 so simply writing $6.00 doesn't tell me they understood the procedure. Likewise 2*3=5 is obviously a lapse of attention to detail, but the mathematics is clear.
Of course, all students should master the skills expected at each level before proceeding to the next and we know that that is not universally the case. I especially think that understanding fractions in their various forms is a weakness and essential for success in mathematics. Many students don't really accept fractions  and mixed numbers  as numbers.
I hope this post isn't too long. Thank you for the question!
Katherine :)



