This seems interesting because it addresses the issue of "show your work." Many years ago, I spent a semester teaching the freshman algebra course at the nearby Big 10 university. This is the course that you take if you don't get into calculus. My students were bright kids -- they were all admitted to the state flagship school -- but not mathematicians.
There was huge variation in the preparation that kids brought with them from high school. In particular, very few of them understood what "show your work" means. They were told "show your work," but nobody told them what it really entails. Is it just to provide evidence that you did some work, to deter cheating, or is it something else? Many of my students were taught "test taking skills" such as the guess-and-try method. So on one exam, a question was:
x^3 = 27
One student's work:
1^3 = 1
2^3 = 8
3^3 = 27
Answer = 3
I asked the professors to tell me what "show your work" means. None of them had a good answer! These were the top mathematicians in the world. I wanted to talk with my students about it, but I'm not even sure that my own answer was very good.
But if we did well in math, then we just know what it means. It's not just evidence that you did the work. It doesn't mean "turn in all of your chicken scratch along with the answers." It means something along the lines of supplying a step-by-step argument, identifying the premises and connecting them with the conclusion, in a language that is "accepted," i.e., that mimics the language of the textbook / teacher. In fact, the reason to read the textbook and attend lectures, is to learn that language. (It's not so different in the humanities courses).
At least, that's my take on it, as just one teacher with one semester's worth of experience.
In my view, a problem solving tool that actually addresses the process of building the argument and not just determining the answer, would be beneficial to students.
There was huge variation in the preparation that kids brought with them from high school. In particular, very few of them understood what "show your work" means. They were told "show your work," but nobody told them what it really entails. Is it just to provide evidence that you did some work, to deter cheating, or is it something else? Many of my students were taught "test taking skills" such as the guess-and-try method. So on one exam, a question was:
x^3 = 27
One student's work:
1^3 = 1
2^3 = 8
3^3 = 27
Answer = 3
I asked the professors to tell me what "show your work" means. None of them had a good answer! These were the top mathematicians in the world. I wanted to talk with my students about it, but I'm not even sure that my own answer was very good.
But if we did well in math, then we just know what it means. It's not just evidence that you did the work. It doesn't mean "turn in all of your chicken scratch along with the answers." It means something along the lines of supplying a step-by-step argument, identifying the premises and connecting them with the conclusion, in a language that is "accepted," i.e., that mimics the language of the textbook / teacher. In fact, the reason to read the textbook and attend lectures, is to learn that language. (It's not so different in the humanities courses).
At least, that's my take on it, as just one teacher with one semester's worth of experience.
In my view, a problem solving tool that actually addresses the process of building the argument and not just determining the answer, would be beneficial to students.