The end of homework
Cross-posted to POWIP.
Hanging out at one of my regular spots lately, I noticed an ad for Bing. It had some generic picture of a chalkboard with equations on it linking to this search.
So teachers don't have to worry just about students copying-and-pasting from Wikipedia for term papers, but also search engines that do the kids' algebra homework.
And the tools developed for the the arms race in English essay will be useless in math -- for plagiarized papers, one can look for copied text. One expects the exact same stuff in math problems, because while there may be a few ways to get to the answer, the end answer is supposed to be the same for everybody.
So my modest proposal is just to get rid of [graded] homework. Sure, give students exercises to do, so they can check themselves for comprehension, but when every class's homework can be done just by going to a search box, there's really no point in grading it.
So let's not waste anybody's time, and make everyone do their work in class itself. Short, daily quizzes ought to do the trick. Also, do them at the very beginning of class. Should inspire punctuality. Oh, of course, no calculators or iPhones allowed...
I'm a big proponent of technology use in instruction [after all, I teach online], but often people think that because a computer can do it for them, they don't need to learn to do it in their heads. After having dealt with one too many college calculus students who didn't know algebra [and forget about arithmetic] I wrote the following:
Why am I allowed now to use the computer programs that I disallow my students? Because I already know how to do these and through my experience, know what answers to expect. Technology nowadays allows the taking of a derivative, minimization of a function, numerical and symbolic integration, plotting of a complicated function, and much more difficult mathematical tasks with little effort on the part of the user of the technology. However, students often get incorrect answers, mainly because they are asking the wrong questions.
Of course, Wolfram Alpha came out last year, and long before that, HP and TI made plenty of calculators that did symbolic operations, even taking derivatives for the students. But they often got wrong answers, as noted in that post from 2000. Just as some students often copy-and-paste stupidly from Wikipedia, I wouldn't be the least surprised that those using Bing to do their algebra will get some basic things, like order of operations messed up.
So to answer all the students I had, who wondered why I banned calculators from my class, and to answer "When am I going to use this? Why do I have to do it by hand when the computer can do all the tedious stuff for me?" I respond:
A computer or calculator will give error messages if you misspell a command, don't give it enough inputs, or ask it to calculate something impossible (like log(-3)... a calculator will probably spit at you, but Maple will give you an answer... try it out, and think about it). However, a calculator or computer will not yell at you: "Those are the wrong limits for that integral!", "No, you're solving for the wrong variable!", "You want to multiply, not divide!". These are things only your brain will tell you, and you must train it accordingly.
The "tedious" math you practice now will give you mathematical intuition and flexibility. The math problems you will be doing in 40 years are not the math problems you are doing now; you will probably not have answers in the back of the book or examples you can copy. You may do no math problems whatsoever, you think. How about planning for retirement? How about estimating the surface area of walls you need to paint? What about comparing two possible car buying options? What about trying to understand newspaper articles about statistical results of medical research? Or demographic change? These are not necessarily about using a calculator, but knowing what you need to calculate.
Hanging out at one of my regular spots lately, I noticed an ad for Bing. It had some generic picture of a chalkboard with equations on it linking to this search.
So teachers don't have to worry just about students copying-and-pasting from Wikipedia for term papers, but also search engines that do the kids' algebra homework.
And the tools developed for the the arms race in English essay will be useless in math -- for plagiarized papers, one can look for copied text. One expects the exact same stuff in math problems, because while there may be a few ways to get to the answer, the end answer is supposed to be the same for everybody.
So my modest proposal is just to get rid of [graded] homework. Sure, give students exercises to do, so they can check themselves for comprehension, but when every class's homework can be done just by going to a search box, there's really no point in grading it.
So let's not waste anybody's time, and make everyone do their work in class itself. Short, daily quizzes ought to do the trick. Also, do them at the very beginning of class. Should inspire punctuality. Oh, of course, no calculators or iPhones allowed...
I'm a big proponent of technology use in instruction [after all, I teach online], but often people think that because a computer can do it for them, they don't need to learn to do it in their heads. After having dealt with one too many college calculus students who didn't know algebra [and forget about arithmetic] I wrote the following:
Why am I allowed now to use the computer programs that I disallow my students? Because I already know how to do these and through my experience, know what answers to expect. Technology nowadays allows the taking of a derivative, minimization of a function, numerical and symbolic integration, plotting of a complicated function, and much more difficult mathematical tasks with little effort on the part of the user of the technology. However, students often get incorrect answers, mainly because they are asking the wrong questions.
Of course, Wolfram Alpha came out last year, and long before that, HP and TI made plenty of calculators that did symbolic operations, even taking derivatives for the students. But they often got wrong answers, as noted in that post from 2000. Just as some students often copy-and-paste stupidly from Wikipedia, I wouldn't be the least surprised that those using Bing to do their algebra will get some basic things, like order of operations messed up.
So to answer all the students I had, who wondered why I banned calculators from my class, and to answer "When am I going to use this? Why do I have to do it by hand when the computer can do all the tedious stuff for me?" I respond:
A computer or calculator will give error messages if you misspell a command, don't give it enough inputs, or ask it to calculate something impossible (like log(-3)... a calculator will probably spit at you, but Maple will give you an answer... try it out, and think about it). However, a calculator or computer will not yell at you: "Those are the wrong limits for that integral!", "No, you're solving for the wrong variable!", "You want to multiply, not divide!". These are things only your brain will tell you, and you must train it accordingly.
The "tedious" math you practice now will give you mathematical intuition and flexibility. The math problems you will be doing in 40 years are not the math problems you are doing now; you will probably not have answers in the back of the book or examples you can copy. You may do no math problems whatsoever, you think. How about planning for retirement? How about estimating the surface area of walls you need to paint? What about comparing two possible car buying options? What about trying to understand newspaper articles about statistical results of medical research? Or demographic change? These are not necessarily about using a calculator, but knowing what you need to calculate.