Homework and Worksheets

This Foxtrot cartoon strip has been circulating on the internet these days and raises the question of the relevance of completing homework or in-class worksheets.

Adults may recall that when math homework was being assigned in the 1950s,60s,70s instructors often said, "Do questions 1, 4, 7 and 9" There were two reasons for this. First, those were the questions that had the correct answers in the back of the textbook--the answers to 2,3,5,6 and 8 were wrong. There was a famous study of math textbooks that found that something like 38% of the answers in textbooks were wrong, because *sloppy*. Wrong answers in textbooks drove students insane, of course, as they worked and reworked questions trying to figure out why their (correct) answer didn't correspond with the (incorrect) answer on the answer key. On the whole, textbooks are held to a higher standard these days (in math, anyway) so that's less likely the reason your instructor is skipping questions now.

Which bring us to the second reason: worksheets and textbooks have more questions than necessary to demonstrate a student's knowledge. Pratice makes perfect (okay, makes satisfactory) but some students need more practice than others. Even great students are going to blow the occasional question through some silly mistake or through misunderstanding the concept. Consequently, they need a second or third practice question to see if they have the concept or can avoid careless mistakes this time. Weaker students may need to work through half a dozen examples before feeling confident they have it. So I don't have a problem with worksheets/homework that provides a lot of examples, or with teachers who chose questions 1 and 4 to start with, because 1 tests a different concept than 4, so teacher needs to see both of those, but not necessarily 2 and 3 if 1 was done correctly.

But that does bring us to the question raised by the above meme: if a student has demonstrated his proficiency with a sufficient sample, should we be wasting the student's time by penalizing not completing every question. Obviously they can't stop half-way through the sheet because later questions may get harder, and we need to see if the student is up for the more challenging examples; or later questions may test quite different concepts. But young Mr. Fox has it right when he did a representative sample of questions from which it would be reasonable to coonclude he had mastered the skill being tested. Too often teachers confuse means and goals, enforcing completeness rather than trying to identify if the student has particular skills and knowledge. The purpose of any assessment is to find out what students know and can do, so that the teacher can (a) reteach missed concepts and (b) know whether it is possible to move on to the next learning objective. Too often, however, worksheets and homework become about which students can tolerate tedium, are the most compliant, and who never question whether directions make sense.

I like to think most teachers are interested in teaching concepts and skills, not subservience to authority figures. Yet I regularly encounter instructors who say things like, "This student is one of my best, they know the material backwards and forwards, but I can only give them 50% because they never complete their work." No, that's not a bad student, it's bad assessment. If your sense is the student knows their stuff, and (if one took the time to actually look at their worksheets/homework rather than just run over it with an answer key to document whether they are covering all the necessary concepts and difficulty levels, then assigning them a lower grade is simply inaccurate. If you're going to use worksheets/practice homework, get it right.