Of Babies and Bathwater

Thanks, John, for those kind words.  And yes, I plan on presenting more proofs.

These last two weeks have been busy with end-of-quarter grades, projects, etc.  (A forthcoming post will be "High-school level projects that involve actual mathematics," but I digress.)  This post is reflecting on the not-entirely-successful first iteration of our "no homework grade" policy: nightly homework assignments don't count towards students' grades, but frequent unannounced quizzes use representative homework problems as an incentive to complete assignments and an assessment of whether students know how to do the math.

The data are in and the following seem clear:

• Students are completing less homework.  How much less is unclear, because in the past, the marks on students' papers didn't always correspond to thoughtful effort expended on mathematical problems, but in my upper-level classes, it's typical for only about half the students to have attempted a significant number of problems, and in previous years, it was more like 80%.  In the past, I doubt that the typical homework assignment was copied/scribbled from answers by 30% of my students.  Lower-level classes are doing better on most days.
• Students perceive the policy as "you don't have to do homework," which seems like a misreading to me.  More accurate would be "homework isn't graded and factored into your overall grade." 
• Students are doing less well on in-class tests than they did on last year's tests, although results vary by class.  Classes that are giving a lot of homework quizzes are finding less dropoff, but those same classes have younger students.

In his fabulous book, So Much Reform, So Little Change, Charles Payne dissects the etiology of failed reform efforts, discovering that a pervasive symptom is simply discarding changes that don't work, rather than examining and adjusting them.  In that light, our department is trying to revise our new homework strategy rather than revert to one we found problematic.  Some questions and possible answers:

1.  Why don't students do homework under the new policy, when they can see their grades dropping?  First, they may not see the connection between doing homework thoughtfully and actually getting better at math: it's telling that large numbers of students describe the policy (to parents, counselors, and teachers) as "you don't have to do homework" rather than "homework is important to learning, but you're only graded on what you learn, not what homework you do."  Second, they have a lot of other work--we're suffering from being the "first movers" in responding to Race to Nowhere.  When a student is up at midnight and choosing whether to do math or go to bed, the threat of a possible homework quiz is clearly not enough incentive to do a handful of math problems.

2.  What can we do to improve the situation without throwing everything out?  First of all, we can communicate better about what we think it takes to learn serious mathematics.  Maybe we should take a cue from the advertising folks, and make posters saying "192 minutes is not enough" or comparing time spent doing math to time spent doing other valuable activities?  What if we change the homework quiz policy so that homework quizzes are frequent but expected, for example every Monday and Friday?  What if we specifically identify which homework problem serves as the basis for each quiz question?

3.  What other ways are there to get students to do math outside of class without increasing incentives to cheat or skate by?  Webassign?

This is a tough time for us:  we want to do things differently and better, so we need to figure out how to adjust our course rather than simply u-turning.  Any ideas and suggestions are welcome; we'll take them in the comments.