I’m a great believer in luck and I find the harder I work, the more I have of it. -Thomas Jefferson
It’s the end of the semester at my college as well as at many schools across the world, and I’ve spent the last week or so grading final exams. And while I was doing it, I noticed something astonishing. But let me start at the beginning.
Introductory physics — without calculus — is one of the most notoriously challenging and rigorous classes that students pursuing a career in health, including doctors, nurses, pharmacists, veterinarians, and physical therapists, face in their college career. It also has a reputation for wiping students out, and (among faculty) for giving even the best professors terrible evaluations.
The reputation of introductory physics at my college is no different. So when they asked me to teach introductory physics this past year, I knew what I was getting myself into. And the first question I asked my department chair? “How does homework work for this course?”
Why should this be so important? There are three main ways I know of to do it while still requiring each student to do their own individual homework (which I support). Each has its own advantages and disadvantages. What are they?
- The classical way: students work and turn in the homework, the professor grades and returns it. The advantage? Students get their homework evaluated with the greatest care and accuracy, and get the best feedback they can: direct from the professor. They will find out what they did wrong and where they made their mistakes. The cons? It takes a long time for one professor with many other time commitments to do this. This is not just a con for the professor, it’s a disadvantage for the student, who has to wait for the professor to grade every homework in the class — by which time they’re usually mired in the next assignment — before they learn what they did wrong.
- The expedient way: students still work and turn in the homework, but instead of grading it, the professor makes up an answer key and hires a grader. The advantage to this is that students still get their homework evaluated and checked by a person, and they’ll get it back more quickly (within a day or two for a good grader). The feedback they get will still often be useful and helpful, but is usually lower in quality than you’d get from the professor directly. The same downside still exists, however. By time a student gets their graded assignment back and learns what they did wrong, they’re on to the next unit in class. But there is an option for faster feedback…
- The instant-feedback way: students turn in the homework online. As unbelievable as it may seem, this is relatively new to the scene (within the last decade or so), but it’s catching on in popularity for one major reason: instant feedback. As students work through the problems, they submit their answers as they go, and are immediately told by the program whether they got it right or not. In other words, they get to learn whether they’re doing it right or not as they’re doing it. The cons are that — while the expediency of the feedback they get is unparalleled — the quality of the feedback that they get is much lower than the other two cases.
And that’s really it: the three major options. My department was going with the second one, but I wasn’t sure that was the best route. What did I decide to do?
I went with the online assignments, with the caveat that I would hold office hours and run a help session every week the day before homework was due for people who needed more guidance than the online system could offer. I think the homework system was set up to run very well, despite the bugs inherent in any online homework.
But it also allowed me to do something very interesting: set up online grading to my specifications. I chose to allow students an unlimited number of tries on each problem, and to give them no penalties for incorrect answers. So long as they were willing to work through their difficulties until they got the right answer, I reasoned, they should receive full credit for their homework. Who cares if you get it right the first time? I care that you get it right in the end.
My idea behind it was that students who were diligent — regardless of their initial aptitude — would learn the skills they needed to in order to do well. And I thought that, if this idea were any good, their grades would bear this out. And I was quite pleasantly surprised; over a third of my students worked hard enough to get 99% or more of the points available on the homework throughout the semester. There were also many who did most (but not all) of the homework, usually giving up on a few problems that gave them the most difficulty. And finally, there were the people who — I would say — didn’t take the homework very seriously. These were the students who did the homework when they felt like it, but didn’t even attempt some of the problems, and maybe had weeks where they didn’t do one of the assignments at all. Any student with a homework score of 85% or lower fell into this last category.
But would it matter? Would the more diligent students perform better than the others? Would the kids who didn’t do all of their homework prove to me that they didn’t need to do all of that homework? Well, it’s the end of the semester, so we can look at the data. If I divide my students up by homework scores, how did they fare overall in the class?
(Each category of student has been normalized to 100%. And yes, some of you will lament the grade inflation. It’s okay, I can take it.)
Amazing! Of the kids who worked through practically all of the homework, there was one B+, and everyone else got A’s or A-’s. While if you look at the kids who often gave up on the homework, not a single one scored better than a B.
And before you think to yourself, “well, Ethan probably just counted the homework heavily in their final grade,” I’d like to show you something else. Here — again, organized by the amount of homework successfully done — are the averages of the three groups on the final exam.
I even made a deal with everyone in the class: if you score better on the final exam than your cumulative grade to this point, your grade on the final will be your grade in the class. In other words, if you can achieve the goals of the course by the end of class, that trumps everything else; a student who did no homework but got an A on the final would get an A in the course.
And what did I find? A bunch of people got A’s on the final and hence A’s in the course, but of the students who did the least amount of homework? The highest grade on the final was a B. The best indicator of how well a student did was how diligently they approached the homework. It didn’t matter whether it took them one hour a week or fifteen hours a week; what mattered was whether they worked until they got it. This was something I should’ve expected from reading Malcolm Gladwell’s Outliers, but I had never expected my class’ results to show this stark of a difference.
So I got to see — as a teacher — just how plainly hard work pays off. If you do your work until you get it right, you succeed, and if you don’t, you don’t. I’m sure many of you have far better stories than I just told about how important diligence and a solid work ethic is, and I’m sure that many of my students next year won’t believe me even after I show them this data. But whether they believe it or not doesn’t make it any less true, and I’ll show you next year’s results when I have them! But enough from me; what are your thoughts?
(And to those of you wondering if this post is two days late because it took me that long to figure out how to generate charts like this in Excel, you’re way off. It shamefully took me two days to give up on Excel and do it in OpenOffice.)
Update: This is the scatter plot of homework score vs. final exam score that James @3 asked for. (See below.)