Bimodal

I talked with a senior colleague a couple of weeks ago and he mentioned that grade distributions have become increasingly bimodal. There are kids who have high scores and kids with very low scores, and very few students in between. The colleague said it didn’t use to be like that, that the students 20-30 years ago used to simply be better on average, and grade distributions used to be the beloved normal (Gaussian) distributions.

I don’t know how students used to be, but I can attest that the bimodal distribution is the norm rather than the exception in many of my courses. There are students who are obviously getting the material and who could probably take on even more challenge. And there are the kids who are so far behind and who have so many deficiencies from lower-level courses that it’s unclear what it is that they are actually getting from the class, if anything.

The problem with this profile is that you don’t know whom to aim your lectures at. My best-ever teacher in grad school said “20% of the students will do great no matter how poorly you teach, 20% will do poorly no matter how well you teach, but there are 60% of students where how you teach really affects what they learn and how well they do; you want to tailor your lectures towards the 60%.” The thing I see is that there are 40% who are doing well and 40% who are doing really poorly, and 20% who are doing so-so. The people who are consistently doing really poorly likely shouldn’t even be in this major, but I am not sure what to do about it. On account of them, I can’t do what I could do in class with the students who are doing really well. Rather than a near-continuum of abilities, we have a pretty big chasm, such that most of the class is either really bored or really lost. It seems that there are very few people near the average, for whom the middle-centric teaching approach of my former teacher would work.

What I do is try to assign extra homework with some brain teasers for additional credit, and I already give 2-3 extra problems per exam that require a little non-trivial thinking. But the lectures do still get dragged towards the lowest common denominator, which leaves some kids really bored. I am not sure how to teach to a class with such a wide range of skills. Ideally, the students at the very bottom of the curve would get sent back to take some remedial courses, but I can’t see that being a widely acceptable practice as college costs money and everyone is interested in funneling the students all the way through to a degree, somehow. We as teachers are discouraged from failing students, but then the value of a BS degree of good students drops with every poor students graduating despite having learned squat.

Who is the one who tells a student “Maybe this is not a major for you” or “You need to go back and learn some calculus and then re-take the class”? The thing is that what’s best for the student may not be the best for enrollment numbers on which department budgets hinge. Consequently, we go soft on the people who really should not be getting our degrees. I try to mind my own business and am no rebel, but this issue makes me wish I were. It makes me sick that everything is always only about money, and that even our core mission — educating students — has to deteriorate for this reason.

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18 comments

  1. I’m an undergrad at a medium-sized state school, and I’ve observed the same in many of my science classes. It’s frustrating to be in the higher end of the distribution, because most professors handle the problem by teaching to the lowest common denominator. I don’t blame professors for it, but I do find myself skipping class to study the textbook faster, or I’ll start doing homework (either for the same class or a different one) during class.

  2. This sounds like a real problem with the set of classes offered. Why can’t you have an AdvancedBunnyHopping for experts and a basic BunnyHoppingWithoutCalculus for remedials?

  3. y3l2n, many thanks for the comment! I know there are students who would appreciate and likely crave more challenge in how we cover the material, and I know they are frustrated and bored when the class is too easy. All I can try is to offer some delicious nuggets for them to ponder, but not require the rest of the class to do it for credit…

    qaz, this is an advanced elective course for majors, and the material cannot be done without the required math. While it makes sense to offer remedial courses in freshman and sophomore years (e.g. there’s freshman calculus and then there’s the remedial version for those who didn’t really have precalculus properly), once students are juniors or seniors, taking advanced electives and majoring in this field, they need to be able to cut it. We need to ensure they don’t advance to this level, after passing multiple courses, with so many glaring holes in their preparation that they are completely unable to do the work. Maybe being more stern about sending them to remedial courses early on is necessary, but students (and parents) object as it prolongs their studies…

  4. Not only are these students juniors and seniors, this is an elective. It should be OK to have hard electives that require you to really know the math and some easy electives for people who should have majored in sociology.

    What is sad about the bigger picture is I have a colleague who is very big on dumbing it down to be progressive but also thinks we need to send more students to grad school. He is mystified about why the grad schools aren’t interested in our students. It just be that they are irrationally prejudiced!

  5. I can see you’re not an engineering professor. Since we have an obligation to the profession to make sure that the ones who graduate are at least marginally competent, we have no hesitation failing students who can’t (or won’t) do the work. Failure rates of 1/3 are not unusual in beginning engineering courses, partly because people in other fields have been shirking their jobs and giving social promotions to students who did not learn the prerequisite material. Usually upper division electives have low failure rates, because only those students who are interested in the material take them, and students looking for an easy path avoid instructors known for high standards.

    It is common for physics departments to take the same attitude as engineering departments, but unusual for biology to do so (they seem to think that their job is to provide huge numbers of unprepared students for med schools to try to sort through).

    It saddens me when administrators focus more on retention of students than on how much learning those students retain.

    Bimodal distributions of student performance occur in one of my classes that is taken by a mixture of grad students and seniors—most years the grad students average a B+ and the undergrads a B-. There are often one or two students who fail, generally by not turning in half the work—some have failed the course repeatedly, even though the programming assignments change very little from year to year. The gap between the two modes (B+ and B-) is small, but the gap between those who pass and those who don’t is enormous.

  6. I say teach at the level that the material requires, offer advice for things students who struggle can do to catch up, and let the grades fall where they may. If you teach this class frequently, you could record some “lectures to help you catch up” and post them on YouTube. Or you could find an EdX class with lectures that would help the lower performers catch up and recommend those.

    The other thing I’d consider is the fact that sometimes students rise to the level of work expected of them. I can think of several times in college where I felt hopelessly out of my league in the first couple of weeks and ended up with an A.

    But I do not have to deal with the pressures of administrators, so my advice is basically useless!

    @Alex- sociology can actually involve quite a lot of math, and even when it doesn’t- qualitative research requires rigorous thinking, too. I’m not even a sociologist and your comment struck me as unnecessarily mean.

  7. Gasstationwithoutpumps, that was a pretty obnoxious comment.

    I can see you’re not an engineering professor. Since we [engineers] have an obligation to the profession to make sure that the ones who graduate are at least marginally competent, we have no hesitation failing students who can’t (or won’t) do the work.
    All professions have the same duty; I don’t see how engineers’ duty to adequately educate is greater than that of other professions. For instance, I fully expect competence from middle-school Spanish teachers, pediatric nurses, and accountants.

    It is common for physics departments to take the same attitude as engineering departments, but unusual for biology to do so (they seem to think that their job is to provide huge numbers of unprepared students for med schools to try to sort through).
    Making these sweeping derogatory statements about whole fields does no good to anyone. And physical science departments are hardly uniform in what they expect of and provide to students, either for one discipline across the country or across disciplines within a single university.

  8. I am a biologist with a spouse in engineering, and I fail students at about the same rate that he does at our R1.

  9. gasstationwithoutpumps-

    I am not sure that physics is a model of rigor and standards. I teach in a physics department. A few things to keep in mind:
    1) At the intro level, there’s a national movement to “reform” introductory classes. Yes, yes, they swear up and down that they want to improve learning, not lower standards. And yes, one can use certain approaches to engage students without lowering the level of the class. However, there’s a definite reduction of the emphasis on math in all of their workshops and recommended course materials. They are absolutely determined to make the US second-rate in introductory physics. Meanwhile, they go on about how we need more Americans in grad school, while urging that we lower the level at which American undergrads are taught.

    There are also some rumors, which I will not repeat, of more recent administrative….suggestions to improve retention in “bottleneck” courses. I’m not saying anybody followed those suggestions…this time. But keep the pressure up, and have the intro classes taught by the people with the least security, and what do you think will eventually happen?

    2) At the advanced level, there’s long been an understanding that the tests will be hard but the curve will be generous. If passing a 4-question test with 40% meant that somebody got one hard calculation completely correct and got significant parts correct on one other, well, great. They know how to do one hard thing and do it well, and they know at least something about something else. Give them a passing grade. If, OTOH, it means that they got bits of partial credit here and there, that’s a problem.

    And in the economic downturn low-enrollment majors have been under a lot of pressure to either grow or shut down. In an environment like that, does anybody really think that standards will go _up_ at most schools? You really think that the push to retain more people will raise standards?

    Cloud-

    I grant that sociology research can be very challenging and rigorous. Any field of scholarly inquiry can be pursued in a rigorous manner. However, some majors definitely attract stronger students than others. The quality of a randomly-selected undergrad is a different issue than the quality of high-caliber faculty research.

  10. In my uni, we say the same thing not about sociology majors, but about poli sci majors (in fact, my DH used to teach in the engineering dept that was the middle of many a student’s path from EE to Poli Sci– it was demoralizing). At the uni where my mom works, it’s communications majors. At my undergrad it was linguistics, at my grad it was business. All these majors can be hard-core or they can be trivial, depending on where they are. I assume sociology is just the gut major at Alex’s school.

  11. I apologize for the snideness of my comments. I agree that all fields *should* have similar duty to ensure competence of their graduates and my remarks about biology departments were too strongly worded. I have not noticed that faculty in all fields feel that it is their duty to ensure competence in their grads—some seem to think that is their duty to provide BA degrees independent of performance.

    It has been my experience (at a very small number of universities, so possibly a very biased sample), that the engineering departments have experienced much less grade inflation and have much more willingness to prosecute academic integrity cases than other departments.

  12. xykademiqz, over the years, have you also noticed at you place that more and more students have to work and earn money on the side as a necessity. I wonder the bimodal distribution is correlated with that.

  13. Good point, TheGrinch. I don’t really know what percentage of students have to work on the side and if that’s changed in the last couple of decades…

  14. I *increasingly* see this bimodal distribution in my classes. Some of those at the lower performance levels are definitely a result of trying to do too much. Many of my students work full time jobs and try to go to school full time too and usually are also raising families. They just can’t keep up and they end up doing nothing really well.

    But my other observations are that there really are two groups of students who are widely separated in their skill sets. I believe it has a lot to do with socioeconomic status. Those students who come from more affluent families have had better schools, more help at home and are much more prepared for college.

    I teach at a public university (research intensive). We, along with many other state universities have implemented rules about graduation numbers. Here it is called “low yield”. The short description is that every program has to be graduating a certain number of students. If you don’t meet those numbers, then the state can and will simply eliminate your program – whether you have tenure or not doesn’t matter. Of course, departments such as biology & chemistry can usually attract enough students so that this doesn’t affect them. But other programs such as geology and physics may not. So there is huge pressure on us to just graduate students no matter their skill level.

    The nation has been brainwashed into believing and treating universities just like businesses – and students are just like cars on an assembly line, except that no quality control is required (except for programs that require testing to meet certification). The bottom line is that if you require them to meet your standards, and if they don’t and you fail them, you could be out of a job pretty quickly. Even the best of us can give up in the face of that (after all we have families to feed too).

    Regarding the comment about separating such classes as described in this blog into two: Here again we are forced to not do that because it is all about money. In order for universities to make money or even break even, we are being pushed to teach fewer classes and to larger audiences. It is all about money and FTEs. If your department doesn’t bring in enough FTEs (e.g. teach more students per cost of the faculty member) then they eliminate the entire department (once again tenure doesn’t matter). So we are teaching fewer and fewer specialized courses and instead are being forced to create classes that attract greater numbers of students – and part of that attraction means dumb it down. Our astronomy course for example is a complete joke. Students can get an A in that class for just paying for the credit.

  15. I switched over to a 2 “midterm” system, and this seems to improve things a bit. Rather than have a midterm in the middle of the semester, I have two exams 1/3 and 2/3 of the way through. After the first exam, a lot of the unprepared students drop (this is a required sophomore level science course with calculus as a prereq). This year, I lost close to 20% of my enrollment from the first day of classes to now.

    My first exam is extremely bimodal, with a nearly empty middle (but a higher mean grade). My second exam has a lower mean grade, but is less bimodal, with more students in the C-B range. It looks like a lot of the weaker students either drop or take their awful grades as a kick in the pants to get to work. Since this is a required course, I have had the same students as many as three times before they manage to pass.

    I have the same problem you mention with my lectures, though. I have a hard time leveling my material. I try to include some tasty tidbits from my research and from the current literature, and I have had some great discussions with my more advanced students in my office hours. Even since I started with this course 5 years ago, I have seen major deterioration of the math skills my students have. I now send them to remedial websites. Almost all the professors I know have noticed that many students now seem to regard prereqs as checkboxes towards their degree rather than preparation for more advanced material, and act shocked when they are expected to demonstrate mastery of background material in a new class. I feel like I am one of the few holding the line against dropping to the lowest common denominator at times, though, and it is tiring. The mean grade in my course is relatively low, and my course is often the lowest grade my students will receive.

    PS I like your new blog. I admit I got overwhelmed with life and had to give mine up for now…

  16. Prodigal, it’s really good to hear from you! I hope things are going well. You must be going up for tenure soon, right?
    N.B. Prodigal Academic and I started blogging around the same time way back in 2010 (I think Female Computer Scientist started around that same time, too.)

  17. A long time ago Eli noticed at the sharp end of a needle, a long one, that quacks hate chemistry professors such as he is but loved their medical school. why is that he asked, well simply no one fails out of medical school because G and O Chem pretty much do the sifting for them, that and the MCATS.

    This, and some sense of self preservation gave rise to the thought that it was not the job of chemistry departments to play the bad guys with the ambitions of all the students in the world.

    The way to do that of course is to figure out why the students are failing, and a bit of looking at the cross-correlation with math placement tests and other things showed that well, the best predictor was math skills, so we upped the pre-rec to pre-calc. (There is some good research on this from Robert Tai at UVa and it goes for all of STEM, that the best predictor is the last math class in HS)

    At which point the School of Nursing went upside our heads to the Provost. Of course, they would not send their students to a Health Sciences Chemistry course we had set up.because their accreditors would not have that.

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