Tuesday, November 30, 2010

Shift, paradigm, shift!

This morning was painful.

I had the uncomfortable task of watching 30 of the students in my morning Calc I section puzzle their way through a difficult (but fair, I feel) exam, their last "mid-term" exam of the semester and a traditionally hard one (on applications of the derivative). This awful duty was the last straw.

The penultimate one came yesterday: I was called upon to help adjudicate a case of "academic dishonesty" (to use the lovely euphemism) in a colleague's class. This colleague wanted to know if the students in question had indeed "cheated" (to stop beating around the bush). After cursory (and then more in-depth) inspection, I agreed that yes, indeed they had.

However, to me the incident said more about the culture of the academy than it did about the "dishonesty" in which the students were involved. More specifically, the students were clearly guilty of "cheating," but to me the more crucial issue concerned why it is they felt the need to "cheat" in the first place.

To "cheat" requires that there be a "game," and that it matter that people follow the rules of that game, and further that it matter that in order to succeed at the game one must "do better" than anyone else playing the game. This was definitely the case in this particular course: the students had been given a (very) high-stakes exam, which to them was more than an assessment instrument; it was moreover one of a very small few means of receiving feedback on the degree to which they were mastering the concepts of the course the exam was given in. To them, "cheating" on the exam was a natural response, given the way in which they've been acculturated to consider the exam a must-win game in which success is measured by high marks.

The point I'm getting at is the following: the more we as educators eliminate, or to the greatest extent possible downplay, the competitive aspect of education (high-stakes testing, rigid and number-driven grading schemata, individualistic learning paradigms, etc.), the less likely we are to find our students "gaming" the system by engaging in "cheating." In some regards, "cheating" will cease to exist, as it simply will have been defined away.

As I hinted above, most "cheating" (I truly believe) is undertaken as an act of desperation, a means of coping with failure as measured by receipt of lower-than-average academic grades. "Cheating" is a means of striving to succeed within a system which provides extrinsic rewards for optimal performance rather than intrinsic rewards for authentic mastery and authorship. I cannot but believe that the vast majority of students would welcome an academic system in which the goal is not to earn high marks but rather to learn, and that students accustomed to this system would see no need to game the system by "cheating." I'm not so naive as to suppose that every student will respond well: there will always be those so acculturated by thirteen-plus years of a largely competitive educational system that it's in their blood to fight tooth and nail for every last percentage point that might tip them from a B+ to an A-...but I believe that even those who are very comfortable with this traditional system will abandon it if given the chance to do so.

All of this gets me back to this morning, and the thoughts I had as I watched my Calc I students (even the strongest of them) wiggle and squirm in completing their in-class exam, stressing out not over whether or not they'd really learned the concepts we've been working on together for the past few weeks, but rather over the grades that will unmercifully adorn their papers when they get them back tomorrow morning.

My thoughts can be boiled down into two short words: no more.

No more in-class exams. Ever. I'm through with them. The one I gave this morning (and will give again in a couple of hours) will be my last.

For quite some time now I've not given in-class exams in my upper-level courses, feeling that little meaningful could be asked on such exams, aside from requiring students to parrot already-proven theorems or give short answers to requests for definitions. In these courses, in-class exams offer none of the opportunity offered by take-home exams to ask authentically engaging and probative questions, and therefore I've found them pointless time-sinks.

For quite some time now I've resisted the banishment of in-class exams from my first-year courses, thinking, I suppose, as I've heard some of my colleagues to think: "there are certain computational techniques the students will have to learn to perform, and to perform quickly." True, but even the most straightforward computational skills will be as well developed (and much more readily understood) if performed in the service of completing the more meaningful, authentically engaging exercises included on take-home exams. This is as true in Precalc or Calc I as it is in Abstract Algebra I or Topology. Even in lower-level courses take-home exams offer a much more meaningful sort of assessment, and even if those exams are still meant as individual exercises and not collaborative ones (of the sort with which I've been experimenting in Linear Algebra this semester) they go much further than do in-class exams in encouraging a culture of collaborative engagement, simply by downplaying high-stakes individualistic assessment.

Keep in mind that I'm not boo-hissing exams entirely: exams offer students a means of reflecting on the ideas they've learned for the past ___ weeks, and if properly responded to they're fantastic tools for giving students feedback. Well-designed and well-delivered exams give students a healthy way of furthering their learning and assimilating their knowledge as they think critically about it. Exams are here to stay.

In-class exams, however, for me will soon be a thing of the past.

I've already responded to a couple of concerns I anticipate colleagues (and even some students...very bright ones, in fact) might have about this decision of mine, but let me respond to a couple more hypotheticals.

Colleague/student: "If you de-emphasize high-stakes individualistic exercises like in-class exams, some students will game the system and prop themselves up on others' work without really learning anything themselves."

Me: "No matter how you set the system up, students are always going to find a way to game it. Gaming the system I propose means cheating themselves out of learning. Gaming the system as it currently stands involves engaging in a behavior that's viewed as sociopathic but is really little more than a symptom of deeper systemic problems. I find the former course far less pernicious. Sure, there'll always be students who frankly don't give a shit, but we're not going to serve them well in any system, and with a system more conducive to authentic learning, they might just pick up a thing or two along the way."

Colleague/student: "You can tilt at as many windmills as you'd like to in your own little class, but you've got to assign grades at the semester's end, anyway. Won't the system you propose result in massive grade inflation?"

Me: "My response to this concern is twofold. First, in courses in which I've begun doing away almost entirely with individualistic activities (begun in Foundations, Topology, and Abstract Algebra I and II in previous semesters, and taken to the extreme in my Linear course this semester), I've seen little noticeable change in the final grades for the courses. This was true even in Topology, in which students had unlimited opportunity to revise and resubmit all work, with no constraint on collaboration. I simply don't see evidence for grade inflation. Second, even if there were grade inflation, so what? It would be incredibly difficult to determine whether students' grades were made higher because they were bracing themselves on each other ("gaming" the system in the sense expected by my first colleague above), or simply because they'd actually managed to more richly and more fully understand the ideas addressed by the course. That is, maybe the grades are higher for a reason: the students are actually, for the first time in their lives, getting it."

I truly feel this way.

Moreover, I truly feel that I've become proficient enough as an educator that my courses offer the sort of rich collaborative learning environment wherein in-class exams no longer serve a meaningful purpose. They're simply anathema to my teaching philosophy, and they're counterproductive to my goal of establishing a safe, stressless, and supportive setting in which we can all learn from one another in robust and authentic ways. From here on out, they're gone.

Before I leave, let me pass my apologies on to the students currently enrolled in my Calc I course: I'm sorry that you had to suffer through the last iteration of this practice. I know how hard the topics you're being tested on are, and I'll keep that in mind as I respond to the exams tonight. I'll respond to them not with an eye toward giving you a grade, but with an eye toward letting you know how well you're learning. I hope you'll receive them back from me with the same thoughts in mind.

One last note: I should point the interested reader in the direction of Alfie Kohn's No contest: the case against competition, about which I've blogged before, and which over the years has probably proven to be the single book which has exerted the greatest influence on me as a teacher. It should be required reading for all educators, at every level.


Anonymous said...

Thanks for sharing all of these thoughts with us. With having no experience of living in an academic world where an emphasis on grades was put away and an emphasis on really learning and understanding was put in place, this peaks my interest. As someone that is looking at teaching and facing the same issues, I find the idea of not giving in-class exams and trying to accurately and fairly test knowledge with take-home exams to be a rather daunting task. I hope that as you journey into doing this with all of your classes you will continue to provide us with feedback about how this concept is playing out among your 100 levels classes.

Good luck and thanks for your investment into the learning of so many young people!

Anonymous said...

As a student (and a former student of yours), I honestly don't know if I would do well without competition. I don't know if it's because that's how I've always been taught, or if it's because I'm competitive by nature, but competition is a driving force for me in class. Of course I do care about absorbing and retaining knowledge more than the rush of competition, but it is a fun push. I've never liked take-home exams, unless they're in the form of an essay for a humanities class. I feel like an in-class exam tests my learning better and provides me with more useful feedback than a convoluted take-home exam. Take-home math tests always feel like a puzzle, you work with it and you piece it together- but, then what? It's always such a stretch from the basic course concepts that it ends up appearing (at least to me) as if it has nothing to do with the core concepts, and therefore doesn't reflect my knowledge of the subject. The stress shifts from caring to learn and score well on exams, to just solving that puzzle so I can turn it in- and score well on it. So essentially, competition remains if you're competitive (like me), and your focus will shift to your ability to solve puzzles with little regard to what has been learned or how it can be applied outside of this puzzle. How can you (the professor) or I (the competitive, traditional student) transform this thought process? How can I believe in this initiative and cope with it? Basically, how can I see, through take-home exams/puzzles/exercises, that I can apply what I (hopefully) learned to everyday, mundane questions in a practical work-field?

I think you're an amazing professor, and I'm not trying to rain on your parade - but I'm just sparking conversation, asking questions from the mind of a competitive student. I understand that there's no way to make everyone happy, and I don't expect everyone to be comfortable with my suggestions. These are just ideas I thought I'd share with you, presenting a different side of the argument.

Anonymous said...

As a current student in your calc 1 second section, I feel like I just completely bombed that test. I felt good about the concepts but once I saw it I just fell apart. I couldn't stop looking at the clock and hear other students moan. That's right, I heard people moan. I dont think the test was unfair, at all. I just don't think I realized the complexity and depth of some of the concepts on the test.

I once had a chemistry class where the instructor had a lot of hope problems (namely an epilleptic newborn daughter) so we almost always had take home exams. I feel like my knowledge of chemistry to this day is better than that of some other people who took her on a different semester. When I have the ability to work on something at home, I have the ability, then, to perfect my work. The hardest chemistry test I ever took was a take home exam that took me 10 whole hours. I got a 100 on it.

I agree with you, I do not think that forced, in class tests are the way to go. There are about a billion arguments that can be made for an against this. But I'm for it. This is not because of my dismal performance on your test today, that is solely my fault. I am sorry for not putting forth the effort for you that you put forth for us.

DocTurtle said...

My immediate response to Anonymous #1 would be the following: are you sure that the goal of a course is to instill an understanding of "core concepts"? Wouldn't a better goal be to help students learn how to solve realistic problems (even if they sometimes appear as though they are quite far removed from those "core concepts")?

My second response would be that you likely are the way you are because you've been trained by those 13-plus years of education to be competitive. You can't help who you are, and I don't want you to change, at all. The best we can do, perhaps, is to learn to get along with one anothers' idiosyncratic ways of doing business.

Thank you for your advocacy of the other side! I honestly don't know who you are, but I can tell you're a thoughtful student. I definitely don't claim this is a one-sided, cut-and-dried argument; I don't claim cogent arguments simply don't exist for the other side...I do, however, claim that to me the benefits of in-class testing are outweighed by the detriments.

Bret Benesh said...

Hi DocTurtle,

You go, and I hope to follow soon. As always, post your detailed plans for next semester to the weblog as an example of what teaching could be like.

I am proud that you are doing this.

sylvier said...

The fact that nearly all of my exams during college were take home exams has made graduate school much more difficult for me. If you have students who are considering grad school, they really need to be familiar with, and have some practice taking timed tests. It starts with the subject GREs but then there are Quals, and then since you need to take Quals, all of the exams in every class are timed. Whether it's the most efficient way to test knowledge or not, it's a skill one needs as a student.

As much as in class tests are stressful, and don't always reflect how well I know the material, the fact that anything we've learned could be on the exam usually forces me to relearn everything. After an exam, I usually feel totally caught up in a class.

I could understand giving in-class exams less weight to discourage cheating, but I don't think you should eliminate them all together.

Bertrand said...

Broken into two comments, Blogspot sucks.

This is really less of a comment and more of a diatribe; I took the liberty of disguising this fact by inserting Roman numerals at random points.

I've combated anxiety issues for quite a large chunk of my life. My grades were in the toilet. It got to a point where, in middle school, I tested separately. My grades improved.

My way of thinking changed. I went from asking "Is this good enough?" to asking "Is this right?".

If even "normal" students resort to trying to game the system, what happens to ones (such as myself) that are disadvantaged from the start? Testing is still a pretty frightening prospect for me.

II. i.
In-class tests aren't a test of how much a student knows. They're not a test of how well the student can synthesize information. They're a test of how fast the student can write stuff down on a piece of paper.

You (the professor) are encouraged to break your test up into small portions. Why? If a student hangs up, they can skip it and move on. You are encouraged to make each question worth only a small fraction of the test's overall score. Why? If a student makes a small mistake, it won't count against them. Typos are worth the same as arithmetical errors are worth the same as a misapplication of concepts.

II. ii.
You'd like to stop me and protest. The ten-point question, you point out, simply requires that my students apply the concepts we learned in class! The question, by design, will award points to the student that knows what the question is asking, regardless of their ability.

First point. You can always get "brownie points". Unless you're evil, a ten-point question will be broken up into chunks (see above point). Maybe you have five two-point sub-questions. These can be worked around using the above strategies.

Second point. You can always lose points by making typos. Lose half a point for introducing a spurious negative sign, one points for misidentifying a character's sibling, one point for misspelling "hyperkalemia", one and a half points for failing to convert Hz into sec^-1 in a formula.

It's clear, when grading, that the student understands that this is an extended application of Bresenham's Second Theorem. But they forgot the x^2 term, so they lose one point every time they apply it.

They got it all right, they just lost 5 points. Same as the other student who stopped partway through because they didn't know.

Your question, little did you realize, is designed to trip everyone into the mud at the same point.

II. iii.
Your students moan and groan when you say that there will be an essay portion. They beg, they plead, they bargain. We can't do two essays, they whine, you already have 30 multiple-choice questions. You ask yourself: why are they complaining? You know they can write. You've seen it, you've graded their out-of-class essays. The dirty secret is that they can't, won't, or don't want to write for the portion of the test. Essays are minefields for a lot of reasons. They're worth a lot of points. You could be the kind of professor who counts off for spelling and grammar. Worse yet, you could be the kind of professor who requires a chart/organizer/etc. alongside the essay.

Did you ever notice that when an essay question requires a chart, there are only ever three bubbles? Those bubbles could say anything. Nobody reads them. But they're worth points. They have to be filled in. The essays get filled in first. They're 30, sometimes 40 percent of the test's value. The prompt gets skimmed over. Key words are inserted at random intervals; the entire essay is garbage.

Anonymous said...

I believe you already provide for a supportive (and motivating) learning environment (at least in my experience). I couldn't tell you whether this elimination of competition will improve the learning experience for students in lower level classes, so I won't even speculate. But know that you are a progressive teacher and you deserve all the support in your paradigm shift, whether it proves successful or not.

Leigha said...

Not in graduate school yet, but I agree with sylvier. Most upper-level physics classes were exclusively take-home exams, with the exception of the final. I have always been good at time tests but found I had a surprisingly hard time with the stress of an in-class final after being used to take-homes, and although I would agree with you that those in-class finals are still the same problem and I think the take-homes totally *did* give me a deeper understanding of what I was doing as well as a chance to pursue perfection because I'm just that kind of a worker...if graduate school is going to be remain in time-test mode but way harder, then, I can appreciate that I need that preparation.

Graduate school paradigm shifts...oh man. Let's not go there.

But that's not fair. If you have a vision, then you ought to try it because change won't happen until somebody does. I would advocate for balance: don't drop the in-class, just don't do them all the time.

Anonymous said...

Anonymous #1 here. Realistic problems are perfect, but if I can't relate to them and apply them practically, then it's very difficult for me to see them as an appropriate test of my knowledge. I assume that this is the case for many students, since math goes into several fields and there's no way you can include all of them.

I agree with you that my thinking is the product of several years of traditional schooling, and that it could've been better developed your way. This is why I think your idea would be revolutionary for younger students. It would be great to see elementary, middle, and high school teachers following your ideas and instilling them within younger brains.

Regardless, it's nice to see a professor putting so much thought and effort into his students' well being. I respect you for your dedication and creative ideas.

Anonymous said...

I think take-home tests can be very valuable; I remember being challenged (and hence learning) quite a bit with some of those. But they allow a HUGE opportunity for people to not just "game" the system, but to completely fake it all the way through to their doctorate. At least some of the time, you should be making sure that THIS particular student does in fact understand what they've submitted (even if they got to that point by collaborative work with others). For a disturbing article on what happens with "take home" work like dissertations, reach this (probably less likely to be an issue in math/science, but not necessarily):

DocTurtle said...

Thanks to Anonymous#...well, to the commenter indicating what might happen with collaboration run amok...for pointing out a scary eventuality. Speaking as a very engaged professor, my main response to that is: this is highly unlikely to happen in any class in which the professor both offers several different means of robust assessment (challenging students to demonstrate development of several different skills sets) and communicates openly and frequently with her students.

The first action ensures that students must demonstrate understanding in varied enough ways that it's harder to "game" the system. The second ensures that the professor really knows each student, so that it's very unlikely for a student to get away with passing off work that isn't hers at any point in the semester. Secondarily, and as an eternal optimist (I wouldn't teach the way I do if I weren't!), I would argue that open communication leads to the sort of strong rapport and sense of mutual respect and understanding that discourages academic dishonesty in the first place. (See my teaching philosophy.)

I suspect that the situation described in the Chronicle article linked to arises almost entirely in relatively large classes in which the professor barely knows her students and their individual potentials. An engaged professor employing a broad array of assessment techniques will be able to spot a fraud a mile away. In-class exams are only one way of getting at the information you need.

blaw0013 said...

Kudos, for being bold, and for being true to yourself. As a fellow math educator, I too have refused the pernicious classification of our (Western?) ways of being that "grading" enhances, maybe institutionalizes, or dare I say cements. (Notice: beef too is "graded.")

Two simple points I wish to contribute.

1) Considering subset of people/adults enrolled in a Calculus course, let alone a college course, is an already highly classed/ranked/graded "select" group of folks. They possess many similarities that are untrue of the population as a whole; one of these is that they thrive in, or at least subscribe to playing the game.

2) To be concerned about "cheating" within the worldview that assumes the "game," is a story of power and control. These are obtained and regulated through the creating and enforcing of the rules of the game. Inasmuch, I find no personal loss or offense when a student "cheats;" my being, my self is not wrapped up in this need for control.

chunga said...

Thanks for sharing your experience and your epiphany. It's heartening to hear of teachers working to support intrinsic motivation and reduce competition.

I'm not clear on the distinction you're making between in-class and out of class exams and how the later somehow are still valuable. This recent article at http://www.theglobeandmail.com/news/technology/science/tests-get-high-marks-as-a-learning-tool/article1824878/singlepage/#articlecontent describes how more frequent testing benefits learning. Notably, the testing described is low-stakes. Isn't this really what's important for students be able to utilize tests as a learning tool?

DocTurtle said...

@chunga: it may very well be that you and I are arguing for the same sort of assessment instrument and classroom practice. I completely agree that lowering the stakes makes for a more effective learning tool (whether one is writing to learn, computing to learn, synthesizing to learn, etc.), and in my classes the primary means of lowering the stakes is to move examinations out of the classroom itself and into the students' relatively boundless out-of-class time, alleviating in a number of ways the pressure students feel to perform.

This said, as you point out (and as the article you link to indicates), it is possible to design effective in-class exams.

The fact remains, however, that the vast majority of in-class exams in college-level mathematics courses are not low-stakes. Rare are my colleagues who weight exams less heavily than, say, homework or other out-of-class projects. For many math instructors, exams still account for upwards of 70% or 80% of a student's course grade, and are often the sole sources of feedback for students' performance. (I lament the fact that many of my colleagues fail to collect and respond to homework on a regular basis, but sadly this failure is common at the college level.)