## What does academic rigor look like?

I got an email from a fellow edu-blogger a couple of days ago asking for my input on the subject of academic rigor. Specifically this person asked:

Is the quest for more rigor an issue for you? Is it good, bad, meaningless? What does rigorous teaching look like in your classroom?

I hope she doesn’t mind my sharing the answer, because after writing it I thought it’d make a good blog post. I said:

For me, “rigor” in the context of intellectual work refers to thoroughness, carefulness, and right understanding of the material being learned. Rigor is to academic work what careful practice and nuanced performance is to musical performance, and what intense and committed play is to athletic performance. When we talk about a “rigorous course” in something, it’s a course that examines details, insists on diligent and scrupulous study and performance, and doesn’t settle for a mild or  informal contact with the key ideas.

Example: A rigorous course in geometry goes beyond just memorization of formulas, applications to simple geometric exercises, and “hand-waving” attempts at proof. Instead, such a course treats details as important, the ability to explain on a deep level the truth of formulas and results as a key goal for students, and sets a high bar for the exactitude of mathematical arguments. Euclid’s “Elements” for example is the prototype of the rigorous treatment of geometry. It’s not a difficult work to understand, necessarily; in fact one of the enduring qualities of the Elements is the clarity and precision of not only each individual proposition but also in how the overall collection of propositions fits together. By contrast, many modern books on geometry are highly non-rigorous, omitting details, putting theorems out of order, and defining a proof as a “reasonable explanation” only.

Is rigor good? It depends on the audience and the goals of the class. When I teach a geometry course for junior and senior Math Education majors, rigor is of the utmost importance because I want those pre-service teachers to go into their classrooms with tough, precise minds for the sake of their students. If I were to teach a geometry class for fifth-graders, on the other hand, I think rigor would obscure the subject, and I would depend a lot more on intuitive explanations and perhaps constructivist techniques for discovering key ideas in geometry and save rigorous proofs for another day. Similarly, when I teach calculus at my college, the audience is about 50% business majors, and so we designed the course not to cover much theory. This is not a rigorous treatment of calculus, but it is more effective for the students than if we included the epsilon-delta proofs and what not.

The quest for more rigor is most important in the post-calculus courses I teach (geometry, abstract algebra, and introduction to proof). These are subject areas where precision and detail-orientation are essential for a complete understanding of the material. Students are not allowed to give examples when a proof is called for, and I nitpick every little thing in their proofs up to and including the choice of punctuation and prepositions. [If any of the five who took this course from me this past semester are reading this, feel free to chime in with an “Amen.” – RT.] At the calculus level and below, I lay off on the theory but the rigor in the course comes from getting details of mechanical calculations right. And this is a big issue, because students in high school are generally taught only to produce a correct answer, not a clear and detailed solution. I am on a mission to make sure students can not only get right answers but also communicate their methods in a clear and audience-appropriate way, and that’s what “rigor” looks like there.

[After-the-fact note: To clarify, in calculus I insist on details in mechanical calculations but also on the details of processes and in paying attention to nuances in solving application-style problems. For example, students know that if you just set $f''(x) = 0$ and solve for $x$, that this doesn’t give you an inflection point; and in an optimization problem you can’t just find the critical number of the model function, you must also test it with the First or Second Derivative Test to see if it really yields a maximum. Or at least, they don’t complain when they forget to do it and I take off points!]

I have two kids, ages 3 and 5. (There’s a third one on the way in three weeks, but that’s another story!) I’m pretty rigorous with them, too — when the 5-year old says “Mimi comed to our house this weekend” I correct her grammar, and she gets it right the next time. You have to do it in a gentle way, but getting details right now will help them get the more complicated things right later. If I were to project myself out of higher ed and into the K-12 sphere I could see my teaching being “rigorous” in that kind of way — insisting that kids get the details right and not gloss over things, but doing it in a lovingly persistent way. I wish more K-12 teachers would do this, though, because it’s obvious from my freshmen in the last 4-5 years that this isn’t happening (or at least it’s not sticking).

[Final note: That last sentence isn’t a slam on either my freshmen, who were really quite excellent this year in calculus, or their teachers. It’s an observation, and I stand by it. I can show you their work at the beginning of the semester if you don’t believe me. Why this kind of “rigor” is not sticking with them is something I can’t fully explain because I don’t know what was going on with them in high school. Is it them? Is it their teachers? Is it the system? Is it the preponderance of standardized testing, which makes rigor more or less irrelevant? Comment!]

Filed under Calculus, Education, Geometry, High school, Teaching

## OMG! Another video on how to cheat on a test

When I put up this post, highlighting a hilariously bad YouTube video on how to cheat on a test, one of the things I discovered was that there is actually an entire genre of “how to cheat” videos on YouTube. I didn’t realize I had tapped into such a resource, but I did. Since the earlier post got lots of comments, I thought I’d do another. This one is much cleverer and better-produced. Enjoy (I guess):

Like I said, a lot cleverer — and a lot harder to detect. The big hurdle here is that many classrooms don’t allow food or drink in the classroom, and even if they did, a prof could simply ban food and drink to circumvent this particular trick. But the problem there is that a student could perform this trick on anything with a label, and so if you ban pop bottles you might as well ban everything. Which some teachers and testing facilities do.

This trick also assumes that the person cheating has enough skill with Photoshop to create the fake label, and that’s a very big stretch. And if somebody is that smart then probably they don’t need to cheat in the first place.

The main problem with both this cheat and the one in the earlier post is that the cheaters are assuming something wrong about the basic nature of tests, at least at the college level. They are assuming that tests are about storage and recall of information. Maybe some (most?) tests in high school are like this. But at least in my classes, having a few bytes of information embedded into some kind of object using steganography just isn’t going to do you much good if you don’t know how to use the information to solve a problem. You might be able to smuggle in the limit definition of the derivative successfully into a calculus test, but if you can’t use the definition to calculate the derivative, that successful smuggling won’t have helped much. In that case, trying to look inconspicuous as you squint nearsightedly at your Coke bottle trying to read off the value of Planck’s constant is the least of your problems.

If these two videos are any indication of the state of the art in cheating on a test, the simplest way to foil attempts to cheat is simply to make tests less about storage and recall of information and more about problem solving and logical deduction. On final exams in my freshman courses, I allow students to make up their own notecard on the front and back of a 3×5 index card and bring it to the exam precisely because I do not want them to think that the exam is about storage and recall. “Legalizing” the cheat sheet has basically eliminated academic dishonesty from my final exams, and in fact students find that making up the card is an excellent way to review.

A far more dangerous form of cheating would be a system where a student taking a test communicates information about the test itself to another student, such as two students sharing solution techniques in real time to a problem on a test they are taking. There are ways to do this, but I haven’t seen a clever (or un-clever) video on YouTube yet about that.

Filed under Education, Student culture, Teaching

## When students fail, who’s responsible?

This story out of Norfolk State University has been lighting up the internet in general and the edu-blogosphere in particular. It revolves around Steven Aird, a biologist at Norfolk, who was denied tenure for failing too many students:

The report from [Dean Sandra DeLoatch] said that Aird met the standards for tenure in service and research, and noted that he took teaching seriously, using his own student evaluations on top of the university’s. The detailed evaluations Aird does for his courses, turned over in summary form for this article, suggest a professor who is seen as a tough grader (too tough by some), but who wins fairly universal praise for his excitement about science, for being willing to meet students after class to help them, and providing extra help.

DeLoatch’s review finds similarly. Of Aird, she wrote, based on student reviews: “He is respectful and fair to students, adhered to the syllabus, demonstrated that he found the material interesting, was available to students outside of class, etc.”

What she faulted him for, entirely, was failing students. The review listed various courses, with remarks such as: “At the end of Spring 2004, 22 students remained in Dr. Aird’s CHM 100 class. One student earned a grade of ‘B’ and all others, approximately 95 percent, earned grades between ‘D’ and ‘F.’” Or: “At the end of Fall 2005, 38 students remained in Dr. Aird’s BIO 100 class. Four students earned a grade of ‘C-’ or better and 34, approximately 89 percent, received D’s and F’s.”

These class records resulted in the reason cited for tenure denial: “the core problem of the overwhelming failure of the vast majority of the students he teaches, especially since the students who enroll in the classes of Dr. Aird’s supporters achieve a greater level of success than Dr. Aird’s students.”

But you really have to go read the whole thing to get the full complexity of the issue. Read especially the comments at the end. This situation has really touched a nerve among higher ed people.

And it’s not hard to see why, either. This story brings up in great clarity a profound conundrum in college teaching: When students fail, whose fault is it? Is it:

• the students‘ fault, for not working hard enough or putting forth enough effort or so forth?
• the professor’s fault, for not working hard enough to reach and help his/her students?
• the university’s fault, for creating a culture of low expectations? (This is Aird’s argument.)
• the students’ high schools’ fault for not adequately preparing them for college?
• somebody else’s fault, for example the admissions department for allowing students who are knowingly unprepared for college to enroll, thereby forcing the university to hold lower standards in order to maintain decent retention rates?
There is no one-size-fits-all answer, of course; every instance of student failure is some linear combination of faults. Looking at Aird’s case, it’s not obvious what that combination is. Is Aird simply an uncaring elitist — or an outright racist, as some critics are claiming (Aird is white, and Norfolk State is a historically black university) — who is refusing to help students who need it? Is Norfolk State pulling a Benedict College and enabling an academic climate so anemic that any professor who assesses students with halfway-decent standards ends up flunking the vast majority of his students? How did it get to the point where only 10% of his intro biology students are earning a C or higher?
• The overwhelming instinct among professors is to lay the blame somewhere else besides themselves. One look at the comments at the IHE article will tell you so. And this instinct may be justified; the plain fact is that many students do fail in spite of the resources available to them, because they are not prepared, or because they have too many distractions in life, or because they are lazy and won’t utilize what’s available to them. But I think profs must beware of transferring the behavior of some students to the behavior of all students. How many of Prof. Aird’s students were adequately prepared to do well in the course, and would have done so with a little more work on Aird’s part or the students’ advisors’ parts?
• The overwhelming instinct among some other people is to lay the blame squarely at the feet of the professor. “If students fail, then it’s the teacher that failed” is the common aphorism. But this simply isn’t true all of the time. One of the main distinguishing factors between education at the college and university level from that at the K-12 level is the degree to which students are responsible for their own learning. A university education is a meeting of the minds. The professor’s job is to craft a well-structured course that enables students to learn. But the professor cannot make learning happen — the student must pick up the ball at some point and take initiative, by doing homework (especially when it’s not required), coming to office hours, asking questions, and investing time in struggling with material that might be difficult. If the professor does her/his part and the student opts out and then fails, it’s not the professor’s fault for not going farther and doing more of the student’s work for him or her. Some times — many times — teachers pass but students fail.
• The university or college itself bears a big responsibility: To create and foster a campus culture where the two-part meeting of the minds I just described takes place on a daily, ever-increasing basis. And by implication, it’s the university’s responsibility to eradicate anything that stands in the way of this. If the university fails to enforce its own academic rules (which appears possibly to have been the case at Norfolk regarding an “80% attendance” rule), or allows co-curricular or athletic activities to usurp the primary role of teaching and learning on campus, then nobody is going to win.
If more universities would simply take up the challenge of being intentional about the primacy of academics on campus, and conduct itself likewise, then I think fewer cases like this would happen.

Filed under Education, Higher ed, Life in academia, Teaching

## Ranking schools for athletics and academics

Via Phi Beta Cons, here’s a ranking of the Top 50 schools for successfully combining athletics and academics. PBC wants a ranking of the bottom 50 schools using these criteria. I’d be happy if the original article would have stopped to consider that their rankings only include NCAA Division I universities and that there is more to a ranking like this than combining existing academic rankings with existing sports rankings. Small colleges, particularly Division III schools like mine and some of the NAIA schools, often do a very good job of combining athletics and academics, probably moreso than most of the Top 50 schools ranked here. The NCAA’s own web site says:

Colleges and universities in Division III place highest priority on the overall quality of the educational experience and on the successful completion of all students’ academic programs. They seek to establish and maintain an environment in which a student-athlete’s athletics activities are conducted as an integral part of the student-athlete’s educational experience.

But you’ll never hear about it because we don’t participate in the BCS circus and don’t have massive research budgets.