Partially Ordered Thoughts

We’ve already covered the fact that I write long course policy documents. The Spring 2010 Applied Combinatorics (MATH 3012) Course Policies and Expectations are seven pages long. Last time I taught this course, they were four. However, last time I wasn’t doing as many different types of assessments and wasn’t using much active learning in class. This time, I had a lot of explaining to do up front. Inspired by Maria Anderson’s post over at Teaching College Math, I decided to get my students to actually read at least part of the course policies by crowdsourcing them. Read more »

This post started as a comment on Nick Hamblet’s blog post about changing calculus. When I realized it was incomplete and almost 700 words long, I decided that I should probably put my thoughts up here instead and link to Nick’s post.

I have to agree with Robert Talbert’s comment that most of this dialog is taking place at liberal arts colleges. This is great for liberal arts colleges and their students. Unfortunately, the behemoths that educate the masses really need to get on board and realize that the way we’ve been doing it for generations is not necessarily the best way any more. I have seen some signs at Georgia Tech that it’s possible things may start to change at the top-tier research universities in the future. The Harvard physicist Eric Mazur (leading proponent of peer instruction and clickers in science courses) is a great example of someone who asked these same questions about his physics classes a while back (and did something about it!) and is also widely-respected as a scientist. We need more people like him in every discipline to create change at the Georgia Techs and UVAs of the world. Another problem with using liberal arts colleges as the proving ground for new instructional methods is that faculty at Big State U almost always say “That’s great in your class of 25. I have 250 and just can’t imagine it working in my class.” Well, the specific things being used might not work, but there are things that can be effective in that context, too.

What are my thoughts on what calculus should be and how we should accomplish this? I’ll admit their not fully-formed, but they’re getting further along as time passes. I’ll do my best at outlining them, but I should point out that I’m writing this at 34,000 feet on four hours of not-so-great sleep.

Foremost, every course needs designated learning outcomes. These should be broad and determined by consensus from within the department, the professional community, and the “consumer departments” that require our courses for their majors. For Calculus I or II, I don’t think “Be able to integrate a function using partial fractions.” is a good learning outcome. Unfortunately, this is the most common type of learning outcome written now to satisfy accreditation bodies. I’ve seen Georgia Tech’s ABET outcomes for the lower-division math courses, and they’re sadly almost all like this. Instead, learning outcomes should lay out how we expect our students to think differently when they leave the course. What are the concepts they should know about? For calculus, I’m much more concerned about students understanding the derivative as a rate of change and how that connects to the integral and area. Instead of caring if students can graph functions, we should care about if they understand what the derivative tells us about the graph of a function. I bet if you asked most mathematics professors how they want their students to think differently after their calculus course, you’d get similar answers. Unfortunately, too many people don’t understand that our teaching and learning activities, feedback and assessment mechanisms, and learning outcomes all need to be aligned. It does no good to want your students to be able to do these things and then just teach them a bunch of algebra tricks and test them on meaningless manipulation of symbols.

Learning outcomes at every level (from remedial courses to graduate courses) need to include communication (reading, writing, and oral) in the discipline. We cannot teach our students everything, so they will have to learn by reading in the future. This is easier if we help them when they’re getting started. If we genuinely care about concepts, they need to communicate their understanding in a meaningful way, often in the context of an application. We need to teach our students to critically evaluate their work to determine if it makes sense. How many times have we seen students compute a volume using calculus techniques and give a negative number as an answer without batting an eye? In evaluating my precalculus students’ work at the end of this semester, I realized that some of them still don’t have BS detectors when reviewing others’ (or their own) work. Students need to be able to take a result that they get (by hand or from a computer) and determine if it makes sense in the context of the problem. (In case of my class, when answering a question that asks for the total amount of interest paid over the life of a loan, a percentage is usually not the right thing to give.)

Once you’ve got your learning outcomes laid out, let people teach the course how they want to (even graduate students). Those of us who think that students should not be glorified calculators should be allowed to focus on concepts, writing, and communicating. The old guard who like meaningless manipulation of symbols can go ahead and do that. They’ll retire soon enough, so it’s just not worth our time to change them (although it may be worth the effort to keep them away from the froshlings). Common exams need to be eliminated, as I’ve only seen them leave everyone unhappy. (The only exception being when a course “czar” writes the exam. Then he/she is happy and everyone else is unhappy.) With learning outcomes and good assessment schemes, you just hold every instructor accountable for providing evidence that students met the learning goals. This may be through questions from the final exam, mastery exams, projects, papers, whatever the instructor believes documents it (and is generally considered valid assessment in the professional community).

A potential pitfall here is the issue of sequence courses. At a liberal arts college, this is not so much of a problem, I imagine. It’s likely that if you took Calc I from Prof. X, then Prof. X will also be teaching Calc II the next semester. At Big State U, this is less likely (and almost unheard of at science/engineering school like Georgia Tech). A student who comes out of a concept-driven calculus course will struggle immensely in the sequel if his/her instructor wants fast-paced symbol manipulation. I don’t think there’s a great solution to this problem. However, Duke has come close. They’ve instituted two calculus sequences. One is traditional (no computers, symbol manipulation, etc.) and taught primarily by senior, tenured faculty. The second is reform (lots of calculators, computers, labs, but concept-heavy) and taught primarily by non-tenure-track (but full-time and under long-ish term renewable contracts) and graduate students. They help the advisors from the various majors understand which sequence is better for which types of students. I think the idea is that as the old guard retires, the traditional course will go by the wayside. (I should note here that I’m not a big proponent of the reform movement. I think they’ve done a lot of things wrong politically and caused an artificial schism that makes young mathematicians feel like they need to choose a “side”.)

Yes, this is all pie in the sky at the moment. We’re probably decades away from this, and it may not work at all. However, I think we’re failing our students if we don’t try. This is also the heart of my career conundrum. I’ve been educated solely at medium-large public research universities and know them well. Apparently there is some belief that I can make a career of working at one (at least that’s what I’m inferring from the fellowship I just got). However, I question whether I can do the research I enjoy and need to do in order to get tenure at such an institution while also trying to create change in how we teach mathematics, even if it’s just in my own courses. Where does the time come from for the professional development required to keep current on these matters? Is there a reward other than a pat on the back (at a research university) for really doing something about undergraduate education? One of the reasons I feel like I should take that career path is to influence the future generations of mathematicians. No one in the Georgia Tech School of Mathematics is seriously evaluating how we teach introductory courses other than graduate students. We were the beneficiaries of a course from our Center for the Enhancement of Teaching and Learning that made us reevaluate our views. We’ve all changed how we teach, although the degree varies, because we’re fortunate to teach in a unit that gives us a lot of latitude. Many mathematics graduate students, however, seem to just be exposed to the status quo when it comes to teaching. Others learn about different approaches but are discouraged from pursuing them because of the time it takes the first time around.

Again, apologies for any incoherence. This is pushing 1500 words, so I should probably edit it. However, that’s no fun on an airplane, so I’ll leave it as is.

Two blog posts in one day after two months off? Well, apparently I have a lot to say today (and I don’t want to prep my class on trig identities for tomorrow).

On MARTA on the way home tonight, I was reading an article from Inside Higher Ed about the Graduate Employees Organization at the University of Illinois going on strike. Why have they gone on strike? My short version of it is simply that unions are bad for graduate students. They create an unnecessarily adversarial and hostile relationship between GTAs/GRAs and the administration. This strained relationship leads to breakdowns in communication, and those breakdowns lead to pure craziness.

The craziness here is just plain dumb. The GEO and the administration are bargaining a contract. It’s not surprising that tuition waiver policy would come up in such negotiations. The GEO proposed language “requiring the university to bargain in the event of ‘any changes in the tuition waivers of any bargaining unit member or members.’” That seems reasonable, until you realize that it would mean the administration couldn’t make any change to the tuition waiver of any GTA or GRA, even one who was totally ignoring his/her responsibilities and needed to be terminated. According to the IHE article “[t]he university rejected that language, opting instead to agree to bargain any changes in ‘tuition waiver policy’ made by the Board of Trustees.” That also seems reasonable, until the GEO points out that the board’s policy only covers the in-state portion of tuition.

A reasonable group (such as the Georgia Tech Graduate SGA) representing the graduate students would say “Hey, this is all about semantics, let’s get it worked out.” However, the GEO being a union, a conspiracy theory is in order. They immediately assumed the administration is up to something nefarious because of their proposed choice of language. According to the union, the administration, in proposing language that would, if strictly interpreted, apply only to the in-state portion of tuition, must be scheming to take away the tuition waivers of out-of-state students! Let’s go on strike!

A rational representative of graduate students would realize that the University of Illinois would be incapable of recruiting nonresident graduate students (the majority of graduate students most places) if they didn’t offer them tuition waivers. A research university of the size of Illinois cannot operate without graduate students. The administration, no matter how dire the budget situation, is not going to do something so stupid as cutting tuition waivers for nonresident students. However, when graduate students unionize, rationality goes out the window, and nobody stops to ask what the issue is. They just assume the other side has hostile motives and prepare for war. Usually these battles are stopped before an actual strike, but not in this case.

I should close by pointing out that while I’ve not collectively bargained a contract, I have had to intervene on behalf of graduate students whose employment classifications and tuition waivers were impacted at one point. I sat down with the appropriate administrators, learned why it was being done, and got the data on how many students were being impacted. We then figured out a way to minimize the adverse impacts on the handful of masters students being directly and immediately impacted. (The policy change was important go prevent abuse of graduate students and tuition waivers, and so was implemented with a few individuals grandfathered in.) A successful solution was found in a collegial way. If we’d had a union, I can only imagine the strike threats that would have run around over that issue, since it was a bigger deal than what the issue at Illinois.

In a recent issue of the Forum, Josh Swanson, who I have known for many years, has an opinion piece discussing how he thinks leaders from the business sector (specifically Doug Burgum) would make excellent candidates for NDSU’s next president. Some of what Josh says makes sense. However, a lot of it is nonsense. Much of the most absurd nonsense is at the expense of a faculty member for whom I have immense respect, Amy Rupiper Taggart. I’m hoping that Jack Zaleski sees fit to run my response, but in case he doesn’t, I’m going to post it here as well. (Note that I’m having a hard time telling from the Forum website if Josh’s piece ran on Monday or Tuesday. I’ve let Mr. Zaleski know that he should correct for the appropriate date if necessary, but I’ll leave this in terms of the way I originally wrote it.)

I read with concern Josh Swanson’s opinion piece in Tuesday’s (Nov. 17) Forum about the North Dakota State University presidential search. I do not doubt that Mr. Swanson wants what is best for NDSU. However, his arguments show a lack of understanding of what it takes to lead a research university. I would like to take this opportunity to provide greater insight from an NDSU alumnus (B.S. Mathematics, 2004) who will in May 2010 earn a Ph.D. from the Georgia Institute of Technology, a top 10 public research university. At both NDSU and Georgia Tech, I have served as a student leader and worked closely with senior administrators. These experiences have given me a understanding of the type of person NDSU should seek.

One cannot argue that Doug Burgum has not been successful in business or that he does not have many of the qualities the next president of NDSU should have. However, a university is not a corporation. One of a university president’s responsibilities is to recommend which faculty members should be granted tenure after extensive review by faculty committees. This is unlike any hiring or promotion decision a corporate executive will ever make. Faculty members are not unreasonable in expecting that the person making the final recommendation will have experience with the type of activities on which they are evaluated. I fail to see how Mr. Swanson’s comparison to Shakespeare can be applied here. Professor Rupiper Taggart did not claim that only those with a Ph.D. are capable of producing materials suitable for instruction. Instead, she was simply quoted as saying that faculty want to be able to seek leadership from someone who understands what they do.

Success in the business world often does not translate well to leadership in higher education. An example is Chancellor Erroll B. Davis Jr. of the University System of Georgia. Mr. Davis, who has an MBA, was hired to lead the USG after a career as an energy industry executive. His prior experience in higher education was sitting on the governing boards of the University of Wisconsin System, Carnegie Mellon University, and the University of Chicago. Shortly after being named chancellor in 2006, he surprised college and university presidents with a plan to fix each student’s tuition rate for four years. The plan was quickly approved by the Board of Regents and worked until the economic crisis struck. Now, USG institutions are hamstrung in terms of budgets and must find backdoor ways to increase student fees in the middle of the year to offset for budget cuts and the inability to raise tuition. Mr. Davis and his initiatives are not very popular within the USG
community. The fixed tuition program has already been discontinued for new students. Other changes will likely be undone or significantly revised when he leaves.

A Ph.D. does not automatically give someone the credentials to lead a research university like NDSU. In fact, there may be excellent academic leaders with other terminal degrees who have served as faculty members and should be considered. There may also be individuals of interest who have spent time in both the private sector and the academy. For instance, the current president of the California Institute of Technology and past chancellor of the University of Wisconsin–Madison both have had success in industry, as faculty members, and as university administrators. NDSU’s next president need not have followed the traditional path to that role, but it would be a disservice to the institution and the state to hire someone who does not have experience as a faculty member at a research university of comparable or greater stature. Mr. Swanson is correct to point out that the wrong choice of president can lead to a significant setback for NDSU. I hope the public and the media will allow the decision to be made by those who truly understand what is at stake.