Grade inflation: The View from the Trenches

When I began teaching at my current university, I received precise instructions governing grades for multisection calculus classes and no guidance for grading upper level classes. The multisection classes have many sections with different instructors but share a common syllabus and a common final exam. Department policy aims to ensure that grading is uniform across all sections; students with comparable performance should receive comparable grades, even if they are in different sections. The method for approximating this uniformity of grades is simple. Final exams are graded in common, and the exam grades are submitted to an administrator. The administrator looks at historical grade distributions, consults with senior instructors, and sets a curve for the final exam. Individual instructors are then required to set a grade distribution for their sections which approximates their sections' grade distribution on the final. Thus, if 10% of my students make an A on the final, I should award A's to approximately 10% of my students (not necessarily the same 10% who scored an A on the final). Grade inflation is minimal in courses subject to this grading regimen.

Upper level courses are an entirely different game. When I began teaching here, I approached prior instructors of my assigned upper level courses and asked them what grade distributions they had assigned when they taught the course. Upper level courses typically have a computational component, a knowledge component, and a proof component. Grading proofs has a significant subjective element. It is easy to decide that an argument is wrong; incompleteness or clumsiness, however, are much more subjective. There is no universal meter stick to use to decide what grade to assign. It is, however, usually easy to partially order the students. This clump is better than that clump. What I have to decide is whether the clumps are B's and C's or A's and A-'s. So, when I teach calculus classes, I feel virtuous for keeping grade inflation so far below what we see in the humanities. When I teach upper level courses, I sometimes have grades concentrated in the nosebleed territory between B- and A. I don't know how I would distribute grades in a humanities class where so much of the grading is subjective.

What is the harm in grade inflation? The most interesting argument I have heard is an economic one: if grades are inflated, students are not pushed to migrate to majors where they hold a relative competitive advantage. Thus a student who is not gifted in, say English, may major in English and receive grades on a par with more gifted writers, rather than being pushed into a business or econ class, where they may earn a lower grade than in their English class, but outperform more of their peers. I also imagine grade inflation makes college transcripts less useful for employers in hiring recent graduates. When I write letters of recommendation for unspectacular students, I always tell the employer not only what grades the student earned in my classes but also where he ranked in the class, in order to obviate the grade inflation problems. I suppose we would need more data about the correlation between academic success and job success to understand whether grade inflation inconveniences employers.

If grade inflation is accompanied by a watering down of the course material, the harm to students is obvious. In my department, I have seen little evidence of decreasing course rigor. In fact, I believe that mathematics courses have become more rather than less rigorous during my time here.

What are the causes of grade inflation? Economists offer one of the most amusing explanations of the fact that grades in the humanities are so much higher than in mathematics, chemistry, and economics departments. They observe that the average mathematician's midcareer salary is approximately 50 % higher than that of a psychology major. They conclude that a good grade in a psych class is worth less than a good grade in a mathematics class. The good grade in psych should therefore cost less. The relevant currency is student effort. This leads to inflation of grades if psych is to retain enrollments. I like the argument because it makes math look good (or at least profitable), but I have met few students who know average salaries by major and fewer still who don't think they will be the exceptions. Hence, I don't believe the economic argument explains the reality. On the other hand, it is very believable that instructors inflate grades in order to keep enrollments up and course evaluation numbers high. When faculty have low enrollments or poor evaluations from their students, the department administration notices and seeks explanation. Consistently poor enrollment and evaluation numbers can lower chances of promotion of junior faculty and can depress salaries for tenured faculty. Strict grading policies can lead to low enrollment and lower evaluations. The resulting pressure to inflate grades is real.

Because many of the incentives to inflate grades stem from worries about administration response to the possible consequences of tougher grading, the administration can easily tighten grading standards if it chooses to do so. If the departmental administration requests that its faculty assign certain grade distributions, then enough faculty will cooperate to slash grade inflation. Departmental administrations, however, also worry about overall departmental enrollments. Hence they are unlikely to act alone unless they are over enrolled. If the university requests that all departments enact tighter grading standards, then much departmental resistance would disappear. Unfortunately, there is a significant faction of the humanities faculty that opposes tighter grading for political/philosophical reasons which I have never understood and will not, therefore, try to explain here.

Though, grade inflation is real, I am unsure of its negative consequences. It is, however, easily addressed if the university administration is willing to buck the politics of a minority of faculty opposed to rigorous grades.

A Newcomer's Guide to State Political Conventions

I recently attended my first state GOP political convention. The convention occupied the better part of a weekend, and I never strayed far from the question: is this activity worth my time? In this post, I will describe aspects of the convention and my answer to the preceding question.

Before the convention, I assumed that the main business of the meeting would be working out the party platform. One of my colleagues in the county GOP, however, told me that the resolutions would be more interesting than the platform. As homework before the convention, I studied the platform proposed by the Platform Committee and sought and identified logical inconsistencies, incoherent statements, violations of my idea of small government conservatism, and impolitic planks. I was unsure how one addressed these at the convention.

Day 1: The convention met in a large hall. The delegates were seated by county. I was the only delegate from my county. We began with a prayer, the presentation of colors, the Pledge of Allegiance, the National Anthem, and a welcome speech from the state party chairman. A large part of the work of the convention then focused on the rules for running the convention itself. The state party chairman appointed the convention officers. In particular, the party chairman does not chair the convention. I assume the rationale for this is that the party chairman generates so much animosity in his capacity as chairman that it makes for a friendlier convention if an outsider is appointed chair of the convention. The next order of business is the report of the Credentials Committee. This committee rules on which people have passed the necessary hurdles to become delegates (and therefore given voting rights). Amusingly, the prospective delegates are asked to vote to accept this report; i.e., we vote on whether we have the right to vote. This process takes a surprisingly large amount of time, especially as there were inevitable omissions which needed to be corrected. Now that we had voted to grant ourselves voting rights, the Rules Committee proposed rules for running the convention, in particular, rules for voting and rules for debating. There was little debate over the rules of debate, and we quickly passed the proposed rules.

I assumed, as a naive newcomer, that the next item on the agenda, amending the state GOP rules of organization, would be comparably pro forma. Apparently, rules changes are the outgrowth of old internecine party fights. There was extended debate about the proposed rules. I had no opinion on (or understanding of) the issues and simply listened and watched the nature of floor debate. The final item on the agenda for the day was voting on the party platform.

My assumption that the party platform would be the heart of the convention was mistaken. There were few proposed amendments. I decided to address a substantive issue. Although I am comfortable speaking before large audiences of mathematicians, I was self conscious addressing the convention. There were microphones spaced along the four aisles dividing the hall. I approached a mike and received permission to speak from the chairman. I gave my name and county and then suggested we amend one of the social planks to delete federal references. I believe it will lead to better electoral prospects for Republicans if we stick to our constitutional principles and treat most social issues as the proper domain of the state governments - not the federal government. My amendment was promptly seconded, and then I was given a second opportunity to approach the mike and take two minutes to argue my case. I had not observed this part of the process and was unready with additional rhetoric. I merely added that conservatives were always ill served when social issues were federalized. I then returned to my seat. At this point other delegates had the opportunity to approach a microphone and argue for or against the amendment. Before any substantive discussion began, a delegate from a nearby county proposed postponing indefinitely debate on the amendment. The convention chairman then explained to us that this was a parliamentary procedure to kill an amendment without expressing an opinion on it. This motion passed killing my amendment. A few minutes later, someone proposed voting to cut off all further debate on the platform. This passed by the required two thirds majority, and we shortly thereafter approved the platform, warts and all. We then adjourned for the day.

The judicial candidates invited the delegates to visit their 'hospitality suite' in the evening. This consisted of a suite in a hotel with free booze and hors d'oeuvres. You had to pass a phalanx of candidates to reach the refreshments. The rooms were too packed with bodies for me to bother to enter.

Day 2 began like day 1: prayer, the presentation of colors, the Pledge of Allegiance, the National Anthem, and welcome speeches. Various candidates for statewide offices were paraded across the stage and allowed to make a few remarks. The top of the ticket (whom I had met that morning) made a long speech. We then broke out for various 'training sessions', addressing topics such as how to employ facebook and twitter in campaigns. Lunch followed. Lunch with the top of the ticket was an (expensive) option.

After lunch we reconvened in the convention hall. After numerous speeches, many quite good, we once again heard from the Credentials Committee. Once again it took quite a bit of time to vote on who could vote. My county delegation swelled to eight people on day 2. The rest of the day was devoted to voting on resolutions. The Resolutions Committee had prepared a list of proposed resolutions covering numerous topics such as repealing Obamacare, opposing a VAT, and calling for sanctions against Iran. Several handouts proposing resolutions, not supported by the committee, also circulated.

The debate over resolutions was much more heated than the debate over platform. Delegates formed long lines at the microphones, waiting their turn to speak. I was extremely impressed by the informed and thoughtful arguments, articulate speeches, and mastery of parliamentary maneuvers. Of course some delegates made statements I thought absurd, but it was heartening hearing so many concerned citizens from so many different walks of life making subtle and intelligent arguments - even if I did disagree with many of them. The silent majority of delegates, however, seemed to prefer to accept the committee reports essentially unaltered.

By the time 5:30 rolled around, I was ready to join a vote to close discussion and accept the amended report. The convention ended, and I went home. Because this was my first convention, I had looked at every aspect of it with a view to answering the question: is this worth my time? At times I wondered if the convention is primarily a vehicle for rallying the troops, rather than seeking their input. I am sure this is one objective of the convention (and a reasonable one), but my current assessment is that the debate over issues and platform is more important than merely adding an egg to a cake mix. I will try to return next year.

How to play public intellectual

Most scholars spend the bulk of their time focused on issues which, though important for their fields, are of little immediate interest to the general public. How should these scholars contribute their expertise to public discourse? In some fields this is easily done. It is always interesting to hear what Middle East scholar Bernard Lewis has to say about current affairs in the Middle East. I always enjoy hearing any four economists give their six different prescriptions for optimal economic policy. For a mathematician studying, say, nonlinear partial differential equations or algebraic K theory, however, it is not clear how his expertise contributes to public discourse.

Among my nonacademic mathematical contributions is the fielding of mathematical queries from the general public. Often these questions require little mathematics beyond 8th grade algebra. The (usually college educated) questioners are chagrined if I point this out to them; so, I have learned to keep this observation to myself. I wonder if high school teachers receive similar queries.

Many questions are just bizarre. Once a man phoned to ask me what were the names of the large numbers after million and trillion. Perhaps he was doing research for Nancy Pelosi's budget advisor. I pointed out that this was not a mathematics question and the answer was surely available on Wikipedia, but he didn't take the hint; so, I pulled the answer off the internet while he was explaining why he needed this information. My answer (or more accurately Wikipedia's answer) satisfied him, but then he wanted me to connect him to someone in the physics department who could answer his questions about stellar evolution. When I told him that I couldn't connect him, he replied, "Hah. You know all those big numbers but don't know how to use a telephone." Some of these folk just seem to want to talk. I always give them a moment to convince me that they don't intend to donate money to the Department before sending them on their way. A month or two ago I received a call from a man who told me that he had received an advertisement for a mathematics book sale, and he wanted me to be aware of the low prices. I asked him if he wanted to donate books (not a good way to use his funds). He said, "No." Was he a salesman? "No." Then why was he calling me? He just wanted me to be aware of the low prices. I didn't bother to tell him how many flyers and emails I get from publishers every week, but I did get him off the phone quickly.

Enthusiastic amateurs are a more difficult group to satisfy. The Department receives a constant trickle of manuscripts from amateur mathematicians who claim to have solved some famous conjecture or, more often, claim to have solved some problem that mathematicians proved a hundred years ago has no solution. Folks, if we have proved that there is no solution, then as far as we are concerned, the problem is finished. We are not going to spend lunch reading through manuscripts so that we can tell the authors what their mistakes are. Sometimes I try to farm out amateurs' manuscripts to postdocs to read, but I rarely get any takers. Most requests to review these are left unanswered. Since manuscripts can be posted on the arxiv, I don't feel too guilty about this.

The last category of query consists of students at other schools trying to get me to do their homework for them. I had a long spate of requests from students with Turkish email addresses, wanting help with engineering calculus homework . I don't know how I got on their list. I decline all such requests.

I bet no one writes Bernard Lewis to ask him for help on their homework.

Vouchers, Libertarians, and Our Failing Public Schools

Libertarians argue that, as no public school can satisfy the disparate needs and priorities of everyone in society, citizens should not be coerced to pay taxes to support public education. For example, your neighbor might object to paying taxes to support sex education classes. You might object to paying to have your children learn French but not Chinese. With private schooling, you pay for the education which is closest (among available options) to your values and priorities. Since a fundamental libertarian principle is that government should not coerce its citizens except to protect their rights, this inability to meet simultaneously the priorities of all taxpayers is sufficient justification in the libertarian view to junk the public school system.

Public education is the most important potential leveler of opportunity in our society. Each generation has the opportunity to obtain a solid education, with its attendant economic benefits. Closing down this path for economic advancement would fundamentally alter Americans' view of the wealthy. Most of us view wealth positively, in part, perhaps because we can easily imagine ourselves or our children acquiring wealth someday. At least once a week I give my children (albeit tongue in cheek) some duty I wish them to perform for me once they are `rich and famous.' The absence of public education would fundamentally alter our view of the fluidity of the socio-economic strata, leading to more class warfare than even Nancy Pelosi can gin up.

Of course our public schools have often failed to provide a decent education. Anyone who has ever homeschooled a child rapidly discovers that children can easily learn at double the rate at which they are taught in most schools (caveat: my children have only attended 4 of the N x 100,000 schools in the U.S; so I may have some sampling error here in my treatment of 'most'.) My children have had English teachers who don't know grammar and speak substandard English, geometry teachers who don't know geometry, and history teachers who don't know anything. They have also had many good teachers, but I still resent how much time the bad teachers have wasted. So, public education as an economic equalizer is an ideal which is not always realized.

Like most small government conservatives, I assume that private schools have the potential to provide a better education than public schools, especially in large school districts, which bring out the worst in the education bureaucracy and have the potential for the greatest variety of private options. I strongly support education vouchers. Economically, however, they only make sense if they are means tested. I would be willing to wager that most private school students have parents in the top 5-10 percent of wage earners. I agree with the libertarians here: why should the middle wage earners support via voucher or tax credit the education choices of the upper and upper middle class of wage earners? A much more interesting experiment would be initially to fund vouchers only for those below the poverty level. The vouchers should also fund an amount significantly less than the current cost of public education. This will test the claim that private education can be provided more cheaply and reduce the overall cost of education.

If private schools can provide both a better and a cheaper education, then vouchers would save money and eventually lead to the founding of many more private schools and the closing of many public schools. As private schools which are not targeted at the upper income levels proliferate, perhaps more people would choose to opt out of the public schools. As the public school system shrinks, perhaps it would reform itself to survive. If not, then a growing number of private school options targeted at lower and middle class students might lead so many people to opt out of the public schools, that we would achieve a variant of the libertarian school system : a system where all or most schools are private, but public funds ensure that the poor have access to an education of sufficiently high quality that each new generation has the opportunity to exit poverty.

Once the education for the poor is guaranteed, ensuring that children are not overly constrained by the sins of their fathers, my resistance to the libertarian argument against public education lessens, but I would like to see the effects of vouchers for the poor before revisiting the debate.