The dynamical systems conference is especially excellent. It happens every other year at Snowbird Ski Resort, on top of a mountain outside of Salt Lake City, Utah. The scientific program is always stimulating, but what really makes the conference special is the group of people who attend. Everyone is just so nice, and I mean that in the best possible way. I had many good times catching up with old friends and colleagues and making new ones.

My one pet peeve about this conference is its location. Not that there's anything wrong with the specific locale. The scenery is amazing, the hotel is posh, and the service and food are excellent (albeit a bit pricey). However, Utah is a problem for me.

As a gay man, I have few rights in Utah. Utah doesn't recognize my marriage. This has many implications for me, but as one example, if I am hurt while traveling in Utah and go to the hospital, my husband has no legal standing to visit me (much less act as a family member in any other capacity). Lest you think I am alarmist about this, please see this news about a gay man arrested at his hospitalized partner's bedside. This is merely one example of many similar situations. Furthermore, sexual orientation is not protected under Utah hate crimes law. This makes me feel less safe when I travel to Utah.

The good folks at SIAM are considering a change of venue for the dynamical systems conference starting in 2017. However, the alternative location that has been proposed is in Arizona. In addition to having many of the same issues for gay people that Utah does, Arizona is terrible place for persons of foreign origin -- or even persons of domestic origin who might be mistaken for persons of foreign origin -- to travel. This is because of the hateful SB107 "papers please" law.

In the past, I raised the issue of conference site selection with various individuals at SIAM. The response I received was sympathetic, but emphasized that it is desirable to "avoid politics" in conference site selection. I find this response to be perplexing. This is a question of policy, not politics. The policies in place in various states make them unfriendly venues for certain constituencies in the professional society's membership.

After a wonderful week at my conference, I decided to raise the issue again. I'm appending below the letter that I sent to a few individuals at SIAM. If your professional organizations face a similar situation, I hope you'll think about addressing it with them (and you are free to use my letter as a template).

Dear [redacted],

Once again, I have returned from the dynamical systems conference at Snowbird convinced it is amongst the most outstanding conferences in the world. Thanks to SIAM and to all of you for a stimulating and enjoyable week.

While I was not able to be present for the business meeting, I heard that there was a conversation about the location of the meeting from 2017 onwards.

I know that finding an appropriate meeting location is a difficult task. I also recognize that the primary considerations for site choice need to be cost and suitability for the meeting. That said, there are real, concrete issues that make both choices I've heard mentioned -- Utah and Arizona -- unfriendly locations for some SIAM members. Arizona's SB1070 law penalizes people who are approached by law enforcement and do not have proof of legal presence on their person. In Arizona and Utah, same-sex couples are not protected by any hate-crimes laws, do not have their marriages recognized, and do not have hospital visitation rights. There are other issues with these states as well.

I often hear the argument that people "don't want to inject politics" into processes like conference site selection. Consideration of the aforementioned issues constitutes policy, not politics, and this is a crucial distinction. Lack of rights for persons of foreign origin (or even perceived foreign origin) and LGBT persons are real issues that could affect SIAM members traveling to the states in question.

In short, for future meetings, I hope you will consider alternative locations that are more friendly to all SIAM members.

Respectfully,
Chad

If you only read one thing about human learning, read How People Learn, Chapter 6: The Design of Learning Environments. In case you are unfamiliar with this book, it was published in 2000 by the National Research Council of the U.S. National Academies. The book gives an overview of what is known about human learning from multiple disciplinary perspectives, including neuroscience, psychology, sociology, and so forth. Even though it should go without saying, I will point out that the National Academies are a credible source. This is solid work.

The whole book is useful, but Chapter 6 is a real gem. First, it gives some useful historical context for educational goals, outlining how these are (and always have been) in flux. But the main attraction of the chapter is a discussion of four characteristics that successful learning environments have. These learning environments are

• knowledge-centered
• learner-centered
• assessment-centered, and
• community-centered.

Knowledge centeredness refers to attending to the bodies of knowledge that we want students to have. Generic "thinking skills" are not enough. For example, a successful learning environment in the field of history will pay a decent amount of attention to, well, history.

I can feel you rolling your eyes at me because this is so obvious, but it is worth articulating. What is much less obvious -- and much more important to articulate -- is that knowledge centeredness is not enough to constitute a successful learning environment. This means that if you are a brilliant historian, if you are at the forefront of historical theory and knowledge, even if you have a better command of both the facts and ideas of history than anyone else in the world, even if you are the most outgoing, charming, and engaging lecturer in the world who weaves course lectures with meaningful examples and entertaining yet relevant anecdotes, if what your course consists of is you talking at students for 60 minutes three times a week, you have not come close to designing the most effective learning environment possible.

There is so much more to worry about besides knowledge. To my eyes, most of the higher education system still puts knowledge at the center, largely to the exclusion of other factors. In doing so, the system embraces a now-antiquated understanding of human learning, envisioning the endeavor of education as an expert pouring knowledge into the brain of a novice. We now know that this is a totally inaccurate model. We must pay attention to other aspects of learning.

Learner centeredness means paying attention to the "knowledge, skills, attitudes, and beliefs" that learners bring to their experience. In short, learners all differ from each other in ways that impact their educational experience, and you have to pay attention to these differences. One size does not fit all.

Assessment centeredness means giving students ongoing opportunities for formative feedback which they might use to impact their own learning. For example, courses that have only one or two assignments (say, a midterm and a final paper) are far from being well-designed. What feedback do students receive on their learning during the intervening weeks?

Community centeredness has several aspects, including creating the classroom environment as a community, and also connecting what happens in the classroom to the larger communities of students' lives: their neighborhoods, states, countries, and so forth. Courses that don't create a classroom community and/or don't connect the course to something bigger fall short of providing the most effective educational experience.

These aren't my opinions. This is what the National Academies think, based on their aggregation of evidence from numerous sources who investigated learning through a variety of disciplinary perspectives.

Why am I thinking about all of this today? I am prompted by discussion around MOOCs, which I have written about in this post and this post. In brief, most (but not all) MOOCs are almost exclusively knowledge centered. This means they won't provide the most effective educational experience. Some MOOC boosters are thinking about the economics of MOOCs and not considering the poor experience being provided. (Again, the experience doesn't have to be poor, but so far, it usually is.) At the same time, some of those faculty decrying MOOCs seem to fear that a MOOC will displace them. A message to these faculty: the more you address the four characteristics addressed above, the harder it is going to be for a MOOC to replace you. You will be providing a vastly superior experience.

Relatedly, and somewhat more broadly, someone recently made a comment to me that "active learning (and perhaps even some of the online media that you want to distinguish from MOOCs) transform the instructor's role," and if I understood correctly, the implication was that this was bad, and constitutes a threat to higher education. I, however, think this is as it should be. We know more than we ever have known about how human learning takes place. We also have better technology than we ever have. These changes suggest why it no longer makes sense to send kids to school with horn books.

In short, it is entirely appropriate that the role of the instructor change to keep up with our expanding technological capabilities, and even more importantly, our expanding understanding of human learning.

For those interested, I have migrated my old blog and other content (at www.integralmathsolutions.com) over to this site, so all of my postings will appear in one place.

This past week's news contained the story of a scientific study that found that electroshocking the brain might improve certain mathematical abilities. And of course, as for a response to this story, the Onion nailed it, as usual.

I want to talk about a few points that have been raised to me.

First, the author of this piece and this piece wrote a thoughtful response to my original post. His comments included:

MOOC's are "threatening to destroy higher education as we know it." And you seem to think that this is incorrect. But I think the difference between us is not our opinion of MOOCs but of the politics through which the MOOC thing is happening. I live in California, where the MOOC-booster rhetoric that you find so irritating is being spoken by politically connected Silicon Valley entrepreneurs and lawmakers, who are right now literally pushing actual legislation which would require all California public universities to accept MOOCs as transfer credit. This is not something that might someday happen; it is happening right now, being pushed by profiteers who want to make money off CA's broke-ass universities and by lawmakers who want to weasel out of funding them. The fact that MOOCs as they now exist "suck" has not dissuaded them. If you pretend that this isn't happening--or pretend that other states aren't watching and preparing similar measures--then I suppose it can seem like it's a lot of sound and fury about nothing.

I am not a fact denier. It is an undeniable truth that this is happening. I also agree that this is bad because most MOOCs, per my previous post, suck. For this reason -- also per my previous post -- I think a discussion of actual pedagogy is very important (an issue to which I will return momentarily). People pushing this legislation are mostly concerned with the economics and not with the educational outcomes. I think that if such a law passes, it will (at least in the short term) result in a lot of bad education for a lot of students.

All that said, excuse the trite saying, but I think MOOCs will represent an evolution (of degree still to be determined) and not a revolution. But higher education has always been evolving. For instance, we no long have a system (at least, in this country) where a select few students receive a tutorial-style education from an expert. We have higher education on a much more massive scale.

I've also been involved in a stimulating Facebook conversation with an old friend from college. He is a smart guy whom I respect a lot, so I am taking his ideas and his framing (with which I stringently disagree, at least right now) very seriously. One fascinating aspect of the conversation is that (in a very respectful way) he has attached my ideas to conservative rhetoric. This is not something I am used to being accused of!

I hope it's ok with him for me to share some of what he wrote (to the author: I am happy to take this down if you want me to).

But I'm wary of the way your post seems to shift attention to this ("If you are someone who speaks strongly against MOOCs, I ask you to ask yourself what steps you have taken recently to improve your own pedagogy"). This seems to be a shift away from the political and toward an ethical language of conscience and individual responsibility. It recalls recent talk about improving secondary education by firing bad teachers--not that there aren't bad teachers, but that that was a rhetorical move appealing conservative ideology through a protestant moral language, and it drew attention from the political stakes to our imagination of bad teachers. Your purpose is nobler, but to me the post seems to internalize the same rhetoric. I would argue that the obverse of this rhetoric, in current talk about education, is an emphasis on measurable results that supplants other ways of talking about education as a collective undertaking. On the one side, individual conscience and effort, and on the other, measurable results and so a logic of efficiency, which presently encourages corporate privatization. I think it makes sense to call this a neoliberal reshaping of universities. Insofar as it's not only an ideological tendency but also a conscious political goal of some Republicans, it aims to mitigate the institution's critical function and make it more subservient to capital. I'm sometimes struck when the (usually liberal/progressive) proponents of MOOCs and active learning, including both the utopians you mentioned and the grad students involved in active learning research, seem to share the conservatives' vocabulary.

He also said:

I interpret the present attacks on tenure and academic freedom, together with the moves to use technology to make teachers disposable, to create shared curricula, and to reduce faculty governance in favor of administration by businesspeople, as efforts to control these critical functions. (I would go further and say that the tendency is to integrate the institution as part of a smoothly operating machine of capital.) These efforts are explicit in the Republicans' "war on education," and the goals I've described have been clearly enunciated on occasion, but I'm equally concerned that the Republicans are only the hard edge of neoliberal ideology that both parties share, and that what universities are facing at the moment (in a form exacerbated by the possibility of technological solutions) is the logical extension of neoliberal economy.

My friend also speaks against active learning and related modalities:

I would argue, given the right forum, that MOOCs and active learning (and perhaps even some of the online media that you want to distinguish from MOOCs) transform the instructor's role, and that this transformation harmonizes with other institutional changes like tenure elimination and use of adjunct faculty. So when I wrote about making teachers disposable, I was talking about making them *individually* disposable. Alterations in the nature of instruction turn faculty (like primary and secondary teachers) into a more manageable labor pool, with instructors hired and fired as needed, except for research faculty at top schools and in fields where research is not privatized. I would also speculate that these shifts are correlated with changes in the relation between students and instructors, e.g. the customer service model of higher education.

I feel some of this gets a bit far afield of the original topic of MOOCs, but here's where I start to have a problem with the overall framing. To my friend, I think the central political economic question is about the preservation of the system of higher education that we have (from the point of view of the people who are part of that system). To me, I think the central political economic question is about students, and, from the perspective of class, I feel troubled by his framing. We tell people in this country that higher education is transformative and is a gateway to achieving the American dream, and then we charge an amount for it that causes most individuals/families to undertake financial hardship, sometimes extreme. Much like the proposed California legislation, this is a real, measurable fact. I think that the people sacrificing for a college education are entitled to have the best possible education, and to have some evidence that it is effective. And this goes back to why I think we must talk about pedagogy. I wonder if worrying about preserving the internal structure of higher education and protecting it from change is a privilege of the people who work in it.

One small thing I want to comment on is my friend's statement that "active learning (and perhaps even some of the online media that you want to distinguish from MOOCs) transform the instructor's role." Yes, they do! What I don't get is why this is bad. I think it has to do with an evolved understanding of how human learning takes place. I could be misreading his statement, but it seems to value the "sage on a stage" model of learning. While this model can certainly be effective if/when done well, I think modern learning science demonstrates that an equally important part of instruction is having the instructor serve as a guide and facilitator as the student constructs meaning from a variety of different types of learning experiences. The criticism of "active learning" is new to me!

Please stop freaking out about MOOCs. Seriously.

The national conversation about MOOCs is driving me bonkers. Like some of you, I have read (too) many articles on the topic of Massive Open Online Courses. I already feel saturated, but over the past few days, two more snippets have appeared in my Facebook feed:

The MOOC moment and the end of reform

A moment of dreaming about higher education

and these have put me over the edge. These are both written by the same author, a graduate student at Berkeley. I don't mean to single out this guy, but his writing encompasses one of the extremes of the MOOC debate: naysayers who decry MOOCs as threatening to destroy higher education as we know it.

On the other end of the spectrum, we have the MOOC boosters -- including the producers and some of the consumers of these courses -- who praise MOOCs as a revolution, a panacea, or both.

The writing I see from both sides is full of inaccuracies and misconceptions. It is probably fruitless for me to try to straighten out the national conversation, but I am a stupid optimist, so I will try. So everyone, please think about the following points, via which I will attempt to inject a dose of reality. In my re-reading of this post, it definitely comes off as more critical of the MOOC critics. That said, I want you to know that I find both sides to be equally irritating.

Point #1: MOOCs are sucking up all the oxygen in the world of online courses. There are online courses that take formats other than that of a MOOC. I should know. I am teaching one, and it is nothing like a MOOC. Unfortunately, many people use the word MOOC synonymously for "online course." This has two negative effects. First, it confuses the conversation. Second, it makes some of the critics discount online formats and technologies that might be incredibly useful to them.

Point #2: MOOCs are sucking up all the oxygen in the world of pedagogy in general. The more we talk about MOOCs, the less we talk about what we are doing in our on-the-ground courses. I hate to be biased, but I especially find fault with the critics here. Do the critics of MOOCs look inward and scrutinize their own on-the-ground courses? If you are someone who speaks strongly against MOOCs, I ask you to ask yourself what steps you have taken recently to improve your own pedagogy. What is needed is a culture of self-reflection and continual improvement for all instructors of all types of courses. Most faculty do not live in such a culture.

Point #3: Many principles of good pedagogy are the same on the ground as they are online. Professors who suck on the ground will suck online. Professors who are great on the ground might be great online if they think about the additional constraints and affordances of that environment.

Point #4: It is not bad to divide lecture material into small bits. I often hear criticism of MOOCs that divide lecture material into small (5 - 20 minute) snippets. The specific complaint is that this division contributes to and/or caters to students' short attention spans, and progresses the shallow TED-talk-ification of education. The critics are simply wrong. Learning scientists know a lot about cognitive (over)load. There is a real benefit to letting students absorb 60 minutes worth of material in three parts, and with the affordances of pause and rewind buttons. To the critics, I say this: why on earth do you think students have absorbed everything in your 60 minute in-class lecture? Do you really think that the mere fact of them being in the room and the mere fact of you talking for 60 minutes means that an effective educational experience has taken place?

Point #5: Related to some previous points, I actually think MOOCs as they exist now suck, but they don't have to. I am sure they don't all suck, but most of them do. The sucky ones consist of an on-the-ground class that is video captured and slapped online, possibly with a few graded or ungraded assessments. This results in a MOOC that is little more than a textbook, and as we know, a textbook is not a course. MOOCs could be much more than this, but there are two reasons they aren't. First, the field simply needs more time to evolve. Second, what garners attention for many MOOCs is the fame of the faculty member teaching it. Their fame usually stems from stature within the world of research. I don't mean to malign the teaching of accomplished researchers, but as there are only 24 hours in the day, it seems plausible that the more research intensive a faculty member is, the less time they will devote to pedagogical improvement and innovation. I am sure this comment will piss off a lot of people. Maybe every MOOC should be co-taught by a famous faculty member and a faculty member who is extremely well-versed in pedagogy and instructional design.

I am sure there is more I should say, but my fingers are tired of ranting.

In conclusion, everyone, please calm the %*&# down about MOOCs and start thinking about good teaching in general.

I can already hear the political economy people writing me hate mail.

Love,

Chad

I feel privileged to be a professor of applied mathematics at Macalester College. I also feel very lucky that you are part of the Macalester community, that you share your presence with us here on campus, and that you operate your wonderful bookstore right in our backyard.

I'm writing because I heard a rumor -- always a dangerous thing, I know -- about a remark you may have made at a Macalester event on May 8, namely that "It is possible to live a very good life in America without any math. They won't tell you that at Macalester, but it's true." You're half right -- we won't tell them that at Macalester!

It might be strictly true that it is possible, but this is not a very useful assessment, and is probably misleading to the casual listener. After all, many things are possible! It's possible that I might win the lottery tomorrow and retire. Well actually, I won't, because I am not a gambling man. But you get my drift. It's possible that I might get invited to my neighbor's house for dinner, but this is unlikely because I have only lived in Minnesota for a mere six years.

Math skills have always been fundamentally important, but that is more true today than ever. Our students need these skills. Math plays a role not only in... well, math... but in almost everything. Just look at the burgeoning field of the digital humanities! Look at the explosion of societally-pivotal problems related to "big data"! Look at the economic problems our nation is struggling with! Students who have math skills will be better equipped to be better citizens of the world. This is what we care about at Macalester.

Let me leave you with a question and an invitation. The question is: why is math society's punching bag? I suspect we would never tell people "you can have a very good life in America without any reading." The invitation is: swing by my office sometime. I'd love to chat with you more about this.

Cheers and best wishes,

Chad Topaz
Macalester College
Associate Professor of Mathematics

Instead of talking about my feelings here, I will present you with some quantitative food for thought.

There are 31 states that have enacted constitutional gay marriage bans of one sort or another. I've taken the data on that link and compiled it into a publicly accessible Google Doc so that you can mess around with the data if you wish.

I don't have it in me right now to do any fancy modeling (I am still too angry) but I did upload the data into Wolfram Alpha. I've blogged before about Alpha, which is a great tool. If you upgrade to a pro subscription (I am not a salesman... I do find the upgrade to be a little pricey) you can access even more convenient features, like uploading data sets and such. This is what I did with the marriage amendment data. I didn't even know what I wanted to do with the data, so I simply typed the name of my data set as the query, and Alpha decided on all kinds of analyses to spit back out at me. Here is some of it. I guess that if there is a pedagogical point here, it's that the way a quantitative modeler often gets started is just by plotting things.

Here's a geographic heat map where the shading corresponds to the fraction of votes supporting a discriminatory measure in a given state. The reason Nevada shows up as over 100% is that there were two votes in Nevada, one in 2000 and one in 2002 (each one receiving in the high 60%'s range). At any rate, I don't see too much structure in this map.

Here's a histogram of the years in which the discriminatory amendments passed.

You can see that 2004/05 were busy years. Here's what I think are the most interesting plots, namely a histogram of the discriminatory vote percentage and a distribution fit (which you can get a feel for via the quantile plot on the right). Alpha finds that the best fit distribution is uniform.

I am not yet sure what I want to do with any of this, but it at least lets me start trying (perhaps in vain) to make sense of the hate in this country.

Two posts ago, I talked about "the unreasonable effectiveness of mathematics" -- the surprising and amazing success that mathematics has had describing phenomena in the real world. I also showed this graph I put together of the number of Facebook users over time:

Then, last time I went on a big long digression to introduce you to differential equations. I introduced the differential equation

[frac{dx}{dt} = rx ]

which describes a particular scenario of growth in continuous time. More specifically, the left side of the equation is just formal mathematical notation for change, known as a derivative. If is the amount of money in your savings account, what this equation says is that at every moment in time, the way your bank account changes is that it accrues times the amount of money currently in the account. This is called continuous compounding. The solution to the differential equation -- meaning the formula that actually follows -- is

[ x(t) = x_0 mathrm{e}^{r t} ]

Since we are in the midst of an economic depression, let's talk about money. Suppose you have a savings account that yields interest on whatever you current balance is. And say that you deposit 100.41. We can write this as

[100 (1+0.004074)^1 = 100.82.]

This is called compounding. After the second month, you didn't just earn interest on your original 105.00. ]

We say that the annualized percentage rate is 5%. In other words, in terms of your bottom line, earning 0.4074% per month 12 times a year on an untouched account is that same as earning 5% one time at the end of the year.

This example so far has ben set in what we call discrete time. Compounding happens at distinct moments (for instance, the end of each month). But what if instead of happening at distinct moments, things happen at every moment in time? In case that made your brain explode, suppose that instead of earning 0.4074% once per month, you earned half of that, namely 0.2037%, twice a month. In this case, instead of ending up with 100.05 and an additional 1/2 cent. This is close to, but not the same as, our original example. And then imagine that you earned a quarter of the original interest rate, but compounding happened four times a month. Then you'd end up with 105.01. In short, you'd earn a whopping extra cent due to the continuous, rather than discrete, compounding.

A common way to describe a problem where something grows in continuous time is to use a differential equation. I'm about to write down a simple differential equation which I call "the most important differential equation in the world." My students know it by this name. If you ask them "what's the most important differential equation in the world," they will write down this equation. If you write down the equation and ask them the name, they'll tell it to you. The equation is

[frac{dx}{dt} = rx. ]

This equation can describe our continuously compounded interest problem. In that case, is the amount of money in your savings account, and it depends on time measured in months. The left side of the equation is just formal mathematical notation for change, known as a derivative. I'll post more on derivatives another time. For now, when you see , you should replace it in your head with "how quickly my bank balance is changing over time." Then there's an equals sign, which means that on the right hand side of the equation, we are going to put in the proper rule describing a savings account. The parameter is the rate of continuous compounding. So the equation says that at every moment in time, the way your bank account changes is that it accrues times the amount of money currently in the account. If we want to have an annualized rate of 5%, it turns out that we need to choose to be about 0.0040658, which is close to, but not the same as, the value of 0.004074 needed to earn 5% annual when compounding only takes place 12 times a year, rather than continuously. To restate: if your 105.

One advantage of having a differential equation description of something is that it is sometimes possible to solve the differential equation, that is, to write down a formula for the unknown function which in our case describes the amount of money in the bank account over time. If you start out with r=0.0040658ttt = 12x(12) = .

Believe it or not, we are now ready to move back to Facebook... tomorrow. But I swear, I am going to make you say "whoa!" and it will have been worth the wait.