On Master's Programs in Economics
With the large demand for graduate education in economics by Chinese students, many economics departments have recently established terminal master’s programs in economics, or are seriously considering doing so. (A terminal master’s program is one that is separate from the PhD program and typically does not lead to a PhD in the same department.) I was Director of the Master of Applied Economics (MAE) Program at the University of Michigan from July 2010 to December 2012, so I wanted to share some thoughts about master’s programs in economics.
The University of Michigan Master of Applied Economics Program. The MAE program at the University of Michigan was well-established long before I arrived as an assistant professor at the University of Michigan in 1987. The composition of the student body has shifted over the years, but the basic nature of the program has not. Our MAE program is very flexible. The formal requirements can be found on the MAE website, but a surprisingly close approximation to the requirements is that there are 5 semester core courses, and then an additional 6 courses that in practice can be almost anything suitably advanced. (There is no master’s thesis in our MAE program.) Students greatly value this flexibility. Here are some examples of different categories of students in our MAE program:
- Mid-career government officials who come to increase their knowledge of economics and their skills before returning to government service. For example, in 2012 we admitted employees of the Central Banks of Japan, Korea, Turkey, Mexico, and Chile, and employees of other government agencies in Afghanistan, Pakistan, Kazakhstan, Korea, Japan, Singapore, Indonesia, Thailand, and China.
- Dual-degree students in other programs at the University of Michigan who realize the value of learning more economics. For example, in 2012 we had dual degree students who were also pursuing a degree in Public Policy, Financial Engineering, MBA and PhD from the Ross Business School, Kinesiology, Urban Planning, Natural Resources, Psychology, Statistics, Education, Health Services Organization and Policy, Industrial and Operations Engineering.
- Students who have recently received a bachelor’s degree who hope to prepare for a career in government service, including service in international organizations such as the World Bank and the IMF.
- Students who have recently received a bachelor’s degree who hope to prepare for a career in finance.
- Students who tried and failed to get into a Ph.D. program who need a way to further their economics training while they figure out what to do next in their lives if their plan of getting a Ph.D. looks impossible.
- Students who belatedly realized their interest in economics and want to switch into economics from another discipline.
- Students with a wide range of other objectives. Here is a list drawn from admittees this year: (a) more analytical rigor to further a business career, (b) understand economics better after having been an economic reporter, (c) get a job in a think tank, as a consultant, as an economic analyst, or in an NGO, (d) understand the art market better, and (e) have a better chance of success as an entrepreneur or running a company.
Most students can easily complete the program in 3 semesters, though a large minority choose to stay 4 semesters, given the attractions of being in our program and being in Ann Arbor. The 5 core courses are all specially designed for the MAE students. They are:
- Math for Economists
- Microeconomics
- Macroeconomics
- 2 Semesters of Econometrics
For their other 6 courses, MAE students fan out to a wide variety of courses. With a few exceptions, the number of MAE students in any one course they take as an elective is so few that they can easily be accommodated. These electives are all classes that would exist even if we didn’t have an MAE program. For example, MAE students take many advanced undergraduate economics classes. Our advanced undergraduate classes are at the right level for most MAE students, given how rigorous our undergraduate program is. But MAE students also take many classes from other departments and schools within the university: math classes, statistics classes, public policy classes and business school classes. (The University of Michigan has modest transfers between units to compensate units for doing part of the education having students from other schools in their classes. These are sufficient that other units don’t mind having our MAE students in their classes.)
Preparation for PhD Programs? One of my biggest surprises when I became the Director of our MAE program was learning how small our role is in preparing students for PhD programs. As the examples I gave above, the bulk of our students had other goals. Indeed, the modal goal was to do something much like an MBA, but with less networking and more economic rigor. For those students who did want to go on to a PhD program, I had to tell them that our MAE program had no special magic in that regard. Noah Smith and I give our advice about getting into economics PhD programs in “The Complete Guide to Getting into an Economics PhD Program.” But getting a master’s degree is not a key component of that advice. I would be interested in the placement results of other master’s programs into PhD programs, but I felt lucky when we had a handful of our MAE graduates accepted into PhD programs. (Some PhD programs give a preference to graduates of their department’s master’s program. Michigan’s PhD program does not. So I am talking primarily about admission to the PhD programs of other universities.)
Resource Cost: What this means is that the incremental faculty resources needed to keep our MAE program going are only the equivalent of fielding 6 classes: the 5 core classes, plus 1 course worth of administrative time on the part of the Director. In addition, there is a staff coordinator (who has some other non-MAE duties in the department as well). Our MAE program also spends a few hundred dollars a year on parties. (My main innovations as Director of the program were aimed at fully integrating the MAE students into our department socially and making sure they interacted with one another socially as well.) That is about it.
I wish we had more resources devoted to career counseling for MAE students. I think the extra resources that would be needed are quite reasonable in magnitude. There have been discussions in our department about doing exactly that. Also, we have had discussions about adding one elective specifically for MAE students directed at research.
Demand for Master’s Programs: I was amazed at the quality of the applicants to our MAE program. And it isn’t just the grades and test scores. The essays are heartfelt and impressive as well. Of the students we admitted, about 1 in 3 came to our program the first year I did admissions, and almost 1 in 2 came to our program the last year I did admissions. The overwhelming bulk of our applicants (75% or so) were from China. Yet we had no problem in filling out our MAE classes with good students even back in the days when China did not yet believe in students getting an education in Neoclassical economics. So the demand of students for an education in our MAE program far exceeds the number of slots we have. If we were a regular business, we would expand much more than we have. But elite universities remain elite by restricting the supply of spaces in their programs. And the elite reputation of a university spills over from one department to the next. So we are not allowed to expand our program beyond a target of about 50 students in each entering class. I suspect some other economics departments face similar constraints. To the extent existing master’s programs do not expand to meet the demand, it makes sense for additional departments to set up master’s programs.
Conclusion: My main piece of advice to economics departments thinking of setting up a terminal master’s program in economics is to consider the University of Michigan’s low-overhead model of running its MAE program. This is not just a matter of money. Staffing requires also finding faculty who meet our high standards. So programs that rely on larger increments of faculty time are likely to run into staffing headaches that go beyond just needing to pay the salaries.
Mary O'Keeffe on Slow-Cooked Math
Mary O'Keeffe was my Ec 10 teacher back in 1977-1978. She has appeared previously on supplysideliberal.com in “My Ec 10 Teacher Mary O’Keeffe Reviews My Blog” and “Another Reminiscence from My Ec 10 Teacher, Mary O’Keeffe.” She gave me permission to share this Facebook post she made in response to the post “Cathy O'Neill on Slow-Cooked Math”:
I am also a slow-cook mathematician, for the most part. I find I have to get into a state of flow in order to really think math through. Often I find it takes me a while to really understand exactly what the problem is getting at—but after a while, it just sinks in and becomes blindingly crystal clear and beautiful. I am rather glad that I didn’t experience buzzer-style or any kind of timed math contests as a kid—they might have permanently discouraged me and induced me into giving up on doing anything mathematically related. I think one of the reasons my husband and I were such a good partnership (professionally) was that he was good at blazing fast insights and I was good at thinking things through more rigorously and deeply. (This is somewhat of a stereotype. We didn’t always fit neatly into these separate boxes, but it is a pretty good first approximation description.)
Quartz #45—>Actually, There Was Some Real Policy in Obama's Speech
Here is the full text of my 45th Quartz column, “Actually, there was some real policy in Obama’s speech,” now brought home to supplysideliberal.com. It was first published on January 29, 2014. Links to all my other columns can be found here.
If you want to mirror the content of this post on another site, that is possible for a limited time if you read the legal notice at this link and include both a link to the original Quartz column and the following copyright notice:
© January 29, 2014: Miles Kimball, as first published on Quartz. Used by permission according to a temporary nonexclusive license expiring June 30, 2015. All rights reserved.
In National Review Online, Ramesh Ponnuru described last night’s State of the Union speech as “… a laundry list of mostly dinky initiatives, and as such a return to Clinton’s style of State of the Union addresses.” I agree with the comparison to Bill Clinton’s appeal to the country’s political center, but Ponnuru’s dismissal of the new initiatives the president mentioned as “dinky” is short-sighted.
In the storm and fury of the political gridiron, the thing to watch is where the line of scrimmage is. And it is precisely initiatives that seem “dinky” because they might have bipartisan support that best show where the political and policy consensus is moving. Here are the hints I gleaned from the text of the State of the Union that policy and politics might be moving in a helpful direction.
- The president invoked Michelle Obama’s campaign against childhood obesity as something uncontroversial. But this is actually part of what could be a big shift toward viewing obesity to an important degree as a social problem to be addressed as communities instead of solely as a personal problem.
- The president pushed greater funding for basic research, saying: “Congress should undo the damage done by last year’s cuts to basic research so we can unleash the next great American discovery.” Although neither party has ever been against support for basic research, budget pressures often get in the way. And limits on the length of State of the Union addresses very often mean that science only gets mentioned when it touches on political bones of contention such as stem-cell research or global warming. So it matters that support for basic research got this level of prominence in the State of the Union address. In the long run, more funding for the basic research could have a much greater effect on economic growth than most of the other economicpolicies debated in Congress.
- The president had kind words for natural gas and among “renewables” only mentions solar energy. This marks a shift toward a vision of coping with global warming that can actually work: Noah Smith’s vision of using natural gas while we phase out coal and improving solar power until solar power finally replaces most natural gas use as well. It is wishful thinking to think that other forms of renewable energy such as wind power will ever take care of a much bigger share of our energy needs than they do now, but solar power is a different matter entirely. Ramez Naam’s Scientific American blog post “Smaller, cheaper, faster: Does Moore’s law apply to solar cells“ says it all. (Don’t miss his most striking graph, the sixth one in the post.)
- The president emphasized the economic benefits of immigration. I wish he would go even further, as I urged immediately after his reelection in my column, “Obama could really help the US economy by pushing for more legal immigration.” The key thing is to emphasize increasing legal immigration, in a way designed to maximally help our economy. If the rate of legal immigration is raised enough, then the issue of “amnesty” for undocumented immigrants doesn’t have to be raised: if the line is moving fast enough, it is more reasonable to ask those here against our laws to go to the back of the line. The other way to help politically detoxify many immigration issues is to reduce the short-run partisan impact of more legal immigration by agreeing that while it will be much easier to become a permanent legal resident,citizenship with its attendant voting rights and consequent responsibility to help steer our nation in the right direction is something that comes after many years of living in America and absorbing American values. Indeed, I think it would be perfectly reasonable to stipulate that it should take 18 years after getting a green card before becoming a citizen and getting the right to vote—just as it takes 18 years after being born in America to have the right to vote.
- With his push for pre-kindergarten education at one end and expanded access to community colleges at the other end, Obama has recognized that we need to increase the quantity as well as the quality of education in America. This is all well and good, but these initiatives are focusing on the most costly ways of increasing the quantity of education. The truly cost-effective way of delivering more education is to expand the school day and school year. (I lay out how to do this within existing school budgets in “Magic Ingredient 1: More K-12 School.”)
- Finally, the president promises to create new forms of retirement savings accounts (the one idea that Ramesh Ponnuru thought was promising in the State of the Union speech). Though this specific initiative is only a baby step, the idea that we should work toward making it easier from a paperwork point of view for people to start saving for retirement than to not start saving for retirement is an idea whose time has come. And it is much more important than people realize. In a way that takes some serious economic theory to explain, increasing the saving rate by making it administratively easier to start saving effects not only people’s financial security during retirement, but also aids American competitiveness internationally, by making it possible to invest out of American saving instead of having to invest out of China’s saving.
Put together, the things that Barack Obama thought were relatively uncontroversial to propose in his State of the Union speech give me hope that key aspects of US economic policy might be moving in a positive direction, even while other aspects of economic policy stay sadly mired in partisan brawls. I am an optimist about our nation’s future because I believe that, in fits and starts, good ideas that are not too strongly identified with one party or the other tend to make their way into policy eventually. Political combat is noisy, while political cooperation is quiet. But quiet progress counts for a lot. And glimmers of hope are better than having no hope at all.
Matt Rognlie on Misdiagnosis of Difficulties and the Fear of Looking Foolish as Barriers to Learning
Matthew Rognlie when he was an undergraduate at Duke, before going to the Ph.D. program in economics at MIT. Here is Matt’s blog.
I have been very impressed with Matthew Rognlie ever since our debate “Sticky Prices vs. Sticky Wages.” In addition to my being pleased with that debate, it is one of the most popular posts on supplysideliberal.com and had this wonderful review from Simon Wren-Lewis:
Yet debates among macroeconomists about whether and why wages are sticky go on. As this excellent example (I’ve been wanting to link to it for some time, just because of its quality) shows, they are not just debates between Keynesians and anti-Keynesians, so I do not think you can put this all down to some kind of ideological divide.
So I was delighted to get this email from Matt, which he gave me permission to share with you, after light editing.
Like many others, I enjoyed your and Noah’s article on math learning. In general, I’ve found that most students are puzzlingly quick to conclude that their failure to understand some concept is due to some innate ability, even when it’s hardly plausible that there is any kind of innate barrier. My favorite example of this comes from my high school chemistry class, where I remember talking with one of my classmates about studying for the big exam, and when the time came to talk about some class of reactions she said “oh, I’m not very good at that type of reaction”. And it wasn’t “I keep forgetting that part, so I need to study it more” - the vibe was more “I am just not talented enough to figure out that part of the class, so I’m going to write it off and spend my time elsewhere”.
I remember thinking that this was totally insane - she had mastered all kinds of very similar material in the class, and there was no reason why this particular material should be any more difficult. Even if we do have sizable innate differences in various high-level cognitive skills (memory for facts, memory for ideas, analytical skills, etc.), it is inconceivable that these differences could be so fine-grained that they would prevent her from learning about reactions B, D, and F when she already understood the very similar A, C, and E. Instead, clearly what had happened was that some tiny ambiguity in the presentation of B, D, and F confused her, and with a little more time and exposure she could have resolved it. And it wasn’t that she was unwilling to devote this time due to laziness. Instead, she honestly believed that there was something fundamental barring her from ever understanding this part of the course.
In that case, it was easy for me to see that her belief was ridiculous, but in all honesty I’ve displayed the exact same pattern on many instances. So many times I’ve seen references to some unfamiliar and mysterious concept of math or economics, and nearly written it off as something I’d need ages to understand - and then, when I finally decide to just learn it, I realize that the basic idea is really quite simple. And now, even though intellectually I know that it is very unlikely that any particular concept I encounter is beyond me, it can be very difficult to shake the attitude “oh, X is so confusing, that’s just a hopeless dead zone for me”. I suspect that many students who struggle with math have a much more pervasive and crippling case of the same basic mental block.
One amateurish theory of mine is that the young are better than the old at learning in large part because they are less susceptible to this mental block. This is related to my wife’s theory that the young are better at learning languages because they are less reserved about charging ahead and trying to speak in a new language. Once someone has already mastered one language, it is easy to become hesitant and neurotic when venturing into a new one - it’s incredibly frustrating to formulate your thoughts in the language of a 2nd grader when you could sound immeasurably more sophisticated in English. Yet this process is essential to learning.
The same is true of math. I’ve encountered many articulate and intelligent people who break down in the face of even elementary math. My theory for these people is that their mathematical ineptitude is driven mainly by fear - they know that they won’t be able to converse in math with nearly the same style and intelligence as in English, and are embarrassed to even try. Over time this attitude reinforces itself.
Matt Waite: How I Faced My Fears and Learned to Be Good at Math
Matt Waite
The Bible says “Cast your bread upon the waters, for you shall find it after many days.” When Noah and published “There’s One Key Difference Between Kids Who Excel at Math and Those Who Don’t,” it didn’t take many days at all before we received many reactions that I feel add a lot to the case we tried to make. One of those reactions was from Matt Waite. I am grateful for his permission to reproduce his post
here as a guest post.
“You might think the principal coder behind PolitiFact took naturally to math. You’d be wrong.”
Somewhere in middle school, I had convinced myself that I was bad at math. It was okay: My mom was bad at math too. So were lots of people I looked up to. “Bad at math” was a thing — probably even genetic — and it was okay.
I so thoroughly convinced myself that I was bad at math that I very nearly didn’t graduate from high school. It took tutors and hours a week to squeak through an advanced algebra class my friends had all breezed through on their way to much harder classes.
But it was okay. I was bad at math. They weren’t. Simple as that.
And it was all a lie.
“Bad at math” is a lie you tell yourself to make failure at math hurt less. That’s all it is.Professors Miles Kimball and Noah Smith wrote in The Atlantic that many of us faced a moment in our lives where we entered a math class that some of us were prepared for and some of us weren’t. Those that got it right away were “good at math” and those who didn’t, well, weren’t. Or so we believed. Those who were good kept working to stay good, and those of us who were bad at it believed the lie.
Now, Kimball and Smith write that bad at math is “the most self-destructive idea in America today.”
Well, Professors Kimball and Smith, welcome to journalism, where “bad at math” isn’t just a destructive idea — it’s a badge of honor. It’s your admission to the club. It’s woven into the very fabric of identity as a journalist.
And it’s a destructive lie. One I would say most journalists believe. It’s a lie that may well be a lurking variable in the death of journalism’s institutions.
Name me a hot growth area in journalism and I’ll show you an area in desperate need of people who can do a bit of math. Data. Programming. Visualization. It’s telling that most of the effort now is around recruiting people from outside journalism to do these things.
But it doesn’t end there. Name me a place where journalism needs help, and I’ll show you more places where math is a daily need: analytics, product development, market analysis. All “business side” jobs, right? Not anymore.
Truth is, “bad at math” was never a good thing in journalism, even when things like data and analytics weren’t a part of the job. Covering a city budget? It’s shameful how many newsroom creatures can’t calculate percent change. Covering sports? It’s embarrassing how many sports writers dismiss the gigantic leaps forward in data analysis in all sports as “nerd stuff.”
In short, we’ve created a culture where ignorance of a subject is not only accepted, it’s glorified. Ha ha! Journalists are bad at math! Fire is hot and water is wet too!
I’m not going to tell you how to get good at math by giving you links to online materials or MOOCs or whatever. I’m not. You can Google. You should do that. No, I’m going to tell you a story.
Through grit and luck and a Hail Mary pass of a grade on a final exam, I did graduate from high school. And in 1993 I went to the University of Nebraska-Lincoln, where the College of Journalism and Mass Communications at the time said the curricular equivalent of “Math? Why the hell do you need math?” I thought this was great. No math? I must be in heaven.
Twenty years later, I’m now a professor in that same journalism school that let me skip out of math. We don’t do that anymore, but our math requirements are pretty thin and universally reviled by students, most of whom would say they’re bad at math. As a professor, I can take classes for free. And it’s abundantly obvious to me that journalism’s problems aren’t with journalism — they’re about money. Where does one go to learn about money? Business school.
So I thought I would get an MBA to better understand the business side of journalism. I walked over to the business college and told them I wanted to do this. “Have you had calculus as an undergrad?” Oh. Uh, no. “Have to have it. It’s an admission requirement.”
So almost two decades to the day that I set foot on campus, there I was, taking a math placement exam. This exam is given to all incoming freshmen to determine which math class they should start with. I took it and could barely read the questions. If they had given me a grade, I would have bombed it. I tested straight into a remedial math class for students who didn’t get enough in high school. Congrats, Math Department: Your test nailed it.
I probably could have crammed and watched Khan Academy videos for hours, taken it again, and landed in a higher math class. But I would have felt like I cheated my way in. And that would have been terrifying. So, I took the class. Math 100A. Just a 37-year-old professor and 30 or so 18-year-old freshmen. Totally normal; I didn’t stick out at all. The instructor was in first grade when I was last in a math class. She asked me what I was doing there. Told her my story. Her reaction: She was bad at math too, until she got to college. Now, she’s getting a Ph.D. in it.
Given all that, I lived in absolute terror that I wouldn’t do well. I sat in the front row. I asked questions non-stop. I did all the homework. I did extra practice problems. I raised my hand to answer questions so much the instructor asked me to stop. I studied for hours.
And I got an A+. I was shocked. And elated. In spite of the fact that I’m a grownup and should get an A in a remedial course, I was pumped up. I can’t remember my last A in math.
On to the next class. Math 101: College Algebra. Just the name gave me chills. I could barely pass high school algebra; how the hell was I going to handle college algebra? Here I was, a grown man with a family and a house and a job and a resume, sweating bullets and losing sleep about a class freshmen take.
Same plan, same result: Work hard, get A+.
I’m halfway through calculus this semester. I have never in my life worked this hard in a class. I’ve never sat awake at night worrying about a class like I have tossing and turning thinking about how to calculate the derivative of something. I can go speak in front of 1,000 people with less than five minutes of preparation and be downright calm compared to the feeling I have going to take a test.
Right now, I’ve got a B+. And if I walk out of there with it, it’ll easily be the most proud of a grade I’ll ever have been.
Why? Because at this level, I’m seeing the consequences of how a student approaches math. On each test, the median score has been around a high F or a low D. The last test saw more than half the class fail. It’s brutal. Of the 111 students in the class, I’m guessing 70 of them will be taking it again.
The only advantage I have over my classmates? I know exactly how to fail at math: Don’t put any effort in. Blow it off. Do something else. A glass of wine and a rerun of Big Bang Theory kicks the crap out of applications of extrema using derivatives, even if you hate wine and loathe Big Bang Theory.
But that’s the lesson I’ve learned: The difference between good at math and bad at math is hard work. It’s trying. It’s trying hard. It’s trying harder than you’ve ever tried before. That’s it.
So do me a favor: Try. Stop with the jokes. Stop telling me, “Oh, I could never do that” when you ask me about math. Because it’s not true. You can. If you try.
You can be good at math.
Matt Waite is a professor of practice at the College of Journalism and Mass Communications. Previously, he was senior news technologist at the St. Petersburg Times, where he was the principal developer of the Pulitzer Prize-winning PolitiFact.
Quartz #43—>That Baby Born in Bethlehem Should Inspire Society to Keep Redeeming Itself
Here is the full text of my 43d Quartz column, “That baby born in Bethlehem should inspire society to keep redeeming itself,” now brought home to supplysideliberal.com. It was first published on December 8, 2013. Links to all my other columns can be found here.
I followed up the main theme of this column with my post “The Importance of the Next Generation: Thomas Jefferson Grokked It.” I followed up the gay marriage theme with my column “The Case for Gay Marriage is Made in the Freedom of Religion.” I also have a draft column on abortion policy that is waiting for a news hook as an occasion to publish it.
If you want to mirror the content of this post on another site, that is possible for a limited time if you read the legal notice at this link and include both a link to the original Quartz column and the following copyright notice:
© December 8, 2013: Miles Kimball, as first published on Quartz. Used by permission according to a temporary nonexclusive license expiring June 30, 2015. All rights reserved.
Among its many other meanings, Christmas points to a central truth of human life: a baby can grow up to change the world. But it is not just that a baby can grow up to change the world; in the human sense, babies are the world: a hundred-odd years from now, all of humanity will be made up of current and future babies.
Babies begin life with the genetic heritage of humankind, then very soon take hold of, reconfigure, and carry on the cultural heritage of humanity. The significance of young human beings as a group is obscured in daily life by the evident power of old human beings. But for anyone who cares about the long run, it is a big mistake to forget that the young are the ultimate judges for the fate of any aspect of culture.
Since those who are now young are the ultimate judges for our culture, it won’t do to neglect instilling in them the kind of morality and ethics that can make them good judges. I have been grateful for the lessons in morality and ethics that I had as a child in a religious context, and with my own children, I saw many of these lessons instilled effectively in short moral lessons at the end of Tae Kwon Do martial arts classes. I don’t see any reason why that kind of secularized moral lessons can’t be taught in our schools, along with practical skills and a deep understanding of academic subjects, especially if we do right by kids by giving them time to learn by lengthening the school day and year.
In at least two controversies, the collective judgments of the young seem on target to me. Robert Putnam of Bowling Alone fame came to the University of Michigan a few years ago to talk about the research behind his more recent book with David Campbell, American Grace: How Religion Divides and Unites Us. He expressed surprise that many young people are becoming alienated from traditional religion when attitudes toward abortion among the young are similar to attitudes among those who are older. But the alienation from traditional religion did not surprise me at all given another fact he reported: the young are dramatically more accepting and supportive of gay marriage than those who are older. I am glad that the young are troubled by the conflict between reproductive freedom and reverence for the beginnings of human life presented by abortion on the one hand and abortion restrictions on the other. But there is no such conflict in the case of gay marriage, which pits the rights of gay couples to make socially sanctioned commitments to one another and enjoy the dignity and practical benefits of a hallowed institution against ancient custom, theocratic impulses, and misfiring disgust instincts that most of the young rightly reject. In this, the young are (perhaps without knowing it) following the example of that baby born in Bethlehem, who always gave honor to those who had been pushed to the edges of the society in which he became a man.
The hot-button controversy of gay marriage is not the only area of our culture due for full-scale revision. Our nation and the world will soon become immensely richer, stronger, and wiser if young people around the world reject the idea I grew up with that intelligence is a fixed, inborn quantity. The truth that hard work adds enormously to intelligence can set them free. What will make an even bigger difference is if they also enshrine their youthful idealism in a vision of a better world that can not only motivate them when young, but also withstand the cares of middle-age to guide their efforts throughout their lives.
Knowing that those who are now young, or are as yet unborn, will soon hold the future of humanity in their hands should make us alarmed at the number of children who don’t have even the basics of life. By far, the worst cases are abroad. The simplest way to help is to stop exerting such great efforts to put obstacles in the way of a better life for them. But whether or not we are willing to do that, it is a good thing to donate to charities that help those in greatest need. Also, I give great honor to those economists working hard trying to figure out how to make poor countries rich.
For those of us already in the second halves of our lives, the fact that the young will soon replace us gives rise to an important strategic principle: however hard it may seem to change misguided institutions and policies, all it takes to succeed in such an effort is to durably convince the young that there is a better way. Max Planck, the father of quantum mechanics, said “Science progresses funeral by funeral.” In a direction not quite as likely to be positive, society evolves from funeral to funeral as well—the funerals of those whose viewpoints do not persuade the young.
It is a very common foolishness to look down on children as unimportant. The deep end of common sense is to respect children and to bring to bear our best efforts, both intellectually and materially, to help them become the best representatives of our species that the universe has ever seen.
Cathy O'Neil on Slow-Cooked Math
Math is sometimes better when it is marinated and cooked slowly; timeless truths take time. Cathy O'Neil, who blogs as Mathbabe, makes that point in her Q&A post “How do I know if I’m good enough to go into math?” She kindly gave me permission to reblog it here. I talk about my own experiences after the text of her post.
Q:
Hi Cathy,
I met you this past summer, you may not remember me. I have a question.
I know a lot of people who know much more math than I do and who figure out solutions to problems more quickly than me. Whenever I come up with a solution to a problem that I’m really proud of and that I worked really hard on, they talk about how they’ve seen that problem before and all the stuff they know about it. How do I know if I’m good enough to go into math?
Thanks, High School Kid
A:
Dear High School Kid,
Great question, and I’m glad I can answer it, because I had almost the same experience when I was in high school and I didn’t have anyone to ask. And if you don’t mind, I’m going to answer it to anyone who reads my blog, just in case there are other young people wondering this, and especially girls, but of course not only girls.
Here’s the thing. There’s always someone faster than you. And it feels bad, especially when you feel slow, and especially when that person cares about being fast, because all of a sudden, in your confusion about all sort of things, speed seems important. But it’s not a race. Mathematics is patient and doesn’t mind. Think of it, your slowness, or lack of quickness, as a style thing but not as a shortcoming.
Why style? Over the years I’ve found that slow mathematicians have a different thing to offer than fast mathematicians, although there are exceptions (Bjorn Poonen comes to mind, who is fast but thinks things through like a slow mathematician. Love that guy). I totally didn’t define this but I think it’s true, and other mathematicians, weigh in please.
One thing that’s incredibly annoying about this concept of “fastness” when it comes to solving math problems is that, as a high school kid, you’re surrounded by math competitions, which all kind of suck. They make it seem like, to be “good” at math, you have to be fast. That’s really just not true once you grow up and start doing grownup math.
In reality, mostly of being good at math is really about how much you want to spend your time doing math. And I guess it’s true that if you’re slower you have to want to spend more time doing math, but if you love doing math then that’s totally fine. Plus, thinking about things overnight always helps me. So sleeping about math counts as time spent doing math.
[As an aside, I have figured things out so often in my sleep that it’s become my preferred way of working on problems. I often wonder if there’s a “math part” of my brain which I don’t have normal access to but which furiously works on questions during the night. That is, if I’ve spent the requisite time during the day trying to figure it out. In any case, when it works, I wake up the next morning just simply knowing the proof and it actually seems obvious. It’s just like magic.]
So here’s my advice to you, high school kid. Ignore your surroundings, ignore the math competitions, and especially ignore the annoying kids who care about doing fast math. They will slowly recede as you go to college and as high school algebra gives way to college algebra and then Galois Theory. As the math gets awesomer, the speed gets slower.
And in terms of your identity, let yourself fancy yourself a mathematician, or an astronaut, or an engineer, or whatever, because you don’t have to know exactly what it’ll be yet. But promise me you’ll take some math major courses, some real ones like Galois Theory (take Galois Theory!) and for goodness sakes don’t close off any options because of some false definition of “good at math” or because some dude (or possibly dudette) needs to care about knowing everything quickly. Believe me, as you know more you will realize more and more how little you know.
One last thing. Math is not a competitive sport. It’s one of the only existing truly crowd-sourced projects of society, and that makes it highly collaborative and community-oriented, even if the awards and prizes and media narratives about “precocious geniuses” would have you believing the opposite. And once again, it’s been around a long time and is patient to be added to by you when you have the love and time and will to do so.
Love, Cathy
I especially like what Cathy says about fast and slow. I think of myself as a slow mathematician. It often takes me half an hour to wrap my head around a math problem or much more if it is a big one. I have gotten used to the confusion I regularly experience for that first chunk of time. If I keep wrestling with the problem, and come at it from different angles, usually the mental fog eventually clears.
Jing Liu: Show Kids that Solving Math Problems is Like Being a Detective
Noah and I have received a flood of overwhelmingly positive email about our Quartz column ”There’s One Key Difference between Kids Who Excel at Math and Those Who Don’t.” I am very gradually making my way through the electronic pile. I was delighted to read near the top of the pile this note from Jing Liu, which has an insight into math education that seems right on the mark to me. Jing kindly gave permission to reprint a slightly revised version of her note here.
I just read the article that you and Noah Smith wrote on Quartz,
“There’s One Key Difference Between Kids Who Excel at Math and Those Who Don’t.”
I’m writing to you because this is an issue that is close to my heart and I have been thinking about it for a long time. I have two kids in K-12 schools, both love math, and I have been worried about what they are learning at school for years. I have talked with teachers and school principles and, of course, many parents. A lot of the things that I’ve heard are concerning and reflect a general lack of understanding from the educators on what math really is and what math can do for students who will not be mathematicians. I finally started a math enrichment program at our neighborhood elementary school and have taught advanced 4th and 5th graders through that program for four years now (this is my main community volunteer work). So I’m sure you can tell why articles such as yours really strike a chord with me.
The issues that you raised in your article are all excellent and educators and parents should think hard about them. I’m also glad that you mentioned the starkly different attitudes toward sports and toward math. It’s not that Americans don’t understand the value of hard work and that effort can definitely make up (to a certain extent) for lack of talent, it’s just that this somehow gets lost in math education. But I also think that there are another couple of very important issues that contribute no less to the current state of math education:
- There is a tendency to treat math as a set of discrete skills, procedures and facts for students to learn each year, not as a coherent and logical way of thinking that students will develop continuously through the years. The amount of rote memorization is, honestly, overwhelming. It is also quite clear that some teachers think that solving math problems is to follow a series of set steps. They miss the point that solving math problems is actually a quite creative process, in which one assesses the situation, assesses the tools in his/her toolboxes and zeros in gradually on how to connect what one knows and what one needs to know. It’s a detective’s work. So the question is: even if we make the kids not fear math, even if they are willing to work hard on math, are they truly learning the essence of math in the classrooms?
- The strong tendency to protect kids from feeling deficient also affects those who are perceived to be capable math students. The math work tends to be very simple, kids are kept at a low level for a very long time until they are absolutely sure that they “have got it”. The slow pace and the lack of depth and challenge at each level can really turn kids off, even for those who are very capable. I’ve read that a whopping 60% of American students actually think that they are not challenged enough in math. In today’s high-stakes college entrance game, it is probably detrimental for a student to score a 70 on a math test. But in many other countries, East Asian or not, 70 is a perfectly OK score for good students. They know that they will apply a large set of math concepts and skills in various ways for a long time, and each time they apply these concepts and skills they have an opportunity to be better at it, and they know that it’s OK to make mistakes. After all, who is a good math student? Someone who only solves very simple problems and gets them all correct? Or someone who tackles very challenging problems but sometimes gets it wrong? In the US, the lack of challenge in the content, the lack of appreciation of math as a creative yet logical endeavor, and the high-stakes evaluation system together might just breed students who are risk-averse in their academic pursuit and who don’t get to see the true beauty of math. And this might be one reason why even the advanced students can be ill-prepared in math.
Quartz #36—>There's One Key Difference Between Kids Who Excel at Math and Those Who Don't
Here is the full text of my 36th Quartz column, and 2d column coauthored with Noah Smith, “There’s One Key Difference Between Kids Who Excel at Math and Those Who Don’t.” I am glad to now bring it home to supplysideliberal.com, and Noah will post it on his blog Noahpinion as well. It was first published on October 27, 2013. Links to all my other columns can be found here. In particular, don’t miss my follow-up column
The warm reception for this column has been overwhelming. I think there is a hunger for this message out there. We want to get the message out, so if you want to mirror the content of this post on another site, just include both a link to the original Quartz column and to supplysideliberal.com.
“I’m just not a math person.”
We hear it all the time. And we’ve had enough. Because we believe that the idea of “math people” is the most self-destructive idea in America today. The truth is, you probably are a math person, and by thinking otherwise, you are possibly hamstringing your own career. Worse, you may be helping to perpetuate a pernicious myth that is harming underprivileged children—the myth of inborn genetic math ability.
Is math ability genetic? Sure, to some degree. Terence Tao, UCLA’s famous virtuoso mathematician, publishes dozens of papers in top journals every year, and is sought out by researchers around the world to help with the hardest parts of their theories. Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught. But here’s the thing: We don’t have to! For high school math, inborn talent is just much less important than hard work, preparation, and self-confidence.
How do we know this? First of all, both of us have taught math for many years—as professors, teaching assistants, and private tutors. Again and again, we have seen the following pattern repeat itself:
Different kids with different levels of preparation come into a math class. Some of these kids have parents who have drilled them on math from a young age, while others never had that kind of parental input.
On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it—maybe 80 or 85%, a solid B.
The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes, and fall further behind.
The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are “math people,” and work hard in the future, cementing their advantage.
Thus, people’s belief that math ability can’t change becomes a self-fulfilling prophecy.
The idea that math ability is mostly genetic is one dark facet of a larger fallacy that intelligence is mostly genetic. Academic psychology journals are well stocked with papers studying the world view that lies behind the kind of self-fulfilling prophecy we just described. For example, Purdue University psychologist Patricia Linehan writes:
A body of research on conceptions of ability has shown two orientations toward ability. Students with an Incremental orientation believe ability (intelligence) to be malleable, a quality that increases with effort. Students with an Entity orientation believe ability to be nonmalleable, a fixed quality of self that does not increase with effort.
The “entity orientation” that says “You are smart or not, end of story,” leads to bad outcomes—a result that has been confirmed by many other studies. (The relevance for math is shown by researchers at Oklahoma City who recently found that belief in inborn math ability may be responsible for much of the gender gap in mathematics.)
Psychologists Lisa Blackwell, Kali Trzesniewski, and Carol Dweck presented these alternatives to determine people’s beliefs about intelligence:
You have a certain amount of intelligence, and you really can’t do much to change it.
You can always greatly change how intelligent you are.
They found that students who agreed that “You can always greatly change how intelligent you are” got higher grades. But as Richard Nisbett recounts in his book Intelligence and How to Get It,they did something even more remarkable:
Dweck and her colleagues then tried to convince a group of poor minority junior high school students that intelligence is highly malleable and can be developed by hard work…that learning changes the brain by forming new…connections and that students are in charge of this change process.
The results? Convincing students that they could make themselves smarter by hard work led them to work harder and get higher grades. The intervention had the biggest effect for students who started out believing intelligence was genetic. (A control group, who were taught how memory works, showed no such gains.)
But improving grades was not the most dramatic effect, “Dweck reported that some of her tough junior high school boys were reduced to tears by the news that their intelligence was substantially under their control.” It is no picnic going through life believing you were born dumb—and are doomed to stay that way.
For almost everyone, believing that you were born dumb—and are doomed to stay that way—is believing a lie. IQ itself can improve with hard work. Because the truth may be hard to believe, here is a set of links about some excellent books to convince you that most people can become smart in many ways, if they work hard enough:
So why do we focus on math? For one thing, math skills are increasingly important for getting good jobs these days—so believing you can’t learn math is especially self-destructive. But we also believe that math is the area where America’s “fallacy of inborn ability” is the most entrenched. Math is the great mental bogeyman of an unconfident America. If we can convince you that anyone can learn math, it should be a short step to convincing you that you can learn just about anything, if you work hard enough.
Is America more susceptible than other nations to the dangerous idea of genetic math ability? Here our evidence is only anecdotal, but we suspect that this is the case. While American fourth and eighth graders score quite well in international math comparisons—beating countries like Germany, the UK and Sweden—our high-schoolers underperform those countries by a wide margin. This suggests that Americans’ native ability is just as good as anyone’s, but that we fail to capitalize on that ability through hard work. In response to the lackluster high school math performance, some influential voices in American education policy have suggested simply teaching less math—for example, Andrew Hacker has called for algebra to no longer be a requirement. The subtext, of course, is that large numbers of American kids are simply not born with the ability to solve for x.
We believe that this approach is disastrous and wrong. First of all, it leaves many Americans ill-prepared to compete in a global marketplace with hard-working foreigners. But even more importantly, it may contribute to inequality. A great deal of research has shown that technical skills in areas like software are increasingly making the difference between America’s upper middle class and its working class. While we don’t think education is a cure-all for inequality, we definitely believe that in an increasingly automated workplace, Americans who give up on math are selling themselves short.
Too many Americans go through life terrified of equations and mathematical symbols. We think what many of them are afraid of is “proving” themselves to be genetically inferior by failing to instantly comprehend the equations (when, of course, in reality, even a math professor would have to read closely). So they recoil from anything that looks like math, protesting: “I’m not a math person.” And so they exclude themselves from quite a few lucrative career opportunities. We believe that this has to stop. Our view is shared by economist and writer Allison Schrager, who has written two wonderful columns in Quartz (here and here), that echo many of our views.
One way to help Americans excel at math is to copy the approach of the Japanese, Chinese, and Koreans. In Intelligence and How to Get It, Nisbett describes how the educational systems of East Asian countries focus more on hard work than on inborn talent:
“Children in Japan go to school about 240 days a year, whereas children in the United States go to school about 180 days a year.”
“Japanese high school students of the 1980s studied 3 ½ hours a day, and that number is likely to be, if anything, higher today.”
“[The inhabitants of Japan and Korea] do not need to read this book to find out that intelligence and intellectual accomplishment are highly malleable. Confucius set that matter straight twenty-five hundred years ago.”
“When they do badly at something, [Japanese, Koreans, etc.] respond by working harder at it.”
“Persistence in the face of failure is very much part of the Asian tradition of self-improvement. And [people in those countries] are accustomed to criticism in the service of self-improvement in situations where Westerners avoid it or resent it.”
We certainly don’t want America’s education system to copy everything Japan does (and we remain agnostic regarding the wisdom of Confucius). But it seems to us that an emphasis on hard work is a hallmark not just of modern East Asia, but of America’s past as well. In returning to an emphasis on effort, America would be returning to its roots, not just copying from successful foreigners.
Besides cribbing a few tricks from the Japanese, we also have at least one American-style idea for making kids smarter: treat people who work hard at learning as heroes and role models. We already venerate sports heroes who make up for lack of talent through persistence and grit; why should our educational culture be any different?
Math education, we believe, is just the most glaring area of a slow and worrying shift. We see our country moving away from a culture of hard work toward a culture of belief in genetic determinism. In the debate between “nature vs. nurture,” a critical third element—personal perseverance and effort—seems to have been sidelined. We want to bring it back, and we think that math is the best place to start.
Follow Miles on Twitter at @mileskimball. Follow Noah at @noahpinion.
Visionary Grit
TED Weekends, which is associated with Huffington Post, asked me to write an essay on my reaction to Angela Duckworth’s wonderful talk about grit as the secret to success. Here is a link to my essay on TED Weekends:
Below is the full text of my essay. It pushes further the themes in the Quartz column I wrote with Noah Smith: “Power of Myth: There’s one key difference between kids who excel at math and those who don’t.”
Grit, more than anything else, is what makes people succeed. Psychologist Angela Duckworth, who has devoted her career to studying grit, defines grit this way:
Grit is passion and perseverance for very long-term goals. Grit is having stamina. Grit is sticking with your future, day in, day out, not just for the week, not just for the month, but for years – and working really hard to make that future a reality. Grit is living life like a marathon, not a sprint.
But where does grit come from? First, it comes from understanding and believing that grit is what makes people succeed:
- understanding that persistence and hard work are necessary for lasting success, and
- believing that few obstacles can ultimately stop those who keep trying with all of their hearts, and all of their wits.
But that is not enough. Grit also comes from having a vision, a dream, a picture in the mind’s eye, of something you want so badly, you are willing to work as hard and as long as it takes to achieve that dream. Coaches know how powerful dreams – dreams of making the team, of scoring a goal, of winning the game, or of winning a championship – can be for kids. Dreams of knowing the secrets of complex numbers, graduating from college, rising in a career, making a marriage work, achieving transcendence, changing the world, need to be powerful like that to have a decent chance of success.
Grit is so powerful that once the secret is out, a key concern is to steer kids toward visions that are not mutually contradictory. Not everyone can win the championship. Someone has to come in second place. But almost everyone can learn the secrets of complex numbers, graduate from college, rise in a career, make a marriage work, achieve transcendence, and change the world for the better.
What can adults do to help kids understand and believe that grit is what makes people succeed, and to help them find a vision that is powerful enough to motivate long, hard work? Noah Smith and I tried to do our bit with our column “Power of Myth: There’s one key difference between kids who excel at math and those who don’t.” We were amazed at the reception we got. Our culture may be turning the corner, ready to reject the vicious myth that out of any random sampling of kids, many are genetically doomed to failure at math, failure at everything in school, failure in their careers, or even failure at life. The amazing reception of Angela Duckworth’s TEDTalk is another good sign. But articles and TEDTalks won’t do the trick, because not everyone watches TEDTalks, and – as things are now – many people read only what they absolutely have to. So getting the word out that grit, not genes, is the secret to success, will take the work of the millions who do read and who do watch TEDTalks, to tell, one by one, the hundreds of millions in this country and in other countries with similar cultures about the importance of grit.
What can adults do to help kids get a vision that is powerful enough to motivate long, hard work? Many are already doing heroic work in that arena. But other would-be physicians among us must first heal ourselves. How many of us have a defeatist attitude when we think of the problems our nation and the world face? How many of us lack a vision of what we want to achieve that will motivate us to long, hard work, stretching over many years?
Visions don’t have to be perfect. It is enough if they are powerful motivators, and good rather than bad. And it is good to share our visions with one another. Here are some of the things that dance before my mind’s eye and motivate me: 1, 2. I hope everyone who reads this will think about how to express her or his own vision – a vision that motivates hard work to better one’s own life and to better the world. That is the example we need to set for the kids.
Lately, since I started reading and thinking about the power of hard, deliberate effort, I have been catching myself; when I hear myself thinking “I am bad at X” I try to recast the thought as “I haven’t yet worked hard at getting good at X.” Some of the skills I haven’t yet worked at honing, I probably never will; there are only so many hours in the day. But with others, I have started trying a little harder, once I stopped giving myself the easy excuse of “I am bad at X.” There is no need to exaggerate the idea that almost everyone (and that with little doubt includes you) can get dramatically better at almost anything. But if we firmly believe that we can improve at those tasks to which we devote ourselves, surprising and wonderful things will happen.
Among the many wonderful visions we can pursue with the faith that working hard – with all of our hearts and all of our wits – will bear fruit, let’s devote ourselves to getting kids to understand that grit is the key to success. Let’s help them find visions that will motivate them to put in the incredibly hard effort necessary to do the amazing things that they are capable of, and help them tap the amazing potential they have as human beings.
Ideas are not set in stone. When exposed to thoughtful people, they morph and adapt into their most potent form. TEDWeekends will highlight some of today’s most intriguing ideas and allow them to develop in real time through your voice! Tweet #TEDWeekends to share your perspective or email tedweekends@huffingtonpost.com to learn about future weekend’s ideas to contribute as a writer.
Learning to Do Deep Knee Bends Balanced on One Foot
I am 53 now and sometime think forward to some dangers of getting older. I read a few years ago that Tai Chi exercises improve balance enough to significantly reduce falls that can sometimes break older bones. I don’t know where to find time for Tai Chi itself in my schedule, so I cut corners. I just do a daily set of deep knee bends balanced on one foot: 18 reps on the right leg, and 20 reps on the left leg, because that one is weaker and needs more strengthening. I had a pretty tough time getting so I could do that many repetitions without toppling over again and again and having to catch myself with my hands. But gradually, gradually, I could do a few more repetitions in a row before toppling over, until now I don’t have too much trouble doing 18 or 20 in a row.
I think of this as a good analogy for a lot of learning: making mistakes and carefully correcting them, over and over again, until very gradually the number of mistakes diminishes. If you aren’t willing to fall–many times–in order to learn, you will fail.
Marc F. Bellemare's Story: "I'm Bad at Math"
Link to “I’m Bad at Math: My Story” on Marc’s blog
I think it is very valuable to share one another’s stories about what the idea that math ability is primarily genetic did to our lives. My story is at this link. Marc Bellemere wrote his story on his blog, and kindly agreed to let me publish it here on supplysideliberal.com as well.
Last week, Miles Kimball and Noah Smith, two economists (one at Michigan, one at Long Island) had a column on the Atlantic’s website (ht: Joaquin Morales, via Facebook) in which they took to task those who claim that math ability is genetic.
Kimball and Smith argue that that’s largely a cop-out, and that there is no such thing as “I’m bad at math.” Rather, being good at math is the product of good, old-fashioned hard work:
Is math ability genetic? Sure, to some degree. Terence Tao, UCLA’s famous virtuoso mathematician, publishes dozens of papers in top journals every year, and is sought out by researchers around the world to help with the hardest parts of their theories. Essentially none of us could ever be as good at math as Terence Tao, no matter how hard we tried or how well we were taught. But here’s the thing: We don’t have to! For high-school math, inborn talent is much less important than hard work, preparation, and self-confidence.
How do we know this? First of all, both of us have taught math for many years—as professors, teaching assistants, and private tutors. Again and again, we have seen the following pattern repeat itself:
- Different kids with different levels of preparation come into a math class. Some of these kids have parents who have drilled them on math from a young age, while others never had that kind of parental input.
- On the first few tests, the well-prepared kids get perfect scores, while the unprepared kids get only what they could figure out by winging it—maybe 80 or 85%, a solid B.
- The unprepared kids, not realizing that the top scorers were well-prepared, assume that genetic ability was what determined the performance differences. Deciding that they “just aren’t math people,” they don’t try hard in future classes, and fall further behind.
- The well-prepared kids, not realizing that the B students were simply unprepared, assume that they are “math people,” and work hard in the future, cementing their advantage.
Kimball and Smith’s column resonated deeply with me, because I discovered quite late (but just in time) that hard work trumps natural ability any day of the week when it comes to high-school math–if not when it comes to PhD-level math for economists.
My Story
What follows is a story which, although I have mentioned it to a few colleagues in the past, I’ve never told publicly until I posted it on my blog on November 6.
Until my early 20s, I never knew that one could become good at math. In high school, I failed tenth-grade math. That year, I’d had mono, so that provided a convenient excuse that I could use when I would tell people that I had to take tenth-grade math again in the summer.
That summer, though, I worked really hard at math, and I did very well, scoring something like a 96% score. But I ascribed my success to the people I was competing with rather than to my own hard work. The class, after all, was entirely composed of other failures, and in the kingdom of the blind, the one-eyed man is king.
When I began studying economics in college, I enrolled in a math for economists course the first semester. I quickly dropped out of it, thinking it was too difficult (and to be sure, the textbook was somewhat hardcore for a first course in math for economists). The following semester, I enrolled in the same course, which was taught by a different instructor, one who seemed a bit more laid-back and who taught it at a level that was better suited for someone like me.
As it turns out, that instructor was a Marxian, so one of the things he taught was the use of Leontief matrices, or input-output models. Like the clueless college student that I was back then, I decided that that stuff was not important, and so skipped studying it for the final.
Much to my surprise, 60% of the final was on Leontief matrices, and so I failed the course and had to take it again the next semester. Even that second time around, I didn’t do that great, scraping by with a C+ (which, if I recall correctly, was the average score in core econ major courses at the Université de Montréal back then).
After finally passing Math for Economists I, I realized I had to take Math for Economists II, which was reputed to be very difficult. But for some reason, it was then that I remembered my tenth-grade math summer course, and how my hard work had seemed to yield impressive results back then. So I decided to really apply myself in that second Math for Economists course, and I got an A.
When I saw my transcript that semester, I finally saw the light: I had been terrible at math all my life because I hadn’t worked hard at it; in fact, I hadn’t worked at all up until that point, and here I was, getting an A in one of the hardest classes in the major.
I graduated with a 3.2 GPA, which wasn’t great considering that my alma mater has a 4.3 scale. But it was enough to get admitted into the M.Sc. program in Economics at the Université de Montréal, and so I applied and got in. But then, I remembered that my hard work had paid off handsomely during my senior year, and I decided to apply myself in every single class. Lo and behold, I did well. So well, in fact, that I finished my M.Sc. with a 4.1 GPA, which allowed me not only to get admitted for a Ph.D. in Applied Economics at Cornell, but to get a full financial ride, including a fellowship for my first year.
Perhaps more importantly, my cumulative experience with the hard work–excellent results nexus boosted my confidence, and it taught me that I could do well in a graduate program in applied economics. Indeed, Cornell was then known for the difficulty of its qualifier in microeconomic theory (which was administered back then by the economics department and was on all of Mas-Colell et al. and more). In any given year, half of all the students (i.e., applied economics, business, and economics students) taking it would fail.
To be sure, I had to work very, very hard during my first year, but I managed to pass my qualifying exam the first time around (thankfully, us applied economics students didn’t have to take the macro qualifier; we only needed to get a B- in one of the core macro courses). In fact, many of my classmates who seemed to rely on their “natural” ability to do math (including folks who had been math majors in college) ended up failing the micro qualifier.
That series of successes followed by hard work was eventually what gave me the confidence to do a little bit of micro theory: in the first essay in my dissertation, I developed a dynamic principal-agent model to account for the phenomenon I was studying empirically. And ultimately, I published an article in the American Journal of Agricultural Economics (AJAE) that relied entirely on microeconomic theory (and thus on quite a bit of math), an article for which my coauthor and I won that year’s best AJAE article award.
Ironically enough, in that article, we cited Miles Kimball’s 1990 Econometrica paper on prudence.
How the Idea that Intelligence is Genetic Distorted My Life—Even Though I Worked Hard Trying to Get Smarter Anyway
Miles in Copenhagen, September 2013
The idea that intelligence is inborn makes us less intelligent by discouraging effort. It also distorts our lives in other ways. I wanted to share my story–a story Noah Smith and I couldn’t figure out how to fit into our column “Power of Myth: There’s one key difference between kids who excel at math and those who don’t.” Here is my story. Along the way, you will see how competitive I am. I hope you don’t come to hate me too much as a result!
For most of my life, I believed firmly in the idea that intelligence was mostly genetic, and much of my identity was wrapped up in “being the smartest kid on the block”—with as big a “block” as possible. But, I knew I couldn’t convince others of how smart I was without working hard in some sense. The trick to convincing both myself and others of my intelligence was to work hard in ways that were off the books. Working hard in a class I was actually in: not cool. Browsing in the math section of a nearby university library, honing public speaking skills on the debate team, reading the encyclopedia, reading Isaac Asimov’s science and history books, and reading the New York Times and the Wall Street Journal: cool. Listening to the teacher with both ears: not cool. Double-tasking by inventing a new game or fiddling with mathematical equations while the English teacher was talking and still doing my best to dominate the class discussion: cool. To avoid feeling I was just a grind, working hard like the peons obsessed by getting good grades, I always tried to find a bigger game to play, like learning things that would help once I got to college rather than learning things for my high school classes.
Once I actually got to college, with many other smart competitors, I knew I would have to work hard in ways more directly related to classes. But the desire to impress my classmates with the appearance of little input for high performance was still there. I still get a frisson of joy remembering the time one of my classmates expressed awe that I managed to survive in college despite not studying on Sunday. What he didn’t realize was that–in terms of time available for studying–my religious strictures against drinking and carousing more than made up for my rule against studying on Sunday.
What I hope you get from the story so far is not the fact that I must have seemed insufferable, but this: one way or another, I figured out ways to work very hard while never seeming to work hard. I fooled even myself, at least in part, especially by routinely working hard on things other than what I was supposed to be working on at the moment.
Despite having a strategy that spared me the worst excesses of smart-kid laziness, the idea that being innately smart was what counted rather than hard work caused me a lot of psychic pain along the way. There came a point in my career when I wondered why other economists were passing me by in prestige and honors. At long last I realized that being a successful economist isn’t just about proving one is smart. The currency of the realm is writing academic papers and shepherding them through endless rounds of revision to get them published in academic journals. There is a limit to how much of my time I am willing to spend on that activity. So this realization alone did not rocket me to the top of the profession. But at least I understand what is going on. Hard work is needed not only in order to get smarter, but also to get the payoff from being smart–whatever type of payoff I choose to pursue.
The Myth of 'I'm Bad at Math'
Link to the column on The Atlantic website
This is the Atlantic’s layout for my Quartz column with Noah Smith: “There’s one key difference between kids who excel at math and those who don’t.” This is only the second time I have cracked the Atlantic. (Both Quartz and the Atlantic website are owned by the Atlantic Company, so they freely syndicate to one another, but they are editorially separate.)
Noah and I have been overwhelmed with a flood of positive reactions to this column, which I have not had a chance to process because of my trip to the Federal Reserve Board this week. I am retweeting many of the wonderful responses I have seen on Twitter. One notable tweet is this one by the World Economic Forum (@davos), which is followed by a total of 1,962,107 humans and bots.
Some of the responses that are the most moving are readers whose faith in their own ability to learn math has gone up.
There's One Key Difference Between Kids Who Excel at Math and Those Who Don't
An early working title was “The Most Self-Destructive Idea in America."
The Unavoidability of Faith
Sometimes we think of faith as something optional, and something directed toward the supernatural. Not so. Faith is unavoidable, and faith directed toward the supernatural is a small part of all faith.
As for many discussions of faith, the starting point for my discussion of faith are the words of the (unknown) author of the Epistle to the Hebrews. Using William Tyndale’s translation with modern spelling, Hebrews 11:1 reads
Faith is a sure confidence of things which are hoped for and a certainty of things which are not seen.
In my book, the more evidence we have to go on and the less faith we have to depend on, the better. That is, I disagree with the words the resurrected Jesus is reported to have said to a doubting Thomas (John 20:29, Tyndale):
Thomas, because thou hast seen me therefore thou believest: Happy are they that have not seen and yet believe.
Rather, happy are they who have much evidence to base their choices on. But choices–to act, or not to act–often have to be made when evidence is scarce. That is where faith comes in.
One might be tempted to think of faith as a Bayesian prior. But it isn’t that simple. In Bayesian decision-making, “prior beliefs” are left unexplained. But in the real world they come from different ways of responding to and reasoning about past experience. New data sometimes simply updates prior beliefs within the same paradigm, as Bayesian theory suggests. But other times, new data upends the thin tissue of reasoning and reaction that was crucial for the formation of those prior beliefs, resulting in a much bigger change in views than straightforward Bayesian updating would imply. And sometimes additional reasoning–in the absence of any additional data whatsoever–can dramatically change one’s views.
A simpler point is that what is prior to one set of events is posterior to earlier events. Putting both points together, faith is what one believes at a given moment in time, however one has managed to cobble together those beliefs.
In situations where one is willing to think of one choice as inaction, with costly actions having debatable benefits, one can distinguish between a “belief in nothing” that leads one to continue in inaction, and a “belief in something” that leads one to act. When proponents of action say “Have faith!” they are advocating a belief in a high enough marginal product of action to make it worth the costs. That is very much the perspective of the Lectures on Faith, which were once part of the Mormon canon, but now enjoy only semi-canonical status. (The full text of the Lectures on Faith can be found here.) Let me quote a passage from the Lectures on Faith that has stuck with me, again modernizing the spelling:
If men were duly to consider themselves, and turn their thoughts and reflections to the operations of their own minds, they would readily discover that it is faith, and faith only, which is the moving cause of all action, in them; that without it, both mind and body would be in a state of inactivity, and all their exertions would cease, both physical and mental.
Were this class to go back and reflect upon the history of their lives, from the period of their first recollection, and ask themselves, what principle excited them to action, or what gave them energy and activity, in all their lawful avocations, callings and pursuits, what would be the answer? Would it not be that it was the assurance which we had of the existence of things which we had not seen, as yet? Was it not the hope which you had, in consequence of your belief in the existence of unseen things, which stimulated you to action and exertion, in order to obtain them? Are you not dependent on your faith, or belief, for the acquisition of all knowledge, wisdom and intelligence? Would you exert yourselves to obtain wisdom and intelligence, unless you did believe that you could obtain them? Would you have ever sown if you had not believed that you would reap? Would you have ever planted if you had not believed that you would gather? Would you have ever asked unless you had believed that you would receive? Would you have ever sought unless you had believed that you would have found? Or would you have ever knocked unless you had believed that it would have been opened unto you? In a word, is there any thing that you would have done, either physical or mental, if you had not previously believed? Are not all your exertions, of every kind, dependent on your faith? Or may we not ask, what have you, or what do you possess, which you have not obtained by reason of your faith? Your food, your raiment, your lodgings, are they not all by reason of your faith? Reflect, and ask yourselves, if these things are not so. Turn your thoughts on your own minds, and see if faith is not the moving cause of all action in yourselves; and if the moving cause in you, it it not in all other intelligent beings?
Application 1: The Cognitive Economics of Human Capital
Let me apply this idea to Jill’s decision of whether to go to college and learn economics or not. Some consequences of college might be relatively easy to discern, such as the costs, and if she is relatively well informed, the likely effect on her future wage. But what about the benefits learning economic analysis might have for her future decision-making? A tempting approach to analyzing Jill’s problem would be to think of her computing what her life would be like (or a probability distribution thereof) if she does go to college, as well as what her life would be like if she doesn’t go to college, compare the two to see which one she prefers, and make that choice. But in this case, Jill can't compute what her life will be like if she goes to college and learns economics because she doesn’t know now the analytical tools that could influence her life in critical ways if she does go to college and learn economics. In other words, she can’t make a fully rational choice (according to the demanding standards of most economic models) of whether or not to go to college without knowing the very things that she would be learning in college. But if she knew those things already, she wouldn’t need to go to college!
The Handbook of Contemporary Behavioral Economics: Foundations and Developments, page 343 points to the more general conundrum of which Jill’s problem is an example:
The inability to formulate an optimization problem that folds in the cost of its own solution has become known as the “infinite regress problem,” with Savage (1954) appearing to be the first to use the regress label.
Application 2: The Cognitive Economics of R&D
Another good example of the infinite regress problem is the decision of which lines of research to pursue. The issue is stark in a decision of whether or not to undertake a research project in mathematical economic theory. There is no way to make a fully rational decision according to the demanding standards of most economic models because the most economic models assume that information processing (as distinct from information acquisition) comes free, but the issue is precisely whether one’s own finite thinking ability will allow one to find a publishable theoretical result within a reasonable amount of time. Therefore, one must make the decision according to a hunch of some sort–or in other words, by faith. The analogy that makes one believe that a proof might exist is not itself the proof, and may fall apart. But that analogy makes one willing to take the risk. Except in cases where undecidability of the sort that shows up in Goedel’s theorem comes into play, the only fully rational probability that one could find a proof would be either 0 or 1, because one would already know the answer. But that just isn’t the way it is when you make the decision. You have some notion of the probability you will be able to find a proof–a probability that by its nature cannot have a firm foundation, yet still guides one’s choice: faith.
Application 3: The Cognitive Economics of Economic Growth
Growth theory faces a similar problem. It would be a lot easier to form a sensible probability distribution for future technological progress if one actually knew the technology already. Someday, economists studying the economics of other planets under the restriction of Star Trek’s (often violated) Prime Directive of non-intervention may be able to do growth theory that way. But we 21st century economists must do growth theory in ignorance of scientific and engineering principles that may be crucial to future economic growth. It would be nice to know the answers to questions such as how hard it is to make batteries more efficient, for example, or whether theoretically possible subatomic particles that could catalyze fusion exist or not. (My friend, theoretical physicist James Wells, has worked on the theory. The right kind of heavy, but relatively stable negatively charged particle could do it by taking the place of electrons in hydrogen atoms and making the exotic hydrogen atoms much smaller in size.) If it were all just a matter of getting experimental results, the economic model might be standard, but what if just thinking more clearly with the evidence one already has could make it possible to get to the answer with one decisive experiment instead of an inefficient series of 100 experiments.
Just as with the standard approach to human capital, we often look at technological progress from the outside, in a relatively bloodless way: a shifter in the production function changes. But the inside story of most technological progress is that in some sense we were doing something stupid, but now have stopped being stupid in that particular way. I say “in some sense” because–while our finite cognition is painful–it is possible to be smart in recognizing our cognitive limitations and making reasonable decisions despite having to walk more by faith that we would like in making decisions that depend on technologies we don’t yet know exist.
Application 4: Locus of Control
A central life decision is whether to attempt to better one’s life by making an effort to do so. Information acquisition and learning how to process information are themselves costly, so the initial decision of whether to do the information acquisition and other learning that are a logical first step must be made in a fog of ignorance. Some people are lucky enough to have parents who instill in them confidence that effort to gain knowledge, learn and grow will be well rewarded in life, at least on average. It is good luck to have that belief, because it seems to be true for most people. But believing that it is true for you–that your efforts to better your life will be rewarded–must be an act of faith. For you are not exactly like anyone else. And even knowing that most people are similar in this regard is a bit of knowledge that might cost you dearly to acquire if you are not so lucky to as to have your parents, or someone else you trust tell you so.
If you decide that it is not worth the effort trying to better your life, you will not collect much evidence on the marginal product of effort, and so there will be precious little that could provide direct evidence to change your mind. In such a low-effort trap, it will not be hard evidence about your own marginal product of effort that switches you from believing in an external locus of control (outside forces govern outcomes with little effect of own effort) to an internal locus of control (own efforts have an important effect on quality of outcomes). If you escape the trap of believing in an external locus of control, it will be by believing some kind of evidence or reasoning that is much less definitive.
Conclusion
I do not believe in the supernatural. So for me, faith is not about the supernatural. Yet still we must walk by faith. Walking by the light of evidence is better, but such is not always our lot.
Not only must we sometimes walk by faith–whether we like or not–so must others. It matters what kind of faith we instill in those around us, to the extent we have any influence.
To me, faith in progress and human improvability–both individually and collectively–is a precious boon. It is not enough for us to have that faith. Many are caught in what I believe to be the trap of believing they can not better their lives. I believe it is important for them to have faith in progress and human improvability as well. If you believe in progress and human improvability as I do, let us together seek for better and better ways of transmitting that faith to those who do not yet believe.
Daniel Coyle on Deliberate Practice
The Talent Code on Amazon.
Video trailer for The Talent Code.
This post is part of my series on deliberate practice (also called deep practice or purposeful practice), which I consider very important for understanding education and human capital accumulation more broadly.
In the last few years, I have often taught an introductory macroeconomics class. Both at the beginning of the semester, and whenever a student comes to me puzzled that they have done worse-than-expected on an exam, I recommend that they read the book The Talent Code. What I hope they get from the book is a sense of what it means to study in a deep way, rather than just “going over the material.” In case students don’t read the book, I have had teams of students from an honors section of the class give a presentation on the book to the entire class of about 250 students. I strongly recommend this
which they generously gave me permission to post. I had the audience vote on this and presentations about 5 other books. This was voted best of all 6 presentations. I agreed with the audience’s assessment. (The other books were
- Red Ink, by David Wessel,
- The White Man’s Burden: Why the Efforts of the West to Aid the Rest Have Done So Much Ill and So Little Good by William Easterly
- The Better Angels of Our Nature: Why Violence Has Declined by Steven Pinker (a book I dearly love)
- The Rational Optimist by Matt Ridley, and
- Happiness: Lessons from a New Science by Richard Layard (which I include partly so I can critique its ideas as I do on my happiness sub-blog.)
Here is the essence of the 3 key slides in Hrishikesh’s and Madeline’s Powerpoint file:
Deep Practice
Chunk it up
- Absorb–get involved with practice: imitation
- Break it into chunks–organize practice into smaller pieces
- Slow it down–take time to practice correctly
Repeat
Learn to feel it
Self-Learning Connection
Master Coaching
- Having someone inspire you to keep working can be effective
- However, your greatest coach is yourself
Ignition
- Make yourself passionate about learning
- Find your own source of ignition
Deep Practice
- Absorb–study deeply, not necessarily a lot
- Break it into chunks–all-nighters are less effect than spreading it out
- Slow it down–take time to make sure you are learning
- Repeat–practice makes perfect!
in the text above, I bolded a thought that got a particularly strong audience reaction: the greater effectiveness of spreading study out over time, instead of concentrating it in one all-nighter.
Eric Hanushek on the Importance of Improving Teacher Quality
I recently ran across Eric Hanushek’s October 19, 2010 Wall Street Journal op-ed “There is No ‘War on Teachers.’” Here are two key excerpts from what he has to say:
No longer is education reform an issue of liberals vs. conservatives. In Washington, the Obama administration’s Race to the Top program rewarded states for making significant policy changes such as supporting charter schools. In Los Angeles, the Times published the effectiveness rankings—and names—of 6,000 teachers. And nationwide, the documentary “Waiting for 'Superman,’” which strongly criticizes the public education system, continues to succeed at the box office….
My research—which has focused on teacher quality as measured by what students learn with different teachers—indicates that a small proportion of teachers at the bottom is dragging down our schools. The typical teacher is both hard-working and effective. But if we could replace the bottom 5%-10% of teachers with an average teacher—not a superstar—we could dramatically improve student achievement. The U.S. could move from below average in international comparisons to near the top.
The principle that a small fraction of employees usually causes most of the trouble for productivity is well known in manufacturing. (I think of that as one of the ideas behind the “Six Sigma” approach to process improvement.) Eric is applying that principle to education.
I did some illustrative calculations using the assumption of a normal distribution of teacher effectiveness. (If the distribution of teacher effectiveness has fat tails, the results below would be more dramatic.) On the left is the fraction of teachers at the bottom of the distribution who are fired (firing the same percentage of the replacement teachers until none of the teachers that remain are in the bottom of the distribution). On the right is the resulting change in the mean of the distribution of teacher effectiveness in standard deviations of the original distribution of teacher effectiveness.
Mass deleted Improvement in performance
5% +.11 cross-teacher standard deviations
10% +.20 cross-teacher standard deviations
15% +.27 cross-teacher standard deviations
20% +.35 cross-teacher standard deviations
[The left column is the normal distribution function of x, solved for 5%, 10%, 15% and 20%; the right column is the normal density function–giving an incomplete expectation integral–divided by one minus the normal distribution function.]
To help in interpreting the meaning of these improvements measured in standard deviations, I converted the average teacher effectiveness after deleting the bottom of the distribution into the percentile in the original distribution of a teachers of a teacher who has the same effectiveness as the average effectiveness of teachers after the bottom of the distribution has been fired.
Mass deleted Average quality = what percentile of original distribution?
0% 50
5% 54.3
10% 57.9
15% 60.6
20% 63.7
[The right column is the normal distribution function of the performance improvements in the table above.]
Update: @aryal_ga flags some nice graphs of the contribution of teacher quality to long-run student outcomes created by Raj Chetty, John Friedman and Jonah Rockoff:
The Long Term Impacts of Teachers: Teacher Value-Added and Student Outcomes in Adulthood.