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## Gender And The Harvard Math Department

This is a guest post by Meena Boppana, a junior at Harvard and former president of the Harvard Undergraduate Math Association (HUMA). Meena is passionate about addressing the gender gap in math and has co-lead initiatives including the Harvard math survey and the founding of the Harvard student group Gender Inclusivity in Math (GIIM).

I arrived at Harvard in 2012 head-over-heels in love with math. Encouraged to think mathematically since I was four years old by my feminist mathematician dad, I had even given a TEDx talk in high school declaring my love for the subject. I was certainly qualified and excited enough to be a math major.

Which is why, three years later, I think about how it is that virtually all my female friends with insanely strong math backgrounds (e.g. math competition stars) decided not to major in math (I chose computer science). This year, there were no female students in Math 55a, the most intense freshman math class, and only two female students graduating with a primary concentration in math. There are also a total of zero tenured women faculty in Harvard math.

So, I decided to do some statistical sleuthing and co-directed a survey of Harvard undergraduates in math. I was inspired by the work of Nancy Hopkins and other pioneering female scientists at MIT, who quantified gender inequities at the Institute – even measuring the square footage of their offices – and sparked real change. We got a 1/3 response rate among all math concentrators at Harvard, with 150 people in total (including related STEM concentrations) filling it out.

The main finding of our survey analysis is that the dearth of women in Harvard math is far more than a “pipeline issue” stemming from high school. So, the tale that women are coming in to Harvard knowing less math and consequently not majoring in math is missing much of the picture. Women are dropping out of math during their years at Harvard, with female math majors writing theses and continuing on to graduate school at far lower rates than their male math major counterparts.

And it’s a cultural issue. Our survey indicated that many women would like to be involved in the math department and aren’t, most women feel uncomfortable as a result of the gender gap, and women feel uncomfortable in math department common spaces.

The simple act of talking about the gender gap has opened the floodgates to great conversations. I had always assumed that because no one was talking about the gender gap, no one cared. But after organizing a panel on gender in the math department which drew 150 people with a roughly equal gender split and students and faculty alike, I realized that my classmates of all genders feel more disempowered than apathetic.

The situation is bad, but certainly not hopeless. Together with a male freshman math major, I am founding a Harvard student group called Gender Inclusivity in Math (GIIM). The club has the two-fold goal of increasing community among women in math, including dinners, retreats, and a women speaker series, and also addressing the gender gap in the math department, continuing the trend of surveys and gender in math discussions. The inclusion of male allies is central to our club mission, and the support from male allies at the student and faculty level that we have received makes me optimistic about the will for change.

Ultimately, it is my continued love for math which has driven me to take action. Mathematics is too beautiful and important to lose 50 percent (or much more when considering racial and class-based inequities) of the potential population of math lovers.

## Nick Kristof is not Smarter than an 8th Grader

This is a post by Eugene Stern, originally posted on his blog sensemadehere.wordpress.com.

About a week ago, Nick Kristof published this op-ed in the New York Times. Entitled Are You Smarter than an 8th Grader, the piece discusses American kids’ underperformance in math compared with students from other countries, as measured by standardized test results. Kristof goes over several questions from the 2011 TIMSS (Trends in International Mathematics and Science Study) test administered to 8th graders, and highlights how American students did worse than students from Iran, Indonesia, Ghana, Palestine, Turkey, and Armenia, as well as traditional high performers like Singapore. “We all know Johnny can’t read,” says Kristof, in that finger-wagging way perfected by the current cohort of New York Times op-ed columnists; “it appears that Johnny is even worse at counting.”

The trouble with this narrative is that it’s utterly, demonstrably false.

My friend Jordan Ellenberg pointed me to this blog post, which highlights the problem. In spite of Kristof’s alarmism, it turns out that American eighth graders actually did quite well on the 2011 TIMSS. You can see the complete results here. Out of 42 countries tested, the US placed 9th. If you look at the scores by country, you’ll see a large gap between the top 5 (Korea, Singapore, Taiwan, Hong Kong, and Japan) and everyone else. After that gap comes Russia, in 6th place, then another gap, then a group of 9 closely bunched countries: Israel, Finland, the US, England, Hungary, Australia, Slovenia, Lithuania, and Italy. Those made up, more or less, the top third of all the countries that took the test. Our performance isn’t mind-blowing, but it’s not terrible either. So what the hell is Kristof talking about?

You’ll find the answer here, in a list of 88 publicly released questions from the test (not all questions were published, but this appears to be a representative sample). For each question, a performance breakdown by country is given. When I went through the questions, I found that the US placed in the top third (top 14 out of 42 countries) on 45 of them, the middle third on 39, and the bottom third on 4. This seems typical of the kind of variance usually seen on standardized tests. US kids did particularly well on statistics, data interpretation, and estimation, which have all gotten more emphasis in the math curriculum lately. For example, 80% of US eighth graders answered this question correctly:

Which of these is the best estimate of (7.21 × 3.86) / 10.09?

(A) (7 × 3) / 10   (B) (7 × 4) / 10   (C) (7 × 3) / 11   (D) (7 × 4) / 11

More American kids knew that the correct answer was (B) than Russians, Finns, Japanese, English, or Israelis. Nice job, kids! And let’s give your teachers some credit too!

But Kristof isn’t willing to do either. He has a narrative of American underperformance in mind, and if the overall test results don’t fit his story, he’ll just go and find some results that do! Thus, the examples in his column. Kristof literally went and picked the two questions out of 88 on which the US did the worst, and highlighted those in the column. (He gives a third example too, a question in which the US was in the middle of the pack, but the pack did poorly, so the US’s absolute score looks bad.) And, presto! — instead of a story about kids learning stuff and doing decently on a test, we have yet another hysterical screed about Americans “struggling to compete with citizens of other countries.”

Kristof gives no suggestions for what we can actually do better, by the way. But he does offer this helpful advice:

Numeracy isn’t a sign of geekiness, but a basic requirement for intelligent discussions of public policy. Without it, politicians routinely get away with using statistics, as Mark Twain supposedly observed, the way a drunk uses a lamppost: for support rather than illumination.

So do op-ed columnists, apparently.

## Fingers crossed – book coming out next May

As it turns out, it takes a while to write a book, and then another few months to publish it.

I’m very excited today to tentatively announce that my book, which is tentatively entitled Weapons of Math Destruction: How Big Data Increases Inequality and Threatens Democracy, will be published in May 2016, in time to appear on summer reading lists and well before the election.

Fuck yeah! I’m so excited.

p.s. Fight for 15 is happening now.

## I accept mathematical bribes

Last Friday I traveled to American University and gave an evening talk, where I met Jeffrey Hakim, a mathematician and designer who openly bribed me.

Don’t worry, it’s not that insidious. He just showed me his nerdy math wallet and said I could have one too if I blogged about it. I obviously said yes. Here’s my new wallet:

It’s made of the same kind of flexible plastic they use on the outside of buildings. Or something. I expect it will last for many years.

You might notice there is writing and pictures on my new wallet! They are mathematical, which is why I don’t feel bad about accepting this bribe: it’s all in the name of education and fun with mathematics. Let me explain the front and back of the wallet.

The front is a theorem:

Here’s the thing, I’ve proven this. I have even assigned it to my students in the past to prove. We always use induction. This kind of identity is kind of made for induction, no? Don’t you think?

Well Jeffrey Hakim had an even better idea. His proof of Nicomachus’s Theorem is represented as a picture on the back of the wallet:

It took me a couple of minutes to see why this is a proof.

Here’s what I’d like you all to do: go think about why this is a proof of the above identity. Come back if you can’t figure it out, but if you can, just go ahead and pat yourself on your back and don’t bother reading the rest of this blogpost because it’s just going to explain the proof.

I’ll give you all a moment…

OK cool here’s why this is a proof.

First, convince yourself that this “pattern,” of building a frame of square boxes around the above square, can be continued. In other words, it’s a square of 4 1×1 boxes, framed by 2×2 boxes, framed by 3×3 boxes, and so on. It could go on forever this way, because if you focus on one side of the outside of the third layer, there are 4 3×3 boxes, so length $4 \cdot 3$, and we need it to also be the length inside the 4th frame, which has 3 boxes of length 4. Since $4\cdot 3 = 3\cdot 4$, we’re good. And that generalizes when it’s the $n$th layer, of course, since the outside of the $n$th layer will have $n+1$ boxes, each of length $n,$ making the inside of the $n+1$st have $n$ boxes, each of length $n+1$.

OK, now here’s the actual trick. What is the area of this box?

I claim there are two ways to measure the area, and one of the ways will give you the left hand side of Nicomachus’s Theorem but the other way will give you the right hand side of Nicomachus’s Theorem.

To be honest, it’s just one bit more complicated than that. Namely, the first way gives you something that’s 4 times bigger than the left hand side of Nicomachus’s Theorem and the second way gives you something 4 times bigger than the right hand side of Nicomachus’s Theorem.

Why don’t you go think about this for a few minutes, because the clue might be all you need to figure it out.

Or, perhaps you just want me to go ahead and explain it. I’ll do that! That’s why I got the wallet!

OK, now imagine isolating the top right quarter of the above figure. Like this:

That’s a square, obviously, so its area is the square of the length of any side. But if you go along the bottom, the length is obviously $1 + 2 + 3 + 4,$ which means the area is the square of that, $(1 + 2 + 3 + 4)^2.$

And since we know we can generalize the original figure to go up to $n$ instead of just 4, one quarter of the figure will have area $(1 + 2 + 3 + 4 + \dots + n)^2,$ which is to say the entire figure will have area $4(1 + 2 + 3 + 4 + \dots + n)^2.$

That’s 4 times the right-hand side of the theorem, so we’re halfway done!

Next, we will compute the area of the original figure a different way, namely by simply adding up and counting all the differently colored squares that make it up. Assume that we continue changing colors every time we get a new layer.

So, there are 4 1×1 squares, and there are 8 2×2 squares, and there are 12 3×3 squares, and there are 16 4×4 squares. In the generalized figure, there would be $4n$ $n\times n$ squares.

So if you look at the area of the generalized figure which is all one color, say the $n$th color, it will be of the form $4\cdot n \cdot n^2 = 4 \cdot n^3.$

That means the overall generalized figure will have total area:

$4 \cdot 1^3 + 4 \cdot 2^3 + 4 \cdot 3^3 + \dots + 4 \cdot n^3 = 4 \cdot (1^3 + 2^3 + 3^3 + \dots + n^3).$

Since that’s just 4 times the left-hand side of the theorem, we’re done.

Notes:

• this would be a fun thing to do with a kid.
• there’s more math inside the wallet which I haven’t gotten to yet.
• After staring at the picture for another minutes, I just realized the total area of the whole (generalized) thing is obviously $(n\cdot (n+1))^2,$ which is to say that either the left-hand side or right-hand side of the original identity is one fourth of that. Cool!
Categories: math, math education

## Guest Post: A Discussion Of PARCC Testing

This is a guest post by Eugene Stern, who writes a blog at Sense Made Here, and Kristin Wald, who writes a blog at This Unique* Weblog. Crossposted on their blogs as well.

Today’s post is a discussion of education reform, standardized testing, and PARCC with my friend Kristin Wald, who has been extremely kind to this blog. Kristin taught high school English in the NYC public schools for many years. Today her kids and mine go to school together in Montclair. She has her own blog that gets orders of magnitude more readers than I do.

ES: PARCC testing is beginning in New Jersey this month. There’s been lots of anxiety and confusion in Montclair and elsewhere as parents debate whether to have their kids take the test or opt out. How do you think about it, both as a teacher and as a parent?

KW: My simple answer is that my kids will sit for PARCC. However, and this is where is gets grainy, that doesn’t mean I consider myself a cheerleader for the exam or for the Common Core curriculum in general.

In fact, my initial reaction, a few years ago, was to distance my children from both the Common Core and PARCC. So much so that I wrote to my child’s principal and teacher requesting that no practice tests be administered to him. At that point I had only peripherally heard about the issues and was extending my distaste for No Child Left Behind and, later, Race to the Top. However, despite reading about and discussing the myriad issues, I still believe in change from within and trying the system out to see kinks and wrinkles up-close rather than condemning it full force.

Standards

ES: Why did you dislike NCLB and Race to the Top? What was your experience with them as a teacher?

KW: Back when I taught in NYC, there was wiggle room if students and schools didn’t meet standards. Part of my survival as a teacher was to shut my door and do what I wanted. By the time I left the classroom in 2007 we were being asked to post the standards codes for the New York State Regents Exams around our rooms, similar to posting Common Core standards all around. That made no sense to me. Who was this supposed to be for? Not the students – if they’re gazing around the room they’re not looking at CC RL.9-10 next to an essay hanging on a bulletin board. I also found NCLB naïve in its “every child can learn it all” attitude. I mean, yes, sure, any child can learn. But kids aren’t starting out at the same place or with the same support. And anyone who has experience with children who have not had the proper support up through 11th grade knows they’re not going to do well, or even half-way to well, just because they have a kickass teacher that year.

Regarding my initial aversion to Common Core, especially as a high school English Language Arts teacher, the minimal appearance of fiction and poetry was disheartening. We’d already seen the slant in the NYS Regents Exam since the late 90’s.

However, a couple of years ago, a friend asked me to explain the reason The Bluest Eye, with its abuse and rape scenes, was included in Common Core selections, so I took a closer look. Basically, a right-wing blogger had excerpted lines and scenes from the novel to paint it as “smut” and child pornography, thus condemning the entire Common Core curriculum. My response to my friend ended up as “In Defense of The Bluest Eye.”

That’s when I started looking more closely at the Common Core curriculum. Learning about some of the challenges facing public schools around the country, I had to admit that having a required curriculum didn’t seem like a terrible idea. In fact, in a few cases, the Common Core felt less confining than what they’d had before. And you know, even in NYC, there were English departments that rarely taught women or minority writers. Without a strong leader in a department, there’s such a thing as too much autonomy. Just like a unit in a class, a school and a department should have a focus, a balance.

But your expertise is Mathematics, Eugene. What are your thoughts on the Common Core from that perspective?

ES: They’re a mix. There are aspects of the reforms that I agree with, aspects that I strongly disagree with, and then a bunch of stuff in between.

The main thing I agree with is that learning math should be centered on learning concepts rather than procedures. You should still learn procedures, but with a conceptual underpinning, so you understand what you’re doing. That’s not a new idea: it’s been in the air, and frustrating some parents, for 50 years or more. In the 1960’s, they called it New Math.

Back then, the reforms didn’t go so well because the concepts they were trying to teach were too abstract – too much set theory, in a nutshell, at least in the younger grades. So then there was a retrenchment, back to learning procedures. But these things seem to go in cycles, and now we’re trying to teach concepts better again. This time more flexibly, less abstractly, with more examples. At least that’s the hope, and I share that hope.

I also agree with your point about needing some common standards defining what gets taught at each grade level. You don’t want to be super-prescriptive, but you need to ensure some kind of consistency between schools. Otherwise, what happens when a kid switches schools? Math, especially, is such a cumulative subject that you really need to have some big picture consistency in how you teach it.

Assessment

ES: What I disagree with is the increased emphasis on standardized testing, especially the raised stakes of those tests. I want to see better, more consistent standards and curriculum, but I think that can and should happen without putting this very heavy and punitive assessment mechanism on top of it.

KW: Yes, claiming to want to assess ability (which is a good thing), but then connecting the results to a teacher’s effectiveness in that moment is insincere evaluation. And using a standardized test not created by the teacher with material not covered in class as a hard percentage of a teacher’s evaluation makes little sense. I understand that much of the exam is testing critical thinking, ability to reason and use logic, and so on. It’s not about specific content, and that’s fine. (I really do think that’s fine!) Linking teacher evaluations to it is not.

Students cannot be taught to think critically in six months. As you mentioned about the spiraling back to concepts, those skills need to be revisited again and again in different contexts. And I agree, tests needn’t be the main driver for raising standards and developing curriculum. But they can give a good read on overall strengths and weaknesses. And if PARCC is supposed to be about assessing student strengths and weaknesses, it should be informing adjustments in curriculum.

On a smaller scale, strong teachers and staffs are supposed to work as a team to influence the entire school and district with adjusted curriculum as well. With a wide reach like the Common Core, a worrying issue is that different parts of the USA will have varying needs to meet. Making adjustments for all based on such a wide collection of assessments is counterintuitive. Local districts (and the principals and teachers in them) need to have leeway with applying them to best suit their own students.

Even so, I do like some things about data driven curricula. Teachers and school administrators are some of the most empathetic and caring people there are, but they are still human, and biases exist. Teachers, guidance counselors, administrators can’t help but be affected by personal sympathies and peeves. Having a consistent assessment of skills can be very helpful for those students who sometimes fall through the cracks. Basically, standards: yes. Linking scores to teacher evaluation: no.

ES: Yes, I just don’t get the conventional wisdom that we can only tell that the reforms are working, at both the individual and group level, through standardized test results. It gives us some information, but it’s still just a proxy. A highly imperfect proxy at that, and we need to have lots of others.

I also really like your point that, as you’re rolling out national standards, you need some local assessment to help you see how those national standards are meeting local needs. It’s a safeguard against getting too cookie-cutter.

I think it’s incredibly important that, as you and I talk, we can separate changes we like from changes we don’t. One reason there’s so much noise and confusion now is that everything – standards, curriculum, testing – gets lumped together under “Common Core.” It becomes this giant kitchen sink that’s very hard to talk about in a rational way. Testing especially should be separated out because it’s fundamentally an issue of process, whereas standards and curriculum are really about content.

You take a guy like Cuomo in New York. He’s trying to increase the reliance on standardized tests in teacher evaluations, so that value added models based on test scores count for half of a teacher’s total evaluation. And he says stuff like this: “Everyone will tell you, nationwide, the key to education reform is a teacher evaluation system.” That’s from his State of the State address in January. He doesn’t care about making the content better at all. “Everyone” will tell you! I know for a fact that the people spending all their time figuring out at what grade level kids should start to learn about fractions aren’t going tell you that!

I couldn’t disagree with that guy more, but I’m not going to argue with him based on whether or not I like the problems my kids are getting in math class. I’m going to point out examples, which he should be well aware of by now, of how badly the models work. That’s a totally different discussion, about what we can model accurately and fairly and what we can’t.

So let’s have that discussion. Starting point: if you want to use test scores to evaluate teachers, you need a model because – I think everyone agrees on this – how kids do on a test depends on much more than how good their teacher was. There’s the talent of the kid, what preparation they got outside their teacher’s classroom, whether they got a good night’s sleep the night before, and a good breakfast, and lots of other things. As well as natural randomness: maybe the reading comprehension section was about DNA, and the kid just read a book about DNA last month. So you need a model to break out the impact of the teacher. And the models we have today, even the most state-of-the-art ones, can give you useful aggregate information, but they just don’t work at that level of detail. I’m saying this as a math person, and the American Statistical Association agrees. I’ve written about this here and here and here and here.

Having student test results impact teacher evaluations is my biggest objection to PARCC, by far.

KW: Yep. Can I just cut and paste what you’ve said? However, for me, another distasteful aspect is how technology is tangled up in the PARCC exam.

Technology

ES: Let me tell you the saddest thing I’ve heard all week. There’s a guy named Dan Meyer, who writes very interesting things about math education, both in his blog and on Twitter. He put out a tweet about a bunch of kids coming into a classroom and collectively groaning when they saw laptops on every desk. And the reason was that they just instinctively assumed they were either about to take a test or do test prep.

That feels like such a collective failure to me. Look, I work in technology, and I’m still optimistic that it’s going to have a positive impact on math education. You can use computers to do experiments, visualize relationships, reinforce concepts by having kids code them up, you name it. The new standards emphasize data analysis and statistics much more than any earlier standards did, and I think that’s a great thing. But using computers primarily as a testing tool is an enormous missed opportunity. It’s like, here’s the most amazing tool human beings have ever invented, and we’re going to use it primarily as a paperweight. And we’re going to waste class time teaching kids exactly how to use it as a paperweight. That’s just so dispiriting.

KW: That’s something that hardly occurred to me. My main objection to hosting the PARCC exam on computers – and giving preparation homework and assignments that MUST be done on a computer – is the unfairness inherent in accessibility. It’s one more way to widen the achievement gap that we are supposed to be minimizing. I wrote about it from one perspective here.

I’m sure there are some students who test better on a computer, but the playing field has to be evenly designed and aggressively offered. Otherwise, a major part of what the PARCC is testing is how accurately and quickly children use a keyboard. And in the aggregate, the group that will have scores negatively impacted will be children with less access to the technology used on the PARCC. That’s not an assessment we need to test to know. When I took the practice tests, I found some questions quite clear, but others were difficult not for content but in maneuvering to create a fraction or other concept. Part of that can be solved through practice and comfort with the technology, but then we return to what we’re actually testing.

ES: Those are both great points. The last thing you want to do is force kids to write math on a computer, because it’s really hard! Math has lots of specialized notation that’s much easier to write with pencil and paper, and learning how to write math and use that notation is a big part of learning the subject. It’s not easy, and you don’t want to put artificial obstacles in kids’ way. I want kids thinking about fractions and exponents and what they mean, and how to write them in a mathematical expression, but not worrying about how to put a numerator above a denominator or do a superscript or make a font smaller on a computer. Plus, why in the world would you limit what kids can express on a test to what they can input on a keyboard? A test is a proxy already, and this limits what it can capture even more.

I believe in using technology in education, but we’ve got the order totally backwards. Don’t introduce the computer as a device to administer tests, introduce it as a tool to help in the classroom. Use it for demos and experiments and illustrating concepts.

As far as access and fairness go, I think that’s another argument for using the computer as a teaching tool rather than a testing tool. If a school is using computers in class, then at least everyone has access in the classroom setting, which is a start. Now you might branch out from there to assignments that require a computer. But if that’s done right, and those assignments grow in an organic way out of what’s happening in the classroom, and they have clear learning value, then the school and the community are also morally obligated to make sure that everyone has access. If you don’t have a computer at home, and you need to do computer-based homework, then we have to get you computer access, after school hours, or at the library, or what have you. And that might actually level the playing field a bit. Whereas now, many computer exercises feel like they’re primarily there to get kids used to the testing medium. There isn’t the same moral imperative to give everybody access to that.

I really want to hear more about your experience with the PARCC practice tests, though. I’ve seen many social media threads about unclear questions, both in a testing context and more generally with the Common Core. It sounds like you didn’t think it was so bad?

KW: Well, “not so bad” in that I am a 45 year old who was really trying to take the practice exam honestly, but didn’t feel stressed about the results. However, I found the questions with fractions confusing in execution on the computer (I almost gave up), and some of the questions really had to be read more than once. Now, granted, I haven’t been exposed to the language and technique of the exam. That matters a lot. In the SAT, for example, if you don’t know the testing language and format it will adversely affect your performance. This is similar to any format of an exam or task, even putting together an IKEA nightstand.

There are mainly two approaches to preparation, and out of fear of failing, some school districts are doing hardcore test preparation – much like SAT preparation classes – to the detriment of content and skill-based learning. Others are not altering their classroom approaches radically; in fact, some teachers and parents have told me they hardly notice a difference. My unscientific observations point to a separation between the two that is lined in Socio-Economic Status. If districts feel like they are on the edge or have a lot to lose (autonomy, funding, jobs), if makes sense that they would be reactionary in dealing with the PARCC exam. Ironically, schools that treat the PARCC like a high-stakes test are the ones losing the most.

Opting Out

KW: Despite my misgivings, I’m not in favor of “opting out” of the test. I understand the frustration that has prompted the push some districts are experiencing, but there have been some compromises in New Jersey. I was glad to see that the NJ Assembly voted to put off using the PARCC results for student placement and teacher evaluations for three years. And I was relieved, though not thrilled, that the percentage of PARCC results to be used in teacher evaluations was lowered to 10% (and now put off). I still think it should not be a part of teacher evaluations, but 10% is an improvement.

Rather than refusing the exam, I’d prefer to see the PARCC in action and compare honest data to school and teacher-generated assessments in order to improve the assessment overall. I believe an objective state or national model is worth having; relying only on teacher-based assessment has consistency and subjective problems in many areas. And that goes double for areas with deeply disadvantaged students.

ES: Yes, NJ seems to be stepping back from the brink as far as model-driven teacher evaluation goes. I think I feel the same way you do, but if I lived in NY, where Cuomo is trying to bump up the weight of value added models in evaluations to 50%, I might very well be opting out.

Let me illustrate the contrast – NY vs. NJ, more test prep vs. less — with an example. My family is good friends with a family that lived in NYC for many years, and just moved to Montclair a couple months ago. Their older kid is in third grade, which is the grade level where all this testing starts. In their NYC gifted and talented public school, the test was this big, stressful thing, and it was giving the kid all kinds of test anxiety. So the mom was planning to opt out. But when they got to Montclair, the kid’s teacher was much more low key, and telling the kids not to worry. And once it became lower stakes, the kid wanted to take the test! The mom was still ambivalent, but she decided that here was an opportunity for her kid to get used to tests without anxiety, and that was the most important factor for her.

I’m trying to make two points here. One: whether or not you opt out depends on lots of factors, and people’s situations and priorities can be very different. We need to respect that, regardless of which way people end up going. Two: shame on us, as grown ups, for polluting our kids’ education with our anxieties! We need to stop that, and that extends both to the education policies we put in place and how we collectively debate those policies. I guess what I’m saying is: less noise, folks, please.

KW: Does this very long blog post count as noise, Eugene? I wonder how this will be assessed? There are so many other issues – private profits from public education, teacher autonomy in high performing schools, a lack of educational supplies and family support, and so on. But we have to start somewhere with civil and productive discourse, right? So, thank you for having the conversation.

ES: Kristin, I won’t try to predict anyone else’s assessment, but I will keep mine low stakes and say this has been a pleasure!

## Guest post: Be more careful with the vagina stats in teaching

This is a guest post by Courtney  an assistant professor of mathematics at Hamilton College. You can see her teaching evaluations on ratemyprofessor.com. She would like you to note that she’s been tagged as “hilarious.” Twice.

Lately, my social media has been blowing up with stories about gender bias in higher ed, especially course evaluations.   As a 30-something, female math professor, I’m personally invested in this kind of issue.  So I’m gratified when I read about well-designed studies that highlight the “vagina tax” in teaching (I didn’t coin this phrase, but I wish I had).

These kinds of studies bring the conversation about bias to the table in a way that academics can understand. We can geek out on experimental design, the fact that the research is peer-reviewed and therefore passes some basic legitimacy tests.

Indeed, the conversation finally moves out of the realm of folklore, where we have “known” for some time that students expect women to be nurturing in addition to managing the class, while men just need to keep class on track.

Let me reiterate: as a young woman in academia, I want deans and chairs and presidents to take these observed phenomena seriously when evaluating their professors. I want to talk to my colleagues and my students about these issues. Eventually, I’d like to “fix” them, or at least game them to my advantage. (Just kidding.  I’d rather fix them.)

However, let me speak as a mathematician for a minute here: bad interpretations of data don’t advance the cause. There’s beautiful link-bait out there that justifies its conclusions on the flimsy “hey, look at this chart” understanding of big data. Benjamin M. Schmidt created a really beautiful tool to visualize data he scraped from the website ratemyprofessor.com through a process that he sketches on his blog. The best criticisms and caveats come from Schmidt himself.

What I want to examine is the response to the tool, both in the media and among my colleagues.  USAToday, HuffPo, and other sites have linked to it, citing it as yet more evidence to support the folklore: students see men as “geniuses” and women as “bossy.” It looks like they found some screenshots (or took a few) and decided to interpret them as provocatively as possible. After playing with the tool for a few minutes, which wasn’t even hard enough to qualify as sleuthing, I came to a very different conclusion.

If you look at the ratings for “genius”  and then break them down further to look at positive and negative reviews separately, it occurs predominantly in negative reviews. I found a few specific reviews, and they read, “you have to be a genius to pass” or along those lines.

[Don’t take my word for it — search google for:

rate my professors “you have to be a genius”‘

and you’ll see how students use the word “genius” in reviews of professors. The first page of hits is pretty much all men.]

Here’s the breakdown for “genius”:

So yes, the data shows that students are using the word “genius” in more evaluations of men than women. But there’s not a lot to conclude from this; we can’t tell from the data if the student is praising the professor or damning him. All we can see that it’s a word that occurs in negative reviews more often than positive ones. From the data, we don’t even know if it refers to the professor or not.

Similar results occur with “brilliant”:

Now check out “bossy” and negative reviews:

Okay, wow, look at how far to the right those orange dots are… and now look at the x-axis.  We’re talking about fewer than 5 uses per million words of text.  Not exactly significant compared to some of the other searches you can do.

I thought that the phrase “terrible teacher” was more illuminating, because it’s more likely in reference to the subject of the review, and we’ve got some meaningful occurrences:

And yes, there is a gender imbalance, but it’s not as great as I had feared. I’m more worried about the disciplinary break down, actually. Check out math — we have the worst teachers, but we spread it out across genders, with men ranking 187 uses of “terrible teacher” per million words; women score 192. Compare to psychology, where profs receive a score of 110.  Ouch.

Who’s doing this reporting, and why aren’t we reading these reports more critically?  Journalists, get your shit together and report data responsibly.  Academics, be a little more skeptical of stories that simply post screenshots of a chart coupled with inciting prose from conclusions drawn, badly, from hastily scanned data.

Is this tool useless? No. Is it fun to futz around with? Yes.

Is it being reported and understood well? Resounding no!

I think even our students would agree with me: that’s just f*cked up.

Aunt Pythia has something in the works for you dear people, but it’s not quite ready yet, and you’ll have to wait another week. Rest assured, it will be worth it. And apologies to mathbabe.org subscribers who received an errant test post this week.

In the meantime, Aunt Pythia is going to write a quick column today from a Montreal hotel room after an amazing workshop yesterday which she will comment on later in the week.

So quick, get some tea and some flannel-lined flannel, because damn it’s wintery outside, all snowy and shit. Aunt Pythia’s about to spew her usual unreasonable nonsense!

From earlier this week in Montreal.

LET’S DO THIS PEOPLES!!! And please, even if you’ve got nothing interesting to say for yourself, feel free to make something up or get inspired by Google auto complete and then go ahead and:

By the way, if you don’t know what the hell Aunt Pythia is talking about, go here for past advice columns and here for an explanation of the name Pythia.

——

Dear Aunt Pythia,

This may not really be an “Aunt Pythia” question. But could either you or Mathbabe comment on this article on sexism in academic science?

I can imagine many ways they could be misrepresenting the statistics, but I don’t know which.

No Bias, Really?

Dear No Bias,

I was also struck by the inflammatory tone and questionable conclusions of this article. But you know, controversy sells.

So, here are a couple of lines I’ll pull out. First:

Our country desperately needs more talented people in these fields; recruiting more women could address this issue. But the unwelcoming image of the sexist academy isn’t helping. Fortunately, as we have found in a thorough analysis of recent data on women in the academic workplace, it isn’t accurate, either.

And second:

Many of the common, negative depictions of the plight of academic women are based on experiences of older women and data from before the 2000s, and often before the 1990s. That’s not to say that mistreatment doesn’t still occur — but when it does, it is largely anecdotal, or else overgeneralized from small studies.

I guess right off the bat I’d ask, how are you collecting data? The data I have personally about sexist treatment at the hands of my colleagues hasn’t, to my knowledge, been put in any database. The sexist treatment I’ve witnessed for pretty much all of my female mathematics colleagues has, equally, never been installed in a database to my knowledge. So yeah, not convinced these people know what they are talking about. It’s famously hard to prove something doesn’t exist, especially when you don’t have a search algorithm.

One possibility for the data they seem to have: they interviewed people after the fact, perhaps decades after the fact. If that’s the case, then you’d expect more and better data on older women, and that’s what we are currently seeing. There is a lag on this data collection, in other words. That’s not the same as “it doesn’t exist.” A common mistake researchers make. They take the data as “objective truth” and forget that it’s a human process to collect it (or not collect it!). Think police shootings.

The article then goes on to talk about how the data for women in math and other science fields isn’t so bad in terms of retention, promotion, and other issues. For there I’d say, the women have already gone through a mighty selection process, so in general you’d expect them to be smarter than their colleagues, so in general their promotion rates should be higher, but they aren’t. So that’s also a sign of sexism.

I mean, whatever. That’s not actually what I claim is true, so much as another interpretation of this data. My overall point is that, they have some data, and they are making strong and somewhat outrageous claims which I can dismiss without much work.

I hope that helps!

Aunt Pythia

——

Dear Aunt Pythia,

In his November “Launchings” column, David Bressoud has presents some interesting data on differences between male and female college calculus students. As much as I’ve appreciated all of Bressoud’s careful explorations of mathematics education, I find I’m a bit irritated by his title, “MAA Calculus Study: Women Are Different,” because it appears to take the male experience as the norm.

Perhaps I was already annoyed because of a NYTimes op-ed, “Academic Science Isn’t Sexist”, in which Wendy Williams and Steven Ceci claim that “[w]e are not your father’s academy anymore,” and that the underrepresentation of women in math-intensive fields is “rooted in women’s earlier educational choices, and in women’s occupational and lifestyle preferences.” Here, too, the message seems to be “don’t worry about changing the academy — women are different from the norm, which is (naturally) that which works for men.”

My question for you, Aunt Pythia, is this: am I overreacting here?

I received my PhD in mathematics in 1984, and I’ve seen significant change for the better in the academy since then. Child care at AMS meetings? A crowd in the women’s rest room at same? Unthinkable when I started. But if women are still disproportionately “choosing” to go into other fields, might we look a little more closely at the environments in which girls and women are making their educational and “lifestyle” choices?

I welcome your thoughts. If you’re eager for more data analysis, I’d also love to hear your take on the paper by Williams, Ceci, and their colleagues.

Still One of the Underrepresented After All These Years

Dear SOotUAATY,

Without even reading that article, I can say without hesitation that yes, it’s a ridiculous title, and it’s infuriating and YOU ARE NOT OVERREACTING. To be clear, that is bold-faced, italicized, and all caps. I mean it.

The word “different” forces us to compare something to a baseline, and given that there is no baseline even mentioned, we are forced to guess at it, and that imposes the “man as default” mindset. Fuck that. I mean, if the title had been, “There are differences between male and female calculus students,” I would not have been annoyed, because even though “male” comes first, I’m not a stickler. I just want to acknowledge that if we mention one category, we mention the other as well.

To illustrate this a bit more, we don’t entitle a blog post “Whites are different” and leave it at that, because we’d be like, different from whom? From blacks? From Asians? From Asian-Americans? See how that works? You need to say different from some assumed baseline, and the assumed baseline has to be a cultural norm. And right now it’s white male. Which is arguable one reason that calculus students act differently when they are men (har!).

As for the other article, I already shit on that in the previous answer but I’m happy to do it once again. It’s bullshit, and I’m disappointed that the Times published it.

As for the article, I don’t have time now but I’ll take a look, thanks!

Aunt Pythia

——

Dear Aunt Pythia,

I am twenty years old, near the halfway point in my senior year of a mathematics BS at a large, well-regarded public university in the Northeast. I’ve been aiming my energies at graduate school, and I am now looking at PhD program applications. Most apps ask for two or three letters of recommendation from a faculty member who is familiar with your work. This poses a very big problem, because all of my professors hate me.

Okay, maybe it’s not quite like that. But I’ve had a really lousy time in the math department at LWRPUN. My fellow students are dispassionate, unresponsive, and unfriendly. My professors are dry, uncommitted to their students, and the ones who aren’t mathematically incompetent are lousy teachers. On top of all this, a crippling bureaucracy has prevented me countless times from taking classes I’m interested in (few as they are in this catalog), substituting instead ANOTHER REQUIRED SEMESTER OF ANALYSIS.

So I haven’t made any personal connections of the sort that might benefit me in the form of a letter of rec. My work hasn’t even been that good; my depression and anxiety (in general as well as re all this) have increasingly prevented me from completing even easy homework assignments. Nobody here has seen my best mathematical work, and for that matter, nobody anywhere else has either*.

And for four years, everyone I’ve come to with this gathering creeping progressively life-eating concern has given me the same old BS about You should really put yourself out there! and It’s just so important to go to your professor’s office hours! without considering maybe — I’ve tried, I really have.

What can I do, Aunt Pythia? I’m really passionate about mathematics, but I’m worried I won’t be able to pursue my studies without these magic papers.

Anxiously,
Reports Embargoed by Crummy Lecturers, Earnestly Seeking Solace

*I thankfully have a professor from an outside experience willing to write about my teaching credentials, but that one letter is surely not sufficient to show my potential as a graduate student and researcher.

Dear RECLESS,

I am afraid I will have to call bullshit on you, RECLESS. Plus your sign-off doesn’t actually spell anything.

Here’s the thing, there are no mathematically incompetent lecturers at large, well-regarded public universities. There are, in fact, mathematically very competent people who can’t get jobs at such places. Such is the pyramid-shaped job market of mathematics. So whereas I believe you when you say your lecturers have been uninspired, and uncommitted to their students, the fact that you added “mathematically incompetent” just makes me not believe you at all, in anything.

Here’s what I think is happening. You think you’re really into math, but you’ve never really understood your classes, nor have you understood that you’ve never understood your classes, because your self-image is that you’re already a mathematician, and that people have just not acknowledged your brilliance.

But that’s not how math actually works. Math is a social endeavor, where you have to communicate your ideas well enough for others to understand them, or else you aren’t doing math.

I’m not saying you haven’t had bad luck with teachers. It’s a real possibility. But there’s something else going on as well, and I don’t think you can honestly expect to go to the next level without sorting stuff out. In other words, even if you don’t love the teacher, if you loved the subject, got into it, and did the proofs, you’d still be getting adequate grades to ask for letters. The thing about writing letters, as a math prof, is that you don’t have to like the student personally to write a good letter, you just need to admire their skills. But since you can’t do that either, you won’t get good letters, and moreover I don’t think you’d deserve good letters. And therefore I don’t think you should go to grad school.

Suggestion: look carefully at your own behavior, figure out what it is you are doing that isn’t working. Maybe think of what you love about math, or about your own image of being a mathematician, and see if there’s something you really know you’re good at, and other people know it to, and develop that.

Good luck,

Aunt Pythia

——

Dearest Aunt Pythia,

I have a sex question for you! Kind of. You have to get through the boring back story first…I’m a 19 year old female physics major. I’m quiet, rather mousy, and awkward. A lot of the time I feel like I have more to prove than the boys do, because I’m a girl, and because of the aforementioned shyness.

People seem to automatically assume I’m unintelligent. I think I’m just as intelligent as the boys in my program, but I don’t come off that way! Point is, I want to be this cool, strong, independent, successful, respectable girl who doesn’t take shit from misogynistic people who assume I’m inferior.

However, I feel extremely guilty about my sexual preferences. I’m pretty submissive. I’d like power exchange in my relationships…hair pulling, bondage, spanking, being bossed around, the whole bit. I like to be dominated by men. Older men. Smart older men. Hopefully I’ve successfully conveyed my dilemma. I want to be respected by the men (and women, and others) I’m surrounded by in my academic life, but taken control of as a girlfriend.

Why does what I despise happening to me in an academic setting please me so much in a romantic/sexual one? Agh, I feel like such a bad girl! (and not in the arousing way…)

Help!
Much Love,
Conflicted

Dear Conflicted,

This is such a relief – finally, a sex question! – and it’s honestly one of the best questions I’ve ever gotten, ever, in Aunt Pythia or elsewhere. I’m so glad I can answer this for you.

It is absolutely not in conflict to want something in a sexual context that is abhorrent to you in normal life. It is in fact a well-known pattern! You shouldn’t feel at all weird about it! Lots – LOTS – of the submissives I’ve met are, in their day jobs, the boss, literally. They have companies and are extremely fancy and in control. And then they love to be bossed around and spanked. Seriously. If anything, my feeling is that your sexual proclivities point to being alpha in real life, but maybe I’m going overboard.

So yeah, no problem here. You are killing it. And in 3 or 4 years I want you to write back and explain to me how you’ve found an amazing lover who gives you what you want in the bedroom and worships your physics prowess outside it. There will, in fact, be people lining up for this role.

And those people in your program? Do your best to ignore them. Men are just impossibly arrogant at that age, but time will humble them somewhat even as your confidence will rise as you learn more. I’m not saying it ever evens out entirely but it does improve.

Also: find other women (and super cool men) to study with. Surround yourself with supportive people. Take note of obnoxious people and avoid them. Trade up with friends whenever possible.

Love always,

Aunt Pythia

——

Well, you’ve wasted yet another Saturday morning with Aunt Pythia! I hope you’re satisfied! Please if you could, ask me a question. And don’t forget to make an amazing sign-off, they make me very very happy.

## Educational feedback loops in China and the U.S.

Today I want to discuss a recent review in New York Review of Books, on a new book entitled Who’s Afraid of the Big Bad Dragon? Why China Has the Best (and Worst) Education System in the World by Yong Zhao (hat tip Alex). The review was written by Diane Ravitch, an outspoken critic of No Child Left Behind, Race To The Top, and the Common Core.

You should read the review, it’s well written and convincing, at least to me. I’ve been studying these issues and devoted a large chunk of my book to the feedback loops described as they’ve played out in this country. Here are the steps I see, which are largely reflected in Ravitch’s review:

1. Politicians get outraged about a growing “achievement gap” (whereby richer or whiter students get better test scores than poorer or browner students) and/or a “lack of international competitiveness” (whereby students in countries like China get higher international standardized test scores than U.S. students).
2. The current president decides to “get tough on education,” which translates into new technology and way more standardized tests.
3. The underlying message is that teachers and students and possibly parents are lazy and need to be “held accountable” to improve test scores. The even deeper assumption is that test scores are the way to measure quality of learning.
4. Once there’s lots of attention being given to test scores, lots of things start happening in response (the “feedback loop”).
5. For example, widespread cheating by students and teachers and principals, especially when teachers and principals get paid based on test performance.
6. Also, well-off students get more and better test prep, so the achievement gap gets wider.
7. Even just the test scores themselves lead to segregation by class: parents who can afford it move to towns with “better schools,” measured by test scores.
8. International competitiveness doesn’t improve. But we’ve actually never been highly ranked since we started measuring this.

What Zhao’s book adds to this is how much worse it all is in China. Especially the cheating. My favorite excerpt from the book:

Teachers guess possible [test] items, companies sell answers and wireless cheating devices to students, and students engage in all sorts of elaborate cheating. In 2013, a riot broke out because a group of students in Hubei Province were stopped from executing the cheating scheme their parents purchased to ease their college entrance exam.

Ravitch adds after that that ‘an angry mob of two thousand people smashed cars and chanted, “We want fairness. There is no fairness if you do not let us cheat.”’

To be sure, the stakes in China are way higher. Test scores are incredibly important and allow people to have certain careers. But according to Zhao, this selection process, which is quite old, has stifled creativity in the Chinese educational system (so, in other words, test scores are the wrong way to measure learning, in part because of the feedback loop). He blames the obsession with test scores on the fact that no Chinese native has received a Nobel Prize since 1949, for example: the winners of that selection process are not naturally creative.

Furthermore, Zhao claims, the Chinese educational system stifles individuality and forces conformity. It is an authoritarian tool.

In that light, I guess we should be proud that our international scores are lower than China’s; maybe it is evidence that we’re doing something right.

I know that, as a parent, I am sensitive to these issues. I want my kids to have discipline in some ways, but I don’t want them to learn to submit themselves to an arbitrary system for no good reason. I like the fact that they question why they should do things like go to bed on time, and exercise regularly, and keep their rooms cleanish, and I encourage their questions, even while I know I’m kind of ruining their chances at happily working in a giant corporation and being a conformist drone.

This parenting style of mine, which I believe is pretty widespread, seems reasonable to me because, at least in my experience, I’ve gotten further by being smart and clever than by being exactly what other people have wanted me to be. And I’m glad I live in a society that rewards quirkiness and individuality.

## Student evaluations: very noisy data

I’ve been sent this recent New York Times article by a few people (thanks!). It’s called Grading Teachers, With Data From Class, and it’s about how standardized tests are showing themselves to be inadequate to evaluate teachers, so a Silicon Valley-backed education startup called Panorama is stepping into the mix with a data collection process focused on student evaluations.

Putting aside for now how much this is a play for collecting information about the students themselves, I have a few words to say about the signal which one gets from student evaluations. It’s noisy.

So, for example, I was a calculus teacher at Barnard, teaching students from all over the Columbia University community (so, not just women). I taught the same class two semesters in a row: first in Fall, then in Spring.

Here’s something I noticed. The students in the Fall were young (mostly first semester frosh), eager, smart, and hard-working. They loved me and gave me high marks on all categories, except of course for the few students who just hated math, who would typically give themselves away by saying “I hate math and this class is no different.”

The students in the Spring were older, less eager, probably just as smart, but less hard-working. They didn’t like me or the class. In particular, they didn’t like how I expected them to work hard and challenge themselves. The evaluations came back consistently less excited, with many more people who hated math.

I figured out that many of the students had avoided this class and were taking it for a requirement, didn’t want to be there, and it showed. And the result was that, although my teaching didn’t change remarkably between the two semesters, my evaluations changed considerably.

Was there some way I could have gotten better evaluations from that second group? Absolutely. I could have made the class easier. That class wanted calculus to be cookie-cutter, and didn’t particularly care about the underlying concepts and didn’t want to challenge themselves. The first class, by contrast, had loved those things.

My conclusion is that, once we add “get good student evaluations” to the mix of requirements for our country’s teachers, we are asking for them to conform to their students’ wishes, which aren’t always good. Many of the students in this country don’t like doing homework (in fact most!). Only some of them like to be challenged to think outside their comfort zone. We think teachers should do those things, but by asking them to get good student evaluations we might be preventing them from doing those things. A bad feedback loop would result.

I’m not saying teachers shouldn’t look at student evaluations; far from it, I always did and I found them useful and illuminating, but the data was very noisy. I’d love to see teachers be allowed to see these evaluations without there being punitive consequences.

## Guest Post: Bring Back The Slide Rule!

This is a guest post by Gary Cornell, a mathematician, writer, publisher, and recent founder of StemForums.

I was was having a wonderful ramen lunch with the mathbabe and, as is all too common when two broad minded Ph.D.’s in math get together, we started talking about the horrible state math education is in for both advanced high school students and undergraduates.

One amusing thing we discovered pretty quickly is that we had independently come up with the same (radical) solution to at least part of the problem: throw out the traditional sequence which goes through first and second year calculus and replace it with a unified probability, statistics, calculus course where the calculus component was only for the smoothest of functions and moreover the applications of calculus are only to statistics and probability. Not only is everything much more practical and easier to motivate in such a course, students would hopefully learn a skill that is essential nowadays: how to separate out statistically good information from the large amount of statistical crap that is out there.

Of course, the downside is that the (interesting) subtleties that come from the proofs, the study of non-smooth functions and for that matter all the other stuff interesting to prospective physicists like DiffEQ’s would have to be reserved for different courses. (We also were in agreement that Gonick’s beyond wonderful“Cartoon Guide To Statistics” should be required reading for all the students in these courses, but I digress…)

The real point of this blog post is based on what happened next: but first you have to know I’m more or less one generation older than the mathbabe. This meant I was both able and willing to preface my next point with the words: “You know when I was young, in one way students were much better off because…” Now it is well known that using this phrase to preface a discussion often poisons the discussion but occasionally, as I hope in this case, some practices from days gone by ago can if brought back, help solve some of today’s educational problems.

By the way, and apropos of nothing, there is a cure for people prone to too frequent use of this phrase: go quickly to YouTube and repeatedly make them watch Monty Python’s Four Yorkshireman until cured:

Anyway, the point I made was that I am a member of the last generation of students who had to use slide rules. Another good reference is: here. Both these references are great and I recommend them. (The latter being more technical.) For those who have never heard of them, in a nutshell, a slide rule is an analog device that uses logarithms under the hood to do (sufficiently accurate in most cases) approximate multiplication, division, roots etc.

The key point is that using a slide rule requires the user to keep track of the “order of magnitude” of the answers— because slide rules only give you four or so significant digits. This meant students of my generation when taking science and math courses were continuously exposed to order of magnitude calculations and you just couldn’t escape from having to make order of magnitude calculations all the time—students nowadays, not so much. Calculators have made skill at doing order of magnitude calculations (or Fermi calculations as they are often lovingly called) an add-on rather than a base line skill and that is a really bad thing. (Actually my belief that bringing back slide rules would be a good thing goes back a ways: when that when I was a Program Director at the NSF in the 90’s, I actually tried to get someone to submit a proposal which would have been called “On the use of a hand held analog device to improve science and math education!” Didn’t have much luck.)

Anyway, if you want to try a slide rule out, alas, good vintage slide rules have become collectible and so expensive— because baby boomers like me are buying the ones we couldn’t afford when we were in high school – but the nice thing is there are lots of sites like this one which show you how to make your own.

Finally, while I don’t think they will ever be as much fun as using a slide rule, you could still allow calculators in classrooms.

Why? Because it would be trivial to have a mode in the TI calculator or the Casio calculator that all high school students seem to use, called “significant digits only.” With the right kind of problems this mode would require students to do order of magnitude calculations because they would never be able to enter trailing or leading zeroes and we could easily stick them with problems having a lot of them!

But calculators really bug me in classrooms and, so I can’t resist pointing out one last flaw in their omnipresence: it makes students believe in the possibility of ridiculously high precision results in the real world. After all, nothing they are likely to encounter in their work (and certainly not in their lives) will ever need (or even have) 14 digits of accuracy and, more to the point, when you see a high precision result in the real world, it is likely to be totally bogus when examined under the hood.

## Love StackOverflow and MathOverflow? Now there’s StemForums!

Everyone I know who codes uses stackoverflow.com for absolutely everything.

Just yesterday I met a cool coding chick who was learning python and pandas (of course!) with the assistance of stackoverflow. It is exactly what you need to get stuff working, and it’s better than having a friend to ask, even a highly knowledgable friend, because your friend might be busy or might not know the answer, or even if your friend knew the answer her answer isn’t cut-and-paste-able.

If you are someone who has never used stackoverflow for help, then let me explain how it works. Say you want to know how to load a JSON file into python but you don’t want to write a script for that because you’re pretty sure someone already has. You just search for “import json into python” and you get results with vote counts:

Also, every math nerd I know uses and contributes to mathoverflow.net. It’s not just for math facts and questions, either, there are interesting discussions going on there all the time. Here’s an example of a comment in response to understanding the philosophy behind the claimed proof of the ABC Conjecture:

OK well hold on tight because now there’s a new online forum, but not about coding and not about math. It’s about all the other STEM subjects, which since we’ve removed math might need to be called STE subjects, which is not catchy.

It’s called stemforums.com, and it is being created by a team led by Gary Cornell, mathematician, publisher at Apress, and beloved Black Oak bookstore owner.

So far only statistics is open, but other stuff is coming very soon. Specifically it covers, or soon will cover, the following fields:

1. Statistics
2. Biology
3. Chemistry
4. Cognitive Sciences
5. Computer Sciences
6. Earth and Planetary Sciences
7. Economics
8. Science & Math Education
9. Engineering
10. History of Science and Mathematics
11. Applied Mathematics, and
12. Physics

I’m super excited for this site, it has serious potential to make peoples’ lives better. I wish it had a category for Data Sciences, and for Data Journalism, because I’d probably be more involved in those categories than most of the above, but then again most data science-y questions could be inserted into one of the above. I’ll try to be patient on this one.

Here’s a screen shot of an existing Stats question on the site:

The site doesn’t have many questions, and even fewer answers, but as I understand it the first few people to get involved are eligible for Springer books, so go check it out.

## Nerding out: RSA on an iPython Notebook

Yesterday was a day filled with secrets and codes. In the morning, at The Platform, we had guest speaker Columbia history professor Matthew Connelly, who came and talked to us about his work with declassified documents. Two big and slightly depressing take-aways for me were the following:

• As records have become digitized, it has gotten easy for people to get rid of archival records in large quantities. Just press delete.
• As records have become digitized, it has become easy to trace the access of records, and in particular the leaks. Connelly explained that, to some extent, Obama’s harsh approach to leakers and whistleblowers might be explained as simply “letting the system work.” Yet another way that technology informs the way we approach human interactions.

After class we had section, in which we discussed the Computer Science classes some of the students are taking next semester (there’s a list here) and then I talked to them about prime numbers and the RSA crypto system.

I got really into it and wrote up an iPython Notebook which could be better but is pretty good, I think, and works out one example completely, encoding and decoding the message “hello”.

The underlying file is here but if you want to view it on the web just go here.

## The platonic solids

I managed to record this week’s Slate Money podcast early so I could drive up to HCSSiM for July 17th, and the Yellow Pig Day celebration. I missed the 17 talk but made it in time for yellow pig carols and cake.

This morning my buddy Aaron decided to let me talk to the kids in the last day of his workshop. First Amber is working out the formula for the Euler Characteristic of a planar graph with the kids and after that I’ll help them count the platonic solids using stereographic projection. If we have time we’ll talk about duals (update: we had time!).

I can never remember which one is the icosahedron.

Tonight at Prime Time I’ll play a game or two of Nim with them.

Categories: math, math education

## Guest post: What is the goal of a college calculus course?

This is a guest post by Nathan, who recently finished graduate school in math, and will begin a post-doc in the fall. He loves teaching young kids, but is still figuring out how to motivate undergraduates.

The question

Like most mathematicians in academia, I’m teaching calculus in the fall. I taught in grad school, but the syllabus and assignments were already set. This time I’ll be in charge, so I need to make some design decisions, like the following:

1. Are calculators/computers/notes allowed on the exams?
2. Which purely technical skills must students master (by a technical skill I mean something like expanding rational functions into partial fractions: a task which is deterministic but possibly intricate)?
3. Will students need to write explanations and/or proofs?

I have some angst about decisions like these, because it seems like each one can go in very different directions depending on what I hope the students are supposed to get from the course. If I’m listing the pros and cons of permitting calculators, I need some yardstick to measure these pros and cons.

My question is: what is the goal of a college calculus course?

I’d love to have an answer that is specific enough that I can use it to make concrete decisions like the ones above. Part of my angst is that I’ve asked many people this question, including people I respect enormously for their teaching, but often end up with a muddled answer. And there are a couple stock answers that come to mind, but each one doesn’t satisfy me for one reason or another. Here’s what I have so far.

The contenders.

To teach specific tasks that are necessary for other subjects.

These tasks would include computing integrals and derivatives, converting functions to power series or Fourier series, and so forth.

Intuitive understanding of functions and their behavior.

This is vague, so here’s an example: a couple years ago, a friend in medical school showed me a page from his textbook. The page concerned whether a certain drug would affect heart function in one way or in the opposite way (it caused two opposite effects), and it showed a curve relating two involved parameters. It turned out that the essential feature was that this curve was concave down. The book did not use the phrase “concave down,” though, and had a rather wordy explanation of the behavior. In this situation, a student who has a good grasp of what concavity is and what its implications are is better equipped to understand the effect described in the book. So if a student has really learned how to think about concavity of functions and its implications, then she can more quickly grasp the essential parts of this medical situation.

To practice communicating with precision.

I’m taking “communication” in a very wide sense here: carefully showing the steps in an integral calculation would count.

Not Satisfied

I have issues with each of these as written. I don’t buy number 1, because the bread and butter of calculus class, like computing integrals, isn’t something most doctors or scientists will ever do again. Number 2 is a noble goal, but it’s overly idealistic; if this is the goal, then our success rate is less than 10%. Number 3 also seems like a great goal, relevant for most of the students, but I think we’d have to write very different sorts of assignments than we currently do if we really want to aim for it.

I would love to have a clear and realistic answer to this question. What do you think?

Categories: education, math education

## Getting rid of teacher tenure does not solve the problem

There’s been a movement to make primary and secondary education run more like a business. Just this week in California, a lawsuit funded by Silicon Valley entrepreneur David Welch led to a judge finding that student’s constitutional rights were being compromised by the tenure system for teachers in California.

The thinking is that tenure removes the possibility of getting rid of bad teachers, and that bad teachers are what is causing the achievement gap between poor kids and well-off kids. So if we get rid of bad teachers, which is easier after removing tenure, then no child will be “left behind.”

The problem is, there’s little evidence for this very real achievement gap problem as being caused by tenure, or even by teachers. So this is a huge waste of time.

As a thought experiment, let’s say we did away with tenure. This basically means that teachers could be fired at will, say through a bad teacher evaluation score.

An immediate consequence of this would be that many of the best teachers would get other jobs. You see, one of the appeals of teaching is getting a comfortable pension at retirement, but if you have no idea when you’re being dismissed, then it makes no sense to put in the 25 or 30 years to get that pension. Plus, what with all the crazy and random value-added teacher models out there, there’s no telling when your score will look accidentally bad one year and you’ll be summarily dismissed.

People with options and skills will seek other opportunities. After all, we wanted to make it more like a business, and that’s what happens when you remove incentives in business!

The problem is you’d still need teachers. So one possibility is to have teachers with middling salaries and no job security. That means lots of turnover among the better teachers as they get better offers. Another option is to pay teachers way more to offset the lack of security. Remember, the only reason teacher salaries have been low historically is that uber competent women like Laura Ingalls Wilder had no other options than being a teacher. I’m pretty sure I’d have been a teacher if I’d been born 150 years ago.

So we either have worse teachers or education doubles in price, both bad options. And, sadly, either way we aren’t actually addressing the underlying issue, which is that pesky achievement gap.

People who want to make schools more like businesses also enjoy measuring things, and one way they like measuring things is through standardized tests like achievement scores. They blame teachers for bad scores and they claim they’re being data-driven.

Here’s the thing though, if we want to be data-driven, let’s start to maybe blame poverty for bad scores instead:

I’m tempted to conclude that we should just go ahead and get rid of teacher tenure so we can wait a few years and still see no movement in the achievement gap. The problem with that approach is that we’ll see great teachers leave the profession and no progress on the actual root cause, which is very likely to be poverty and inequality, hopelessness and despair. Not sure we want to sacrifice a generation of students just to prove a point about causation.

On the other hand, given that David Welch has a lot of money and seems to be really excited by this fight, it looks like we might have no choice but to blame the teachers, get rid of their tenure, see a bunch of them leave, have a surprise teacher shortage, respond either by paying way more or reinstating tenure, and then only then finally gather the data that none of this has helped and very possibly made things worse.

Categories: education, math education, news

## How Not To Be Wrong by Jordan Ellenberg

You guys are in for a treat. In fact I’m jealous of you.

I had a little secret about my survival in grad school, and that secret has a name, and that name is Jordan Ellenberg. We used to meet every Tuesday and Thursday to study schemes at the CallaLily Cafe a few blocks from the Science Center on Kirkland Street, and even though that sounds kind of dull, it was a blast. It was what kept me sane at Harvard.

You see, Jordan has an infectious positivity about him, which balances my rather intense suspicions, and moreover he’s hilariously funny. He’s really somewhere between a mathematician and a stand-up comedian, and to be honest I don’t know which one he’s better at, although he is a deeply talented mathematician.

The reason I’m telling you this is that he’s written a book, called How Not To Be Wrong, and available for purchase starting today, which is a delight to read and which will make you understand why I survived graduate school. In fact nobody will ever let me complain again once they’ve read this book, because it reads just like Jordan talks. In reading it, I felt like I was right back at CallaLily, singing Prince’s “Sexy MF” and watching Jordan flirt with the cashier lady again. Aaaah memories.

So what’s in the book? Well, he talks a lot about math, and about mathematicians, and the lottery, and in fact he has this long riff which starts out with lottery math, then goes to error-correcting codes and then to made-up languages and then to sphere packing and then arrives again at lotteries. And it’s brilliant and true and beautiful and also funny.

I have a theory about this book that you could essentially open it up to any page and begin to enjoy it, since it is thoroughly enjoyable and the math is cumulative but everywhere so well explained that it wouldn’t take long to follow along, and pretty soon you’d be giggling along with Jordan at every ridiculous footnote he’s inserted into his narrative.

In other words, every page is a standalone positive and ontological examination of the beauty and surprise of mathematical discovery. And so, if you are someone who shares with Jordan a love for mathematics, you will have a consistently great time with this book. In fact I’m imagining that you have an uncle or a mom who loves math or science, in which case this would be a seriously perfect gift to them, but of course you could also give that gift to yourself. I mean, this is a guy who can make nazi jokes funny, and he does.

Having said that, the magic of the book is that it’s not just a collection of wonderful mathy tidbits. Jordan also has a point about the act of scrutinizing something in a logical and mathematical fashion. That act itself is courageous and should be appreciated, and he explains why, and he tells us how much we’ve already benefited from people in the past who have had the bravery to do so. He appreciates them and we should too.

And yet, he also sends the important message that it’s not an elitist crew of the usual genius suspects, that in fact we can all do this in our own capacity. It’s a great message and, if it ends up allowing people to re-examine their need for certainty in an uncertain world, then Jordan will really end up doing good. Fingers crossed.

That’s not to say it’s a perfect book, and I wanted to argue with points on basically every other page, but mostly in a good, friendly, over-drinks kind of way, which is provocative but not annoying. One exception I might make came on page 256: no, Jordan, municipal bonds do not always get paid back, and no, stocks do not always go up, not even in expectation. In fact to the extent that both of those statements seem true to many people is the result of many cynical political acts and is damaging, mostly to people like retired civil servants. Don’t go there!

Another quibble: Jordan talks about how public policy makers make proclamations in the face of uncertainty, and he has a lot of sympathy and seems to think the should keep doing this. I’m on the other side on this one. Telling people to avoid certain foods and then changing stances seems more damaging than helpful and it happens constantly. And it’s often tied to industry and money, which also doesn’t impress.

Even so, even when I strongly disagree with Jordan, I always want to have the conversation. He forces that on the reader because he’s so darn positive and open-minded.

A few more goodies that I wanted to adore without giving too much away. Jordan does a great job with something he calls “The Great Square of Men” and Berkson’s Fallacy: it will explain to many many women why they are not finding the man they’re looking for. He also throws out a bone to nerds like me when he almost proves that every pig is yellow, and he absolutely kills it, stand-up comedian style, when comparing Ross Perot to a small dark pile of oats. Holy crap he was on a roll there.

So here’s one thing I’ve started doing since reading the book. When I give my 5-year-old son his dessert, it’s in the form of Hershey Drops, which are kind of like fat M&M’s. I give him 15 and I ask him to count them to make sure I got it right. Sometimes I give him 14 to make sure he’s paying attention. But that’s not the new part. The new part is something I stole from Jordan’s book.

The new part is that some days I ask him, “do you want me to give you 3 rows of 5 drops?” And I wait for him to figure out that’s enough and say “yes!” And the other days I ask him “do you want me to give you 5 rows of 3 drops?” and I again wait. And in either case I put the drops out in a rectangle.

And last night, for the first time, he explained to me in a slightly patronizing voice that it doesn’t matter which way I do it because it ends up being the same, because of the rectangle formation and how you look at it. And just to check I asked him which would be more, 10 rows of 7 drops or 7 rows of 10 drops, and he told me, “duh, it would be the same because it couldn’t be any different.”

And that, my friends, is how not to be wrong.

Categories: math, math education

## Interview with a middle school math teacher on the Common Core

Today’s post is an email interview with Fawn Nguyen, who teaches math at Mesa Union Junior High in southern California. Fawn is on the leadership team for UCSB Mathematics Project that provides professional development for teachers in the Tri-County area. She is a co-founder of the Thousand Oaks Math Teachers’ Circle. In an effort to share and learn from other math teachers, Fawn blogs at Finding Ways to Nguyen Students Over. She also started VisualPatterns.org to help students develop algebraic thinking, and more recently, she shares her students’ daily math talks to promote number sense. When Fawn is not teaching or writing, she is reading posts on mathblogging.org as one of the editors. She sleeps occasionally and dreams of becoming an architect when all this is done.

Importantly for the below interview, Fawn is not being measured via a value-added model. My questions are italicized.

——

I’ve been studying the rhetoric around the mathematics Common Core State Standard (CCSS). So far I’ve listened to Diane Ravitch stuff, I’ve interviewed Bill McCallum, the lead writer of the math CCSS, and I’ve also interviewed Kiri Soares, a New York City high school principal. They have very different views. Interestingly, McCallum distinguished three things: standards, curriculum, and testing.

What do you think? Do teachers see those as three different things? Or is it a package deal, where all three things rolled into one in terms of how they’re presented?

I can’t speak for other teachers. I understand that the standards are not meant to be the curriculum, but the two are not mutually exclusive either. They can’t be. Standards inform the curriculum. This might be a terrible analogy, but I love food and cooking, so maybe the standards are the major ingredients, and the curriculum is the entrée that contains those ingredients. In the show Chopped on Food Network, the competing chefs must use all 4 ingredients to make a dish – and the prepared foods that end up on the plates differ widely in taste and presentation. We can’t blame the ingredients when the dish is blandly prepared any more than we can blame the standards when the curriculum is poorly written.

Similary, the standards inform testing. Test items for a certain grade level cover the standards of that grade level. I’m not against testing. I’m against bad tests and a lot of it. By bad, I mean multiple-choice items that require more memorization than actual problem solving. But I’m confident we can create good multiple-choice tests because realistically a portion of the test needs to be of this type due to costs.

The three – standards, curriculum, and testing – are not a “package deal” in the sense that the same people are not delivering them to us. But they go together, otherwise what is school mathematics? Funny thing is we have always had the three operating in schools, but somehow the Common Core State Standands (CCSS) seem to get the all the blame for the anxieties and costs connected to testing and curriculum development.

I see a lot of good in the CCSS. This set of standards is not perfect, but it’s much better than our state standards. We can examine the standards and see for ourselves that the integrity of the standards holds up to their claims of being embedded with mathematical focus, rigor, and coherence.

Implementation of CCSS means that students and teachers can expect consistency in what is being in taught at each grade level across state boundaries. This is a nontrivial effort in addressing equity. This consistency also helps teachers collaborate nationwide, and professional development for teachers will improve and be more relevant and effective.

I can only hope that textbooks will be much better because of the inherent focus and coherence in CCSS. A kid can move from Maine to California and not have to see different state outlines on their textbooks as if he’d taken on a new kind of mathematics in his new school. I went to a textbook publishers fair recently at our district, and I remain optimistic that better products are already on their way.

We had every state create its own assessment, now we have two consortia, PARCC and Smarter Balanced. I’ve gone through the sample assessments from the latter, and they are far better than the old multiple-choice items of the CST. Kids will have to process the question at a deeper level to show understanding. This is a good thing.

What is potentially bad about the CCSS is the improper or lack of implementation. So, this boils down to the most important element of the Common Core equation – the teacher. There is no doubt that many teachers, myself included, need sustained professional development to do the job right. And I don’t mean just PD in making math more relevant and engaging, and in how many ways we can use technology, I mean more importantly, we need PD in content knowledge.

It is a perverse notion to think that anyone with a college education can teach elementary mathematics. Teaching mathematics requires knowing mathematics. To know a concept is to understand it backward and forward, inside and outside, to recognize it in different forms and structures, to put it into context, to ask questions about it that leads to more questions, to know the mathematics beyond this concept. That reminds me just recently a 6th grader said to me as we were working on our unit of dividing by a fraction. She said, “My elementary teacher lied to me! She said we always get a smaller number when we divide two numbers.”

Just because one can make tuna casserole does not make one a chef. (Sorry, I’m hungry.)

Testing is only good for kids when it helps them learn and become more successful – that the feedback from testing should inform the teacher of next moves. Testing has become such a dirty word because we over test our kids. I’m still in the classroom after 23 years, yet I don’t have the answers. I struggle with telling my kids that I value them and their learning, yet at the end of each quarter, the narrative sum of their learning is a letter grade.

Then, in the absence of helping kids learn, testing is bad.

What are the good/bad things for the teachers with all these tests?

Ideally, a good test that measures what it’s supposed to measure should help the teacher and his students. Testing must be done in moderation. Do we really need to test kids at the start of the school year? Don’t we have the results from a few months ago, right before they left for summer vacation? Every test takes time away from learning.

I’m not sure I understand why testing is bad for teachers aside from lost instructional minutes. Again, I can’t speak for other teachers. But I do sense heightened anxiety among some teachers because CCSS is new – and newness causes us to squirm in our seats and doubt our abilities. I don’t necessarily see this as a bad thing. I see it as an opportunity to learn content at a deeper conceptual level and to implement better teaching strategies.

If we look at anything long and hard enough, we are bound to find the good and the bad. I choose to focus on the positives because I can’t make the day any longer and I can’t have fewer than 4 hours of sleep a night. I want to spend my energies working with my administrators, my colleagues, my parents to bring the best I can bring into my classroom.

Is there anything else you’d like to add?

The best things about CCSS for me are not even the standards – they are the 8 Mathematical Practices. These are life-long habits that will serve students well, in all disciplines. They’re equivalent to the essential cooking techniques, like making roux and roasting garlic and braising kale and shucking oysters. Okay, maybe not that last one, but I just got back from New Orleans, and raw oysters are awesome.

I’m excited to continue to share and collaborate with my colleagues locally and online because we now have a common language! We teachers do this very hard work – day in and day out, late into the nights and into the weekends – because we love our kids and we love teaching. But we need to be mathematically competent first and foremost to teach mathematics. I want the focus to always be about the kids and their learning. We start with them; we end with them.

Categories: math, math education

## Interview with a high school principal on the math Common Core

In my third effort to understand the Common Core State Standards (CC) for math, I interviewed an old college friend Kiri Soares, who is the principal and co-founder of the Urban Assembly Institute of Math and Science for Young Women. Here’s a transcript of the interview which took place earlier this month. My words are in italics below.

——

How are high school math teachers in New York City currently evaluated?

Teachers are now evaluated on 2 things:

1. First, measures of teacher practice, which are based on observations, in turn based on some rubric. Right now it’s the Danielson Rubric. This is a qualitative measure. In fact it is essentially an old method with a new name.
2. Second, measures of student learning, that is supposed to be “objective”. Overall it is worth 40% of the teacher’s score but it is separated into two 20% parts, where teachers choose the methodology of one part and principals choose the other. Some stuff is chosen for principals by the city. Any time there is a state test we have to choose it. In terms of the teachers’ choices, there are two ways to get evaluated: goals or growth. Goals are based on a given kid, and the teachers can guess they will get a certain slightly lower score or higher score for whatever reason. Otherwise, it’s a growth-based score. Teachers can also choose from an array of assessments (state tests, performance tests, and third party exams). They can also choose the cohort (their own kids/ the grade/the school). The city also chose performance tasks in some instances.

Can you give me a concrete example of what a teacher would choose as a goal?

At the beginning of year you give diagnostic tests to students in your subject. Based on what a given kid scored in September, you extrapolate a guess for their performance in the June test. So if a kid has a disrupted homelife you might guess lower. Teacher’s goal setting is based on these teachers’ guesses.

So in other words, this is really just a measurement of how well teachers guess?

Well they are given a baseline and teachers set goals relative to that, but yes. And they are expected to make those guesses in November, possibly well before homelife is disrupted. It definitely makes things more complicated. And things are pretty complicated. Let me say a bit more.

The first three weeks of school are all testing. We test math, social studies, science, and English in every grade, and overall it depending on teacher/principal selections it can take up to 6 weeks, although not in a given subject. Foreign language and gym teachers also getting measured, by the way, based on those other tests. These early tests are diagnostic tests.

Moreover, they are new types of tests, which are called performance-based assessments, and they are based on writing samples with prompts. They are theoretically better quality because they go deeper, the aren’t just bubble standardized tests, but of course they had no pre-existing baseline (like the state tests) and thus had to be administered as diagnostic. Even so, we are still trying to predict growth based on them, which is confusing since we don’t know how to predict performance on new tests. Also don’t even know how we can consistently grade such essay-based tests- despite “norming protocols”, which is yet another source of uncertainty.

How many weeks per year is there testing of students?

The last half of June is gone, a week in January, and 2-3 weeks in the high school in the beginning per subject. That’s a minimum of 5 weeks per subject per year, out of a total of 40 weeks. So one eighth of teacher time is spent administering tests. But if you think about it, for the teachers, it’s even more. They have to grade these tests too.

I’ve been studying the rhetoric around the CC. So far I’ve listened to Diane Ravitch stuff, and to Bill McCallum, the lead writer of the math CC. They have very different views. McCallum distinguished three things, which when they are separated like that, Ravitch doesn’t make sense.

Namely, he separates standards, curriculum, and testing. People complain about testing and say that CC standards make testing easier, and we already have too much testing, so CC is a bad thing. But McCallum makes this point: good standards also make good testing easier.

What do you think? Do teachers see those as three different things? Or is it a package deal, where all three things rolled into one in terms of how they’re presented?

It’s much easier to think of those three things as vertices of a triangle. We cannot make them completely isolated, because they are interrelated.

So, we cannot make the CC good without curriculum and assessment, since there’s a feedback loop. Similarly, we cannot have aligned curriculum without good standards and assessment, and we cannot have good tests without good standards and curriculum. The standards have existed forever. The common core is an attempt to create a set of nationwide standards. For example, without a coherent national curriculum it might seem OK to teach creationism in place of evolution in some states. Should that be OK?

CC is attempting to address this, in our global economy, but it hasn’t even approached science for clear political reasons. Math and English are the least political subjects so they started with those. This is a long time coming, and people often think CC refers to everything but so far it’s really only 40% of a kid’s day. Social studies CC standards are actually out right now, but they are very new.

Next, the massive machine of curriculum starts getting into play, as does the testing. I have CC standards and the CC-aligned test, but not curriculum.

Next, you’re throwing into the picture teacher evaluation aligned to CC tests. Teachers are freaking out now – they’re thinking, my curriculum hasn’t been CC-aligned for many years, what do I do now? By the way, importantly, none of the high school curriculum in NY State is actually CC-aligned now. DOE recommendations for the middle school happened last year, and DOE people will probably recommend this year for high school, since they went into talks with publication houses last year to negotiate CC curriculum materials.

The real problem is this: we’ve created these new standards to make things more difficult and more challenging without recognizing where kids are in the present moment. If I’m a former 5th grader, and the old standards were expecting something from me that I got used to, and it wasn’t very much, and now I’m in 6th grade, and there are all these raised expectations, and there’s no gap attention.

Bottomline, everybody is freaking out – teachers, students, and parents.

Last year was the first CC-aligned ELA and math tests. Everybody failed. They rolled out the test before any CC curriculum.

From the point of view of NYC teachers, this seems like a terrorizing regime, doesn’t it?

Yes, because the CC roll-out is rigidly tied to the tests, which are in turn rigidly tied to evaluations of teachers. So the teachers are worried they are automatically going to get a “failure” on that vector.

Another way of saying this is that, if teacher evaluations were taken out of the mix, we’d have a very different roll-out environment. But as it is, teachers are hugely anxious about the possibility that their kids might fail both the city and state tests, and that would give the teacher an automatic “failure” no matter how good their teacher observations are.

So if I’m a special ed teacher of a bunch of kids reading at 4th and 5th grade level even through they’re in 7th grade, I’m particularly worried with the introduction of the new and unknown CC-aligned tests.

So is that really what will happen? Will all these teachers get failing evaluation scores?

That’s the big question mark. I doubt it there will be massive failure though. I think given that the scores were so clustered in the middle/low muddle last year, they are going to add a curve and not allow so many students to fail.

So what you’re pointing out is that they can just redefine failure?

Exactly. It doesn’t actually make sense to fail everyone. Probably 75% of the kids got 2’s or 1’s out of a 4 point scale. What does failure mean when everyone fails? It just means the test was too hard, or that what the kids were being taught was not relevant to the test.

Let’s dig down to the the three topics. As far as you’ve heard from the teachers, what’s good and bad about CC?

My teachers are used to the CC. We’ve rolled out standards-based grading three years ago, so our math and ELA teachers were well adjusted, and our other subject teachers were familiar. The biggest change is what used to be 9th grade math is now expected of the 8th grade. And the biggest complaint I’ve heard is that it’s too much stuff – nobody can teach all that. But that’s always been true about every set of standards.

Did they get rid of anything?

Not sure, because I don’t know what the elementary level CC standards did. There was lots of shuffling in the middle school, and lots of emphasis on algebra and algebraic thinking. Maybe they moved data and stats to earlier grades.

So I believe that my teachers in particular were more prepared. In other schools, where teachers weren’t explicitly being asked to align themselves to standards, it was a huge shock. For them, it used to be solely about Regents, and also Regents exams are very predictable and consistent, so it was pretty smooth sailing.

Let’s move on to curriculum. You mentioned there is no CC-aligned curriculum in NY. I also heard NY state has recently come out against the CC, did you hear that?

Well what I heard is that they previously said they this year’s 9th graders (class of 2017) would be held accountable but now the class of 2022 will be. So they’ve shifted accountability to the future.

What does accountability mean in this context?

It means graduation requirements. You need to pass 5 Regents exams to graduate, and right now there are two versions of some of those exams: one CC-aligned, one old-school. The question is who has to pass the CC-aligned versions to graduate. Now the current 9th grade could take either the CC-aligned or “regular” Regents in math.

I’m going to ask my 9th grade students to take both so we can gather information, even though it means giving them 3 extra hours of tests. Most of my kids pass 2 Regents in 9th grade, 2 in 10th, and 3 in 11th, and then they’re supposed to be done. They only take those Regents tests in senior year that they didn’t pass earlier.

What’s bad is how much time is lost, as we’ve already said. And also, it’s incredibly stressful. You and I went to school and we had one big college test that was stressful, namely the SAT. In terms of us finishing high school, that was it. For these kids it’s test, test, test, test. I don’t think it’s actually improved the quality of college students across the country. 20 years ago NY was the only one that had extra tests except California achievement tests, which I guess we sometimes took as well.

Another way to say it is that we did take some tests but it didn’t take 5 weeks.

And it wasn’t high stakes for the teacher!

Let’s go straight there: what are the good/bad things for the teachers with all these tests?

Well it definitely makes the teachers more accountable. Even teachers think this: there is a cadre of protected teachers in the city, and the principals didn’t want to take the time to get rid of them, so they’d excess them out of the schools, and they would stay in the system.

Now with testing it has become much more the principal’s responsibility to get rid of bad teachers. The number of floating teachers is going down.

How did they get rid of the floaters?

A lot of different ways. They made them go into the schools, take interviews, they made their quality of life not great, and a lot if them left or retired or found jobs. Principals took up the mantle as well, and they started to do due diligence.

Sounds like the incentive system for over-worked principals was wrong.

Yes, although the reason it became easier for the principals is because now we have data. So if you’re coming in as ineffective and I also have attendance data and observation data, I can add my observational data (subjective albeit rubric based) and do something.

If I may be more skeptical, it sounds like this data gathering was used as a weapon against teachers. There were probably lots of good teachers that have bad numbers attached to them that could get fired if someone wanted them to be fired.

Correct, except those good teachers generally have principals who protect them.

You could give everyone a bad number and then fire the people you want, right?

Correct.

Is that the goal?

Under Bloomberg it was.

Is there anything else you want to mention?

I think testing needs to be dialed down but not disappear. Education is a bi-polar pendulum and it never stops in the middle. We’re on an extreme but let’s not get rid of everything. There is a place for testing.

Let’s get our CC standards, curriculum, and testing reasonable and college-aligned and let’s keep it reasonable. Let’s do it with standards across states and let’s make sure it makes sense.

Also, there are some new tests coming out, called PARCC assessments, that are adaptive tests aligned to the CC. They are supposed to replace Regents down the line and be national.

Here’s what bothers me about that. It’s even harder to investigate the experience of the student with adaptive tests.

I’m not sure there’s enough technology to actually do this anyway very soon. For example, we were given \$10,000 for 500 student. That’s not going to go far unless it takes 2 weeks to administer the test. But we are investing in our technology this year. For example, I’m looking forward  to buying textbooks and get my updates pushed instead of having to buy new books every year.

Last question. They are redoing the SAT because rich kids are doing so much better. Are they just trying to get in on the test prep game? Because, here’s the thing, there’s no test that can’t be gamed that’s also easy to grade. It’s gotta depend on the letters and grades. We keep trying to shortcut that.

Listen, this is what I tell the kids. What’s going to matter to you is the letter of recommendation, so don’t be an jerk to your fellow students or to the teachers. Next, are you going to be able to meet the minimum requirements? That’s what the SAT is good for. It defines a lower bound.

Is it a good lower bound though?

Well, I define the lower bound as 1000 in total. My kids can target that. It’s a reasonable low bar.

To what extent do your students – mostly inner-city, black girls interested in math and science – suffer under the wholly gamed SAT system?

It serves to give them a point of self-reference with the rest of the country. You have to understand, they, like most kids in the nation, don’t have a conception of themselves outside of their own experience. The SAT serves that purpose. My kids, like many others, have the dream of Ivy League minus the understanding of where they actually stand.

So you’re saying their estimates of their chances are too high?

Yes, oftentimes. They are the big fish in a well-defined pond. At the very least, The SAT helps give them perspective.

Thanks so much for your time Kiri.

## Billionaire money and academic freedom

If you haven’t seen this recent New York Times article by William Broad, entitled Billionaires With Big Ideas Are Privatizing American Sciencethen go take a look. It generalizes to all of scientific research my recent post entitled Billionaire Money in Mathematics.

My favorite part of Broad’s article is the caption of the video at the top, which sums it up nicely:

Funding the Future: As government financing of basic science research has plunged, private donors have filled the void, raising questions about the future of research for the public good.

In his article Broad makes a bunch of great points.

First, the fact that rich people generally ask for research into topics they care about (“personal setting of priorities”) to the detriment of basic research. They want flashy stuff, bang for their buck.

Second, academics interested in getting funding from these rich people have to learn to market themselves. From the article:

The availability of so much well-financed ambition has created a new kind of dating game. In what is becoming a common narrative, researchers like to describe how they begged the federal science establishment for funds, were brushed aside and turned instead to the welcoming arms of philanthropists. To help scientists bond quickly with potential benefactors, a cottage industry has emerged, offering workshops, personal coaching, role-playing exercises and the production of video appeals.

If you think about it, the two issues above are kind of wrapped up together. Flashy academic content goes hand in hand with flashy marketing. Let’s say goodbye to the true nerd who doesn’t button up their cardigan correctly. And I don’t know about you but I like those nerds. My mom is one of them.

This morning I thought of another way to express this issue, from the point of view of the individual scientist or mathematician, that might have profound resonance where the above just sounds annoying.

Namely, I believe that academic freedom itself is at stake. Let me explain.

I’m the last person who would defend our current tenure system. It’s awful for women, especially those who want kids, and it often breeds a kind of arrogant laziness post-tenure. Even so, there are good things about it, and one of them is academic freedom.

And although theoretically you can have academic freedom without tenure, it is certainly easier with it (example from this piece: “In Oklahoma, a number of state legislators attempted to have Anita Hill fired from her university position because of her testimony before the U.S. Senate. If not for tenure, professors could be attacked every time there’s a change in the wind.”).

But as we’ve seen recently, tenure-track positions are quickly declining in number, even as the number of teaching positions is growing. This is the academic analog of how we’ve seen job growth in the US but it’s majority shitty jobs. And as I’ve predicted already, this trend is surely going to continue as we scale education through MOOCs.

The dwindling tenured positions means there are increasing number of people trying to do research dependent upon outside grants and funding, and without the safety net of tenure. These people often lose their jobs when their funding flags, as we’ve recently seen at Columbia.

Now let’s put these two trends together. We’ve got fewer and fewer tenure jobs, which are precariously dependent on outside funding, and we’ve got rich people funding their own tastes and proclivities.

Where does academic freedom shake out in that picture? I’m going to say nowhere.

Categories: education, math, math education

## Report from an MSRI MOOC conversation

I am back from Berkeley where I attended a couple of hours of conversations about MOOCs last Friday up at MSRI.

It was a panel discussion given mostly by math and stats people who themselves run MOOCs, and I was wondering if the people who are involved have a better sense of the side effects and feedback loops involved in the process. After all, I’m claiming that the MOOC Revolution will lead to the end of math research, and I wanted to be proven wrong.

Unfortunately, I left feeling like I have even more evidence that my fears will be realized.

I think the critical moment came when Ani Adhikari spoke. Professor Adhikari is in the second semester of giving her basic stats MOOC, and from how she described it, she is incredibly good at it, and there’s a social network aspect of the class which seems like it’s going really well – she says she spends 30 minutes to an hour a day on it herself, interacting with students. I think she said 28,000 students took it her first semester in addition to her in-class students at Berkeley. I know and respect Professory Adhikari personally, as I taught for her at the Berkeley Mills summer program for women many years ago. I know how devoted she is to good teaching.

Even so, she lost me late in the discussion when she explained that EdX, the platform which hosts her stats MOOC, wanted to offer her class three times a year without her participation. She said something to the effect that MOOC professors had to be “extra vigilant” about this outrageous idea and guard against it at all costs.

After all, she said, at the end of the day the MOOC videos are something like a fancy textbook, and we don’t hand out textbooks and claim they are courses, so we by the same token cannot hand out MOOC videos (and presumably the social networks associated with them) and claim they are courses.

When I pressed her in the Q&A session as to how exactly she was going to remain vigilant against this threat, she said she has a legal contract with EdX that prevented them from offering the course without her approval.

And I’m happy for her and her great contract, but here are two questions for her and for the community.

First, how long until someone in math or stats makes a kick-ass MOOC and doesn’t remember to have that air-tight legal contract? Or has an actual legal battle with EdX and realized their lawyers are not as expensive? Or believes that “information should be free” and does it with the express intention of letting the MOOC be replayed forever?

Second, how much sense does it make to claim that you and your presence are super critical to the success of a MOOC if 28,000 people took this class and you interacted at most one hour a day? Can you possibly claim that the average student benefitted from your presence? It seems to me that the value proposition for the average MOOC student is very similar whether you are there or not.

Overall the impression I got from the speakers, who were mostly MOOC evangelists and involved with MOOCs themselves, was that they loved MOOCs because MOOCs were working for them. They weren’t looking much beyond that point to side effects.

There was one exception, namely Susan Holmes, who listed some side effects of MOOCs including a decreased need for math Ph.D.’s. Unfortunately the conversation didn’t dwell on this, though, and it happened at the very end of the day.

Here’s what I’d like to see: a conversation at MSRI about the future of math research funding in the context of MOOCs and a reduced NSF, where hopefully we come up with something besides “Jim Simons”. It’s extra ironic that the conversation, if it happens, would be held in the Simons Theater.

Categories: math education