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.
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.
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.
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.
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.
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.
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!
This is a guest post by Courtney Gibbons, 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”:
Similar results occur with “brilliant”:
Now check out “bossy” and negative reviews:
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:
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.
This is a guest post by Becky Jaffe.
It has come to my attention that I am a nerd. I take this on good authority from my students, my friends, and, as of this morning, strangers in a coffee shop. I was called a nerd three times today before 10:30 am, while I was standing in line for coffee – which is to say, before I was caffeinated, and therefore utterly defenseless. I asked my accusers for suggestions on how to be less nerdy. Here was their helpful advice:
Guy in coffee shop: “Wear makeup and high heels.”
Another helpful interlocutor: “Use smaller words.”
My student, later in the day: “Care less about ideas.”
A friend: “Think less like NPR and more like C-SPAN.”
What I wish someone had said: “Is that a dictionary in your pocket or are you happy to see me?”
What I learned today is that if I want to avoid being called a nerd, I should be more like Barbie. And I don’t mean the Professor Barbie version, which – get this – does not exist. When I googled “Professor Barbie,” I got “Fashion Professor Barbie.”
So many lessons in gender conformity for one day! This nerd is taking notes.
Greetings fellow Mathbabers! At Cathy’s invitation, I am writing here about NYCTaxi.info, a public service web app my co-founder and I have developed. It overlays on a Google map around you estimated taxi activity, as expected number of passenger pickups and dropoffs this current hour. We modeled these estimates from the recently released 2013 NYC taxi trips dataset comprising 173 million trips, the same dataset that Cathy’s post last week on deanonymization referenced. Our work will not help you stalk your favorite NYC celebrity, but guide your search for a taxi and maybe save some commute time. My writeup below shall take you through the four broad stages our work proceeded through: data extraction and cleaning , clustering, modeling, and visualization.
We extract three columns from the data: the longitude and latitude GPS coordinates of the passenger pickup or dropoff location, and the timestamp. We make no distinction between pickups and dropoffs, since both of these events imply an available taxicab at that location. The data was generally clean, with a very small fraction of a percent of coordinates looking bad, e.g. in the middle of the Hudson River. These coordinate errors get screened out by the clustering step that follows.
We cluster the pickup and dropoff locations into areas of high density, i.e. where many pickups and dropoffs happen, to determine where on the map it is worth making and displaying estimates of taxi activity. We rolled our own algorithm, a variation on heatmap generation, after finding existing clustering algorithms such as K-means unsuitable—we are seeking centroids of areas of high density rather than cluster membership per se. See figure below which shows the cluster centers as identified by our algorithm on a square-mile patch of Manhattan. The axes represent the longitude and latitude of the area; the small blue crosses a random sample of pickups and dropoffs; and the red numbers the identified cluster centers, in descending order of activity.
We then model taxi activity at each cluster. We discretize time into hourly intervals—for each cluster, we sum all pickups and dropoffs that occur each hour in 2013. So our datapoints now are triples of the form [<cluster>, <hour>, <activity>], with <hour> being some hour in 2013 and <activity> being the number of pickups and dropoffs that occurred in hour <hour> in cluster <cluster>. We then regress each <activity> against neighboring clusters’ and neighboring times’ <activity> values. This regression serves to smooth estimates across time and space, smoothing out effects of special events or weather in the prior year that don’t repeat this year. It required some tricky choices on arranging and aligning the various data elements; not technically difficult or maybe even interesting, but nevertheless likely better part of an hour at a whiteboard to explain. In other words, typical data science. We then extrapolate these predictions to 2014, by mapping each hour in 2014 to the most similar hour in 2013. So we now have a prediction at each cluster location, for each hour in 2014, the number of passenger pickups and dropoffs.
We display these predictions by overlaying them on a Google maps at the corresponding cluster locations. We round <activity> to values like 20, 30 to avoid giving users number dyslexia. We color the labels based on these values, using the black body radiation color temperatures for the color scale, as that is one of two color scales where the ordering of change is perceptually intuitive.
If you live in New York, we hope you find NYCTaxi.info useful. Regardless, we look forward to receiving any comments.
What is Evidence-based Sentencing?
For several decades, parole and probation departments have been using research-backed assessments to determine the best supervision and treatment strategies for offenders to try and reduce the risk of recidivism. In recent years, state and county justice systems have started to apply these risk and needs assessment tools (RNA’s) to other parts of the criminal process.
Of particular concern is the use of automated tools to determine imprisonment terms. This relatively new practice of applying RNA information into the sentencing process is known as evidence-based sentencing (EBS).
What the Models Do
The different parameters used to determine risk vary by state, and most EBS tools use information that has been central to sentencing schemes for many years such as an offender’s criminal history. However, an increasing amount of states have been utilizing static factors such as gender, age, marital status, education level, employment history, and other demographic information to determine risk and inform sentencing. Especially alarming is the fact that the majority of these risk assessment tools do not take an offender’s particular case into account.
This practice has drawn sharp criticism from Attorney General Eric Holder who says “using static factors from a criminal’s background could perpetuate racial bias in a system that already delivers 20% longer sentences for young black men than for other offenders.” In the annual letter to the US Sentencing Commission, the Attorney General’s Office states that “utilizing such tools for determining prison sentences to be served will have a disparate and adverse impact on offenders from poor communities already struggling with social ills.” Other concerns cite the probable unconstitutionality of using group-based characteristics in risk assessments.
Where the Models Are Used
It is difficult to precisely quantify how many states and counties currently implement these instruments, although at least 20 states have implemented some form of EBS. Some of the states or states with counties that have implemented some sort of EBS (any type of sentencing: parole, imprisonment, etc) are: Pennsylvania, Tennessee, Vermont, Kentucky, Virginia, Arizona, Colorado, California, Idaho, Indiana, Missouri, Nebraska, Ohio, Oregon, Texas, and Wisconsin.
The Role of Race, Education, and Friendship
Overwhelmingly states do not include race in the risk assessments since there seems to be a general consensus that doing so would be unconstitutional. However, even though these tools do not take race into consideration directly, many of the variables used such as economic status, education level, and employment correlate with race. African-Americans and Hispanics are already disproportionately incarcerated and determining sentences based on these variables might cause further racial disparities.
The very socioeconomic characteristics such as income and education level used in risk assessments are the characteristics that are already strong predictors of whether someone will go to prison. For example, high school dropouts are 47 times more likely to be incarcerated than people in their similar age group who received a four-year college degree. It is reasonable to suspect that courts that include education level as a risk predictor will further exacerbate these disparities.
Some states, such as Texas, take into account peer relations and considers associating with other offenders as a “salient problem”. Considering that Texas is in 4th place in the rate of people under some sort of correctional control (parole, probation, etc) and that the rate is 1 in 11 for black males in the United States it is likely that this metric would disproportionately affect African-Americans.
Sonja Starr’s paper
Even so, in some cases, socioeconomic and demographic variables receive significant weight. In her forthcoming paper in the Stanford Law Review, Sonja Starr provides a telling example of how these factors are used in presentence reports. From her paper:
For instance, in Missouri, pre-sentence reports include a score for each defendant on a scale from -8 to 7, where “4-7 is rated ‘good,’ 2-3 is ‘above average,’ 0-1 is ‘average’, -1 to -2 is ‘below average,’ and -3 to -8 is ‘poor.’ Unlike most instruments in use, Missouri’s does not include gender. However, an unemployed high school dropout will score three points worse than an employed high school graduate—potentially making the difference between “good” and “average,” or between “average” and “poor.” Likewise, a defendant under age 22 will score three points worse than a defendant over 45. By comparison, having previously served time in prison is worth one point; having four or more prior misdemeanor convictions that resulted in jail time adds one point (three or fewer adds none); having previously had parole or probation revoked is worth one point; and a prison escape is worth one point. Meanwhile, current crime type and severity receive no weight.
Starr argues that such simple point systems may “linearize” a variable’s effect. In the underlying regression models used to calculate risk, some of the variable’s effects do not translate linearly into changes in probability of recidivism, but they are treated as such by the model.
Another criticism Starr makes is that they often make predictions on an individual based on averages of a group. Starr says these predictions can predict with reasonable precision the average recidivism rate for all offenders who share the same characteristics as the defendant, but that does not make it necessarily useful for individual predictions.
The Future of EBS Tools
The Model Penal Code is currently in the process of being revised and is set to include these risk assessment tools in the sentencing process. According to Starr, this is a serious development because it reflects the increased support of these practices and because of the Model Penal Code’s great influence in guiding penal codes in other states. Attorney General Eric Holder has already spoken against the practice, but it will be interesting to see whether his successor will continue this campaign.
Even if EBS can accurately measure risk of recidivism (which is uncertain according to Starr), does that mean that a greater prison sentence will result in less future offenses after the offender is released? EBS does not seek to answer this question. Further, if knowing there is a harsh penalty for a particular crime is a deterrent to commit said crime, wouldn’t adding more uncertainty to sentencing (EBS tools are not always transparent and sometimes proprietary) effectively remove this deterrent?
Even though many questions remain unanswered and while several people have been critical of the practice, it seems like there is great support for the use of these instruments. They are especially easy to support when they are overwhelmingly regarded as progressive and scientific, something Starr refutes. While there is certainly a place for data analytics and actuarial methods in the criminal justice system, it is important that such research be applied with the appropriate caution. Or perhaps not at all. Even if the tools had full statistical support, the risk of further exacerbating an already disparate criminal justice system should be enough to halt this practice.
Both Starr and Holder believe there is a strong case to be made that the risk prediction instruments now in use are unconstitutional. But EBS has strong advocates, so it’s a difficult subject. Ultimately, evidence-based sentencing is used to determine a person’s sentencing not based on what the person has done, but who that person is.