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.
So far only statistics is open, but other stuff is coming very soon. Specifically it covers, or soon will cover, the following fields:
- Cognitive Sciences
- Computer Sciences
- Earth and Planetary Sciences
- Science & Math Education
- History of Science and Mathematics
- Applied Mathematics, and
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:
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”.
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!).
Tonight at Prime Time I’ll play a game or two of Nim with them.
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.
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:
- Are calculators/computers/notes allowed on the exams?
- 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)?
- 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.
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.
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?
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.
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.
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.
As a teacher, what’s good and bad about the CCSS?
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.)
What are the good and bad things for kids about testing?
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.