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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.

Screen Shot 2014-05-29 at 7.21.14 AMThe 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.

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.

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 are the good and bad things about testing?

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

Interview with Bill McCallum, lead writer of Math Common Core

This is an interview I had on 2/4/2014 with Bill McCallum, who is a University Distinguished Professor of Mathematics and member of the Department of Mathematics at the University of Arizona. Bill also led the Work Team which recently wrote the Mathematics Common Core State Standards, and was graciously willing to let me interview him on that.

Q: Tell me about how the Common Core State Standards Mathematics Work Team got formed and how you got onto it.

A: There were actually two separate documents and two separate processes, and people often get confused between them.

The first part happened in the summer of 2009 and produced a document called “College and Career Readiness Standards“. It didn’t go grade by grade but rather described what a high school student leaving and ready for college and career looks like. The team that wrote that pre-cursor document consisted of people from the College Board, ACT, and Achieve and was organized and managed by CCSSO (which represents state education commissioners and the like) and NGA (which represents Governors). Gene Wilhoutthen executive director of CCSSO, led the charge.

I was on that first panel representing Achieve. Achieve does not write assessments, but College Board and ACT do, and I think that’s where the charge that the standards were developed by testing companies comes from. It’s worth noting in the context of that charge that both ACT and College Board are non-profits.

The second part of the process, called the Work Team, took that document and worked backwards to create the actual Common Core State Standards for mathematics. I was the chair of the Work Team and was one of the 3 lead writers, the other two being Jason Zimba and Phil Daro. But the other members of the Work Team represent many educators, mathematicians, and math education folks, as well as DOE folks, and importantly there are no testing or textbook companies represented. The full list is here.

Q: Explain what Achieve is and is not.

A: Achieve is not a testing company, so let’s put that to rest.

Without going into too much historical detail (some of which is available here), Achieve was launched as an initiative of a combination of business and education leaders with the goal to improve education. It’s a non-profit think tank, which came out with benchmarks for mathematics education and tried to get states to align standards to them.

I started working with Achieve around 2005 and pretty soon I found myself chairing a committee to revise the benchmarks, which is how I got involved in the drafting of the first document I talked about above.

One more word about getting states on board with the Common Core State Standards (CCSS). There were 48 states that had committed to being involved in the writing, but not necessarily to adopt the standards. The states were involved in the review process as the CCSS were being written in 2009-2010. And here by “states” we usually mean teams from the various Department of Education, but different states had different team makeups.

For example, Arizona heavily involved teachers and some other states had their mathematics specialists at the DOE look things over and make comments.The American Federation of Teachers took the review quite seriously, and Jason and I met twice over the weekend to talk to teams of teachers assembled by AFT, listening to comments and making revisions.The National Council of Teachers of Mathematics was also quite involved in reviews and meetings.

Q: What are the goals of CCSS?

A: The goal is educational: to describe the mathematical achievements, skills, and understandings that we want students to have by the time they leave high school, broken down by grades.

It’s important to note at this point that this is not a new idea. Indeed states have had standards since the early 1990′s. But those standards were pretty unfocused and incoherent in many cases. What’s new is that we have common standards, and that they are focused and coherent.

Q: So what’s the difference between standards and tests?

A: Standards are descriptions of what you want students to learn. What you do with them is up to you. Testing is something you do if you want to know if they’ve learned what you wanted them to learn. It’s assessment.

Q: What’s your view on tests?

A: I would say that it doesn’t make sense to have no tests, no assessments. It doesn’t make sense to spend the money we spend on education ($12000 per student each year) and then not bother to see if it has had an effect. But nobody tests as much as the United States, and it seems quite overdone. This is a legacy of the No Child Left Behind bill, which had punitive measures for schools based on assessments embedded into law.

From my perspective, education in this country goes between extremes, and right now we are undeniably on the extreme with respect to testing. But I’d like to be clear that standards don’t cause testing.

Q: OK, but it’s undeniable that CC makes testing easier, do you agree?

A: Yes, and isn’t that a good thing? Having common standards also makes good testing easier. I’d also argue that they make it possible to spend less money on testing, and to make testing more centered on what you actually want. It puts more, not less, power into the hands of the consumers of the test. And that’s a good thing.

A word about testing companies. There’s no question that testing companies are trying to grab their share of money for tests. But before they could get paid for 50 different tests based on 50 different standards. What’s better?

There are two new assessment consortia, groups of states which are developing common assessments based on the standards. The consortia will have more power in the marketplace than individual states had.

I believe that people are conflating two separate issues which I’d like to separate. First, do we do a good job of choosing tests? Second, do the CCSS make that worse?

I believe that the CCSS have the power to make things better, although it’s possible that nobody will take advantage of the “commonness” in CCSS. And I’m not saying I’m not worried – the assessment consortia might do a good job but they might fail or get caught up in politics. The campaign for teacher accountability is causing fear and anger. I think you are right to be suspicious of VAM, for example. But that’s not caused by CCSS. Having common standards gives us power if we use it.

I’d also like to make the point that having common standards helps gives power to small players in curriculum publishing. When 50 different states had 50 different standards, the big publishing players with huge sales forces were able to send people to every state and adapt books to different standards. But now we will have smallish companies able to make something work and prove their worth in Tennessee and then sell it in California or wherever.

Q: What would you say to the people who might say that we don’t need more tests, we need to address poverty?

A: I’d say that having good standards can help.

Look, we need a good education system and to eliminate poverty. And having good common standards helps that second goal as well as the first. Why do I say that? A lot of what is good about the CCSS is that they are pretty focused, whereas many of the complaints about the old state standards were that they had tended to be “mile wide inch deep,” meaning having laundry lists of skills which were overall unfocused and incoherent.

We wanted to make something focused, which translated into having fewer things per grade level and doing them right, and making the overall standards a progression which tells a story that makes sense. Good standards, as I believe the CCSS represent, help everybody by providing clear guidance, which particularly helps struggling students and poor schools with less than ideal conditions.

Q: Do CC standards make teachers passive? Are they sufficiently flexible?

A: I don’t even get that.

Here’s the thing, standards are not curriculum.

Curriculum is what teachers actually follow in the classroom. We’ve always had standards, so what changed? Why are we suddenly worried about this new concept which isn’t new at all?

Here’s a legitimate fear: regimented, overly-prescriptive curricula that tell you what to do every day, like in France. Fair enough. But standards don’t say you need to have that. They just say what we want students to learn. It’s true that an overzealous implementation of standards could make teachers passive.

Maybe what’s new is that previously most people ignored their state standards and now people are actually paying attention. But that still doesn’t imply boring or rigid curricula.

Q: Are the CCSS “alive”?

A: How living do we want CC standards to be? Countries like Singapore revise standards on a 10-year cycle. After all we don’t want it to move too quickly, since we need to have time to implement stuff. In fact I’d argue that instability has been a big problem: there’s always a new fad, a new thing, and people never get a chance to figure out what we’re doing with what we’ve got. We should study what works and what doesn’t. And of course there should be revisions when that makes sense.

Q: Is there anything else you’d like to say?

A: Two things. First, I’d like to stress that people are conflating CCSS and testing, and they’re also conflating CCSS and curriculum. It’d be nice for people to separate their issues.

And one last thing. We as a country don’t understand common anything. We don’t see advantages of standards. Think about how useful it is to have standards, though. My recent project is a website called Illustrative Mathematics, which could not exist without standards. it’s a national community of teachers figuring out what they need to know – across state lines. That’s neat, and it’s only one of many benefits of having shared standards.

Categories: math education

Researching the Common Core

I’m in the middle of researching the Common Core standards for math. So far I’ve watched a Diane Ravitch talk, which I blogged about here, which was interesting but raised more questions than it answered, at least for me.

I’ve also interviewed Bill McCallum this week, who was a lead writer and chair of the Work Team that wrote the Common Core standards for mathematics. I’m still writing up that interview but I should have it done soon.

Next up I plan to interview a long-time teacher and current principal of a Brooklyn-based girls school for math and science, Kiri Soares, on her perspective on the Common Core standards and standardized tests in general.

One thing I can say already for sure: people who are not insiders here conflate a bunch of different issues. I’m hoping to at least separate them and understand where people stand on each issue, and if I at the very least get to the point of agreeing to disagree on well-defined points then I will have done my job.

Tell me if you think I need to go further to fully understand the issues at hand. Of course one thing I’m not doing is delving directly into the content of the standards, and that may very well be essential to understanding them. I’d love your thoughts.

Categories: math education
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