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

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

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

——

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Is there anything else you’d like to add?

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

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

Categories: math, math education

## A simple mathematical model of congressional geriatric penis pumps

This is a guest post written by Stephanie Yang and reposted from her blogStephanie and I went to graduate school at Harvard together. She is now a quantitative analyst living in New York City, and will be joining the data science team at Foursquare next month.

Last week’s hysterical report by the Daily Show’s Samantha Bee on federally funded penis pumps contained a quote which piqued our quantitative interest. Listen carefully at the 4:00 mark, when Ilyse Hogue proclaims authoritatively:

“Statistics show that probably some our members of congress have a vested interested in having penis pumps covered by Medicare!”

Ilya’s wording is vague, and intentionally so. Statistically, a lot of things are “probably” true, and many details are contained in the word “probably”. In this post we present a simple statistical model to clarify what Ilya means.

First we state our assumptions. We assume that penis pumps are uniformly distributed among male Medicare recipients and that no man has received two pumps. These are relatively mild assumptions. We also assume that what Ilya refers to as “members of Congress [with] a vested interested in having penis pumps covered by Medicare,” specifically means male member of congress who received a penis pump covered by federal funds. Of course, one could argue that female members congress could also have a vested interested in penis pumps as well, but we do not want to go there.

Now the number crunching. According to the report, Medicare has spent a total of \$172 million supplying penis pumps to recipients, at “360 bucks a pop.” This means a total of 478,000 penis pumps bought from 2006 to 2011.

45% of the current 49,435,610 Medicare recipients are male. In other words, Medicare bought one penis pump for every 46.5 eligible men. Inverting this, we can say that 2.15% of male Medicare recipients received a penis pump.

There are currently 128 members of congress (32 senators plus 96 representatives) who are males over the age of 65 and therefore Medicare-eligible. The probability that none of them received a federally funded penis pump is:

$(1-0.0215)^{128} \approx 6.19\%$

In other words, the chances of at least one member of congress having said penis pumps is 93.8%, which is just shy of the 95% confidence that most statisticians agree on as significant. In order to get to 95% confidence, we need a total of 138 male members of congress who are over the age of 65, and this has not happened yet as of 2014. Nevertheless, the estimate is close enough for us to agree with Ilya that there is probably someone member of congress who has one.

Is it possible that there two or more penis pump recipients in congress? We did notice that Ilya’s quote refers to plural members of congress. Under the assumptions laid out above, the probability of having at least two federally funded penis pumps in congress is:

$1- {128 \choose 0} (1- 0.0215)^{128} - {128 \choose 1}(1-0.0215)^{127} (0.0215)^1 \approx 76.3\%$

Again, we would say this is probably true, though not nearly with the same amount of confidence as before. In order to reach 95% confidence that there are two or moreq congressional federally funded penis pump, we would need 200 or more Medicare-eligible males in congress, which is unlikely to happen anytime soon.

Note: As a corollary to these calculations, I became the first developer in the history of mankind to type the following command: git merge --squash penispump.

## Guest rant about rude kids

Today’s guest post was written by Amie, who describes herself as a mom of a 9 and a 14-year-old, mathematician, and bigmouth.

Nota bene: this was originally posted on Facebook as a spontaneous rant. Please don’t miscontrue it as an academic argument.

Time for a rant. I’ll preface this by saying that while my kids are creative, beautiful souls, so are many (perhaps all) children I’ve met, and it would be the height of arrogance to take credit for that as a parent. But one thing my husband and I can take credit for are their good manners, because that took work to develop.

The first phrase I taught me daughter was “thank you,” and it’s been put to good use over the years. I’m also loathe to tell other parents what to do, but this is an exception: teach your fucking kids to say “please” and “thank you”. If you are fortunate to visit another country, teach them to say “please” and “thank you” in the native language.

After a week in paradise at a Club Med in Mexico, I’m at some kind of breaking point with rude rich people and their spoiled kids. And that includes the Europeans. Maybe especially the Europeans. What is it that when you’re in France everyone’s all “thank you and have a nice day” but when these petit bourgeois assholes come to Cancun they treat Mexicans like nonhumans? My son held the door for a face-lifted Russian lady today who didn’t even say thank you.

Anyway, back to kids: I’m not saying that you should suppress your kids’ nature joie de vivre and boisterous, rambunctious energy (though if that’s what they’re like, please keep them away from adults who are not in the mood for it). Just teach them to treat other people with basic respect and courtesy. That means prompting them to say “please,” “thank you,” and “nice to meet you” when they interact with other people.

Jordan Ellenberg just posted how a huge number of people accepted to the math Ph.D. program at the University of Wisconsin never wrote to tell him that they had accepted other offers. When other people are on a wait list!

Whose fault is this? THE PARENTS’ FAULT. Damn parents. Come on!!

P.S. Those of you who have put in the effort to raise polite kids: believe me, I’ve noticed. So has everyone else.

Categories: guest post, rant

Great to be here, and glad you came.

Please hop on the nerd advice column bus for another week of ridiculous if not damaging guidance from yours truly, Aunt Pythia.

And please, after enjoying today’s counsel to other poor, unsuspecting fools:

think of something to ask Aunt Pythia at the bottom of the page!

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

——

Aunt Pythia,

I’m so SORRY. When I asked your opinion about conference sex the other week I thought I had pasted the link to the article: Will you still medal in the morning? It’s all about the behind the scenes sex at the Olympics.

ORR

Dear ORR,

Let me remind readers of your original question (after giving them a chance to read the article). You (thought you) gave me the link and then made the comment:

If conferences like JMM were to have bowls of condoms at the end of the tables where you pick up your badge do you think people would get the idea and pocket a hand full, then use them?

Answer: no. And that’s a good thing. As much as I’m sex positive, and I truly am, I don’t think what’s going on there in the Olympic Village is really about sex. I mean, that’s super dumb for me to say, because obviously tons of sex is happening, but it’s really about freedom and control and conquests.

So, for example, when you go to college, you notice that the kids who had controlling parents and no freedom in high school are particularly prone to spending too much money, drinking too hard, and fucking anything that moves, even relative to the kids whose upbringing was more relaxed and free. It’s about asserting control over their destiny and their freedom, and it lasts a couple of months and then calms down, hopefully in time for them to pass their classes. I’m absolutely sure of this phenomenon but come to think of it I’ve never seen statistics, which is probably a good thing.

Now think about Olympic athletes. They have lives utterly controlled by their coaches and parents and practices, and between you and me it’s often a neglectful if not abusive situation for those kids. Don’t get me wrong, I’m not saying they hate every minute of it, especially the ones we hear from who win the medals, but if you account for the selection bias for a minute and just think about the childhoods these kids have, your heart breaks for them.

So when they finally get to be somewhere away from their coaches, and this ridiculous pressure is off after their events, they need to somehow assert their freedom to themselves, and the most obvious way to do that is to party hard and fuck anything that moves. Plus it’s even better if they have a long list of conquests, because they’ve been trained to be super competitive.

Now think about math people to contrast this. I’m not saying no condoms are used at a math conference, but generally speaking math people have agency over their own lives, time to have sex when they want and so on, so when they get to a math conference, they just have more of the same. There’s some tension built up before one’s talk, and so in that sense there’s some blowing off of steam, but it’s not Olympic level.

Aunt Pythia

——

Dear Aunt Pythia,

I wrote to you a while ago ranting about how my boss sold me a middle-office IT job as a front-office quant role. Anyways, just wanted to let you know that I did manage to land a quant research role at another buy-side firm, and even though you can’t tell if it’s a scam without being there, it seems promising (I’ll start in about a month). I asked smarter questions this time and the pieces seem to be lining up. I want to thank you for providing a voice of sanity, which is always welcome but especially crucial in trying times where one needs to cut through cognitive dissonance.

Perennial Employee

Dear PE,

Awesome!

Auntie P

——

Dear Aunt Pythia,

Reading about people who are trying to find love or a companion at various places (via online dating or in physical environments) at Aunt Pythia’s Saturday column, why do not you consider creating an online dating site for these high-profile intellectuals?

I considered doing this myself during graduate school when I had many smart and single people around who wanted to have a girl or boy friend but for some reason could not, I did not have the courage or time to invest in this.

How about Aunt Pythia, who has so many followers? I personally checked out some online dating environments, but it was so hard to find really sophisticated people and I did not feel like talking to all those people with the hope that one of them was the good looking nerd I was after.

Idea

Dear Idea,

I like your idea (har har!), but here’s the thing. If I started an online matchmaking thing, I’d first of all not restrict to “high-profile intellectuals,” and second of all it would be very very different from the stuff that already exists.

So for example I’m definitely of the opinion that knowing someone’s age, race, height, and weight and seeing a picture of them makes 99% of all people unfairly unattractive.

It’s a case of knowing the wrong thing about someone. I mean, I’m not saying that you don’t eventually know those things about someone you’re into, but you don’t focus on them if it’s an organic meeting. It’s just the wrong information to provide and makes things less sexy and painfully judgmental.

Let me say it this way. Some woman going online for a date might think she needs the man to be taller than she is, and filter stuff out that way, but in real life she’ll meet someone at a party and be really into him and later realize he’s probably a couple inches shorter than she is and she won’t care at all.

So what information would I ask people to provide instead? That’s a toughie, and I’d love your help, readers, but here’s a start:

1. How sexual are you? (super important question)
2. How much fun are you? (people are surprisingly honest when asked this)
3. How awesome do you smell? (might need to invent technology for this one)
4. What bothers you more: the big bank bailout or the idea of increasing the minimum wage?
5. Do you like strong personalities or would you rather things stay polite?
6. What do you love arguing about more: politics or aesthetics?
7. Where would you love to visit if you could go anywhere?
8. Do you want kids?
9. Dog person or cat person?
10. Do you sometimes wish the girl could be the hero, and not always fall for the hapless dude at the end?

That’s a start. Again, looking for more. I think there should be about 20. Also people should answer in sentences.

Aunt Pythia

——

Dear Aunt Pythia,

I’m a graduate student in a STEM field who happens to also be of the male inclination….oh, and I’m gay.

Now, this normally isn’t so much of an issue (though it has been!) with my social circle/friends outside of the academia, but I’m a bit concerned about disclosing this sort of information to the department, my advisor, and other STEM graduate peers, because, well

1. in my humble opinion, STEM departments are not the most gay friendly. I mean, if you’re a gay male, surely you should be studying creative writing or writing your thesis about continental philosophy’s role in post-WWII imperialism (honestly, the former has been said to me….though the latter sounds like an interesting blog post or two), and
2. my main concern is the future of my academic career. Who are we kidding here, people making hiring decisions in the future may not be that cool with the whole “I’m here and queer!” thing. It could affect my career, negatively. (Ever been to Princeton btw?)

Please feel free to straightsplain to me that I’m being paranoid (though I won’t think I was being paranoid, would I?)

Best,

Sardonic Albeit Distinctly Fearful About Gay-friendliness

First of all, I have been to Princeton, thanks for asking.

Second of all, I don’t think you’re being at all paranoid. In fact it warms the cockles of my heart that you might even feel like you’re being paranoid asking about this, and it’s a testament to how far this country has come since I was a graduate student. Progress!

But only partial progress, to be sure. One of the weirdest things about the academic math market is how you’re expected to up and move to just about anywhere for a one year post-doc or what have you. And many people, especially outside of math, don’t actually want to do that, even if those places are nice places. When you add to that the fact that many of those places aren’t particularly nice, and are still crazy backwards when it comes to accepting gay people, then your job search is getting narrower.

Even so, you might want to take that job in that no-so-nice place, especially if it’s only for one year. I get that.

My short-term advice to you is to do what you need to do to keep your options wide, and if that includes coming out because you’re fed up with this bullshit, then definitely keep that in mind. My long-term advice is to end up eventually in a nice place where you can be accepted. Such places exist and the great news is they are increasing in number.

Love,

Aunt Pythia

——

Please submit your well-specified, fun-loving, cleverly-abbreviated question to Aunt Pythia!

Categories: Aunt Pythia

## The Lede Program has awesome faculty

A few weeks ago I mentioned that I’m the Program Director for the new Lede Program at the Columbia Graduate School of Journalism. I’m super excited to announce that I’ve found amazing faculty for the summer part of the program, including:

1. Jonathan Soma, who will be the primary instructor for Basic Computing and for Algorithms
2. Dennis Tenen, who will be helping Soma in the first half of the summer with Basic Computing
3. Chris Wiggins, who will be helping Soma in the second half of the summer with Algorithms
4. An amazing primary instructor for Databases who I will announce soon,
5. Matthew Jones, who will help that amazing yet-to-be-announced instructor in Data and Databases
6. Three amazing TA’s: Charles Berret, Sophie Chou, and Josh Vekhter (who doesn’t have a website!).

I’m planning to teach The Platform with the help of a bunch of generous guest lecturers (please make suggestions or offer your services!).

Applications are open now, and we’re hoping to get amazing students to enjoy these amazing faculty and the truly innovative plan they have for the summer (and I don’t use the word “innovative” lightly!). We’ve already gotten some super strong applications and made a couple offers of admission.

Also, I was very pleased yesterday to see a blogpost I wrote about the genesis and the goals of the program be published in PBS’s MediaShift.

Finally, it turns out I’m a key influencer, according to The Big Roundtable.

## The US political system serves special interests and the rich

A paper written by Martin Gilens and Benjamin Page and entitled Testing Theories of American Politics: Elites, Interest Groups, and Average Citizens has been recently released and reported on (h/t Michael Crimmins) that studies who has influence on policy in the United States.

Here’s an excerpt from the abstract of the paper:

Multivariate analysis indicates that economic elites and organized groups representing business interests have substantial independent impacts on U.S. government policy, while average citizens and mass-based interest groups have little or no independent influence.

A word about “little or no independent influence”: the above should be interpreted to mean that average citizens and mass-based groups only win when their interests align with economic elites, which happens sometimes, or business interests, which rarely happens. It doesn’t mean that average citizens and mass-based interest groups never ever get what they want.

There’s actually a lot more to the abstract, about abstract concepts of political influence, but I’m ignoring that to get to the data and the model.

The data

The found lots of polls on specific issues that were yes/no and included information about income to determine what poor people (10th percentile) thought about a specific issue, what an average (median income) person thought, and what a wealthy (90th percentile) person thought. They independently corroborated that their definition of wealthy was highly correlated, in terms of opinion, to other stronger (98th percentile) definitions. In fact they make the case that using 90th percentile instead of 98th actually underestimates the influence of wealthy people.

For the sake of interest groups and their opinions on public policy, they had a list of 43 interest groups (consisting of 29 business groups, 11 mass-based groups, and 3 others) that they considered “powerful” and they used domain expertise to estimate how many would oppose or be in favor of a given issue, and more or less took the difference, although they actually did something a bit fancier to reduce the influence of outliers:

Net Interest Group Alignment = ln(# Strongly Favor + [0.5 * # Somewhat Favor] + 1) – ln(#
Strongly Oppose + [0.5 * # Somewhat Oppose] + 1).

Finally, they pored over records to see what policy changes were actually made in the 4 year period after the polls.

Statistics

The different groups had opinions that were sometimes highly correlated:

Note the low correlation between mass public interest groups (like unions, pro-life, NRA, etc) and average citizens’ preferences and the negative correlation between business interests and elites’ preferences.

Next they did three bivariate regressions, measuring the influence of each of the groups separately, as well as one including all three, and got the following:

This is where we get our conclusion that average citizens don’t have independent influence, because of this near-zero coefficient in Model 4. But note that if we ignore elites and interest groups, we do have 0.64 in Model 1, which indicates that preferences of the average citizens are correlated with outcomes.

The overall conclusion is that policy changes are determined by the elites and the interest groups.

We can divide the interest groups into business versus mass-based and check out how the influence is divided between the four defined groups:

Caveats

This stuff might depend a lot on various choices the modelers made as well as their proxies. It doesn’t pick up on smaller special interest groups. It doesn’t account for all possible sources of influence and so on. I’d love to see it redone with other choices. But I’m impressed anyway with all the work they put into this.

I’ll let the authors have the last word:

What do our findings say about democracy in America? They certainly constitute troubling news for advocates of “populistic” democracy, who want governments to respond primarily or exclusively to the policy preferences of their citizens. In the United States, our findings indicate, the majority does not rule — at least not in the causal sense of actually determining policy outcomes. When a majority of citizens disagrees with economic elites and/or with organized interests, they generally lose. Moreover, because of the strong status quo bias built into the U.S. political system, even when fairly large majorities of Americans favor policy change, they generally do not get it.

Categories: #OWS, modeling

## How recently have you experienced democracy? #OWS

A few weeks ago Omar Freilla came to talk to my Occupy group. Omar is a founder of the Green Worker Cooperatives and shared his experience as an organizer.

He is a well-spoken guy and talked passionately about forming community cooperatives, where workers “have a direct role in decision-making and a share of all profits, build community wealth and help make a democratic economy real.”

At one point in his presentation, Omar asked us was how recently we’d “experienced democracy.”

On the face of it I didn’t think it was a fair question, especially when he compared it to experiencing anger or happiness. After all, democracy isn’t an emotion and I can’t experience democracy, say, by myself in a room, but of course I can conjure up emotions by myself in a room, especially if I have a laptop, wifi, and Netflix to help me.

But since his visit, I have to admit I have dwelled on that question and it’s become more and more reasonable in my mind, although I made two decisions on how to interpret it.

First of all, I chose to interpret it not as a formal gesture of democracy, like asking how recently have you voted in a formal election. Instead, it’s a local decision-making process question: how recently has your vote mattered in a local decision that affects a group?

Second, it’s not really about me. It’s about looking around and deciding who around me gets to participate in democratic decisions and who doesn’t.

For example, it might be at work. Although I personally get to make a lot of decisions at work, that fact clearly separates me from tons of people who simply get told what to do by some kind of authority. And there is an important distinction between people who have a manager but get to make decisions internal to their projects and people who have every decision laid out for them.

And that latter workplace anti-democratic situation is, I imagine, maximally soul-crushing, and is the audience that Omar is worried about and is reaching out to. And that’s why his question turns out to be a really good question after all.

I also consider democracy inside my own family. Since I’m the mom of the family, I tend to make more decisions that affect my little group than other people, but now I’m more sensitive to sharing that power there when I can. Turns out my kids love making decisions, it makes them gleeful in fact, even if it’s just what to eat for dinner. And they make good decisions too, which I’m consistently proud of.

My final example is Occupy, which is by construction a direct democracy, and I know how good participating and experiencing democracy actually feels there, and it’s a big part of why it works.

What about you? How recently have you experienced democracy?

Categories: #OWS