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A Conversation About “Intellectual Teachers” with Ben Riley

Ben Riley and I have been talking together about teaching for years. Ben’s day job is Executive Director of Deans For Impact, a non-profit that seeks to bring learning science to teachers before and during their careers. Much of Ben’s work is motivated by a belief that this sort of research could transform the status of teaching by giving the discipline a specialist’s language and knowledge.

Ben and I agree is that teachers have important contributions to make to the intellectual landscape of teaching. When Ben recently wanted to think more about this, he reached out to me. Below is the conversation as it played out over email.


Benjamin Riley: Michael, I feel like you are very interested in questions about how to teach effectively in ways that you find stimulating as a teacher. Put another way, I feel like you find…joy?…in working through the challenges of finding methods to build your students’ mathematical knowledge. So, I guess I’m wondering…do you think of yourself as an “intellectual teacher”? Is there any value to trying to define what that means? Or is this all too cute and erudite by half?

Michael Pershan: I think “teaching as an intellectual craft” can mean two separate things.

The first is maybe closer to what you’re talking about, which is doing intellectual work — let’s call it theoretical work — to make pedagogical decisions. Let’s imagine a teaching problem, maybe that Johnny isn’t engaged in class. There are a lot of ways to deal with this. You might call Johnny’s parents. You might try to find out Johnny’s interests. We could try to offer challenging extension work for Johnny’s sake; we could try to add supportive instruction for the benefit of Johnny. How do we decide which course to take?

There are a lot of Johnny-centric factors involved in this decision, and clearly there is a certain amount of knowledge about teaching — about what we do with students who are like Johnny — that is involved also. I think most teachers don’t have formal, theoretical ideas about what students like Johnny are like and how you deal with situations such as his.

To the extent that you try to develop more of that theoretical knowledge as part of your teaching, I think that’s “teaching as an intellectual craft.”

But I think this is only one thing that we might mean, because there is this whole enterprise of developing and sharing theoretical knowledge about teaching. It’s developed by researchers, consultants, teacher trainers, university professors, and oh-so-rarely by teachers themselves. And I’m also interested in that aspect of “intellectual craft,” because while there are clearly limitations to the sort of generalizations that teachers can make about teaching, there are also things that teachers can add that nobody else can.

I think that both aspects of this intellectual craft are relevant for my professional life. (Clearly, they can’t be totally separated or I’d be weirdly dissociated with myself, or some kind of fraud.) I think the future of teaching could involve more teachers doing this second thing, contributing to the theoretical edifice of teaching knowledge, but there’s no roadmap for how it could get done. There’s a reason that researchers contribute more to the theoretical knowledge than teachers do — most importantly, it’s hard to make generalizations from your own, limited experience. So, if we’re going to get to a world where teachers regularly contribute in this way, it’s not obvious to me what has to change.

Ben: See, I knew you were the right teacher to ask about this. And I think you’ve made an important distinction among two types of “teaching intellectualism,” which pose related but somewhat distinct challenges.

The question of “how should I, a teacher, teach Johnny, this particular student” strikes me as essentially an engineering question. I’ve discovered the hard way that teachers hate the metaphor of “learning engineering,” yet it strikes me as apt — when teachers design a lesson or task for their students, they are trying to get them (the students) to think about something they otherwise might not be inclined to think about. Students are puzzles, and while they can never be fully solved, I think there are ways in which we can help teachers get better at “engineering” experiences that will help Johnny and his classmates learn.

You are right that we rarely give teachers formal ideas about what students are like, but this is where cognitive science can be helpful, right? We could make sure that teachers have at least a basic understanding of how our minds work, and then use that as the foundation for exploring questions about what to do with that knowledge in a teaching context. While we can’t just snap our fingers to make that happen, I at least see a roadmap to get there, and indeed, that’s the work we do at the organization I founded.

Which brings me to your second aspect of teaching as an intellectual craft. What I hear you saying is there’s a big gap right now between the largely theoretical knowledge produced by university professors and such, and the sorts of questions that might only be visible to people who actually spend most of their days with children. Unfortunately, as you hint at, there is no obvious path to make that more valued. I feel like periodically the idea of “teacher-researcher” floats around but never goes very far. The incentives just don’t exist. We could mount a policy push to create them, but that seems like a hard slog.

So what to do? Any ideas?

Michael: I think teacher-researcher as a label is sort of a trap for teachers. Quite obviously, classroom teachers aren’t able to visit a large variety of other teachers and make systematic observations. This means that, for the most part, we’re observing ourselves or our colleagues, severely limiting the generalizations we’re able to make with confidence. There are other research methodologies that are supposed to be available to classroom teachers — we can talk of case studies, action research, or teaching experiments — but I think these are rightly seen as minor contributions to the field.

(To be fair, there are a few well-known case studies and teaching experiments in math education, but they have almost exclusively been performed by academic researchers, not classroom teachers.)

If teacher-researcher is a trap, I think teacher-writer is a much better deal for the teacher. Writers just get to write, and we (I’ll switch to “we”) can try to convince the reader however we like. I think we can contribute to the intellectual landscape by chewing over our own experiences through the lens of research. In other words, we can speak directly about what we know but put it in terms that might be useful to others by relating it to research.

Unfortunately, if not surprisingly, there aren’t a lot of teachers who seem interested in this. I don’t really have any bright ideas on how to change this. Part of the problem, I think, is that teachers don’t tend to write to their advantages. When teachers typically do write it tends to mimic the patterns of consultants and researchers who tediously cite study without speaking personally. We have a weird prejudice against personal experience in education writing. But what’s the point of a teacher writing if they aren’t going to sound like a teacher?

I’ll be honest, this is not a good time to be in this line of work. Everything seemed much better for teacher-writers in the early 2010s when I was coming up. Blogs were still big and there truly was a culture of people in the classroom who wrote. Not a lot of that is still around.

What’s left is books, so I’d encourage teachers to write those.

Ben: You say that teachers can’t visit other classrooms and make systematic observations…but what if they could? I’ll admit I’ve fantasized about a variety of possibilities in this regard. At the most basic level, you could imagine teachers popping into other teachers’ lessons on Zoom — a less-than-ideal format for instruction, I think we’d both agree, but it does eliminate the geographic limitation. The “multiverse” seems like it might be a giant practical joke but again, I can at least imagine a future where teachers can observe other teachers in a virtual learning environment. Or perhaps we could create a one-year teacher fellowship program, where teacher-fellows go around the country (or the world?) to watch other great teachers and learn and write about their experiences. Pricey, but we’ve got lots of philanthropists in this space!

It also occurs to me that, to foster teacher-writing, perhaps we need a prestigious journal dedicated to publishing essays by teacher-writers?  I feel like asking teachers — or anyone — to write books is a pretty big ask. 

Michael: We do have journals that will publish essays by teacher-writers but…they aren’t very interesting. It’s a lot of what I was describing before, that sort of faux research essay, the kind that starts by citing a bunch of Common Core State Standards.

The thing about making systematic observation is that it puts teachers in competition with researchers, and at that point why do we prefer the analysis of teachers? Maybe teachers would ask questions that academic researchers would not — that’s something that Callie Lowenstein has pointed to as a unique advantage that teachers have, and I agree with her on that.

Look, there are a lot of things that need money in education. We need to make sure school buildings are healthy environments. Kids should feel safe in every school. Every kid should get to study science, art, music, that’s a fundamental right. I want smaller class sizes. I want kids to love to think and read. I don’t think that your ability to succeed in school should be your last chance to make it in American society. Compared to these problems, the question of whether teachers have a part in the theory-building edifice of teaching feels like exceedingly small potatoes.

That said — a fellowship is a good idea! And I’m all for more journals, conferences, and so forth. The challenge will always be finding what unique perspective teachers can add. I believe it’s there, but too much teacher writing suffers from trying to be something that it’s not.

Ben: So to summarize our conclusions…

Yes, teaching is an intellectual craft, but this has multiple meanings.

There are things we might do to nurture the intellectual climate of teaching, such as:

  • Encouraging teachers to write more, and in authentic fashion
  • Fostering opportunities for teachers and researchers to explore classroom-relevant questions together
  • Creating fellowships to allow teachers to observe and learn from other teachers

That seems like a reasonable agenda to me, and one that might help attract intellectually curious individuals into the profession of teaching. I’ll let you have the final word — any parting thoughts?

Michael: My only parting thought is that there are many ways to change the composition of the teacher workforce. Teaching, at the end of the day, is incredibly meaningful work. What keeps people out of the profession isn’t the intellectual atmosphere as much as a wide variety of other factors. Yes, pay. But also working conditions. What would the teacher workforce look like if we had fewer behavioral problems to deal with? If we were less likely to be blamed for things beyond our control? When we think about attracting people to the job who might otherwise be in other lines of work, we should think expansively about how people choose whether or not to teach.

Books Received

Every once in a while people send me books. That’s very nice of those people, I always appreciate it, it’s a cool way to stay in touch with what’s going on. But I feel like I should acknowledge receipt in a clearer way. So, here are three books that I recently received and have started to take a look at, along with something nice I’ll say about each of them.

Tools for Teachers, Oliver Lovell: Oliver’s a great guy and he runs a really nice podcast about education research. He had me on to talk about worked examples back when my own book came out, and it was just a very deep conversation, much deeper than most conversations about pedagogy ever tend to be.

“This book summarises the most useful techniquest, strategies, and mental models from sixty in-depth conversations.” One cool thing about the book is that Ollie creates a giant diagram synthesizing all the things he’s learned. It’s an attempt to show how it all hangs together. Impressive and ambitious! It also features an appendix titled “Michael Pershan’s Worked Example Routine,” and I’m proud to be part of Oliver’s teaching journey.

Painless Statistics, Patrick Honner: Thankfully, I don’t have to prepare students for the Regents exams any more. When I did, books like Patrick’s were crucial for the kids. We need high quality study materials out there in the world, and I feel secure knowing that Patrick — who also writes for Quanta Magazine — is writing these things.

The book ends with a fun chapter titled Statistical Literacy that features excellent examples, including a COVID vaccine trial, a certain “large city” considering a congestion pricing plan (god help nyc), and a brief but clear explanation of p-hacking. There are practice problems, solutions, the whole shebang.

Figuring Out Fluency In Mathematics, Jennifer M. Bay-Williams, John J. SanGiovanni: These types of elementary mathematics texts often don’t have much to say about worked examples, but this one does! “Even though the focus is on someone else’s work, worked examples help students notice their own misconceptions or errors, especially when tasks include self-expalantion prompts. The notion that the work comes from a stranger alleviates anxiety and embarrassment that can come about when sharing with classmates. Worked examples offer the opportunity to inject an idea that hasn’t come about during instruction or other practice opportunities. Like any practice resource, they are flexible and adaptable.”

I also noticed some nice fluency games. I always need more nice fluency games.

Pros/Cons of Using Grades and Tests in College Admissions

The hard thing about talking about college admissions in the United States is that the facts don’t matter and the system is insane. The system is a patchwork of private and public colleges, some that admit basically everybody and others that reject 96% of applicants. Private colleges get to determine their own admissions criteria, money makes a big difference, and if you are extremely good at football you get to go wherever you want. There is a magazine nobody reads that ranks schools and everyone — especially the colleges — cares deeply about it. On top of all this, nobody can agree on what the point of college admissions is, anyway, so it’s unclear what we’re even trying to optimize for.

It’s so confusing to me. Who should get into Princeton? I don’t know, who gets to work for Goldman Sachs? Anyway, the vast majority of schools are nothing like Princeton. So: who gets to go to UC or SUNY? I don’t know, it all seems to depend on what you think these schools are supposed to be doing. Are they trying to reward excellence or help whoever they can? What are we doing here?

That said, the two most important factors for college admissions in the US are high school grades and standardized test scores. Some people think this is bad, and that test scores shouldn’t be used. Other people think grades are bad and should not be used. Most people — including the testing companies themselves — seem to think you should use both, because they’re both a little bit bad and a little bit useful.

In her book “Who Gets In?” Rebecca Zwick compares different admissions criteria, attempting to clarify the choices institutions face about selection. Zwick is a researcher who was a professor at UC Santa Barbara and worked for Educational Testing Services, an enormous testing company. You will not be shocked to learn that she likes tests. (She is not a fan of test-optional policies, for instance.) And though I find her book frustrating, as I think she handles the social and moral issues in a narrow and unenlightening way, she has a nice little chapter where she compares the pros/cons of grades and standardized tests. I want to summarize that chapter in this post.

First up, the case for grades. What is good about grades as an admissions criteria?

  • Your grades in high school do a good job predicting your grades in college. “High school grades have typically been found to be a somewhat better predictor than test scores,” Zwick writes. This is widely seen as significant for admissions decisions, a sign that a kid can succeed at your institution. It’s worth thinking hard about whether that makes sense, but lots of schools think it does.
  • Grades are less correlated with socioeconomic status than test scores. Zwick and a colleague studied this and found less of a correlation than other people do. (They looked at the correlation between SES and scores/grades within a school, whereas most people just combine all the data.) Zwick emphasizes that this reduces the correlation, but not all the way: “When we calculated the student-level correlations within high schools and then took the avedrage, we found that the association with SES ranged from .20 to .25 for SAT scores, from .12 to .18 for high school GPA, and from .15 to .21 for class rank.”
  • Grades contain information about your performance over four years; tests are a snapshot of a single moment. “High school grades summarize four years of academic accomplishments,” Zwick writes. Though I put this under a “pro,” it’s only an advantage if you care about this. But it may go some ways towards explaining why GPA does a better job predicting college grades — it presents a larger picture. She points out that grades rely on testing information also, just four years of it.
  • Grades measure more than just knowledge. “Grades reflect ‘scholastic engagement,’ which includes characteristics we might call industriousness, conscientiousness, and perseverence.” If you want that information, grades reflect it.
  • Grades measure the knowledge that schools are attempting to teach. The test and the school may not agree on what students are expected to know. Quoting another ETS researcher Warren Willingham: “Individual assessment by the teacher can be based more closely on the specific material that each student has studied and what each has learned that is possible with a standards-based test.”
  • Grades better predict who will get further credentials after college. “Perhaps the most interesting finding concerns the percentages of students who completed a postbaccalaureate credential by 2013, nine years after high school graduation. The vast majority of the credentials received were either master’s degrees or “professional doctorates,” which included degrees in law, medicine, and dentistry.”

But what are the problems with grades, according to Zwick?

  • Grades collapse towards the top. Too many people have 4.0s to make it useful for elite admissions. “In 2015 an astonishing 37,200 applicants to UC Berkeley had high school GPAs of at least 4.0,” she notes. “They are not very useful for making distinctions at the high end of the scale.”
  • Grades aren’t standardized and some schools grade harder than others. “High school grades can lead to systematic prediction errors because of the differences in grading standards across schools. A student with a high school GPA of 3.0 from a top-notch high school may be well prepared for college, whereas a student with the same GPA from an inferior school may not be.” I don’t like the way she talks about superior/inferior schools, but I understand what she’s talking about. It is possible for adjust GPAs to compensate for this, and some schools do that.
  • Grades are biased by extraneous factors. “Studies and information observations involving college students have suggested that grades can be influenced by the student’s physical attractiveness and charm. Some research on younger students has found that boys receive lower grades than girls because of classroom misbehavior. A 2014 study of high school students found that young women and students with limited English proficiency tended to earn higher grades than other students, after taking test scores and school characteristics into consideration, whie low-income students earned lower grades,” Zwick writes. Just to editorialize for a moment: grades are obviously biased, I don’t dispute that, but Zwick’s argument here is fairly sketchy. Besides, how bad can the bias be if grades do better than tests at predicting college performance? But as a person who has given grades, yes, they are influenced by all sorts of things.
  • Grades are less precise. “One way to think about this is in terms of signal-to-noise ratio…Because they are affected by many nonacademic factors, including the teacher’s stringency and the student’s attitudes and classroom behavior, grades are relatively noisy measures.”

Each of these flaws with grades is itself a point in favor of tests:

  • Tests are more precise and are designed to discriminate between students, even at the high-end of achievement. “[Tests] can help to distinguish among the many applicants to elite colleges who share a GPA of 4.0 or above.”
  • The test are standardized. “Test scores can also provide a means of evaluating home-schooled and international candidates.”
  • Tests are not biased by non-academic factors. “An advantage of admissions tests is their ability to provide efficient comparisons of students whose high school grades are influenced by the schools they attend, the classes they chose, their rapport with their teachers, and many other extraneous factors.”
  • Tests can identify talented students who have not succeeded in school. “As test proponents like to point out, admissions tests can sometimes serve to identify talented students with weak academic backgrounds — those who used to be called “diamonds in the rough” before that label came to be seen as disparaging.” (Editorializing: I was not aware that was a disparaging thing to say.)
  • When tests and grades are combined they do a better job of predicing college grades. Though high school GPA is better at predicting college performance than test scores, using both is better still at predicting college grades. This is why testing companies recommend using both grades and scores to make admissions decisions.

So, what to make of all this? If the thing you care about is how well a student will perform in college, I think there’s a very clear case that both high school grades and tests are imperfect measures of that. Grades, on their own, are better than tests, but grades also have real drawbacks. Tests, however, are also flawed. Put them together and you get something with complementary flaws and benefits.

Of course, maybe you don’t care about predicting college grades! Maybe you just want reward people who did well in school, and you don’t care if grades incorporate behavior. Or maybe you just think that college is stupid and college grades don’t mean anything either, so you don’t care about that. Maybe what you value is a precise standardized competition for a scarce resource and so you like standardized tests because that’s what they are. Maybe you care about social mobility so you want to err on the side of accepting poor students into college, no matter their grades or tests. None of the above can decide between these options, the facts don’t matter when there are all these values to hash out.

But my point, the reason I think this matters, is to remember that none of this is certain or clear. Grades can be biased, yes, I think we all know this. And yet it’s not at all clear that tests do a better job. Even the ETS employee says so. And I think everybody involved in education should remember that we are working with flawed tools that do an imperfect job of measuring the things that most of us care about — and it’s not even clear what it is that we care about! What can you do? That’s education for you. It’s not a science. So don’t fall in love with the tools, acknowledge that they’re flawed, and then use them anyway if they’re the best that we have to work with.

What’s The Deal With the California Math Framework?


It is not easy to talk about what’s happening with math in California right now. Partly this is because it involves an enormous evolving document — the California Math Framework (CMF) — that has a complicated relationship with what actually happens in schools. Partly it’s hard because the document has become caught up in the broader culture war, attracting Fox News hysteria and the attention of political operators.

But a significant part of what’s tricky is that while the CMF itself was written by committee, its presentation to the world has been dominated by Jo Boaler. The CMF itself is a complex, at times vague, grabbag of progressive math education initiatives. But the controversies surrounding it have reflected the particular idiosyncracies of its most prominent supporter. If we want to even begin to understand what exactly is happening, we have to deal with both the issues and the personality involved.

Let’s start with the CMF itself. The framework — full disclosure, I skimmed but did not read most of it — is comprehensive without being entirely coherent. As it reads right now, it basically expresses support for progressive math educational policy and pedagogy without requiring it. Here is what I saw when I skimmed it:

  • The first two chapters are a mashup of UDL, NCTM’s Principles to Action, and YouCubed. Boaler’s work is cited a combination of 24 times.
  • Chapters 3 and 4 read to me like a restatement of Common Core State Standards and NCTM’s standards: emphasis on sensemaking, strategies prior to memorization, multiple strategies, visuals, connections, depth of understanding over speed, emphasis on mathematical processes over content. Potentially controversial but really not much different from Common Core. Boaler is cited 8 times total.
  • Chapter 5 describes CCSS/NCTM’s take on statistics but calls it “data science” and emphasizes the value of showing real data journalism to students. It also describes a culminating high school data science (don’t call it “statistics”) course. Boaler is cited twice.
  • Chapters 6-8 try to organize the k-12 math curriculum around a series of big ideas. For high school, the documents basically rearticulate NCTM’s urging of schools to consider other ways of carving up the content other than Algebra 1/Geometry/Algebra 2. Boaler is cited just a handful of times.
  • Chapter 9 cites Boaler 14 times and expresses concerns with tracking without really coming down against it. “Districts are at liberty to group students as they choose,” it says, but it wants to remind people to keep the pathways into higher tracks open and desegregated. I liked this chapter (which I skimmed) more than I was expecting to, even though it cites this study of Boaler’s which is really quite weak.
  • Chapter 10 cites Boaler once and is basically a call for good professional development.
  • I didn’t read the rest because it looked boring.

The strongest statements in this thing are all still fairly weak. In Chapter 8, the authors clearly have their hearts set against acceleration. And yet they say this: “Some students will be ready to accelerate into Algebra I or Integrated Mathematics I in eighth grade, and, where they are ready to do so successfully, this can support greater access to a broader range of advanced courses for them. At the same time, successful acceleration requires a strong mathematical foundation.”

This has all been revised several times. Its original version contained stronger language. I found this article about the revisions quite helpful — basically, the culture war language was removed in this draft, explicit support for San Francisco’s de-tracking experiments was removed and the recommendations to de-track without acceleration were softened, everything was clarified to be a recommendation and not a call for change. It’s not very surprising that people were provoked by the earlier drafts.

But now, nothing in CMF sounds particularly firm. The statements against tracking and acceleration are fairly cautious. You have no doubt what the authors think in this document — they like teaching towards big ideas, progressive pedagogy, data science, detracking, no-acceleration — but as it currently stands this document has no teeth.

So why is it still so controversial?


At this point it becomes impossible not to talk about Boaler more personally. I want to stick to the facts as I understand them as much as possible, while still drawing an accurate picture.

Let’s start with the emails. I have three to talk about. The first was sent to a professor of engineering and CS at Berkeley. It looks like this:


The second was sent to me by Boaler after I declined to help with a YouCubed project and explained that I had concerns with the way they handle research. (I’ve written about these concerns in “YouCubed is Sloppy About Research” and “YouCubed is More Than Sloppy About Research.”) The response I got from Boaler was that she hadn’t realized I was the author of that “awful blog post” and that she would never want to work with me.

The third email was sent to a person who I can’t name. I don’t want to give any details about the context because I don’t have permission to share any of them, but he had done something entirely inoffensive. He received a message in response from Boaler. She described him as attempting to “discredit” her. She didn’t see any value in what he had written — what was the purpose in being critical? And won’t that just direct people to go after her on Twitter? She requested that he change his writing to sound more respectful to her, and she suggested that the author had ulterior and selfish motives.

OK, on to the research.

As noted, I have described errors or sloppiness in YouCubed/Boaler’s published research. The first post described a straightforward misinterpretation of Moser’s growth mindset study. This was pointed out many times to YouCubed and they reprinted the misinterpretation many times over. (The CMF actually cites the Moser study correctly without the misinterpretation, I was stunned to see.) The second post described failures in the research studying YouCubed’s own initiatives. A third post featured a blatant inconsistency in a research article that has now been corrected without explanation.

There was also the famous Railside paper. Boaler seems to have attracted some genuine harrassment from a pair of professors who were threatened by her work. (People who witnessed this behavior but were otherwise critical of Boaler have described it to me as harrassment. Boaler’s version of the story can be found here.) The mathematicians charged that there were issues with her paper, and I’ve never given it a serious look. What I can report is that when I talk to other mathematics education researchers, they have raised their own concerns about the Railside study. My interpretation of those concerns is that they aren’t allegations of fraud. They are roughly similar to the concerns that I raised in my posts about her more recent work — that there is a kind of carelessness to them that makes them less than fully reliable.

Now, to Twitter.

I once noticed that some YouCubed tasks had been reprinted from other sources without attribution. I posted them on Twitter (somewhat melodramatically):


The response from Boaler was consistent with the perspective expressed via email — basically, why aren’t you being more supportive?

Now, back to current events.

Jelani Nelson’s posting of Boaler’s email made its way around Twitter. Boaler in response created a new website, The first thing posted there was a letter in support of her against the pushback from Twitter. She soon wrote three blogposts.

The first blogpost presents a kind of origin story that has animated Boaler’s passion for her work. It’s the story of her experience of a sexist physics teacher:

There were about 15 girls and 15 boys in the class, and before the national exam everyone takes what is called “a mock exam.” I did not (as was typical for me) do a lot of studying and only got a border line pass. That was true for about 8 students, half of whom were girls and half boys. The teacher then pronounced that all the boys could take the higher-level physics exam paper and all the girls should take the lower-level paper, as although we had got the same results, it was clear that the boys had got them from real understanding and the girls had just worked very hard to get them. I was about 15 at the time and fully aware of the sexism at play. My family argued with the school and got me placed into the higher exam. I ended up getting the highest grade and I still remember the teacher climbing up the grassy bank on a hot day to mumble an apology to me, a few months later. But the damage was done and I decided against studying physics for A-levels. It would have been with the same sexist teacher. The other girls did not argue the decision and ended up with low grades in physics- as that is all that is on offer in the low exam paper

The second blog post describes her mistreatment on Twitter:

On Twitter I feel as safe as I would walking into a bear pit, completely naked and covered with honey, with a sign saying “eat me.” My feed makes if clear that anyone can write anything! I wish Twitter had fact checkers like we see during election season. Instead, people post outrageous lies, and there’s no stopping a salacious tweet from going viral, even if the claims are ridiculous. I have been subject to huge amounts of abuse and name calling, and the culture of bringing down anyone who is successful is rampant. It was Twitter where the attackers of the Framework published personal contracts with my home address. This actually violates Twitter’s rules and when I reported them, their account was locked – briefly. But others retweeted my address – and Twitter did nothing about it.

(A quick fact check on this: the content that was posted was her address in the context of a bill for her contract work for a district. The district published that bill in its public disclosures — all perfectly normal — and it was retweeted by an opponent of the CMF. Twitter says that does not break the rules of Twitter since it’s public information but that they do reserve the right to ask people to take that stuff down, to protect from potential personal harrassment. In fact they temporarily froze the account of the person who shared it and the person took down the post.)

The third blog post describes her warm feelings for a “rule-breaking woman”:

My first memory of Mrs. Marshall was her running up the stairs to our classroom, coming into the room out of breath, throwing herself against the door which she slammed behind her and panting – sharing with relief that she had just missed the head teacher (principal), who would have reprimanded her for wearing dangly earrings. I was immediately in awe of this rule breaking woman – who was so personable and friendly and different from any other maths teacher I had ever known. Then she did something even more remarkable. She told us that we would learn the calculus ideas she was teaching us by talking to each other in groups. This was my first time of discussing mathematical ideas with my friends and it gave me access to a depth of understanding I had not even known possible.

That’s where the story is up to today.


So, what does it all mean?

I have no interest in psychologizing, but the facts say that Boaler sees criticism as personally discrediting and she does not like it. Her research — and at times YouCubed’s publications — have made errors or failed to live up to the highest standards. It has been difficult to get Boaler or YouCubed to correct those errors.

In the context of CMF, she did not write the entire document. Some of the chapters more clearly show her influence than others. Either way, in its current draft form the document as written seems entirely unthreatening to me. (I lack the on-the-ground knowledge of how such a document would be received and implemented in California’s schools, and defer to others on this matter!)

But as a public advocate for CMF, Boaler is prone to see criticism as threatening to the project and will escalate conflicts rather than engage with criticism.

My sense is that as CMF is gaining more attention that people are having a hard time disconnecting Boaler’s public advocacy from CMF itself. Even if there are parts of the CMF that I disagree with, I’m more inclined to shrug than anything else. It seems extremely unlikely to me that this document in its current form will make much of a difference in the daily lives of students, even if passed. (But again I defer to people more familiar with California’s school politics than I am! It would be terrific if someone would report on this aspect of CMF!)

That said, Boaler’s actions seem to fairly invite scrutiny of the document itself. It’s reasonable to ask if those citations of research have any weight. It’s reasonable to ask how fair the document is being when it talks about how neuroscience and other forms of research support what the CMF is calling for.

Most of all, though, I want to call into question this whole way of doing business. Who thought that this — getting an edu celeb who takes criticism poorly to create and then promote an enormous franken-doc containing every controversial idea in math education — would be a good idea? This is not how progress in math education is made, I hope everyone can now plainly see. Ours is a field of millions of teachers who actually decide what is going to happen in classrooms and countless more students and families who set the stage for those decisions. There is no real room for combativeness in education. Teaching isn’t the sort of where you can defeat your enemies. They’re still your enemies, and they’re not defeated! They’re there, and you need them.

There are countless ways to promote equity that look nothing like this. It would be quieter and less attention-seeking. The entire standards-writing project has produced basically no fruits over the past few decades. It’s time to stop looking for warriors and get to work.

Is subject specialization in elementary school worth it?

The problem with elementary school, some might say, is that the teachers aren’t able to focus on mastering their subject. It’s not their fault! They teach everything. There’s no time to specialize. There’s no time to do anything. Do you have any idea how few bathroom breaks an elementary teacher gets during the day? Zero to one. So of course they can’t master the mathematics curriculum.

And in fact there is research showing that different teachers are more effective at teaching some subjects than others.

Here’s a simple solution: every child should have access to a math or reading specialist.

This is an idea that a lot of people love. For example, the National Council of Teachers of Math and a bunch of other organizations officially support the use of math specialists (though they note that math specialists can be used in many ways besides managing classroom instruction, e.g. as coaches, meeting with teachers or individual students, running professional development for the district, and so forth):

A new paper has added to the surprising(?) research literature that argues that this simple solution does not work. In fact, the teaching goes worse when you’re a specialist. It further suggests that the reason is because you lose out on the benefits of a stronger student-teacher relationship when you specialize. The paper is titled “Spread Too Thin: The Effects of Teacher Specialization on Student Achievement” and if you are inclined to read such things I encourage you to read it.

But, before you do, it might be helpful to list every reason why the researchers might be wrong. Why might researchers have messed this one up? Let’s list the ways:

  • Even if teachers are slightly worse at teaching when they’re specialists, schools might be making smart moves about who is best in the classroom and who is best teaching a subject, i.e. Michael isn’t our strongest teacher so we put him in a more targeted role where his knoweldge of math can be put to use
  • Every new professional role is hard, so teachers who become specialists will initially struggle but eventually get the hang of it
  • Schools that move to having specialists will uniformly improve but this won’t be captured by a change in any individual teacher’s effectiveness

To summarize, we want to know that there’s neither a school effect or a teacher effect. And we want to make sure that the researchers aren’t just capturing the difficulty of being effective when you’re transitioning to a new role.

Now, on to the paper.

If a policy paper has no experiment then it begins with a dataset. This one comes courtesy of the Indiana Department of Education, which provided researchers with data on students (4th and 5th Graders), their teachers, and whether their teachers were generalists or specialists over a seven year period. This amounts to 591,311 students and 32,996 teachers. (Co-teachers were excluded, because that’s hard to deal with. That was 10% of the teachers in the sample. Can you think of a reason why excluding co-teachers would mess this up? The researchers couldn’t and neither could I.)

Their primary interest is in the teacher effect. Since they aren’t running an experiment, they look at changes in a techer’s work status as the thing that could cause a change in learning. In their words: “we identify the effect of specialization by comparing the effectiveness of the same teachers in years when they do and do not specialize.” The key assumption being that these changes are not correlated with anything else, i.e. you don’t become a specialist once you’re suddenly great (or awful) at teaching, or you don’t become a specialist when your students suddenly become good (or bad) at reading.

Then they run a giant regression that looks to see what contribution the teacher’s role has in explaining student performance, over and above a bunch of other things.

(These “other things”: a student’s prior test scores, gender, race/ethnicity, whether they get free or reduced cost lunch, enrollment in special services, ELL, class size, whether a teacher has a graduate degree, whether a teacher is new to a school, how big the school is, percent of Black and Hispanic students, percent of students in the school who get free or reduced lunch, how effective this teacher was on average no matter the role, how well the grade scored on these tests on average, how well the school performed on these test on average.)

And then the researchers got nervous that they were only capturing the first year of a teacher’s transition, and maybe they got much better after that first year. So they created a model that paid attention to how many years of experience as a specialist the teacher had — one year, two years, three or more years — and took a look at whether experience mattered.

This is all good, but what about the school effects? Well, they wanted to look at that as well. “Though assigning a teacher to a specialist role may lower an individual teacher’s average effectiveness, students may still be better off if that teacher is better at a particular subject than the other generalists in the school,” they write. So they tested another model i.e. long equation:

I would like to emphasize that if you are familiar with the idea of linear regression these fancy equations should not intimidate you further. We are interested in the impact of the specialization rate of a given school in a specific grade at a time on the scores of kids in that time in that grade at that school. And beta is the slope, so if that slope is high then voila, the specialization rate explains a lot. If it’s low, it doesn’t. Everything else is in a sense the control — the researchers will measure the explanatory power (i.e. control for) all the stuff that I listed in that parentheses above. What we care about is the sope associated with the specialization rate.

Anyway, the results aren’t good if you like specialization. If you just look at specialization of teachers, there’s a significant reduction of teacher effectiveness, especially for math. If you separate by year, it’s clear that things get better when teachers are more experienced but not that much better.

When you compare schools that specialize more to ones that specialize less, the differences aren’t huge but those numbers all have negative signs in front of them which, if you like specialization, is not what you want to see:

They speculate that this could be explained by the way specialization reduces the strength of the teacher’s relationship with their students, and they have an interesting way to test it: look just at the students who happened to work with the same specialist two years in a row. They find that this reduces the costs of specialization compared to working with a generalist (though not all the way):

Do I believe these results? Yes, I do, for a few reasons. First, because this isn’t the first time researchers have found that specialization backfires in elementary school. There was an experiment in Houston a few years back that was particularly interesting with true random assignment and it didn’t work out. There was also a big study of schools in North Carolina that had negative results for specialization. Here are those studies described by the authors of this paper:

But the other thing is that I am a 3rd Grade math specialist. I work hard, and I think have a good understanding of the math and the kids. Yet I frequently come in and realize that I’m walking in to a situation I only partly understand. The kids main teachers have expectations and routines they work on all day with their students. They have different bathroom policies. Kids are working on things emotionally that I sometimes catch a bit of, things like “trying to deal with frustration productively” or “separating yourself from a tough situation.” And I don’t get to know any of this!

Moreover, these kids worship their teachers. They are the adults who care for these children during the day. Meanwhile I come in and it’s more of a gun-for-hire situation. I’m in, I’m out. It’s a very weird situation compared to the rest of my day.

So, no, I don’t find this surprising, and while maybe someday someone will figure out a way to get the benefits of specialization without the costs, I’ve seen enough for now: specialization in elementary school is not worth it.

How Education Helps the Rich Stay Rich

This is a story in three parts, corresponding to three excellent books about the habits of American elites. Those books are:

Pedigree: How Elite Students get Elite Jobs by Lauren A. Rivera

The Sum of Small Things: A Theory of the Aspirational Class by Elizabeth Currid-Halkett

Privilege: The Making of an Adolescent Elite At St. Paul’s School by Shamus Rahman Khan

And, before getting lost in sociology, here is an attempt at summarizing what I took from these books into some bullet points:

  • Education is more important than ever for helping rich people stay rich.
  • For elites, education is sort of about academics, but it also is about how to act rich. (“Act elite,” if you prefer.)
  • There is competition for elite jobs, but to even qualify for those jobs you have to act elite. Knowledge is more like a minimum. How you act, socially, is what will get you hired.
  • A lot of what happens in less-elite spaces is like a watered down version of this dynamic.

This won’t be a comprehensive defense of these ideas, or really a comprehensive anything. But, taking this one book at a time, let’s look at where this picture comes from.


“Pedigree” is about three of the highest paying entry-level jobs in America: corporate law, management consulting, and investment banking. (A brief afterward notes that this book was researched pre-2008. Investment banking is now no longer quite the party that it was, and tech is a bigger part of this picture.)

For her reserach, Rivera interviewed a bunch of people and also worked in HR for one of the consulting firms. She gets some amazing quotes from her interviewees, who speak frankly about who they hire. The most basic fact is that they hire almost exclusively from elite colleges, and a very particular slice of them at that:

We purposely only target certain institutions, so … if [you] didn’t go to the right school, … the odds are stacked against you more … You will find it when you go to career fairs … Someone will show up and say, “Hey, I didn’t go to Harvard Business School, but I am an engineer at MIT and I heard about this fair, and I wanted to come and meet you in New York.” God bless him for the effort, but it’s just not going to work. I mean you never know, but from our experience, we just don’t have the resources. We don’t give that person as much of a chance.

It’s hard to argue that these firms are looking for the “best and the brightest” if they ignore MIT candidates. And, indeed, everybody pretty much admits that this is not the case. This stuff is “not rocket science,” one says:

We like to interview at schools like Harvard and Yale, but people who have 4.0s and are in the engineering department but, you know, don’t have any friends, have huge glasses, read their textbooks all day, those people have no chance here….I have always said, [my firm] is like a fraternity of smart people.

The point is that intelligence is a bar to be cleared, a minimum requirement. Being smarter than the field won’t get you hired, as a matter of fact it might work against you. But what does matter? Your pedigree (e.g. your fancy degree), your social fit (e.g. ability to talk about interesting things), and your polish (e.g. the right degree of confidence).

There is a certain “type of personality” that these firms are looking for. You’re supposed to have interests outside of work, but they can’t be larks. It’s not enough to say, “hey I like crocheting.” You have to be, like, systematically devoted to achieving as a crocheter. You can’t just jog for fun; you want to be a ultra-marathoner, working to beat your own personal best. You can’t like beaches; you have to love exploring other cultures. It’s an ethos of achievement and winning via the ability to act knowledgeable and sophisticated. It goes without saying, this is about acting rich.

Why is it important that these firms who can act the right way? Which is to say, why do they need to act like elites?

It’s partly about attracting the right sort of customers.

If you make a big hiring zoo at Harvard, a bunch of kids from Harvard will know the name of your company. One day down the line these kids will be rich and then need to have a company deal with a tangly legal problem. Who will they turn to? The one that they’ve heard of, the one that recruited on their campus and all their friends work at. Multiple interviewees make this explicit to Rivera.

The other way of seeing this, though, is that it’s about making potential rich customers feel comfortable. The firm acts like they do, even if they don’t make as much money. They talk similarly, dress the same way, share the same values, and so forth.

In short: Competition for positions is fierce, but not based entirely on skills or knowledge. To qualify for a job at a top firm, you have to exhibit a minimum of knowledge but most of all exhibit the appropriate set of social characteristics. Those social characteristics are easily attainable if you grew up in elite culture. If you grew up poor, you’re mostly out of luck.

“Pedigree” is about the elite of the elite, but we might wonder whether what Rivera observes is true for elites more generally. And in “The Sum of Small Things,” we get an answer, and that answer is basically “yeah.”

The Sum of Small Things

The “aspirataional class” is the New Yorker set. They shop organic, exercise regularly, and know interesting restaurants to eat at. They are not necessarily rich, though many are. They might be graphic designers, writers, journalists, and — less commonly — teachers who blog about sociology. Yes, it’s at this point that I can start pulling up a mirror, because “The Sum of Small Things” is most definitely about an Ivy-legacy who reads the New York Times on weekends. Hi, guys.

The “aspirational class” is not necessarily rich, but they (we) are elite. Which is to say, we potentially exhibit the kinds of social qualities that qualify us for the kinds of jobs featured in “Pedigree.”

“Pedigree” was about the kinds of knowledge an interests that help a graduate get into an elite firm. But a watered-down version of those qualities is instantly recognizable to anyone who is familiar with American admission into elite universities. Knowledge — as measured by grades or scores — is necessary, but not enough for elite admission. In interviews and personal essays you need to exhibit not just hobbies, but “extra-curriculars” that show you impose structure and ambition to your leisure time. Most of all, you should be interesting and knowledgeable about the world, good to talk to, someone who would fit in on campus.

The book is a mix of quantitative arguments and (mostly) cultural observations. Currid-Halket describes the aspirational class as “cultural omnivores”:

They pride themselves on going to hole-in-the-wall ethnic restauratns instead of Applebee’s, buying local farmers’ eggs, and wearing TOMS shoes because these signifiers of cultural capital reveal social and environmental consciousness, surely acquired in the pages of the New Yorker and at the elite universities they attended. Even if they have full-time careers, the attainment of such knowledge implies that they either have the conspiculous leisure time to read or stroll farmers’ markets, or that they value the acquisition of this type of information as a worthy use of their time.

Importantly, these cultural signifiers aren’t especially expensive. She brings data that lower and middle classes have actually increased their spending on stuff in recent decades. Access to big-screen TVs and motorcycles has never been greater. Partly because of this, she argues, these possessions have lost their allure as class signals. As it gets easier to knock off expensive items in slightly cheaper versions, it’s harder to use fancy posessions to indicate social status. (Though, of course, not impossible, especially at the highest levels of wealth.)

Instead, elites have started signalling status with inconspicuous consumption, the sort of not-necessarily-expensive spending that shows knowledge and discernment on the part of the spender.

A key part of this argument is that this is making inequality worse in the US. Why? Because elites spend thoughtfully in ways that actually matter: on healthcare, child care, and especially education.

Currid-Halkett view of culture is as of a giant recursive loop, positively feeding back on education. Many of the things that matter in America have been growing more expensive, and life has not improved for the lower or middle classes in decades. The top 10% or so of earners have the means to invest in things that really do matter for improving one’s “life chances”:

Investing in a child’s secondary education, being able to afford fruits and vegetables and regular health checkups, even having the time to breat-feed, all give the next generation a leg up. Having “arrived” used to mean the minivan adn the suburvan house, but those dont’ get the kids into a good university, and that university (and being able to write the tuition check) is increasingly what divides thr ich from everyone else.

Just as you have to qualify socially to compete for elite jobs, you have to qualify socially to qualify for elite educations and the top 10% of jobs. This is not longer the elite-of-the-elites but the wider range of doctors, lawyers, managers, creatives, writers, journalists and much else. The same dynamics present in “Pedigree” play out at a larger scale in “The Sum of Small Things.”

But can an education really inculcate this culture? For that we can turn to Shamus Khan’s “Privilege,” my favorite of the bunch.


Shamus Khan spent a year teaching at St. Paul’s School (an elite US boarding school) while interviewing students and faculty for this book. He gets the clearest picture of how school can produce elite culture, the sort of thing that is most clearly in line with the needs of “top” colleges in the US.

I find a Books and Ideas interview with Khan a pretty clear window into what he saw at St. Paul’s. Part of elite culture is the notion of being a “cultural omnivore”:

It is the idea that high status people have gone from being snobs to being omnivores, that they have gone from people with very particular cultural tastes (say a taste for classical music) to people with quite varied tatstes (from classical music to hip hop or rap or rock music, to jazz…) […] The way the new elite distinguishes itself is as being the most inclusive, democratic, open. This promotes the view of the world as a kind of space of opportunities in Thomas Friedman’s sense of the flat world. It is the people who see its wideness who are able to be successful. Who are the closest minded people, the most likely to listen to their very small range of things, heavy metal or country music? It is poor people. 

It’s these kinds of habits that students learn at school. And if you haven’t been brought up this way, you won’t be able to hide it. Your class is permanently printed on your tastes and values.

Khan, along with the other two authors, are well aware that this has always been the case. What all three authors would argue, I think, is that what’s different is the invisibility of these cultural markers. Today’s elites don’t think of themselves as rich or elite as much as they think of themselves as smart, capable, healthy, worthy. Education — and especially at the university level — is kind of like money-laundering. You take the benefits of class and school turns them into knowledge and values.

It’s not that this makes inequality worse, I think. It just makes class invisible, and Americans have never had a harder time seeing it. That’s the argument, I think. And it means that there is really no way for poor kids to get into Harvard. You can’t make up the class gap.


So, to wrap up:

  • Class matters in American society.
  • For elites (broadly speaking) it matters by raising young people with a minimum baseline of academic knowledge but (more importantly) with the correct tastes, values, interests.
  • These things are at a certain level about acting rich — interesting, worldly, interested in the right things, acting smart in a way that is essentially flattering.
  • If the very rich like acting a certain way, then to a certain level so will the next level down, if they want to have elites as customers.

This basically closes the loop. There are maybe a few other ways out there for people to rise up in American society. (I think a lot of them come through math and science, which probably explains some of the intense feelings surrounding math education in the US.)

These are the basic facts about America — invisible class lines that are drawn much stronger than you might expect. And, in a certain way, it’s all about what it means to act rich and how much education is needed to learn to do it right.

Math for Enthusiastic First Graders

The basic challenge as I see it is that a young child who is enthusiastic about math is generally enthusiastic about numbers. The natural response to such enthusiasm from any reasonable adult is to give that kid more numbers. But this very quickly puts the kid on the path towards accelerating through the school curriculum, making it harder for them to have a good time at school and narrowing their mathematical experiences.

And the other part of the problem is the kid’s maturity and independence. If you have a teen who is enthusiastic about math, that’s fine, they’ll do their schoolwork and then noodle around on Numberphile or Desmos. But younger children frequently lack the ability to direct their own mathematical lives. They want an adult to lead.

If you put those two pieces together — number-centricity and the need for adult guidance — it makes it very hard to give a young child what they want without accelerating them through the K-5 math curriculum.

I maintain that it’s worth trying to avoid as much of the school curriculum at home as you can. If you can get beyond the fun of “hey my six-year old is doing ten-year old math” you’re at risk of making it harder for schools to keep your kid happy. And while I’m not opposed to straight-up acceleration or grade-skipping in some cases, in general I think it’s best to avoid these with very young children, who however advanced they are in math often have totally age-typical emotional needs. (This is why, for all my love of Beast Academy, I don’t typically recommend it to parents.)

I’m trying to speak generally here, but without being super-weird about it I’ve encountered this both at school and at home. My oldest son is very enthusiastic about numbers, and I think it’s in his best interests to not race ahead too far of his classmates. And at school I have tried to express the perspective above to parents of my 3rd and 4th Graders, to mixed success. (Thankfully, most parents get it.)

OK, but all this leads to a question: what do you do with a kid who wants to talk about numbers during breakfast? and on the subway? and over dinner? and after dinner? and at many other times, especially when he’s bored and moody?

It’s in that spirit that I share some of the things that we’ve been talking about in my own home lately. Some of these I proposed to my oldest. Others he came up with on his own. I’ll add that in my teaching life I sometimes encounter accelerated students who totally lack the ability to ask questions independently. That doesn’t make sense to me, since often as kids become more independent they can get more out of their grade-level classes.

Anyway, here are some of the number-centric ideas my son and I have been talking about lately.

Switcheroo Numbers: Take a two-digit number, and swap its digits. 35 and 53. 72 and 27. 19 and 91. Then take the difference of those numbers. You will find that all those numbers are _________________. Why is that? Does it work with three-digit numbers? Four-digit numbers? Consider representing these numbers as sums — 30 + 5 and 50 + 3 — to play with some of these ideas.

Writing a Scratch Program for Counting Factors: My son is most eager to talk about factors, so we often end up drifting towards factor math. Together we made a Scratch program that finds all the factors of a number. I let him tinker around with it and he was able to show some indpenedence there, which I was gratified to see — coding is something unrelated to K-5 math that he can do outside of school. Together we added a factor counter to this program, so he could try to “set records” and find numbers with the most number of factors.

Factor/Number Fraction: Conversations about which numbers had a lot of factors led to discussions about the relationship of the number to its factors. My son loved talking about perfect, abundant, and deficient numbers. I, on the other hand, find this stuff dull as dirt, so I proposed a different question. 3 has two factors, so its factor to number fraction is 2 out of 3, or 2/3. 4 has three factors, so its fraction is 3/4. What numbers have the largest of these sorts of fractions?

Building Bigger Factors: This one also came from me, I thought he would like seeing how you could use multiplication to find factors of bigger numbers. For instance, the factors of 10 are 1, 2, 5, and 10. The factors of 9 are 1, 3 and 9. What are the factors of 9 x 10 = 90? How many factors does it have? And (if this is new territory for you) you might discover that there is a pattern that seems to hold for some, but not all numbers. (For instance, compare the factors of 9 x 10 and 5 x 10.)

Triangular Square Numbers: I don’t know if my boy got into triangular numbers from Marilyn Burns’ books or from Numberblocks, the TV show. But it might have been Numberblocks, with their annoyingly catchy “step squad” chant. You know the one I’m talking about.

That’s the one.

Anyway, are any triangular numbers also square? That made for a few days of fun.

The Difference Between Nearby Multiplications: I don’t know why, a lot of my son’s math has to do with finding the difference between slightly different things. For instance, he came into the kitchen the other day eager to share a “trick.” Start with two numbers, like 2 and 7. Make 2 x 8 and 3 x 7. Find the difference between them. He thought there was a pattern but it took him a few false before he figured out what was going on, and then it was interesting to try to explain what was happening and why.

The Sum of Consecutive Powers: This one came from him, I think. Or maybe it was a book he was reading? I’m not sure. Either way, add consecutive powers of 2, like 4 + 8 = 12 or 32 + 64 = 96. His claim was that these numbers are always divisible by 3. Really cool, right? Try it with other bases besides 2. Why is this happening? Fun times.

The “One and a Half” Sequence: This one is very much kid-math, but I think it’s interesting and it occupied my son for a while. He spent a few days (or weeks? what is time?) looking for numbers that were “one and a halfs.” For example, for him 3 is a one and a half (because it is 2 and half of 2) but 4 is not. The full sequence of “one and a half” numbers for him was: 3, 6, 9, … right! He noticed that these were multiples of 3. And then what about “one and a third” numbers? “One and a fourth”? And so forth. An interesting regularity for him to notice and a challenging one for him to try to explain.

These are just the little number investigations that have landed at home. There are other things to recommend: Prime Climb, Math for Smarty Pants, The I Hate Mathematics Book are the biggest winners in our house at the moment. And of course it partly depends on your child’s taste.

But for parents of enthusiastic young children, I think the most important work at home is to broaden those tastes. Because even if what we love most is calculation and numbers, mathematics is big. Kids, especially those self-professed lovers of math, deserve the chance to explore it.

More YouCubed Research That is Difficult to Explain

Update: This post describes an error in a paper that now appears to have been corrected. See the update at the bottom of the post.

Along with however many people are on YouCubed’s email list, I recently received this message from Jo Boaler:

Hello youcubians,

Three years ago we reached out to everyone who had taken Teaching Mindset Mathematics, a workshop we offer to share the curriculum, ideas and teaching practices from our 2015 summer mathematics camp for middle school students. We asked if they were planning to host a youcubed-inspired summer camp in 2019, and if so, whether they would be willing to participate in a study of student outcomes and teacher change. We heard from many people who were interested in engaging with us and ultimately enrolled 10 different camps and their school districts into our study, sponsored by the Gates Foundation.
The demonstration camp that youcubed hosted in 2015 had resulted in significant improvements in student mathematics understanding and mindsets, and the purpose of the new study was to learn whether this could be replicated by teachers across the US in a variety of settings. Today, we are very excited to announce that the results of this research have been published in the journal Frontiers in Education. I would encourage everyone to read the full study, which can be found here.

So, a published study funded by the Gates Foundation. I clicked and opened up the paper.

Look, you know what’s coming at this point, right? We’ve been down this road before. I’m going to show you that the paper is a mess. And who cares? Nobody. People who care about research, including a great number of math education professors, do not have respect for Boaler’s output. YouCubed’s popularity stems I think from consultants, PD leaders, and from teachers themselves, not from the math education research community. Frankly, I think YouCubed would be just as popular if they never performed any research whatsoever. It’s totally inessential. As am I. As is this post. What am I doing with myself? How am I choosing to spend my life? That’s how I always end up feeling when I write about YouCubed.

Anyway, back to the paper, this is what they did:

A matched comparison analysis was employed to assess the effect of the approach on students’ achievement. School districts provided a variety of achievement measures of both participant and non-participant students (GPA and MARS scores, before and after camp participation; and a baseline math standardized test score), and a battery of control variables (race, ethnicity, gender, free and reduced-price lunch status, English learner status, and special education status). 

OK basically the research team couldn’t run an experiment where they randomly place kids in these camps, so they did a very reasonable next-best thing: they created a control group, of sorts, by matching each child in their camp with a child with similar stats who didn’t go to the camp. So if Michael is a camper and has a GPA of 2.5 and a MARS score of whatever, etc., they tried to find a student Jackson who was not a camper but with the same GPA and MARS score. If Michael (and all the other campers) suddenly are performing much better after the camp than the “control” group then maybe the camp is responsible for it. Or maybe it’s some subtle selection bias.

This is all totally reasonable but in the end totally irrelevant for the issues I’m going to point out. I’m including it because, why not?

By the way, the details of this matching and a quantitative comparison of the groups are not detailed in the paper. Normally a paper would do that, but again that’s not so important in light of what I’m about to say.

OK, so we get to the part of the paper where we’re seeing how campers did compared to their control group. First issue is that in this table it looks like the “non-participants” in the matched group had a higher GPA after the camp than the campers.

The body of the paper says, “This analysis showed that at the end of the first term or semester back at school, the students who attended the youcubed summer camp achieved a significantly higher mathematics GPA (p < 0.01, n = 2,417).” Now this is the exact opposite of what the table says, which is a problem, because either the table is wrong or the sentence is false. And, honestly, I assume that the table is wrong and the entire thing is mislabeled. OK.

The paper goes on: “On average, students who attended camp had a math GPA that was 0.16 points higher than similar non-attendees (i.e., students from the same district and grade and who had a similar baseline math GPA and test score) (Table 4).”

This is a problem because the table also does not say this. The difference between a GPA of 2.679 and 2.622 is 0.057 points. That is not 0.16 points. What am I doing, providing this level of scrutiny to this paper, i.e. basic scrutiny? Shouldn’t I be writing a book? Doing math? Reading something? Was I put on this Earth to fact check these papers, providing infinitely more care than the authors themselves apparently did?

Anyway, presumably the issue is that the body of the paper misinterpreted its own table. The 0.16 is the effect size, provided (and clearly labeled) on the right side of the table, not the GPA.

And now a bit more from the paper: “In addition, compared to control students, camp participants were 6 percentage points more likely to receive a grade of B or higher, and 5 percentage points less likely to receive a grade of D or lower (Table 4).”

This is not right, again I think they must be rounding up the effect sizes and reporting them as a percentage change. Silly stuff, quite honestly, but none of it matters at all, I don’t know.

By the way, there is no supplemental information posted, despite this statement.

So, I don’t know. I wrote to corresponding author a month ago but haven’t heard back, I’m sure he’s busy and I’m not sure what he would say.

It’s absurd that this was published as is, and it obviously doesn’t speak well for YouCubed or Boaler that this was pushed through. I…I am unsure what any of this means. Like, yes, it’s bad. But in a way it’s so bad that it doesn’t really touch her core areas of advocacy. I wish the research she was attempting was better because then it would actually be about something. Instead it’s about nothing besides YouCubed and Boaler herself, who has managed to become the popular voice for math education research in this country while showing complete disdain for the work of research itself.

I need to find a better hobby.

Update 2/28/22: The paper appears to have been corrected with a new Table 4. No explanation at the page explains the update or the source of the error, and I’m not sure why the effect is reported to more decimal places than the means:

What I wrote in 2021

What exactly did I spend time on this year? Hard to say, or maybe it’s just hard to admit that my output this year was all over the place. Let’s sort by topic and see what it amounts to.

Book Stuff

I finished writing this book in summer 2020, and it came out in April 2021.

Was purple the right choice for the cover?

I wrote the sort of book about teaching that I wanted to read — short, personal, aimed more at the working teacher than the teacher-in-training. I thought there were some original perspectives in there, though I think it’s fair to say it’s mostly a synthesis of research ideas.

I wrote a few posts this year that expanded on the techniques from the book:

What is “fading out a worked example” and why would it work and also when?

Good explanations connect particulars to principles

Start class with the good stuff

Making Long Problems Shorter


I was hoping to get started with a second book at some point in 2021, but it never happened. Pedagogically, this was a year of grappling with a million little things, rather than one big one.

Is there a book to be written about whole-class discussion, growth mindset, the equals sign, and math fact memorization? That is the book that (apparently) I am ready to write about teaching, but it just feels like a potpourri to me at this stage.

A Good Eye for Arithmetic

What actually even is a growth mindset?

The Change-Resistance Explanation for Why Kids Struggle So Much with Algebra

A growth mindset is a tendency to explain things in a certain way

These included some of my most popular posts this year, for what that’s worth.

Some questions and answers about whole-class discussions

What People Get Wrong About Memorizing Math Facts


On to the math! Honestly, I didn’t learn very much math this year, though the last few months of the year have been a bit better in that department.

People Actually Really Like Mathematics

Teaching Yourself and Others


Honestly, I know so little about policy. You don’t come to michaelpershan dot com to learn about politics. The best you can say about me is that I’m a dabbler and that I try to react thoughtfully to whatever happens to be causing a fuss at the moment.

Was it a mistake to call KIPP the top recommended charity in the United States?

Teachers are afraid of hybrid learning (picked up here)

What if we ban private schools?

Some basic questions about college admissions

I Don’t Know How To Categorize These

If you trust hitcounts, these pieces were among my most popular. One of them is a would-be takedown of an incredibly popular education figure, another a joke, the last a very brief statement of purpose. I enjoyed writing each of these things but they don’t make it easier to figure out exactly what I’m doing here.

YouCubed is More Than Just Sloppy About Research

All the numbers from 1 to 500, ranked from worst to best by a middleschooler

Where My Cynicism About Education Ends


If you’re reading this, it’s likely because at some point or another I wrote a worksheet that you liked. Or I shared someone else’s worksheet, and you liked it. Or you liked something I wrote about algebra, or whatever. But I spent a lot of time this year writing sorta-funny fiction (or straight up humor) and some of it got published in places.

Is any of this good? I couldn’t tell you. But for completeness, I include it below:

The American Bystander

“I Am Baby, Persecuted in City of New York”


“About the Murderer”

Two Fifty One

“A Mathematical Magic Trick”


“I Am A Mad Scientist, And I Am Begging You To Just Trust Scientists”


For the first summer in years, I didn’t teach. During some of that quiet time I sat down to really try to do service to this essay, something that I’ve been thinking about writing for nearly a decade in one form or another. My teen years were dotted with weird Jewish things that I’m spending my adult life trying to make sense of. Adult religion is so normal. Mostly for better.

“A Time To Die” in Tablet

What am I going for here

I honestly don’t know! Looking back, it’s a lot. But do I regret any of it? Not really. I do wish that I was working on another book. Having a big project is good for me. Having a book is also quite honestly a nice thing for the ol’ ego. Blogging has never really been a “respectable” activity, in the sense that you could talk to family members about it without suffering a paroxysm of shame.

Then again, come to think about it, one of the few times this year that I told someone that I wrote a book, their reaction was to ask how anyone would ever hear about the book, let alone buy it? And then I had to once again shamefully admit that I’m a social media user. So there’s really no way out of the shame of writing. It’s an inherently shameful exercise, and maybe I’ll just try to own that embarrassment in the coming year.