Monthly Archives: January 2013

Spring 2013: These students aren’t really prepared, either.

I’m teaching Geometry and Algebra II again, so I gave the same assessment and got these results, with the beginning scores from the previous semester:


I’m teaching two algebra II classes, but their numbers were pretty close to identical—one class had the larger range and a lower mode—so I combined them.

The geometry averages are significantly lower than the fall freshmen only class, which isn’t surprising. Kids who move onto geometry from 8th grade algebra are more likely to be stronger math students, although (key plot point) in many schools, the difference between moving on and staying back in algebra come down to behavior, not math ability. At my last school, kids who didn’t score Proficient or Advanced had to take Algebra in 9th grade. I’d have included Basic kids in the “move-on” list as well. But sophomores who not only can’t factor or graph a line, but struggle with simple substition ought not to be in second year algebra. They should repeat algebra I freshman year, go onto geometry, and then take algebra II in junior year—at which point, they’d still be very weak in algebra, of course, but some would have benefited from that second year of first year.

Wait, what was my point? Oh, yeah–this geometry class class is 10-12, so the students took one or more years of high school algebra. Some of them will have just goofed around and flunked algebra despite perfectly adequate to good skills, but a good number will also be genuinely weak at math.

On the other hand, a number of them really enjoyed my first activity: visualizing intersecting planes, graphing 3-D points. I got far more samples from this class. I’ll put those in another post, also the precalc assessment.

I don’t know if my readers (I have an audience! whoo!) understand my intent in publishing these assessment results. In no way am I complaining about my students.

My point in a huge nutshell: how can math teachers be assessed on “value-added” when the testing instrument will not measure what the students needed to learn? Last semester, my students made tremendous gains in first year algebra knowledge. They also learned geometry and second year algebra, but over half my students in both classes will test Below Basic or Far Below Basic–just as they did the year before. My evaluation will faithfully record that my students made no progress—that they tested BB or FBB the year before, and test the same (or worse) now. I will get no credit for the huge gains they made in pre-algebra and algebra competency, because educational policy doesn’t recognize the existence of kids taking second year algebra despite being barely functional in pre-algebra.

The reformers’ response:

1) These kids just had bad teachers who didn’t teach them anything, and in the Brave New World of Reform, these bad teachers won’t be able to ruin students’ lives;

2) These bad teachers just shuffled students who hadn’t learned onto the next class, and in the Brave New World of Reform, kids who can’t do the work won’t pass the class.

My response:

1) Well, truthfully, I think this response is moronic. But more politely, this answer requires willful belief in a delusional myth.

2) Fail 50-60% of kids who are forced to take math classes against their will? Seriously? This answer requires a willful refusal to think things through. Most high schools require a student to take and pass three years of math for graduation. Fail a kid just once, and the margin for error disappears. Fail twice and the kid can’t graduate. And in many states, the sequence must start with algebra—pre-algebra at best. So we are supposed to teach all students, regardless of ability, three years of increasingly abstract math and fail them if they don’t achieve basic proficiency. If, god save us, the country was ever stupid enough to go down this reformer path, the resulting bloodbath would end the policy in a year. We’re not talking the occasional malcontent, but over half of a graduating class in some schools—overwhelmingly, this policy impacts black and Hispanic students. But it’s okay. We’re just doing it for their own good, right? Await the disparate impact lawsuits—or, more likely, federal investigation and oversight.

Reformers faithfully hold out this hope: bad teachers are creating lazy students who could do the work but just don’t want to. Oh, yeah, and if we catch them in elementary school, they’ll be fine in high school.

It is to weep.

Hey, under 1000 words!

A new year begins—midyear

As I mentioned, my school runs a block semester schedule—we cover a year in a semester, four classes each semester. So Monday starts the new year.

I will be teaching Geometry and Algebra II again, although the geometry class will be 10-12 instead of the freshmen of my first semester. One Geometry, two Algebra IIs and, for the first time, pre-calculus.

Note that I am teaching four classes, which means no prep period, and 33% more pay. I am pumped. Okay, a little bit because of the pay, but mostly for two reasons.

First: Admins don’t give a teacher extra work unless they are happy with the teacher. I have now had two observations with notes so glowing that I keep checking back to see if the name is mine. I know I’m a good teacher. I’m just not used to the principal agreeing with me. More importantly, the administrators seem to like me for the right reasons. Both the principal, who did my observations, and the AVP of the master schedule (the one who reawakened my algebra terrors ) came to see me teach before making the decision.  They liked my explanations.  They like the fact that I pass most of my students. They like the fact that I engage kids with low abilities or incentives, a skill that that all previous administrators have used for their own purposes, but never acknowledged as rare or useful. It’s very nice, if unusual, to be appreciated.

Second: In my state, a math credential has two levels, basic and advanced. Advanced math teachers are much thinner on the ground. Yet in my first three years of teaching, administrators have on several occasions given advanced math classes colleagues who had not yet passed the tests necessary for advanced math, despite several attempts. They made this decision despite the fact a penalty is attached to using unqualified teachers, requiring  a letter home to the students’ parents alerting them to the unqualified teacher.  The administrators took this penalty instead of giving me classes that I was actually qualified to teach.  Such madness as this is pretty normal, and it’s why teachers laugh hysterically when education reformers yammer on about giving principals complete control over hiring and firing.

As a result of these previous administrator decisions, I have never taught an advanced math class. Not once. Ever. I have no idea how to teach pre-calc. I have no idea how to talk to students who are taking a math class for some other reason than “I need it to graduate”. I have even less idea how to teach an entire class of people who–please, please, PLEASE god—know a positive slope from a negative one. I can’t wait.

I have a friend who is a professor at an elite public university, in a field that requires a lot of math. Back when I was first tutoring and learning math on the job, and got hired to teach a student pre-calc, I asked him “What topics are in pre-calc?” He sniffed, snootily, and said “Precalc isn’t a subject. It’s an administrative category.” I must have learned a lot of math in the intervening years, because I get the joke now.

I’ve got a book, so I’ll figure it out. But if any pre-calc teachers have broad topics to organize around, I’d love to hear about them.

In addition to teaching a full-schedule, no prep period, I start my yearly ACT class on Monday, and in a month I begin my AP US History review classes, two of them. I dropped my English enrichment class, though, so for the first time in seven years, my Saturday mornings are free. I love late winter/spring. But with all this extra money I may just take the summer off for the first time ever.

Algebra 1 Growth in Geometry and Algebra II

Last September, I wrote about my classes and the pre-algebra/Algebra 1 assessment results.

My school covers a year of instruction in a semester, so we just finished the first “year” of courses. I start with new students and four preps on Monday. Last week, I gave them the same assessment to see if they’d improved.

Unfortunately, the hard drive on my school computer got wiped in a re-imaging. This shouldn’t have been a problem, because I shouldn’t have had any data on the hard drive, except I never got put on the network. Happily, I use Dropbox for all my curriculum development, so an entire year’s worth of intellectual property wasn’t obliterated. I only lost the original assessment results, which I had accidentally stored on the school hard drive. I should have entered the scores in the school grading system (with a 0 weight, since they don’t count towards the grade) but only did that for geometry, the only class I can directly compare results with.

My algebra II class, though, was incredibly stable. I only lost three students, one of whom got a perfect score—which the only new addition to the class also got, so balance maintained. The other two students who left got around 10-15 wrong, so were squarely in the average at the time. I feel pretty comfortable that the original scores didn’t change substantially. My geometry class did have some major additions and removals, but since I had their scores I could recalculate.

Mean Median Mode Range
Original just above 10 9.5 7 22
Recalculated just below 10 (9.8) 8 7 22

I didn’t have the Math Support scores, and enough students didn’t take the second test that comparisons would be pointless.

One confession: Two Algebra II students, the weakest two in the class, who did no work, scored 23 and 24 wrong, which was 11 more than the next lowest score. Their scores added an entire point to the average wrong, increased the range by 14 points, and you know, I just said bye and stopped them from distorting the results the other 32 kids. (I don’t remember exactly, but the original A2 tests had five or six 20+ wrong scores.)

So here’s the original September graph and the new graph of January:


The geometry class was bimodal: 0 and 10. Excel refused to acknowledge this and I wasn’t sure how to force it. The 10s, as a group, were pretty consistent—only one of them improved by more than a point. The perfect scores ranged from 8 wrong to 2 wrong on the first test.


In short, they learned a lot of first year algebra, and that’s because I spent quite a bit of time teaching them first year algebra. In Algebra II, I did it with data modeling, which was a much more sophisticated approach than what they’d had before, but it was still first year algebra. In geometry, I minimize certain standards (proofs, circles, solid shapes) in favor of applied geometry problems with lots of algebra.

And for all that improvement, a still distressing number of students answered x2 + 12 when asked what the product of (x+3) and (x+4) was, including two students who got an A in the class. I beat this into their heads, and STILL some of them forget that.

Some folks are going to draw exactly the wrong impression. “See?” these misguided souls will say, nodding wisely. “Our kids just aren’t being taught properly in early grades. Better standards, better teachers, this problems’s fixed! Until then, this poor teacher has to make up the slack.” In short, these poor fools still believe in the myth that they’ve never been taught.

When in fact, they were taught. Including by me—and I don’t mean the “hey, by the way, don’t forget the middle term in binomial multiplication”, but “you are clubbing orphan seals and making baby Jesus cry when you forget the middle term” while banging myself on the head with a whiteboard. And some of them just forgot anyway.

I don’t know how my kids will do on their state tests, but it’s safe to say that the geometry and second year algebra I exposed them to was considerably less than it would have been had their assessment scores at the beginning of class been the ones they got at the end of class. And because no one wants to acknowledge the huge deficit half or more of each class has in advanced high school math, high schools won’t be able to teach the kids the skills they need in the classes they need—namely, prealgebra for a year, “first year” algebra for two years, and then maybe some geometry and second year algebra. If they do okay on the earlier stuff.

Instead, high schools are forced to pretend that transcripts reflect reality, that all kids in geometry classes are capable of passing a pre-algebra test, much less an algebra one test. Meanwhile, reformers won’t know that I improved my kids’ basic algebra skills whilst still teaching them a lot of geometry/algebra II, because the tests they’ll insist on judging me with will assume a) that the kids had that earlier material mastered or b) that I could just catch them up quickly because after all, the only problem was the kids’ earlier teachers had never taught them.

Modeling Probability

This is a lecture class, but I put all the instructions in the handout as well, mostly so I can remember the outlines of the activity.

In the lecture, I explain that video games run on probabilities, that balancing probabilities is an essential element for strategy video games. Any games that give the user a running series of choices has to balance outcomes and create choices with tradeoffs. Otherwise, the user learns that the “good” choices are and the game gets boring. (I have no idea if this is true, but it sounds reasonable.)

Obviously, if the students were really at a software company, these scenarios would be automated, but hey, it’s a math class.

Materials: Scintilla Handout (reproduced here), and 9 Oracle advice cards (3 gryphons, 3 dragons, 3 excaliburs)

Here’s the main handout.

Crossing the Scintilla

You’re an intern at a major software development company! You’ve been assigned to work with the team developing Sorcery & Shadows, a new game scheduled for fall release.

S&S is “retro”, harking back to the 70s and 80s fantasy games—less violence, more strategy. At various points, the player’s choice of avatar must consult the three Oracles for permission and guidance. The Oracles determine the character’s actions, but the response varies based on the avatar chosen:


The software team is working on the following scenario:

The player (Vlad, Dulcinea, or Chaos) is trying to cross the Scintilla River. The Oracles must be consulted. The Oracles will each advise one of the following options:

  1. The gryphon, which swims across.

  2. The dragon, which flies across.
  3. Excalibur, the sword, which magically transports the carrier.


Gryphon                                Dragon                                         Excalibur

The player will follow the Oracles’ advice if the right number of them agree. The Oracles are pleased when the player follows their advice and give the player five silver coins.

If the player can’t follow the Oracles’ advice, then the player must pay 1 silver coin to cross on the ferry.

The software team has already decided that the Oracles’ responses are randomly generated, and they need to determine the probability that each character gets across the river. They’ve asked you to work this out.

Before you start, have a brief group discussion and make your predictions.

    Is it equally probable that Vlad, Dulcinea, and Chao will be able to follow the Oracles’ advice?

  1. If not, who do you think is the most likely to be able to follow the advice?
  2. Least likely?

I wander around to listen in on the predictions. The two most common predictions are Vlad and Dulcinea, which is interesting.

I always do two trials as a class before I set them on their own, stressing that the actual advice—Gryphon, Dragon, Excalibur—is immaterial. They are tracking which character is able to accept the Oracle’s advice. Back to the handout—this is on the flip side.

Experimental Probability
Experimental Probability—Performing an event repeatedly and measuring the results as a ratio of a particular occurrence to the total number of trials: exprob.

Once a pattern has been established, we can rely on this data as an empirical probability.

You are going to perform 30 simulated trials of the event “Asking the Oracles for Advice”.

Each group has three sets of three cards: a gryphon, a dragon, and Excalibur. Three group members will “play Oracle”, by randomly and simultaneously throwing down one of the three cards. (IT MUST BE RANDOM!). The other group member tracks the outcome of each trial, using the table below.


When you have completed 30 trials, compute the experimental probability of each character’s likelihood of following the Oracles’ advice. Remember to keep careful track of how many trials you run, as that’s going to be your denominator.

Send someone from your group up to the front whiteboard and report your results. Report the totals, not the experimental probability percentages. We’re going to calculate the results for the class.


The kids love the trials. They are religiously random, and really get a kick as they see a clear pattern emerge in the results.

After all the results are on the board, I tote them up and calculate the experimental probability for the class.

Then I transition to theoretical probability and discuss the difference between experimental probability—what actually happens in a series of trials—and theoretical, what is expected to happen. I ask for examples of trials that would have no theoretical probability: medical trials, new treatments, new procedures. I point out that researchers run thousands of trials because they want to have a reliable experimental model in order to begin to build theoretical probability.

In other cases—coin tosses, lottery tickets, and asking the Oracles’ advice—the theoretical probability is easily modeled. And that’s what we do next. Back to the handout, page 3.

Who Crosses the River?–Theoretical Probability

In Part B, you ran trials and calculated the experimental probability of each character’s being able to follow the Oracles’ advice. Now you’re going to determine the theoretical probability for each character and compare them.

Theoretical probability can be calculated when the number of possible outcomes is fixed.

In this case, we can define the following:

Sample Space:
The set of all possible outcomes for a trial.
Particular outcome(s) of the sample space. An event may contain other events, each with its own sample space.
Target event:
The desired outcome to be tested.

For example, the sample space for one instance of “asking for an Oracle’s advice” is: gryphon, Excalibur, dragon.

But in this case, we are asking for all the Oracles’ advice. So how do we find all the combinations possible from three Oracle requests?

There are three useful tools to help you model theoretical probabilities for a multiple-event scenario.

  • A tree diagram can help you determine all the possible outcomes for a “compound” (multiple event) outcome, particularly complex events such as this one. Trees model a new “branch” for each component of an event.

  • An area model is simple and easy, but limited to two or three events.
  • A counting diagram is useful for ordering and calculating the number of outcomes.

See the flip side of this page for detailed descriptions of area models and probability trees.

Probability Tree

Working with your team, create a probability tree for all possible combinations of Oracular responses.

Using different colored pens for each character, trace the different outcomes: all three match (Vlad), two match (Dulcinea), no matches (Chaos).

Count up the possible crossings for each character, and the total possible outcomes.

How many different outcomes are possible? __________________

How many outcomes allow Vlad to cross? ________

Dulcinea? _______________

Chaos? _______________

Compare these numbers to your own experimental results, as well as the class totals. How do they compare?

I use a CPM handout (page 14), which isn’t all that great but gives visual examples of both models on one page. All I really want is the visual, which I haven’t gotten around to building for myself yet.

Building the probability tree diagram for “asking the Oracles” is a great activity that really brings home the difference between theoretical and experimental probability. The kids can see why Dulcinea gets the necessary agreement more often, and why Chaos wins more frequently than Vlad.

In earlier years I would have just had the students create the probability tree on paper, in their groups. But earlier in the school year, I came up with a fun way to work on bigger, multi-step problems. I have a lot of whiteboards. So in their groups, the kids go to a whiteboard section, and start working on the assigned problem(s). They have more room, I can see the work and be sure everyone’s got the correct answers. It shoves the math right under the nose of the weaker students, who might otherwise (ahem) sit quietly hoping I don’t notice they aren’t working or paying attention. And it mixes things up, which is always useful. I used this about three times during the year (our semester is a year); here’s a picture of them working on parabolas:


(Note: smudged the faces, took out the color, and asked the kids permission to use the photo.)

As I was driving to school the morning of this class, I suddenly realized that whiteboard work would be perfect for the probability trees. If I had them do it on paper, at least half of the kids would be looking on as someone else did all the work anyway, so I might as well be sure they were actually looking on, instead of tuning out. I usually use this method as review rather than for new concepts, but in this case it was the right call. Each of the groups were all involved in their own tree, and none of them were simply copying some other group’s work—some surreptitious checks to see if they were on the right track, sure. But that’s a bonus.

There were several gorgeous versions done in red, blue, green, and purple that I forgot to photograph before I erased them, but this one is nicely functional. Except the misspelling.

So we take a few minutes to compare the theoretical outcomes with the experimental, and since we have close to 200 trials (8 groups, 25 trials on average), they match up beautifully.

I tell them that science and research engage in experimental probability, but in math, we focus entirely on the theoretical by modeling the possible outcomes. I always start with the most flexible and visual, but the least useful, model. I then outline the other two models I want them to use, both of which I think have limitations, but are much more helpful: the area model and the “counting diagram”.

Counting Diagram

I always snicker at a formal name for a very simple concept. But it’s extremely useful as an organizer.

One blank line for every event. So asking the Oracles, there are three events.

______      ______      _______

How many outcomes are possible for each event? The events are independent of each other.

___3__        __3___        ___3___ = 27

Multiply across. That’s the total number of outcomes that can result in asking the Oracles.

Now, model each character. In these cases, the number of desired outcomes for subsequent events is conditional. (I point out that the Oracles’ response is still random and independent, but the desired response is conditional, and that’s what we’re counting).

Vlad is the easiest. The first event can be any of the three responses. But the second and third events must match the first, so there’s only one acceptable outcome for each.

___3__       __1___       ___1___ = 3

Dulcinea is more complicated, but the trees are very helpful in getting the kids to see that the first two events can have any outcome. The third event must match one of those first two.

___3__       __3___       ___2___ = 18

Finally, Chaos. Why is Chaos twice as likely as Vlad to get the correct Oracle response? The counting diagram helps students see that as each event occurs, he loses the possibility of that outcome—and yet, this gives him more outcomes than Vlad.

___3__        __2___         ___1___ = 6

The diagram can also calculate probabilities of multiple events, but it’s primarily useful for counting.

Right around now, I bring up lottery tickets, and we go through the hugeness of the numbers in a diagram. And here, I mention a key difference between theoretical and experimental probability, aka Why All Math Teachers Tell You Not To Buy Lottery Tickets.

Theoretical probability says it’s utterly pointless to buy lottery tickets. But every time the lottery runs, someone achieves the functional equivalent of getting struck by lightening while finding a four-leaf clover while getting abducted by aliens. Someone wins. Reality occurs. Gambling exists because of experimental probability. So my students won’t get the Lottery Tickets lecture from me. Go ahead and buy. Cross your fingers when your plane takes off, even though the car ride to the airport was the riskier trip. But if you blow your entire salary on poker, find a 12-step program.

Area model

My students are already

For this, I have a handout, because the area model makes the two most important probability operations beautifully clear: when to multiply probabilities, and when to add them.

Limitations—only two sample spaces, alas. You couldn’t model “asking the Oracles” with the rectangle.

So there’s the three basic models that we use for the rest of the unit. I often return to the “intern at the software shop” scenario, which gives me endless possibilities. Here’s a couple more.

This one is usually homework for the first day—what is the probability of getting various payouts? I don’t mean expected value—we go through that the next day, with the original Scintilla scenario and this one.

And here’s one that goes nicely with an area model, which can really help students visualize conditional probability.

Thanks to binomial expansion, probability and elementary combinatorics are sandwiched into second year algebra and it’s hard to go into the subject in depth. AP Stats is pretty joyless. Example 99,521,325 on the list of Why We Need to Offer a Broader Range of Math Classes.

Jo Boaler’s Railside Study: The Schools, Identified. (Kind of.)

A brief, illustrative Jo Boaler anecdote by Dan Meyer, currently one of her doctoral students:

I was talking to Jo Boaler last night (name drop!) and she admitted she didn’t really get the whole blogging thing.

I laughed. Some background:

Jo Boaler, a Stanford professor, conducted a longitudinal study of three schools that’s widely known as the Railside paper. She presented the results to a standing room only crowd at the National Meeting of the National Council of Math Teachers in 2008, convincing almost everyone that “Railside” High School, a Title I, predominantly Hispanic high school outperformed two other majority white, more affluent schools in math thanks to the faculty’s dedication to problem-based integrated math, group work, and heterogeneous classes.

“Reform” math advocates, progressives whose commitment to heterogeneous classes has almost entirely derailed the rigor of advanced math classes at all but the most homogenous schools, counted this paper as victory and validation.

Three “traditionalists” were highly skeptical of Boaler’s findings and decided to go digging into the details: James Milgram, math professor at Stanford University, Wayne Bishop of CSU LA, and Paul Clopton, a statistician. They evaluated Boaler’s tests, the primary means by which Boaler demonstrated Railside’s apparently superior performance, and found them seriously wanting. They identified the schools and compared the various metrics (SAT scores, remediation rates) and demonstrated how Railside’s weak performance called Boaler’s conclusions into question. Their resulting paper, “A close examination of Jo Boaler’s Railside Report”, was accepted for publication in Education Next—and then Boaler moved to England. At that point, they decided not to publish the paper. All three men were heavily involved in math education and didn’t want to burn too many bridges with educators, who often lionize Boaler. One of the authors, James Milgram, a math professor at Stanford, posted the paper instead on his ftp site. Google took care of the rest.

The skeptics’ paper has stuck to Boaler like toilet paper on a stiletto heel; she’s written a long complaint about the three men’s “abusive” determination to get more information from her. From an Inside Higher Ed report on her complaint:

[S]he said she was prompted to speak out after thinking about the fallout from an experience this year when Irish educational authorities brought her in to consult on math education. When she wrote an op-ed in The Irish Times, a commenter suggested that her ideas be treated with “great skepticism” because they had been challenged by prominent professors, including one at her own university. Again, the evidence offered was a link to the Stanford URL of the Milgram/Bishop essay.

“This guy Milgram has this on a webpage. He has it on a Stanford site. They have a campaign that everywhere I publish, somebody puts up a link to that saying ‘she makes up data,’ ” Boaler said. “They are stopping me from being able to do my job.”

Boaler is upset because ordinary, every day, people aren’t merely taking her assertions at face value, but are instead challenging her authority with a link to a paper that, in her view, they shouldn’t even be able to read. So you can see why I laughed. This is a woman with absolutely no idea how the web works. “It’s not even peer-reviewed!!!” That people might find the ideas convincing and well-documented, with or without peer-review, isn’t an idea she’s really wrestled with yet.

Identifying the Schools
As I mentioned a while back, I had a strong reaction four years ago when reading an earlier work by Jo Boaler. A few months later, while still in ed school, I perused her Railside paper, which struck me as equally, er, not credible, a product of wishful deception, maybe? Or maybe just wishful thinking. I googled around to see if I was the only doubter and found the Milgram/Bishop/Clopton paper.

Railside High School

The article indicated that the three schools were identifiable. So I just googled algebra “bay area” boaler and in the first 2-3 pages I found this report on San Lorenzo High School:

San Lorenzo’s relationship with Stanford was based on their participation in a longitudinal study conducted by Professor Jo Boaler and her colleagues at the university. ….According to the CAPP liaison to the project, Weisberg, the researchers also found that SLHS math teachers rated high for their constructivist approach to teaching when compared to teachers at the other two high schools in their study.

Praised for their constructivist approach? In five minutes, I’d not only identified one of the schools. I’d identified the big Kahuna–Railside, the star of Boaler’s report, the school whose dedication to complex instruction, problem-based integrated math, and heterogeneous classes had propelled the Stanford professor to fame and glory. Bow to my greatness.

Happily, Boaler’s paper included CST scores for 2003, so I could match them up (as did MBC in their followup paper):


I could easily confirm that San Lorenzo High School CST scores for freshmen match exactly to Railside’s:

(you can confirm here, it’s in Alameda County. The Algebra column for freshmen only. See? 1% 15% 33% 36% 15%. 188 students. )

San Lorenzo is an California East Bay suburb, so I’m not sure why Boaler would describe Railside as “an urban school”. California has any number of high poverty, Title I suburban schools.

One down, two to go. But the original MBC paper didn’t specify how the men identified the schools, and google gave too many possibilities for the other two study participants. Besides, I had other things to do, like find a teaching job, so I put away childish things.

Greendale High School

Then four years later, Jo Boaler complains and, in his response, James Milgram explains how they identified the schools:

We took the data above from Table 5, and one of us…checked the entire publicly available 2003 California STAR data-base, looking for schools for which any column was identical to one of the columns in Table 5. In each case we found that there was one and only one school that had that data.

Hey. I could do that. I had Access (the database), even. Which you need, because the CST file is too big for Excel.

Using this method, I identified the other two schools.

I downloaded the 2003 data to a text file, imported it to Access. I know mySQL’s interface but have never used Access before. I feel sure there’s an easier way than the path I took, which was to treat poor Access like Excel: go to the TestResults table, highlight the “total students tested” row, and search for 125, looking to the right for 0,6,27,55,12. It sounded something like this:

ClicknoClicknoClicknoClicknoClicknoClicknoClicknoClicknoClickno ClicknoClicknoClicknoClickWAITcrap that was it!go back! What, there’s no Reverse?Christ?Where was it?crapcrapcrapscrollbackscrollbackClicknoClickn…yes! There it is!

What, you don’t see it? Click to enlarge:


I found Greendale!! Whoohoo!

All I had to do was tab to the left a bit and look up the school’s identifying number. Then I went to the form in Access to look up the school and tada!


According to Jo Boaler, “Greendale High School is situated in a coastal community, with very little ethnic or cultural diversity (almost all students are white).”.

Well, she’s half right. Greendale is definitely mostly white, but it’s in the mountains, not in the excessively wealthy mountains, in the much much much Greater Bay Area. Well, really, it’s juuuuust outside the much much much Greater Bay Area. Very pretty place. If you look at it on Google Maps, you would barely see blue, way off to the left.

It is not coastal.

Hilltop High School
Back to Access and clicknoclicknoclickgobackack!clicknoclickstop!tableft and there! I have Hilltop.

Here are the CST scores to match:

Boaler on Hilltop: “Hilltop High School is situated in a more rural setting, and approximately half of the students are Latino and half white.”

Demographics, right. Location, wrong. Boaler has just described Greendale’s location, not Hilltop’s. Find Hilltop’s town on a map and the blue is just to the left. One would describe Hilltop as “coastal”.

So Boaler flipped the school descriptions, but not the demographics? Was that on purpose, or an error?

I feel pretty confident, therefore, that in Boaler’s report:

  • Railside High School is San Lorenzo High School, in San Lorenzo. Title I school, mostly Hispanic.
  • Greendale High School is located in one of the mountain chains surrounding the Bay Area. Rural community, economically diverse, mostly white.
  • Hilltop High School is in a coastal community just outside the Bay Area, half Hispanic, half white. Greendale and Hilltop are not neighbors, but much closer to each other than either is to the edges of the Bay Area, much less San Lorenzo.

I originally planned to reveal the names of all three schools. I used publicly available data and Boaler’s own study to identify them. The schools have nothing to be embarrassed about. They participated in a study to help further knowledge about effective math instruction. How is that a bad thing? Their scores are already available on government website. Boaler isn’t directly critical of any school. No downside is immediately apparent, at least to me.

But still. In San Lorenzo High School’s case, their participation is easily searchable, so I identified the school. But the other two schools take quite a bit of work to find in Google, and the principals might not want to wake up and find their schools in a blog, even if the news wasn’t bad. This way, they can have some warning—again, with the understanding that this is publicly available data. Using Access is the cleanest way to find them, but at the end of this post I will give some other info to help interested people identify them.

So What Does This Mean?

Well, let’s assume that I didn’t miss schools with identical CST scores (I checked every entry, but who knows, I might have clicked too fast) and that these are, in fact, the schools in the study.

With just a bit of effort, interested parties can now review the Milgram/Bishop/Clopton report and confirm its claims about the overall math performance of the three schools. I’ve spot checked a lot of it, and I haven’t found any errors yet.

I’m not terribly detail-oriented, yet I saw two huge issues.

First, the 2003 CST data I matched up? Boaler provides this data as an external validator, showing how well the Railside kids did compared to the other two groups, thanks to the superior instruction of reform math. As is evident from the screen prints of the actual CST data that Boaler is using freshman 2003 data. But in Table 6, reproduced here:


Boaler provides Year 3 data and clearly indicates that the students are juniors in 2003. The freshman algebra scores are not from her cohort. So why is she using this data as evidence of how great the program was? Shouldn’t she be using Algebra II data?

I went back two years to see what algebra scores were like, and discovered San Lorenzo High School (Railside) had fewer than ten freshmen taking algebra—in fact, the school has no math subject-specific scores at all. The other two schools did have freshmen algebra classes. So what, exactly, was Boaler comparing?

Milgram et al cover all of this in greater detail, and they also cover the other big red neon warning I see: if San Lorenzo High, which didn’t track, put all of its freshmen in algebra, while Greendale and Hilltop put their mid-to lower ability students in Algebra while the top freshmen took Geometry and Algebra II, then Boaler should not assert that San Lorenzo High is outperforming the other two schools based on freshman Algebra scores.

Of course, since she’s using the scores from the wrong cohort, she didn’t really demonstrate that the studied cohort from San Lorenzo HS outperformed the other two schools in the CST to begin with.

Why bother?

Like most mathematicians, MBC are vehemently opposed to reform math. Both Milgram and Bishop spend a lot of time working with parents or districts that are trying to get rid of reform curricula. In his rebuttal, Professor Milgram says,

Indeed, a high ranking official from the U.S. Department of Education asked me to evaluate the claims of [the Railside study] in early 2005 because she was concerned that if those claims were correct U.S. ED should begin to reconsider much if not all of what they were doing in mathematics education. This was the original reason we initiated the study, not some need to persecute Jo Boaler as she claims.

However, given both men’s determination to oppose reform math, and their willingness to work with parent groups organizing against reform math, Boaler believes, as Milgram says, that the paper was an attempt to discredit reform math, as opposed to an honest academic inquiry.

I have no opinion on that, but then I spend a lot of time on the Internet. MBC all seem pretty mild to me.

I’m not a traditionalist. I’ve written many times in this blog that for a pro-tracking, pro-testing discovery-averse teacher, I am stupendously squishy. Milgram, Bishop, Clopton, and Professor Wu would undoubtedly disapprove of my teaching methods. My kids sit in groups, I use a lot of manipulatives, I don’t lecture much or give notes, use lots of graphic organizers. To the extent I have a specialty, it lies in coddling low ability, low incentive kids through math classes whilst convincing them to learn something, and what they learn isn’t even close to the rigorous topics that real mathematicians want to see in math class. (Some lesson examples: real life coordinate geometry, modeling linear equations, triangle discovery, factoring trinomials, teaching trig and right triangles.) Nonetheless, I firmly believe that discovery, problem-based math, and complex instruction are ineffective with low to mid ability kids and think tracking or ability grouping is essential. So I’m not really tied to either camp in the math wars.

Besides, the math wars have largely been resolved. Lectures won’t work for low ability kids, but neither does discovery. High ability kids need fewer lectures, fewer algorithms, more open-ended problems, more challenges. Traditionalists have a lot of energy around reform math, but I think they could dial it back. For the most part, reform has lost in schools, particularly high schools.

Since Boaler will, if she acknowledges this post at all, complain about my motives, let me say that I am not a Boaler fan, but my disapproval is based purely on her opinions as revealed through her work: the Amber Hill/Phoenix Park paper, the Railside paper, and yeah, her recent bleat struck me as a big ol’ self-pity fest. But I’m not actively seeking to hurt her reputation, and while my tone is (cough) skeptical, I’m perfectly happy to learn that all of these questions I raise involve perfectly normal research decisions for academics.

However, I am constantly surprised at the unquestioning acceptance of educational research, particularly quantitative research.

Remember, this is a hugely significant paper in the math wars. Boaler is the hero who went out and “proved” that reform math gets better results. Suppose it’s academically acceptable for Boaler to assert that San Lorenzo High School algebra students outperformed the algebra students from two more affluent schools, based on the test results of students not in her study cohort. Would it nonetheless be important for education journalists to point out that the San Lorenzo students included the best students in the school, while the Greendale and Hilltop schools’ best students were in more advanced classes? And that a component of her success metric relied on scores of students who were two years behind her cohort?

To the extent I have an objective, there it is. Educational researchers may, in fact, engage in entirely acceptable behavior that nonetheless hides information highly relevant to the non-academic trying to use the research to figure out educational best practices.

Who’s responsible for bringing that information to light?


Identifying the schools

Ironically, when I was originally searching for the schools four years ago, I came across a link that identified Greendale. I just didn’t realize it for reasons that will be clearer once you find the link. Since MBC discuss the Greendale parents’ demand for a “traditional” program, and the school’s reluctant compliance, I tried to use that history to figure it out, googling (exactly): “interactive mathematics program” california high schools traditional. In the first couple pages, I found a link written by one of the MBC authors that references that parental demand as well. There are several schools mentioned in the paper, but only one of them is rural.

I’d also found a link with the Hilltop school in my initial search but had dismissed it, thinking the schools would all be in the Bay Area. But since MBC mentions that the school district forced Hilltop to cancel, I’d googled “interactive mathematics program” california district canceling. That will bring up, in the first two or three pages, a blog post from a once fairly well-known education specialty blogger (since gone inactive) on the school. This battle went on for some time, and the New York Times covered it earlier, but I won’t give the query for that.

A couple other clues: Many of Jo Boaler’s doctoral students posted in support of her complaint. An early supporter, who has a well-regarded math blog, taught at Greendale High School, although after the years of Jo Boaler’s study. That is probably not a coincidence. Jo Boaler thanks teachers in the paragraph in which she also mentions the schools that participated in her study. Maybe check out those teachers and see where they teach (or taught).

SAT Writing Tests–A Brief History

I have a bunch of different posts in the hopper right now, but after starting a mammoth comment on this brand new E. D. Hirsch post (Welcome to blogging, sir!), I decided to convert it to a post—after all, I need the content. (Well, it was brand new when I started this post, anyway.)

Hirsch is making a larger point about Samuel Messick’s concern with consequential validity versus construct validity but he does so using the history of the SAT. In the 80s, says Hirsch, the ETS devised a multiple choice only method of testing writing ability, which was more accurate than an essay test. But writing quality declined, he implies, because students believed that writing wasn’t important. But thanks to Messick, the SAT finally included a writing sample in its 2005 changes.

I have nothing more than a layman’s understanding of construct vs. consequential validity, and Hirsch’s expertise in the many challenges of assessing writing ability is unquestioned, least of all by me. But I know a hell of a lot about the SAT, and what he writes here just didn’t match up with what I knew. I went looking to confirm my knowledge and fill any gaps.

First, a bit of actual SAT writing assessment history:

  • By 1950, the CEEB (College Board’s original name) had introduced the English Composition Achievement Test. The original test had six sections, three multiple choice, three essay (or free response). The CEEB began experimenting with a full 2-hour essay the next year, and discontinued that in 1956. At that point, I believe, the test was changed to 100 question multiple choice only. (Cite for most of this history; here’s a second cite but you need to use the magnifying glass option.)
  • In 1960, the CEEB offered an unscored writing sample to be taken at the testing center, at the universities’ request, which would be sent on to the schools for placement scoring. (I think this was part of the SAT, but can’t be sure. Anyone have a copy of “The Story Behind the First Writing Sample”, by Fred Godshalk?)
  • In 1963, the English Composition Achievement Test was changed to its most enduring form: a 20 minute essay, followed by a 40-minute multiple choice section with 70 questions.
  • In 1968, the CEEB discontinued the unscored writing sample, again at the universities’ request. No one wanted to grade the essays.
  • In 1971, the CEEB discontinued the essay in the ECAT , citing cost concerns.
  • In 1974, the SAT was shortened from 3 hours to 2 hours and 45 minutes, and the Test of Standard Written English was added. The TSWE was multiple choice only, with questions clearly similar to the English Composition Achievement Test. The score is not included in the SAT score, but reported to colleges separately, to be used for placement.
  • In 1976, in response to complaints, the essay version of the ECAT was reinstated. (It may or may not be significant that four years later, the ETS ran its first deficit.) From what I can tell, the ECAT and the TSWE process remained largely unchanged from 1976 through 1994. This research paper shows that the essay was part of the test throughout the 80s.
  • In 1993, all achievement tests were rebranded as SAT II; the English Composition Achievement Test was renamed to the SAT II Writing exam. At some point, the SAT II was shortened from 70 to 60 questions, but I can’t find out when.
  • In 1994 , there were big changes to the SAT: end to antonyms, calculators allowed, free response questions in math. While the College Board had originally intended to add a “free response” to the verbal section (that is, an essay), pressure from the University of California, the SAT’s largest customer, forced it to back down (more on this later). At this time, the TSWE was discontinued. Reports often said that the SAT Writing exam was “new”; I can find no evidence that the transition from the ECAT to the SAT II was anything but seamless.
  • In 1997, the College Board added a writing section to the PSAT that was clearly derived from the TSWE.
  • In 2005, the College Board added a writing section to the SAT. The writing section has three parts: one 25 minute essay and two multiple choice sections for a total of 49 questions. The new writing test uses the same type of questions as the ECAT/SAT II, but the essay prompt is simpler (I can personally attest to this, as I was a Kaplan tutor through the transition).
  • By the way, the ACT never required an essay until 2005, when compliance with UC’s new requirement forced it to add an optional essay.

I’m sure only SAT geeks like me care about this, but either Hirsch is wrong or all my links are wrong or incomplete. First, even with his link, I can’t tell what he’s referring to when he says “ETS devised a test…”. A few sentences before, he places the date as the early 80s. The 80s were the one decade of the past five in which the College Board made no changes to any of its writing tests. So what test is he referring to?

I think Hirsch is referring to the TSWE, which he apparently believes was derived in the early 80s, that it was a unique test, and that the College Board replaced the TSWE with the required essay in 2005. This interpretation of his errors is the only way I can make sense of his explanation.

In that case, not only are his facts wrong, but this example doesn’t support his point. The SAT proper did not test written English for admissions. The TSWE was intended for placement, not admissions. Significantly, the ACT was starting to pick up market share during this time, and the ACT has always had an excellent writing test (multiple choice, no essay). Without the TSWE, the SAT lacked a key element the ACT offered, and saying “Hey, just have your students pay to take this extra test” gave the ACT an even bigger opening. This may just possibly have played into the rationale for the TSWE.

Colleges that wanted an SAT essay test for admissions (as opposed to placement) had won that battle with the English Composition Achievement Test. The CEEB bowed to the pressures of English teachers not in 2005, but in 1963, when it put the essay back into the ECAT despite research showing that essays were unreliable and expensive. After nine years of expense the CEEB believed to be unnecessary, it tried again to do away with the essay, but the same pressures forced it to use the essay on the English Composition Achievement Test/SAT II Writing Test from 1976 to 2005, when the test was technically discontinued, but actually shortened and incorporated into the SAT proper as the SAT Writing test. Any university that felt strongly about using writing for admissions could just require the ECAT. Many schools did, including the University of California, Harvard, Stanford, and most elite schools.

The College Board tried to put an essay into the test back in the 90s, but was stopped not because anyone was concerned about construct or consequential validity, but because its largest customer, the University of California, complained and said it would stop using the SAT if an essay was required. This struck me as odd at first, because, as I mentioned, the University of California has required that all applicants take the English Composition Achievement test since the early 60s. However, I learned in the link that that Achievement Test scores weren’t used as an admissions metric until later in the 90s. In 1994, UC was using affirmative action so wasn’t worried about blacks and Hispanics. Asians, on the other hand, had reason to be worried about an essay test, since UC had already been caught discriminating against them, and UC clearly felt some placation was in order. Later, after the affirmative action ban, UC did a 180 on the essay, requiring that an essay be added to the SAT in 2005.

Why did the College Board want to put an essay in the SAT in 1994, and why did UC change its position 11 years later? My opinion: by then the College Board was getting more efficient at scoring essays, and the ECAT/SAT II Writing wasn’t catching on with any other than elite schools and UC. If the Writing test was rolled into the SAT, the College Board could charge more money. During the 90s we saw the first big push against multiple choice tests in favor of “performance-based assessments” (Hirsch has a whole chapter in one of his books about these misconceptions), giving the College Board a perfect rationale for introducing an essay and charging a lot more money. But UC nixed the essay until 2002, when its list of demands to the College Board called for for removing analogies, quantitative comparisons, and—suddenly—demanding that the writing assessment be rolled into the main SAT (page 15 of the UC link). I can see no reason for this—at that time, UC still required Subject tests, so why couldn’t applicants take the writing test when they took their other two Subject tests? The only reason—and I mean the only reason—I can see for rolling the writing test into the main SAT comes down to profit: the change made the College Board a hell of a lot of money.

Consider: the College Board already had the test, so no development costs beyond dumbing the test down for the entire SAT population (fewer questions, more time for the essay). So a test that only 10% of the testing population paid for could now be sold to 100% of the testing population. The 2005 SAT was both longer (in time) and shorter (in total questions), and a hell of a lot more expensive. Win win.

So UC’s demand gave the College Board cover. Fair’s fair, since UC had no research rationale whatsoever in demanding the end to analogies and quantitative comparisons, changes that would cost the College Board a great deal of money. Everyone knows that California’s ban on affirmative action has made UC very, very unhappy and if I were to assert without foundation that UC hoped and believed that removing the harder elements of the SAT would reduce the achievement gap and enable the university to admit more blacks and Hispanics, well, I’d still get a lot of takers. (Another clue: UC nearly halved the math test burden requirement at the same time—page 16 of the UC link.) (Oh, wait—Still another clue: Seven years later, after weighting the subject tests more heavily than the SAT and threatening to end the SAT requirement altogether, UC ends its use of….the Subject tests. Too many Asians being “very good at figuring out the technical requirements of UC eligibility”.)

So why does any of this matter?

Well, first, I thought it’d be useful to get the history in one place. Who knows, maybe a reporter will use it some day. Hahahahaha. That’s me, laughing.

Then, Hirsch’s assertion that the “newly devised test”, that is, the TSWE, led to a great decline in student writing ability is confusing, since the TSWE began in 1974, and was discontinued twenty years later. So when did the student writing ability decline? I’ve read before now that the seventies, not the eighties, saw writing nearly disappear from the high school curriculum (but certainly Hirsch knows about Applebee, way more than I do). If anything, writing instruction has improved, but capturing national writing ability is a challenge (again, not news to Hirsch). So where’s the evidence that student writing ability declined over the time of the TSWE, which would be 1974-1994? Coupled with the evidence that writing ability has improved since the SAT has achieved “consequential validity”?

Next, Hirsch’s history ignores the ECAT/SAT II Writing test, which offers excellent research opportunities for the impact of consequential validity. Given that UC has required a test with an essay for 50 years, Hirsch’s reasoning implies that California students would have stronger writing curriculum and abilities, given that they faced an essay test. Moreover, any state university that wanted to improve its students’ writing ability could just have required the ECAT/SAT Writing test—yet I believe UC was the only public university system in the country with that requirement. For that matter, several states require all students to take the ACT, but not the essay. Perhaps someone could research whether Illinois and Colorado (ACT required) have a weaker writing curriculum than California.

Another research opportunity might involve a comparison between the College Board’s choices and those driving American College Testing, creator of the ACT and the SAT’s only competition. I could find no evidence that the ACT was subjected to the on-again, off-again travails of the College Board’s English/Writing essay/no essay test. Not once did the College Board point to the ACT and say to all those teachers demanding an essay test, “Hey, these guys don’t have an essay, so why pick on us?” The ACT, from what I can see, never got pressured to offer an essay. This suggests, again, that the reason for all the angst over the years came not from dissatisfaction with the TSWE, but rather the Achievement/SAT II essay test, and the College Board’s varying profit motives over the years.

Finally, Hirsch’s example also assumes that the College Board, universities, high school teachers, and everyone else in 2005 were thinking about consequential or construct validity in adding the essay. I offer again my two unsupported assertions: The College Board made its 1994 and 2005 changes for business reasons. The UC opposed the change in 1994 and demanded it in 2005 for ideological reasons, to satisfy one of its various identity groups. Want to argue with me? No problem. Find me some evidence that UC was interested in anything other than broadening its admissions demographic profile in the face of an affirmative action ban, and any evidence that the College Board made the 2005 changes for any other reason than placating UC. Otherwise, the cynic’s view wins.

On some later date, I’ll write up my objections to the notion that the essay test has anything to do with writing ability, but they pulled the focus so I yanked them from this post.

By the way, I have never once met a teacher, except me, who gives a damn about helping his or her students prepare for the SAT. Where are these teachers? Can we take a survey?

Every so often, I wonder why I spend hours looking up data to refute a fairly minor point that no one really cares about in the first place and yes, this is one of those times. But dammit, I want things like this to matter. I don’t question Hirsch’s goals and agree with most of them. But I am bothered by the simplification or complete erasure of history in testing, and Hirsch, of all people, should value content knowledge.

Yeah, I did say “brief”, didn’t I? Sorry.

Acquiring Content Knowledge without Hirsch’s Help

I don’t remember not knowing how to read. My mother tells me that she’d first thought I memorized certain Dr. Seuss stories, and it took her a while to figure out that I could read independently. I was 3.

My father’s IQ is probably less than 100, but not much. He has exceptional conversational fluency in languages; put him anywhere in the world and he’s exchanging stories with cab drivers and waiters in less than a week. He’s an equally fluent and improvisational musician. When he learns something it stays learned: he spent two hours explaining to nine-year-old me how airplanes flew and to this day, that’s the best explanation I’ve ever gotten. Ask him about any major plane crash that occurred before 2000 (the year he retired after 45 years in airline operations) and he can tell you exactly who was at fault, why, and what changes were made to reduce the risk of reoccurrence. Unlike my highly concrete father, my mother is a better abstract thinker. She mastered technology easily, moving from shorthand secretary to working with faxes and computers in the 70s and 80s,and moved up the ladder from temp secretary to executive secretary for bigwigs at a major technology company, to network support technician for her last few years when she got tired of secretarying. She has a somewhat higher IQ but none of the improvisational fluency of my dad; you can see this best in their individual approaches to cooking, at which they both excel. Dad never uses recipes, Mom rarely ventures off without a cookbook, both of them produce meals you’ll remember forever. Dad’s second wife got a college degree in her 30s and made the Dean’s list but works as a skilled technician in the same job she had before college; Mom’s second husband has two doctorates from a top ten university, spent his life in a high-octane brain job, but his real love is carpentry and gardening, which he did as a side business before and during retirement. Politically, Dad is a blue-collar Democrat, Mom a hippie-dippie liberal.

At no point did my blue-collar parents take any steps to develop my intellect, even though they were fully aware that I was at or near genius IQ. My mother refused to allow me to move up a year in school because she’d been advanced and didn’t like it. My parents could have sent me to Phillips Academy, all expenses paid; they decided not to. They saw no difference between my going one of the top public universities schools in the country and a local state college except cost, although they did think I should “major in business” (hey, it was the early 80s). I went for cost and in those days, that was a terrible call. In my twenties and thirties, I resented their decisions which seem inexplicable today. However, two master’s degrees at top-tier universities (which took up a lot of my 40s) have convinced me that the only thing I would have gotten from a better education is more amusing stories about how much trouble I caused the schools and how glad they were to get rid of me.

Anyway. Up to a few years ago, I said I was a book and TV lover. Now I know I’m just an obsessive who needs to keep a busy brain. Regardless, I consumed information reflexively as a result of keeping my brain busy. I grew up overseas with no TV, but when we came home for summers I was literally glued to the set. I watched game shows, Bonanza, Medical Center, SWAT, and Scooby Doo until age 10, when I discovered movies and stayed up late to watch whatever was on. (I discovered Star Trek reruns at 12).

TV-watching never interfered with my reading; I read 2-3 books a day (1000 WPM, clocked and reclocked), before, during, and after TV. On weekends during the year when I had no TV, I’d easily go through 5-7 books. I quickly read through the school library. No public library overseas and no English bookstores in that country, and I could only talk my parents into buying me five or six books at airport bookstores, which I ran through in a couple days. I read the back of cereal boxes and Clorox bottles, which was convenient when my baby brother appeared to have taken a swig from the jug. (Unfortunately, we lived in a place that didn’t have ready access to milk, the recommended remedy. But he survived.) My grandfather, bless his heart, used to send me a huge box of paperbacks, picked at random from the general and genre fiction section, which took me a bit longer to run through than books for kids my age—and they had far more interesting plots. So when I ran through Gramps’ gift, I turned to my parents’ books; I know everything there is to know about the works of John D. McDonald, Agatha Christie, and Dick Francis. Just ask me.

Some early reading memories:

  • The Middle Sister, age 5—odd little book, but I’ve found that many remember the plot, if not the story. One of my earliest memories of a “chapter” book; an older cousin was reading it. Most of my reading at this age were junior high basal readers that I stole from school. I hadn’t figured out I could read my parents’ books, and everything else I’d ripped through a year or more earlier, apparently.
  • The Trojan War,age 6: Not until years later did I learn that The Iliad didn’t have the Trojan Horse scene in it, but ended with Hector’s death. I found parts of the story confusing. Not the gods, I figured out what was going on, there; the gods had magical powers and subdivided areas of interest. (An agnostic from birth, best I can tell, I had no bias for or against polytheism. The Greek pantheon seemed an entirely reasonable way of explaining things. But then, I wasn’t entirely clear on the difference between God and Santa Claus.) No, what confused me was why all these battles seem to happen one at a time. What was everyone else doing while Hector was killing Patroclus or Achilles was killing Hector? How did the Greeks have time to discuss who got Achilles’ armor? Where were the Trojans while the Greeks were building the horse? I developed this confused idea of an arena, with the kings watching each scheduled battle—I must have seen a gladiator fight on TV. One thing I was clear on, though: everything was Paris’s fault.
  • King of the Wind, age 7–I am the opposite of artistic, but this image fascinated me. I read every Marguerite Henry book I could find, but I only enjoyed Justin Morgan Had a Horse and Born To Trot.
  • Madame, Will You Talk?, age 7—we were in an isolated European village, and I’d run through my dozen books. Desperate for something to occupy my brain, I picked up this romance-thriller when my mother had finished, thus meeting my earliest genre title. I didn’t quite understand the plot, which had something to do with Nazis and Jews and getting revenge for a Jew that was killed—apparently, Nazis killed Jews? I looked it up later when I got home; it may have been my first intro to WW2 and the Holocaust, although I can’t be sure. I suddenly understood a lot more of Hogan’s Heroes, though. I read Airs Above the Ground a year later, because it had a teenage boy in it and not as much love stuff. Mary Stewart, by the way, is still with us at 96. Holla!
  • David Copperfield, age 7—Suddenly Dora’s gone. David’s sad. What the hell happened to Dora? I had barely figured out what happened to Emily. Something dire with Steerforth. But where did Dora go? I had to read “Another Retrospective” three times before I realized that “Do I know, now, that my child-wife will soon leave me?” meant Dora was dying and when Agnes was sad, she’d died. Wow. Couldn’t you be more specific? I read fast, I miss things.

    Years later, I was quizzing my son on A Tale of Two Cities, which I hadn’t read, and asked him what happened to Madame Defarge. “I don’t know; she just disappears.” “Naw, that can’t be true. I’d have heard if she just disappeared.” So I leaf back through the book. “Oh, here it is. Miss Pross kills her.” “What? Miss Pross? No way? How’d I miss that?” “The bastard buried it in the middle of a paragraph, like he always does.” “That’s annoying.” “Tell me.” (My son’s ACT reading score: 36.)

  • The Black Stallion, age 7—This was the kind of stuff I was looking for when I read all those Marguerite Henry books! Unfortunately, he just kept writing about the same damn horse. But the first one is an awesome read. Still. I tried nibbling seaweed a few times, but ick.
  • Oliver Twist, age 8—I figured out that Nancy died. In fact, I think this was the first time I saw the word “corpse”. But how? He just hit her. You could die from people just hitting you? It didn’t take a gun or a knife? Or a car? Or jumping off a cliff like in Snow White?
  • The Happy Hooker, age 8 or 9—She didn’t seem very happy. But I wasn’t clear what a hooker was. When I figured out it was linked to prostitution, I looked that word up. Still not entirely clear. I had a vague idea that Nancy in Oliver Twist did something like that, but again, not happy. Hmmm.
  • The Quick Red Fox, also age 8 or 9, after The Happy Hooker—ah. Some women don’t charge, some women do. I wasn’t quite sure for what, but McDonald was actually much more informative on this point than the Hooker lady. I wasn’t sure which McGee thought was preferable, although he never seemed to pay.
  • Nerve and Enquiry, age 9—I read Dick Francis books from 1971 until 1999 or 2000; I think the last one I read was To The Hilt. I have fonder memories of him than any other writer, and not just because of his unreasonably perfect heroes (which made much more sense when I learned that his wife wrote most of his books), but because he was a living writer in my life for nearly 30 years. From these first two books, I learned that horseracing wasn’t just about who ran the fastest, but about “steeplechasing”, which involved jumping over fences and mud pools. With the horse. I also learned that marrying first cousins was a bad thing, and that jockeys were a lower “class” than trainers. But I wasn’t sure what “class” was. Not the school kind.
  • Cards on the Table, age 9—I’m reasonably certain this was my first Christie novel. Death on the Nile was second. I didn’t realize it was a bad idea to peek at the end until I was 12, and by then I’d read the entire Christie canon. All those endings, spoiled. But I learned more about this “class” thing, which also had something to do with “titles” (not books). I thought “class” complaints were restricted to the English until a distressingly short time ago. I also became familiar with a number of poisons and confirmed that yes, just getting hit on the head could kill you.

Not a complete list. I know I read Madeleine L’Engle and Laura Ingalls Wilder during these years, and all the Hardy Boys canon. (The Twisted Claw was the bomb.) I read Little Men at 7 or 8, and eventually Little Women. I also read a lot of history books and almanacs. And some really strange books that I can’t remember clearly which is extremely annoying. But these are the memories that seem relevant.

What’s my point? As I’ve mentioned before, my measured vocabulary has spiked hard to the right side of the bell curve, leaving the 99th percentile in the dust since I was first tested at 8. And my vocabulary is far weaker than my analytical reading skills. While I scored a 730 on the SAT (which at that time was 99+ percentile), I scored an 800 on the English Lit Achievement Test (known now as the SAT subject test), which even now is a rare achievement, and much less frequent back then.

And yet, as I hope this little tale has revealed, I did not live the life of a middle class child with that literacy-rich environment that gives children the background content knowledge. Or, based solely on my story, E. D. Hirsch has it wrong:

[Students learn new vocabulary] by guessing new meanings within the overall gist of what they are hearing or reading. And understanding the gist requires background knowledge. If a child reads that “annual floods left the Nile delta rich and fertile for farming,” he is less likely to intuit the meaning of the unfamiliar words “annual” and “fertile” if he is unfamiliar with Egypt, agriculture, river deltas and other such bits of background knowledge.

I am living proof that “understanding the gist” does not require background knowledge, that some people, like me, acquire content knowledge through the books that they read and TV that they watch. In fact, it’s clear that I, god save me, constructed my knowledge of the world through the books that I read. If you were to go by me, the progressives have it exactly right—teach them to read, and knowledge will follow. But you know, progressives are never right about their idealism, so let’s laugh off that possibility and return to Hirsch, who is right, but for the wrong reason.

Hirsch isn’t the only one emphasizing the importance of specific instruction in content knowledge because of poor environment. Lately, advocates on all sides of the debate have been focused on Hirsch’s argument (aka the Core Knowledge solution) “knowledge-rich” environment of the middle class and higher kids, the “language deficient” environment of low income kids, and how the latter group is starting behind.

One might think that these guys think academic achievement is purely a matter of environment, that individual ability has nothing to do with it.

But then, this essay is long enough. More later.

Update: One of the more idiotic commenters I’ve ever run into on this site argues that what I describe is a typical, middle class knowledge-rich environment. Sigh. I called her an idiot. But I’ll update with a bit more information, just in case there’s other zealots who think they’ve got a point.

My reading was considered incredibly weird by everyone who knew me. I was teased constantly. I was “grounded” by losing access to any reading material; my father once upset me terribly by pretending to throw my book out the window of a Greek hotel room when I wasn’t in bed by 10:00. (He hadn’t, but he didn’t let me have it back for a day.) My parents did not have a lot of books, they bought books to read on planes when four kids allowed them the time. They did not read otherwise, but (like me) rarely threw things away, so there were ten years of books lying around the house. The Dickens books were from the library. I was far better-informed than my parents were in a distressing number of subjects, but granted them total expertise on cooking, music, sports, and airplanes—and would accept their knowledge of current and recent events as somewhat reliable but needing confirmation. I was, undoubtedly, incredibly annoying.

As for the traveling, we travelled on passes as an employee benefit. My parents were, and are, extremely adventurous (particularly my mother, who just came back from a month in South Africa). We traveled everywhere and saw everything on the cheap. I hated it a lot of the time, although I’m glad now I did it. I did not gain any content knowledge from the travel, although I learned flexibility and patience.

2012 in review

In October, I reached 100 posts, which is a lot for a slow writer, so I did a summary of my work thus far. I had 37,000 views in October; by year end, I had 67000. Calculated on a purely monthly basis, my blog has 5628 views per month. However, it’s clear that things took off in June, which is when I created a Twitter account. June through December accounts for 60,000 of my 67,000 page views, or 8627 views per month. I did not achieve this by writing more posts; as you can see by my calendar archive at the bottom I wrote 25 posts in January, 13 posts in February, and 10 or less every subsequent month, so I apparently grew my audience. So I thought I’d do a retrospective; maybe new readers would find something that interested them.

Page views by month:


Rather than list posts by viewership, I thought I’d look into the numbers by month, as it’s obvious I started off big, then faded back, then hit my stride over the summer, which I connect to Twitter but may be caused by something else.


  1. The Gap in the GRE, currently 8th in my overall list, has actually gotten more views over time than in its original posting. Steve Sailer discussed it in June, and it’s getting more interest over time. As a 99.999% verbal performer, I’m proud to have increased awareness of that gap.
  2. Teacher Quality Pseudofacts, Part II. This article was responsible for most of the atypically high activity in January and is third on my overall list. Google “teacher SAT scores” and the search returns my article on the first page. I can’t count the number of times I’ve been reading a blog on an entirely unrelated subject and seen commenter A sneer about crappy teacher SAT scores, and commenter B slam back with a link to this article. This is a high information value post that gets used a lot. Deeply satisfying. Eat that, Biggs and Richwine.
  3. Another post that gets a lot of attention, relative to what I expected, is Modeling Linear Equations. Google “linear equations modeling” and it comes up on the first page, and is 13th overall in page views. Teachers use this post as a direct homework assignment or as an example, and its usage has also increased over time.
  4. Oh, yeah, I explained the Voldemort View, a phrase I borrow from an anonymous teacher.


  1. Another sleeper post, Homework and Grades. Joanne Jacobs linked it in, giving it the first boost, but it’s been a big performer over time, and is the seventh most read post.
  2. I think my unit on Twelfth Night has some great ideas.
  3. I also introduced the lurker in the teacher quality debate—namely, race. I’ve returned to this several times with my Mumford posts.

March, April, and May

These were all very slow months, primarily because I didn’t take on hot topics and talked mostly about teaching. No big posts, but I’m very happy with the method outlined in Teaching Trig, and thought this post on induction and its crappiness was good. My History of Elizabethan Theater I, II, and III are worth a read, too. I only wrote 4 posts in May, because I was focusing on a piece I wrote under my own name, but this piece is a lot of fun: Teaching Algebra, or Banging Your Head With a Whiteboard.


  1. Why Chris Hayes Fails got a big immediate reaction, winning links from both Steve Sailer and Razib Khan, and is currently #5 on my overall. This post, too, gets a lot of repeat links because of its disconcerting evidence in two big areas: a) blacks and Hispanics are more likely to get test prep than whites, and b) wealthy blacks score lower than poor whites on the SAT, something I return to often.

  2. What’s the difference between the SAT and the ACT—The difference between these tests will, at some point or another, become relevant to your life, and I’m one of maybe fifty people in the country (and that’s being generous) who have spent a decade prepping wealthy, middle class, and poor kids of all races on both the SAT and the ACT. Please keep it in mind.
  3. Difference between tech and teacher hiring . I’m fifty. It’s frigging brutal, getting hired as a teacher. If you know anyone planning on becoming a second career teacher, send them this link to discourage them from spending a lot of money on the effort.
  4. The problem with fraudulent grades: For seven years, I’ve taught an ACT class to low income, black and Hispanic students, and seen the profound differences in GPA, course transcript and demonstrated ability based on whether or not they went to a charter school or comprehensive high school. My contempt for GPA and AP for all is close to boundless because of my experience.

July was my first huge month, nearly double June, and 60% of January through June combined. I found it intimidating, frankly.

  1. The myth of “they weren’t ever taught”–probably my single favorite post, an effort to explain to non-teachers what it is like to teach a demanding cognitive subject to low to mid-ability kids. Razib Khan and many others linked this in; thanks for the attention!
  2. Google Clarence Mumford and my original post is still on the first page as of today. In August, it was third. This story was completely ignored for four months, in my opinion because it points the way to what will certainly occur (and has occurred) if teacher content knowledge requirements are raised.
  3. The False God of Elementary Test Scores–another idea I return to frequently. Many believe that raising elementary test scores and achievement will lead to stronger high school achievement. No evidence of that, folks.


  1. #1 on the most read list: Algebra and the Pointlessness of the Whole Damn Thing, my “curating”, as it’s called today, of the argument set off by Andrew Hacker. I didn’t take a position but rather explained why everyone else was wrong.
  2. SAT Prep for the ultra-rich and everyone else—another very useful useful primer on test prep.
  3. Why Chris Christie picks on teachers—for that matter, why eduformers pick on teachers and leave cops and firefighters alone. Is it completely a coincidence that teachers are mostly white women and the other two are primarily white men?

A relatively light month, but with a number of pieces I’m happy with.

  1. The Fallacy at the Heart of All Reform—this piece has never gotten all that much attention. Basic idea: both progressives and “reformers” have been pushing legislation onto schools without any research supporting their objectives. Useful overview of education legislation over the past 40 years.
  2. On the CTU Strike—another piece I like a great deal, suggesting why reformers might be failing so spectacularly at winning the hearts and minds of the public.
  3. The Sinister Assumption Fueling KIPP Skeptics—Stuart Buck throws out what he assumes is a gotcha, and I amiably agree.


  1. Escaping Poverty—what advice do you give a 15 year old who wants to get out of poverty? In a little over a month, it achieved second place on my most read list.

  2. Boaler’s Bias—it was opinions like these that made my life at ed school difficult.
  3. Teaching Students with Utilitarian Spectacles—Every so often, I take a piece of academic writing and show what it means when working with a student at ground level. This is one of my favorites; thanks to Joanne Jacobs for discussing it.
  4. Best Movie About Teaching. Ever.–I like writing about movies.


  1. Parental Diversity Dilemma—jumped to six on my overall list. I’m pretty hard on Mike Petrilli, the parents pretending they want diversity, and charter advocates. All in all, a good day’s work. John Derbyshire included me on his dark enlightenment reading list, as did Steve Sailer
  2. More on Mumford—finally, the media noticed the Clarence Mumford story, and I slam down hard on the education pundits who scoff at the “stupid” people who can’t pass the Praxis without cheating.
  3. The End of Pi—Like Twelfth Night, a rare post when I talk about teaching literature.
  4. Algebra Terrors—in which I discuss the PTSD I suffer from teaching all algebra, all the time.


  1. Alternative College Admissions System–#9 on my most read list, an answer to Ron Unz’s controversial article about the myth of american meritocracy
  2. Fake Grades and Big Money–I use KIPP data to show why I think grades are useless, and why KIPP pledges are so problematic.
  3. Push the Right Buttons—another student anecdote that I’m very fond of.
  4. Those who can, teach. Those who can’t, wonk—useful if you want to know the teaching history of most major eduwonks. Answer: not very much.
  5. Diversity Dilemma in Action—Obligingly, the Rancho Elementary School in Novato comes forth to prove why I have such a low opinion of Mike Petrilli’s new book.

So there’s my year. Thanks for reading!