Tag Archives: reform math

Group Work vs. Working In Groups

I sit my kids in groups. But I don’t like “group work”.

No, that’s not a paradox. Sitting in groups isn’t “group work”.

Group work is an activity that falls under the larger rubric of “collaborative learning”, an organizing bubble to collect techniques and strategies like “Think Pair Share”, jigsawing, peer tutoring, and the like. The most fully-realized collaborative learning pedagogy is probably complex instruction, which was developed by Elizabeth Cohen. (That’s CI, not CISC.) To illustrate, CPM curriculum is based on complex instruction, whereas Everyday Math is not.

Complex Instruction had been in development for over 20 years, by the time it caught on  in the early 90s. Jeannie Oakes’ book Keeping Track, a broadside against any sort of ability grouping.  Oakes accused parents and schools of racial discrimination, an argument that found favor with many schools and teachers. Those schools that weren’t favorable to the argument faced lawsuits or the threat of one. A good chunk of the 90s was wasted as districts and states desperately tried to win her approval, and adopting the CI method was often adopted as the strategy. Fortunately, they all ultimately learned it was easier to disappoint her.1

Complex Instruction was also developed by tracking opponents, but opponents who nonetheless cared about learning. It’s explicitly designed to give schools a tool for the havoc that results when kids with a 3 to 8 year range in abilities are put in the same room, and thus was grabbed at by many schools back in the early 90s. Many CI concepts are also found in “reform math”—Jo Boaler’s Railside study on San Lorenzo High School was all about Complex Instruction. Carlos Cabana and Estelle Woodbury, who just co-authored Mathematics for Equity, a book on teaching math with Complex Instruction, both worked at San Lorenzo High School during Boaler’s study.

So start with the theory, articulated here by Rachel Lotan, the late Cohen’s key associate. You should watch this, or at least fast forward through parts, because Lotan clearly articulates the admirable goals of complex instruction minus the castigation, blame, and fuming ideology. Or, Complex Instruction’s major components in written form:

ci3components

Both Lotan and the writeup offer much that is problematic. Reducing the ability range: not good. Creating busywork tasks (writing down questions, getting supplies) to let everyone feel “smart”: not good.

The write up mentions “status problems”. Lotan gives a great account of an absurdly pretentious term, “mitigating status” that is something every teacher in every classroom–no matter how they are seated—should take seriously. Lotan does a better job of explaining it, but since many won’t listen to the video, here’s a written version:

CI targets equity and, in particular, three ideas: first, that all students are smart; second, that issues of status—who is perceived as smart and who is not—interfere with students’ participation and learning; and third, that it is teachers’ responsibility to provide all students with opportunities to reveal how they are smart and develop/recognize new ways of being smart. The complex instruction model aims to “disrupt typical hierarchies of who is ‘smart’ and who is not” (Sapon-Shevin, 2004) by promoting equal status interactions amongst students so that they engage with tasks that have high cognitive demand within a cooperative learning environment.

(emphasis mine)

Ed schools wanting to hammer home how putting kids in groups doesn’t by itself address status usually show this video, but brace yourself. I tell myself that the ignored kid is probably a pest all the time, that everyone in the class is tired of his nonsense, that we’re just seeing a carefully culled selection to maximize the impact of exclusion and of course, race. It doesn’t matter. It’s still hard to watch.

And the video also reinforces the practical message that CI advocates are pushing, as opposed to the theory. In theory, status can be unearned by anyone of any gender or color. In practice, most CI advocates expect teachers to shut down white males. In theory, kids learn that everyone is smart. In practice, kids still know who’s “smart” and who’s not.

But then, CI advocates have their own frustrations. In theory, they’d put teachers in PD designed to indoctrinate them into realizing the error of their racist ways. In practice, teachers who haven’t already drunk the Koolaid either politely fake it until they can find an exit or get really annoyed when they’re called racists, as an excerpt for Mathematics for Equity makes clear:

CIPurpose
Cite: Mathematics for Equity1

Complex Instruction done well is pretty interesting and often thought-provoking. Cathy Humphreys is a long-time advocate of “reform math” and complex instruction. She was at the center of one of those “rich educated parents” meltdowns that you saw over reform math back in the 90s. Humphreys represented the reform side, of course, and further endeared herself to parents by proposing to get rid of tracking at a Palo Alto, CA middle school. That went over like a water balloon down a balcony, she quit, worked as a math coach for a while, and then taught for years at a diverse high school in the Bay Area that had ended tracking. She also teaches at Stanford’s education program, according to her bio. Carlos Cabana, one of the co-authors of Mathematics for Equity, has also been teaching complex instruction for a long time; he’s one of the teachers at Railside, Jo Boaler’s pseudonym for San Lorenzo High School.

You can see both Humphreys and Cabana here at a website put together by the Noyce Foundation to promote the 8 essential practices. (Notice the link between “reform math” and supporting “common core”? As Tom Loveless says, Common Core is a “dog whistle” for reform math. Humphreys and Cabana are teaching high school math in the videos. You can also see Humphreys teaching at what I assume is the middle school that melted down. Humphreys and Cabana are much better demonstrations of complex instruction than the absurdly flashy promos that Jo Boaler puts out.

When I began teaching, I thought sitting kids in groups was absurd. I remember being pleased one of my mentoring teachers put kids in rows. But my primary student teaching assignment required me to sit kids in groups, as we were using CPM, a reform text that requires groups. I adjusted and liked it much more than I thought I would, especially when I took over the class and could group by ability. But my first year out, I happily put my desks in rows, thinking that groups were good, but now I could finally run my class the way I wanted.

Four weeks later, I put the kids in groups. It just….felt better. Year 2, I was teaching all-algebra, all the time, and thought rows would make more sense. The rows lasted 2 weeks and since around September of 2010, the only time my kids sit in rows is for tests.

I have….mixed feelings about CI. When promoted by the fanatic adherents, it’s both Orwellian and despicable. Teachers have to squelch kids who know the answer, force kids who understand the concept to explain, endlessly, to the kids who don’t, and then grade the kids who know the answer not on their demonstrated knowledge but on the success of their explanation and their willingness to do so. Teachers have to pretend to their students that asking a good question or taking notes is just as important as understanding the math (no, say the fanatic adherents, teachers aren’t pretending. These tasks are just as important!).

But while no student is ever going to believe that everyone is smart, “issues of status” do absolutely impact a students’ willingness to participate. Let the “smart kids” talk, everyone thinks, and sits back and zones out.

However, in my opinion and experience, CI methods often achieve exactly what they are defined to avoid, precisely because of their Orwellian insistence on ignoring reality. Kids know who is smart. They shut down if the smart kid is in their group, and go through the motions when the teacher walks by.

Ironically, I “mitigate status” by violating Complex Instruction’s most sacred tenet. Complex Instruction holds that student groups must be heterogeneous. Organization can’t be based on the rigid, academic version of “smart”. But I group my kids by ability as the most effective way of “mitigating status”.

I don’t want the weakest students in my class feeling as if any success short of an “A” is irrelevant. I also don’t want to try and convince them they’re just as “smart” as students who don’t struggle with the same material. That way, my students know that they can talk about math, what they need to know, what questions they have, knowing that other students probably have similar issues.

I don’t want to make it sound as if “mitigating status” is the only reason I sit kids in groups. Groups allow me to differentiate tasks slightly (or extensively) and enables me to quickly give help or new tasks. Groups allow kids to work together, discussing math, developing at their own speed with peers who have similar abilities.

But whether it’s status or some other curricular reason, when I sit them in groups, they start working and talking about math. They discover they are working with peers who won’t make them feel stupid, and they start to have discussions. Should we do this or this? They call me over to adjudicate. They try things. They check their notes, engage in all those excellent student behaviors. Not always, of course. But many times. They are less likely to sit passively and wait until I come by to personally tutor them through problems.

Moreover, because they are working with students of their own ability, they don’t feel alone or stupid. They work to improve. Maybe not great, maybe not good. But better.

Sitting kids in groups is not group work. But sitting kids in groups based on ability and giving them achievable tasks makes them more likely to work, and as math teachers often know, that’s no small thing.

******************************************
1 I was thinking crap, I don’t want to have to look up the whole history of the ebb and flow of tracking and then went hey, Tom Loveless has to have something on this and by golly he does: The Resurgence of Ability Grouping and Persistence of Tracking covers the whole era, Oakes included. I would only quibble slightly with this sentence: Although the call to detrack was not accompanied by conventional incentives—the big budgets, regulatory regimes, and rewards and sanctions that draw the attention of policy analysts—detracking was, in a field famous for ignored or subverted policies, adopted by a large number of schools.

Loveless appears to forget the biggest incentive of all: lawsuit avoidance. Detracking lawsuits were the rage in this time period. Unlike new curriculum or teaching styles, detracking is achieved by executive fiat by district superintendents. No training, no carrots needed. Shazam! But leaving aside that minor quibble, a great piece documenting the move to and then the move away from heterogeneous classrooms (de-tracked).


Teaching Math a Third Way

I was reading Harry Webb’s advice to a new secondary teacher, describing his usual classroom procedure for “senior maths”, as an addendum to his earlier post on classroom management. And I thought hey, I could use this to fully demonstrate the difference in math instruction philosophies.

Harry’s lesson is a starting activity, a classroom discussion/lecture, and classwork.

So here’s what I did on Friday for a trig class, which is certainly “senior maths”: brief classroom discussion, class activity (what Harry would call “group work”), brief classroom discussion. And I think it’s worth showing that difference.

The kids walked in, sat in assigned seats grouped in fours—strong kids in back, weakest in front. I often forget and start before the tardy bell, just laying out what we’ll do that day. I never check homework—the kids take pictures and send it to me, and I eventually get it into the gradebook. I don’t really care if kids do homework or not. They take pictures of it and text or email me. I eventually check. If kids have homework questions, they’re to let me know during the tardy pause and I’ll review them on an as-needed basis. But yesterday, the kids hadn’t had homework, so not an issue.

When the tardy bell rang, I had just finished sketching this:

simrev

(this next bit is what I think Harry would call classroom discussion):

“Can anyone tell me the relationship these triangles have?”

I got a good, solid chorus of “similar” from the room—not everyone, but more than a smattering. I picked on Patti, up front, and asked her to explain her answer.

“They have two congruent angles.”

“Good. Dennis, why do I only need to know about two of the angles?”

Dennis did the wait out game, but I’m better. After a while, he said, “I don’t know.”

“Do you know how many degrees are in a triangle?”

“180. Oh. OK. If they add up to 180, and two of them are equal, the third one has to be the same amount to get to 180.”

“See, you did know. Jeb, if two triangles are similar, what else do I know?”

Jeb, in the back corner, said “The sides have a constant ratio.”

“More completely, the corresponding sides of the triangle have a constant ratio. Good. How many people remember this from geometry?” All the hands are up. “If you had me for geometry, and about eight of you did, you may even remember me saying that in high school math, similarity is much more important than congruence, for high school math, anyway. Trigonometry will prove me right once again. So while I hand out the activity, everyone work the problem.”

When I got back up front, I confirmed everyone knew how to solve that, then I went on to this:
Simreview2

“I don’t want everyone to answer right away, okay? I’ll call on someone. Give people a chance to think. Which one of these variables can be solved without a proportion? Olin?”

Olin, very cautiously: “x?”

“Because…”

“I can just…see what I add to 8 to get 12?”

“Right. Now, that probably seems painfully obvious, but I want to emphasize—always look at the sketch to see what you know. Don’t assume all variables take some massive equation and brain work. Now, how can I find the length of the other side? Alex?”

“I’m just trying to figure that out.”

“You’re assuming the triangles are similar? Can she do that, Jamie?”

“Yes, because the lines are parallel.”

“Hey, great. Why does that help, Mickey?”

“I don’t know.”

“Cast your mind back to geometry. Which you took with me, Mickey, so don’t make me look bad. What did we know about parallel lines and transversals?”

“Oh. Oh, okay. Yeah. the left angles are congruent to each other, and the right ones, too.”

“Because….”

“Corresponding angles,” said Andy. I marked them in.

“Okay. So back to Alex. Got an equation yet?”

“I don’t know what I should match with what.”

“Okay. So this, guys, is the challenge of proportions. What will give me the common ratio that Jeb mentioned? I need a valid relationship. It can be two parts of the same shape, or corresponding parts from different shapes. Valicia?”

“Can I match up 8 and 6?”

“Can she?”

“Yes,” said Ali. “They are corresponding. But we don’t know what the short leg is.”

“We don’t need to,” says Patti. “6 over 8 is equal to y over 12.”

After finishing up on that problem, I turned to the handout.

GMhandout1

“I stole this group of common similar triangle configurations, just as a way to remember when they might show up. But we’re going to focus on the sixth configuration. Can anyone tell me what’s distinctive about it?”

“It’s a right triangle with an altitude drawn,” offered Hank.

“True. Anything unusual?”

“No. All triangles have altitudes.” He looked momentarily doubtful. “Don’t they?”

“They do. So take a look at this” and I draw a right triangle in “upright” position. “Where do I draw an altitude?”

“You don’t need to….Oh!” I hear talking from all points in the room, and pick someone up front. “Oscar?”

“That’s the altitude,” he points. I wait. “The—not the hypotenuse.”

“Melissa? Can you give me a pattern?”

Melissa, in back, quite bright but never volunteers. “If the leg is a base, then a leg is the altitude.”

“True for all triangles?”

“No. Just for rights. Because the legs are perpendicular.”

“Right. So back to Oscar, what’s different about this?”

“The hypotenuse is the base.”

“Right. So it turns out that the altitude to the hypotenuse of a right triangle is….interesting. Turn over the handout.”

The above conversation, which takes a while to write out, took about 15 minutes, give or take. I would expect Harry Webb has similar stories.

The next part of my lesson is the “group work” that Harry and other traditionalist think leads to “social loafing” and wasted time.

gmhandout2

The kids are in ability groups of four; they go to whiteboards spaced all around the room: two 5X10s, 3 4x4s, and self-stick on bulletin boards that works great—I even have graphs attached.

And I just give them instructions and say, “Go.”

Is this discovery math? Hell, no. I give them all sorts of instructions. I don’t want open-ended exploration. What I want for them is to do for themselves and understand what I would have otherwise explained.

In the next 50 minutes, using my instructions, each group had identified the three triangles:

3trianglesgm

There’s always a surprise. In this case, more of the kids had trouble proving the similarity (that is, all angles were congruent) than with the geometric mean. I actually stopped the activity between steps 1 and 2 to ensure everyone understood that the altitude creates two acute angles congruent to the original two–which I frankly think is pretty awesome.

rtwanglesmarked

Even before they’d quite figured out the point of the angles, they’d gotten the ratios:

gmratios

Each of the nine groups found the second step, proving the altitude (h) is the geometric mean of the segments (x & y) on their own; I confirmed with each group. Once they’d established that, I reminded them that the third step was to prove the Pythagorean theorem and to look for algebra that would get them there. Four of the groups had identified the essential ratios, identifying that a2 = xc and b2 = yc.

At that point, I brought it back “up front” and finished the proof, which requires three non-obvious steps.

a2 + b2 = xc + yc (reminding them about adding equations)

Then I waited a bit, because I wanted to see if the stronger kids pick up on the next step.

“Just think, a minute. Remember back in algebra II, when you were solving for inverses.”

“…Factor?” says Andy.

“Oh, I see it,” Melissa. “factor out the c.”

“Right. So then we have a2 + b2 = c(x+y)”

“Holy sh**.” from Mickey.

“Watch the language.”

“That is so cool.” says Ronnie, who is UP FRONT!

“if you don’t know what they’re saying, everyone, look at the diagram and tell me what x+y is equal to.”

And then there were a lot of “Holy sh*–crap” as the kids got it. Fun day.

I wrapped it up by reminding them that we were just doing some preliminary work getting warmed up to enter trig, but that they want to remember some key facts about the geometric mean, the altitude to the hypotenuse of a right triangle. Then I go into my spiel on the essential nature of triangles and we’re all done. Homework: Kuta Software worksheet on similar right triangles, just to give them some practice.

This lesson would rarely be included in a typical trig class, whether reform or traditional. I described the thinking that led to the sequence. But it’s a good example of what I do. (Also, as many bloggers have pointed out, my attention to detail is dismal, both in blogging about math and teaching it. Kids usually pick up on stuff I miss, and if it’s something big, I go back and cover it.)

I vary this up. Sometimes I go straight to an activity they do in groups (Negative 16s and Exponential Functions), other times I do a brief classroom discussion/lecture first (modeling linear equations and inequalities). Sometimes I have an all practice day or two—I’ve covered a lot of material, now it’s time to work problems and gain fluency (that’s when the tunes come out).

I originally had more but somehow the length got away from me, so I’ve chopped this down.

I have developed this method because I was never happy with traditional math, whether lecture or class discussion. The difference is not solely about the method of delivery; my method requires more time, and thus the pace is considerably slower.

The jury’s in on reform math: it doesn’t work well in the best of cases, and is devastatingly damaging to low ability kids. Paul Bruno refers to reform math as the pedagogy of privilege, and I agree. But it’s worth remembering that reform math evolved as a means of helping poor and black/Hispanic kids. Why? Because they weren’t interested in traditional math methods, and were failing in droves.

Ideally, we would stop forcing all kids into advanced math. But since that’s not an option, I think we need to do better than the carnage of high school math as we see it today: high failure rates, kids forced to repeat classes two or three times Given the ridiculous expectations, traditional math is due for some scrutiny, particularly in its ability to leave behind kids without the interest or high ability to carry them through. Let’s accept that most kids can’t really master advanced math. We can still do better. This is how I try for “better”.

I still have problems with students forgetting the material. I still teach kids who aren’t cognitively able to master higher level math. I’m not pretending the problems go away. But the students are willing to try. They don’t feel hopeless. They aren’t bored. I don’t often get the “what will we use this for” question—not because my math is more practical, but because the students aren’t looking for an argument. (And when they do give me the question, I tell them they won’t. Use it.) However, as I mentioned in the last post, I now have had students two or three years in a row. They were able to pass subsequent classes with different teachers, but they haven’t lost the ability to launch into an activity and work it, having faith that I’m not wasting their time. That tells me I’m not doing harm, anyway.


Math Instruction Philosophies: Instructivist and Constructivist

Harry Webb has been on a tear about discovery vs. traditional explanations. The hubbub has pulled the great god Grant Wiggins, originator of backward design, which is a bible of ed schools as a method for developing curriculum.

Now, let us pause, a brief segue, to reflect on those last two words. Developing curriculum. I’m talking about teachers, yes? Teachers, building their own unit lessons, their own tests, their own worksheets. As I’ve written, teachers develop their own curriculum and, to varying degrees, have intellectual property rights (I would argue) to their material. So when reformers, unions, politicians, or whoever stress the importance of curriculum, textbooks, and professional development in implementing Common Core, there’s a whole bunch of teachers nationwide snorfling at them.

So Wiggins and Jay McTighe wrote Understanding by Design, which describes their framework and approach to curriculum. It is, as I said, a bible of ed schools. I have a copy. It’s good, although you have to look past their irritating examples to figure that out.

(Note: See Grant Wiggins’ response below. I’ve reworded this slightly and separated it to respond to his concerns. Also throughout, I changed “direct instruction” to some other term, usually instructivism.)

The book clearly states that there’s no one correct approach for every situation, that arguing between instructivism and constructivism creates a false dichotomy. So I was jokingly sarcastic before, but my point is real: it’s hard to read Grant Wiggins and not think that, so far as K-12 curriculum goes, he leans heavily towards constructivist. As one example, in a text section that discusses the fact that there’s no one right approach, he includes this table on the activities dominant in each approach. When I look at this table, I see a clear preference for constructivist approaches. I also see it in this highly influential essay and much of his writing. But as Wiggins states in the comments, and in the book, he clearly denies this preference. However, Wiggins’ book is the bible of ed schools for a reason, and it’s not for its categoric embrace of all things instructivist. So put it this way: what he says are his preferences and what any instructivist would take away from his preferences are probably not the same thing. I say this as someone who periodically rereads his work because of the value I find in it once I shift my focus away from the trappings and focus in on the substance. I encourage anyone who agrees with my impression of Wiggins’ preference to read him closely, because he’s done a lot over time to inform my approach to curriculum development.

(end major edits–I put the original text at the bottom)

So Wiggins reads all this hooha, and comes out with this outstanding description of lectures and why they are a problem. I agreed with every word of this post (there are two others), so much so that I tweeted on it. (Note: I agree for math. History’s a different issue.) As I did so, I was vaguely disturbed, because look, while I don’t write a lot about ed school per se (and even defend it, slightly), I spent a lot of time in class naysaying. And if they’d been saying reasonable things like this about lectures, what had I been disagreeing about?

And then Harry comes through brilliantly, answering my question and pointing out a huge hole in Wiggins’ 3-part series:

Wiggins writes of a survey of teachers in order to support his view that different pedagogies are required to achieve different aims. Unsurprisingly, the teachers give the right answers; the ones that they probably learnt at Ed School. However, the survey response that is taken to represent lecturing is called, “DIRECT TEACHING Instruction on the knowledge and skills.” Now, although I do not recognise my practice in Wiggins’ definition of lecturing, I do recognise myself in this definition wholeheartedly. And so I think we are being invited here to see all direct teaching – dare I say direct instruction – as non-interactive lecturing that lasts for most of a period.

Hey. Yeah. That’s right! Wiggins naysays the lecture in his essay, but the overall debate is between instructivism, of which lectures are just a part, and it’s , and it’s instructivism that has a bad name in ed school, not solely lectures. Harry says that he explains in classroom discussion, but rarely lectures. Which may sound like someone else.

Harry scoots right by this, because he’s all obsessed about the fuzzy math and constructivist debate, and it occurred to me that this area needs elucidation, because most people—and reporters, I am looking at you—don’t understand this difference.

So here it is: not all explanation is lecture, and not all discovery is constructivist.

In an effort to not turn all my posts into massive tomes (don’t laugh), I’m going to write about this difference later. Here, I’m just going to show you the difference through different teachers.

Before I start: labels are hard. Roughly, the terms reform, student-centered, constructivist, “facilitative” (Grant Wiggins’ term) all refer to the open-ended investigative approach. Instructivist, teacher-centered, traditionalist, direct instruction are all terms used to describe the approach where the teacher either tells you how to do it or wants you to figure out the way (not a way) to do it. (Note: I left “direct instruction” in here, because I believe it’s still an instructivist approach.)

Very few math teachers are pure constructivist. We’re talking degrees. I have no data on usage rates, but I’d be pretty surprised if 80% of all high school math teachers didn’t use traditional instruction-based approach for 90% of their lessons. I speak to a lot of colleagues who dislike pure lecture and would like to teach a more modified instructivist mode, but they aren’t sure how it works. However, most high school math teachers are instructivists who lecture. Full stop.

Constructivist Approach (aka investigation, reform)

Dan Meyer: Dan Meyer’s 3-Act Meatballs
Fawn Nguyen: Barbie Bungee
Fawn Nguyen Vroom Vroom
Michael Pershan: Triangles and Angles (he calls this investigation. I’d personally characterize it as “in between”, but it’s his call.)
Cathy Humphries: Investigation into Quadrilaterals

This is a partial list. Dan’s blog has links to all his various projects, as well as other bloggers committed to the investigative approach.

(By the way, I am dying to do the Vroom Vroom one, but I’m not enough of a mathematician to understand the math behind it. Neither does Fawn, apparently. The math looks quadratic. Is it?)

I’m not a fan of the open-ended reform approach, but I like all sorts of the activities the constructivists come up with. I just modify them to be more instructivist.

Remember that both Meyer and Nguyen use worksheets, practice skills, and many other elements that are pure instructivist. Pershan rarely does open-ended activities. In contrast, Cathy Humphries is very close to pure constructivist math. Total commitment to reform.

Traditional Instructivism (Lectures)

Much MUCH harder to find traditionalists bloggers. I’ve included two of my “lectures” that have relatively little discussion, just to fill out the list:

Me: Geometry: Starting Off
Me: Binomial Multiplication and Factoring with the Rectangle

Dave at MathEquality is traditionalist, a guy who works hard to explain math conceptually, but does so for the most part in lecture form. However, it’s also clear he keeps the lectures fairly short and gives his students lots of in class time for work.

But he’s the only one I can find. Right on the Left Coast appears to be a traditionalist, but he writes more about policy and his disagreement with traditional union views. (Huh, I should have mentioned him in my teacher blogger writeup of a while back.)

In order to give the uninitiated a good idea of what lecture looks like, three google searches are informative:

factoring trinomials power point

holt math power point

McDougall Litell math power point

Many high school teachers build their own power point explanations. Others just take the ones provided by publishers.

Still others use a document camera or, if they’re extremely old-school, transparencies.

What they look like is mostly this:

Khan Academy: Isosceles Right Triangles

Many teachers are really, really irritated at the fuss over Khan Academy because all he does is lecture his explanations—and not very well at that.

The most vigorous voices for traditional direct instruction comes from people who don’t teach high school math. That’s not a dig, it’s just a fact.

Modified instructivist

I’m not sure what to call it. There’s not just one way to depart from instructivist or constructivist. The examples here generally fall into two categories: highly structured instructivist discovery, and classroom discussions with lots of student involvement.

Me:Modeling Linear Equations
Me: Modeling Exponential Growth/Decay
Michael Pershan: Proof with Little Kids
Michael Pershan: Introducing Polar Coordinates
Michael Pershan: The 10K Chart
Ben Orlin: …999…. and the Debate that Repeats Forever.
Ben Orlin: Permutations and combinations

For a complete list of my work, check out the encyclopedia page on teaching. I likewise recommend Pershan and Orlin’s blogs.

A question for Grant Wiggins, and anyone else interested: what differences do you see in these approaches?

A question for reporters: when you write about reform or traditional math, do you have a clear idea of what the fuss is about? And did these examples help?

Question for Harry Webb: You sucked me into this, dammit. Satisfied?

If you have good examples of math instruction that falls into one of these categories, or want to propose it, tweet or add it to the comments. I’m going to write up my own characterizations of this later. Hopefully not much later.

*******

Here’s what I originally said in the changed paragraph:

So Wiggins and Jay McTighe wrote Understanding by Design, which describes their framework and approach to curriculum. It is, as I said, a bible of ed schools. I have a copy. It’s good, although you have to look past their irritating examples to figure that out. The book clearly states that there’s no one right answer, that arguing between direction instruction or constructivism creates a false dichotomy, but then there’s this table on the activities dominant in each approach. Cough. Okay, no one right answer, but a strong preference for facilitative/constructivist.


Dan Meyer and the Gatekeepers

I have at least one more post on reform math, but I got distracted while looking for examples of Dan Meyer’s teaching (as an example of his math in action) then realizing that many of my regular readers wouldn’t know Dan Meyer, and so started to construct a brief bio. In doing so, I got distracted again in considering Meyer’s quick-yeast rise and what it says about the gatekeepers in the education racket and access to microphones.

This may seem like insider baseball, but I hope to illustrate that Dan Meyer is an unobjectionable guy with a good idea, whose unhesitating adoption by the elites represents a real problem with educational discourse in this country. I will probably overstate and paint a picture that suggests plan and intent by those causing the trouble, when in fact it’s fuzzy and reactive with only big picture general directions, but probably not to the extent that Diane Ravitch (or, indeed, Dan Meyer) commit that particular sin.

Dan Meyer, 31, is in the process of becoming a celebrity math teacher (hey, it’s a small group). Much of his rapid trajectory upward can be explained by his message, which involves a digital curriculum that will (he says) instantly engage and perplex kids and thus resolve all classroom management issues (more on this later), a message tailor-made to appeal to both techies, since it implicitly attacks all teachers, and progressive educators, since it is inherently constructivist.

Most of the rest of his said trajectory can be explained by his excellent luck in his early audience—not only were they progressives and techies, but they were influential progressives and techies–Chris Lehmann, O’Reilly Publishing folk like Kathy Sierra, Nat Torkington and Tim O’Reilly himself, Brian Fitzpatrik of Google, and Maggie Johnson of Google and Stanford.

A teeny-tiny bit–ok, maybe more–of that trajectory can be explained by the Great White Hope factor. As I’ve written many times, every corner of education is desperate for young teachers, particularly young male teachers, most especially young white male teachers. Smart young white male pushes technology-based teaching, implicitly or explicitly declaring that all those old teachers (mostly white female grandmas) are doing it wrong. Hard to resist. So attractive message, demographic felicity, and luck. Not bad.

I’m going to summarize what I see as the relevant points of Meyer’s career thus far, but go straight to the source: Meyer describes his teaching career in this excellent video, which I recommend watching to instantly “get” his appeal. Go watch. I’ll wait.

He taught his first year at a Title I school in Sacramento, CA and, as he says above, was both miserable and ineffective, which he blames on his failure to create a “classroom ethos”. The improvement in classroom ethos began during his second year at San Lorenzo Valley High. It apparently never occurred to him to wonder whether the “classroom ethos” improvement at his second school, was helped along by a student demographic that was 87% white. Meyer actually noted the novelty of a non-English speaking Hispanic student which is the only time he ever mentions a minority student on his blog, best I can see.

While he made numerous videos that ended with the tagline, “I like to teach”, he in fact wasn’t all that attached to teaching. At the beginning of his third year, he was already predicting he’d be in school for either an administrative credential or doctorate by the end of the next year (he was off by two), because “I’m just keenly aware how much of my strength as a teacher derives from my ability to relate to student culture, to talk like they talk and dress like they dress” and his awareness that he feels “obliged to entertain”. He often implied that he’d mastered the technical aspects My personal favorite::

I am at a place, for example, where classroom management no longer challenges me. Not that every day is all smiles and hard work, just that I have identified the mix of engaging instruction, mutual respect, and tough love that eluded me for years.

Four ENTIRE years, this eluded him! This meme runs throughout his blog and is, in fact, the seed of his image-based curriculum. Meyer states time and again that he worked hours on end to keep from boring his students, thinks student approval as essential to improved learning outcomes and thus presents his curriculum as a better way to entertain kids, to perplex them in a way they will value, and once entertained and perplexed, they will learn.

Then, at the end of five years, he declared he was quitting teaching because he’d been transformed from “miserable to happy, incompetent to competent” (astonishing, really, how few of the commenters openly laughed at his hubris). He originally planned to attend UC Santa Cruz’s PhD program but his aforementioned contacts got him a year as curriculum fellow at Google, and he taught part-time for one more year. While at Google, he made his first TV appearance on Good Morning America (probably via Google) to discuss his theory as to whether regular or express grocery lanes were faster.

At some point after that, he pulled a TEDx invitation—very nice work if you can get it—which got him onto CNN and good lord, how could Stanford let him get his doctorate at Santa Cruz, after all that publicity? So now he’s at Stanford in year 3 of his doctoral program.

A star was born.

Like most teachers, Meyer’s a good talker; unlike many teachers, he’s good with any audience. He’s a bright guy and his videos are genuinely entertaining (go to the end to catch his early work), and I say that as someone who disagrees with very close to all of his primary assertions. As a young white male teacher he could demand nearly anything, and he nonetheless stayed in algebra and geometry, rather than push for advanced classes that his principal, eager to keep him, would easily grant. I suspect that some of his willingness to stay in low status classes was caused by his short-timer’s attitude, while another part of it was caused by his 70-hour work week. Anyone working that hard and long on classes he’s been teaching for years is unlikely to embrace new subjects. But those stated priorities nonetheless reveal a guy who is well beyond committed and flat out obsessed with doing a good job.

He’s hard to pin down ideologically not because he’s an original thinker but because he was, and is, profoundly uninterested in education policy. So no coherent philosophy, but Me Like, Me No Like. He would disavow the charge that he is on the “reform” side of the math wars, although less vehemently than a few years ago—Jo Boaler, High Priestess of Reform Math, is his adviser, after all. But even now, a few years after starting a Stanford PhD program, he’s very foggy about the specifics of major debates in math education. So he’s been trying to consolidate his positions, but he’s not always sure what the right ones are. In his earlier iterations, for example, before he became well-known, he often adopted strong education (not math) reform positions—he had an “educrush” on Michelle Rhee. In the early years of the blog, he dripped contempt on most teachers, particularly older ones, including coworkers. Early on he harped often on the need for professionalism, and asserting we’d be better off without teachers that do it just for love. But once Stanford put him on the doctoral payroll, he’s become more typically math reform, which means he’s disavowing education reform positions and doing his best to walk all that talk back. Well, not all of it–here he is on a forum last year talking about the need to train teachers on Common Core:

I think if you’ve taught for thirty years under a particular style of teaching, it has to distort what your perception is of math and how it should be taught. It’s unavoidable, to be steeped in that for so long. So to realign yourself, I imagine, is a very difficult thing. So PD that involves problem solving, involves reasoning, argumentation, that’ll be essential going forward.

So the nastiness to older teachers, still there. I don’t blame anyone who wonders if promoters consider that a bug or a feature.

Meyer’s writings never describe his “classroom action” in detail relative to other math bloggers (e.g., Fawn Nguyen, Sam Shah, Michael Pershan, Kate Nowak and, okay, me). He rarely describes the success or failure of a particular lesson, or gives any kind of walkthrough. He never describes a lesson in full detail, down to the worksheets and responses. He often went to the data collection well, and just as often failed, as in his two-month long “Feltron” project in which half the class dropped out early during data collection and had to be given other tasks, or this similar project

Meyer and metrics aren’t a natural fit. A few years ago, he was, comically, shocked by news of California’s Hispanic achievement gap. Dude, didn’t you get the memo? He never blogs about it, never discusses it, then out of the blue: Damn! We’ve got an achievement gap! And then he rarely mentions it again, save for this recap of Uri Treisman’s speech. He almost never discusses his student’s test scores and when he does, they are usually not great, although he mentions once in passing that his algebra students beat the department (no data, though). He cheerfully talked about standards-based grading for a year or two and blew off the commenters who wondered if the students were retaining the skills they’d “mastered” twice in a week. When he did finally get around to looking for that data, the answer was no, and it’s quite clear that he’d never before wondered about this essential element of success. So while I suspect that Meyer was a popular teacher who convinced a lot of kids–mostly white boys–to work hard at math, there’s little evidence of that in his written history of his years teaching.

I can find little evidence of intellectual achievement in education once he left teaching, either. At Google, he and three other curriculum fellows worked for a year on computational thinking projects. When his project shipped he wrote, somewhat obscurely, “Near as I can tell, of the sixty-or-so modules listed, only one of them ….is mine. I always admired Google’s lack of sentiment in deciding when to invest itself and when to divest itself. Still it’s strange to see a year of work reduced to a single entry in a long list.” (emphasis mine)

At Stanford, his qualifying paper was not hailed as an instant masterpiece:

The criticism I remember most vividly: a) my weak review of the literature, b) the sense that I wasn’t really taking myself anywhere new with the study, and c) a claim about equity that had me reaching beyond my data.

In short, he didn’t set the curriculum world on fire at Google, and the critiques of his qualifying paper suggest an analytical lightweight—which is pretty typical for salesfolk. So thus far Meyer has established himself as a stupendous salesman, but not much of an intellectual—at least, not of the sort that Google and Stanford like to pretend they invest in. He was even wrong in the GMA segment. Unsurprisingly, he was unflustered.

Realize that I know all of this because of Dan Meyer’s blog, so he’s not hiding anything. Hell, he doesn’t need to.

But he was brought to Google and then to Stanford and then Apple gets involved, and now we’re talking three of the most elite institutions in the country are pushing him not because they have any evidence of his ability to close the achievement gap, or even whether his digital curriculum works, but simply because he’s Dale Carnegie, and boy oh boy, is that a depressing insight into their motivations, just as his success is indicative of the desires of the larger educational world. It’s not “go develop your ideas and expand and prove them” but “here’s a bunch of elite credentials that will make your sales job easier”. So they dub Dan an “expert” and give him a microphone—which makes it a whole lot easier for a largely ignorant general media to hear him.

No, I’m not jealous. My karmic destiny demands that I enter new communities with neither warning nor fanfare and utterly polarize them within a month, usually without any intention of causing trouble. Lather, rinse, repeat. I gave up fighting that fate fifteen years ago. I have attended two elite institutions in recent memory; one of them ignored me desperately, the other did its best to hork me up like a furball. I don’t want to go back. Academia isn’t for me. And if a corporation handed me money to sell my message, they’d be facing a boycott. My blog has fifty times the readership and influence that I ever imagined, and I love teaching. I am content.

Previous paragraph notwithstanding, this essay will be interpreted by some as an attack on Dan Meyer, who is largely unfamiliar with anything short of worshipful plaudits from eager acolytes (he occasionally heeds polite dissenters, but only occasionally) since he began his blog. But while he’s a dilettante as a teacher, I think his simplistic curriculum ideas have interesting potential in teaching certain demographics, and I wish him all success in developing a coherent educational philosophy. Oh crap, that was snarky. I wish him all success in his academic and business career.

Dan Meyer’s rapid rise isn’t the problem. Dan Meyer himself isn’t the problem. The problem lies with the Gatekeepers: with Stanford, who knows that Dan’s not the solution, with Google, Apple, and publishing companies like Shell Centre (well, they’re in England) and Pearson. That intersection between academia and business, the group that picks the educational platitudes and pushes them hard, while ignoring or banishing dissent. They’re the ones granting Meyer the credentials that cloak him in the illusion of expertise. And I believe that, at least in part, they grant those credentials with a clear eye to the attributes that are diametrically opposed to the attributes they pretend to focus on. It’s no coincidence that Dan Meyer is a young white male. It’s the point. It’s not a fluke that he primarily taught white kids, many of whom were obviously sent to him with strong skills by teachers who valued homework above ability. It’s the only way he could have come up with his curriculum. Yet his message is adopted and embraced by elites who castigate education, particularly teachers, for failing black and Hispanic kids. I don’t know if they do this consciously or if they genuinely believe that all teachers are just meanspirited morons who don’t know math and deliberately deprive certain kids of meaningful math experiences. Ultimately, it doesn’t matter.

I suspect Meyer and others will ignore this essay (Meyer snarked obscurely at my reform piece, assuming this tweet means what I think it does), but whether that’s because he doesn’t like dissent or, more probably, because he subscribes to the Voldemort View, I couldn’t tell you. But maybe this piece will make reporters and educational wonks a bit more wary about the backgrounds of the “experts” they quote, and the gatekeepers who create them.


Who I Am as a Teacher

As I thought about writing specific disagreements I have with reformers, I realized that time and again I’d be having to break off and explain how my values and priorities differed. So I thought I’d do that first.

At my last school’s Christmas party (Year 1 at that school, Year 2 of teaching), the popular, widely respected “teacher at large” showed up an hour late. A PE teacher whose credential had been disallowed by NCLB-wrought changes, he was at that point responsible for coming up with plans to help “at-risk” kids.

“Yeah, I was having all sorts of fun reviewing the Lists.”

“The Lists?” asked another teacher.

“Top 25 Discipline Problems, Top 25 Kids On Probation for Felonies, Top 25 Absentee/Truancy Students, Lowest 25 GPAs, you name it. I look for the kids who aren’t on more than one or two lists and try to reach them before they qualify for more lists.”

“I think I have a few of those kids.” groused a teacher.

“A few? Pity Ed here.” He nodded at me. “Half the kids on each list are in one of your classes.”

I think he made up the felonies list. I hope.

Fall of year two was about as tough a time as I’ve ever had as a teacher.

Getting quiet for teaching was job one. I’d separate inveterate chatters, then I’d move the worst offenders to the front groups, and then, if one of them still didn’t shut up, I’d pull the desk forward all the way to a wall (with the kid in it). The rest of the class would snicker at the talker—at, not with.

“It’s not like I’m going to pay attention to you up here. I’ll just go to sleep,” one of them said, defiantly.

“You say that as if it were a bad thing.”

He or she often did go to sleep, which gave me some quiet from that corner, anyway. Otherwise, I wrote a referral. I also wrote referrals when they called me a f***ing [noun of your choice, profane or not], a sh**ty f**ing boring teacher (boring! I ask you), when they threw things, when they got up and wandered around the room refusing to sit, when they texted in open view and refused to give over the phone, when they left the room without permission, when they howled I HAVE TO PISS at the top of their voices (usually one at a time), and so on—all during the time that I was trying to teach the lesson “up front”. Once I released them for work it got easier, as I wasn’t trying to maintain order and some notion of what I’d been doing before the last interruption, but rather walking around the room helping students and telling others to shut up.

As bad as I make it sound, every senior teacher I worked with was astonished at how well I did, given the pressure; all the previous teachers stuck with all algebra all the time had routinely lost control of the classes and had supervisors posted. Administrators didn’t approve of my approach, alas; since my kids were mostly Hispanic, my referrals were, too. So I was caught between an administration who would really rather I’d have flailed ineffectually than kick kids out for order, and the bulk of my students, who opined frequently that I should boot students more often and earlier.

The beginning of the way back up that year began in second period when I’d thrown out the third kid of the day, and Kiley said “Could you toss out Elijah, while you’re at it?” and much of the class laughed. Elijah stood up and said “Yeah, send me, too! I don’t want to be here! Let me go!”

I tend to stay pretty focused on teaching; rarely do I give A Talk. Today, I have no idea why I made an exception.

“Why don’t you want to be here, again?”

“Because I hate math? F***ing duh.”

“What is it you think I want?”

“You want me to shut up.”

“Well, yeah. But why?”

“So you can teach!”

“Why?”

“Because it’s your job!”

Because I want everyone to pass this class.” And to this day, I thank all that’s holy that I caught the class’s sudden silence and realized that my remark had an impact.

“Maybe I need to make that clearer. I want every single person in here to pass algebra and move onto geometry. Remind me again, how many people have taken algebra more than once?” Almost everyone in the class raised a hand, including Elijah.

“Yeah. Don’t raise your hand, but I know at least ten students in here are taking it for the third time, including some people who get tossed out of class regularly. I don’t kick kids out for fun. I kick them out because I need to teach everyone. I have kids who want to excel in algebra. I have kids who would like to get better at algebra. I have kids who simply would like to survive algebra, although many days they think that’s a pipe dream. And I have kids who don’t want to be here at all. I figure, I kick kids out from the last group, I’m meeting everyone’s goals but mine.” I actually get a couple laughs; they’re listening.

“But make no mistake, that’s my goal. I want everyone in here to pass.” I looked at Elijah, who’d slipped back into his chair, his eyes fixed on me.

“You could tell me about your troubles, and I’ll give you an ear, but here’s a basic truth: there’s not a single situation in your life that gets worse if you pass algebra. And there’s a whole bunch of things that improve.”

“I could get a work permit, for one thing,” Eduardo muttered.

“Get back on the football team,” said DeWayne.

“And now I know some of you are thinking sure, there’s a catch. No. I didn’t say I want you to like algebra. I didn’t even say I want you to understand algebra, although I guarantee that trying will improve your understanding. I’m making a simple commitment: show up and try. You will get a passing grade. No catch.”

The rest of second period, the toughest class, went so well that I decided to repeat that little speech for every class, and in every class, I got utter quiet. I don’t say that all the problems were solved that day, but from that point on far more of the kids “had my back”. Psychologically, their support made it much easier for me to develop a strategy to teach algebra in the face of these challenges.

Here’s how I taught it, and here’s how they did. I only failed 10 kids out of the final 90, or 11%. (Elijah had left. Eduardo got his permit, and DeWayne made it back onto the football team.) That’s the highest failure rate I’ve ever had, but then it’s the last time I taught algebra I. It’s easier to work with kids in geometry and algebra II—they’ve got skin in the game, and graduation becomes a real objective as opposed to the remote possibility it presents to a sophomore taking algebra I for the third time.

The wise reader can infer much about my students and a great deal, although certainly not all, about my values and priorities as a teacher from that tale.

First, I mostly teach kids from the lower third to the middle of the cognitive ability spectrum, with a few outliers on each end. That’s who takes algebra in high school. No more than 10% of my students in any year are capable of genuinely comprehending an actual formal math course in geometry or algebra (I or II). Another 30-50% of the rest are perfectly capable of understanding geometry, algebra and even more advanced topics in applied math, even if they couldn’t really master a formal math course, but they’d have to try a lot harder and want it much more. About a quarter of my students each year are barely capable of learning basic algebra and geometry well enough to apply it in simple, rote situations. A much smaller number can’t even manage that much.

For other teachers, the percentages are skewed heavily to the first and second categories; some of them don’t even know there’s a third and fourth category. A teacher covering precalc and honors algebra II/trig in high-income or Asian suburb, teaching mostly freshmen and sophomores, would have a much higher percentage of students who could master a formal course; their notion of “struggling kids” would be those who aren’t working hard enough. But that’s not my universe—and it’s not the universe I signed up for, although I wouldn’t mind visiting occasionally.

Until this year, my assignments weren’t deliberate. I was just an unimportant teacher who schools didn’t care about losing. In fact, the following year at that same school the administration assigned Algebra II/Trig classes to a teacher who was not qualified to teach the subject while I, who was qualified, was given the lower level Algebra II classes. The administration knew full well about the distinction, which necessitated a “your teacher is not highly qualified” letter to some 90 kids, but that teacher was more valuable than than I was, and so it goes. I’m not bitter, and I’m not marking time until I get “better” kids. I’m doing exactly what I want to do. But every teaching decision I make must be considered in light of my students’ cognitive abilities and, related to that ability, their motivation.

Second, I am a teacher who doesn’t overvalue any individual student at the expense of the class, which means I have no compunction about kicking kids out for the day. You run into these teachers philosophically opposed to removing kids from class; how can these students learn if they aren’t in class, they bleat. These teachers never seem to worry about how all the other kids learn with a disruptive hellion wreaking havoc because, they strongly hint (or outright assert), the right curriculum and caring teachers would eliminate the need to disrupt.

I ask these teachers, politely, do you have kids with tracking bracelets and/or probation officers? Do you have students who have fathered two kids while wearing that tracking bracelet, or gave birth to one? Do you have students who have been suspended or expelled for putting other students in the hospital, or for having a knife in their backpack? Do you have students who routinely tell you to f*** off and don’t bother me? Do you have all of these students plus twelve more who have just enough motivation that, given no distractions, would be able to learn some math but with a distraction will readily jump over to the side telling you to f*** off? And with all that, are you math teachers trying to help students with a four-year range in skills figure out second year algebra? Because otherwise, you can go sing your smug little songs of no student left behind to someone with kids who really shouldn’t be kicked out of the classroom. Okay, maybe not politely.

Come back the next day or even the same day, hat in hand, and no harm, no foul. I don’t only act like it didn’t happen, I have completely forgotten it happened. But get out of my class if you won’t shut up or can’t consider the day a success unless you’ve sucked in three other kids with your distractions.

The biggest pressure on teachers like me these days is the huge pushback they get from administration, district, and state/federal education agencies when they try to maintain an orderly classroom. And charter schools’ ability to a) have none of these kids to start with and b) kick moderately ill-behaved kids back to public school when they act out can’t be overstated as factor in their “success”.

That’s a shame. Because invariably, the bulk of my unmotivated rabble-rousers realize that I really mean it about that whole “passing” thing, if they would just shut up and give the class a shot. And so they do.

Next, I am a teacher who explains. I don’t mean lecture; my explanations always take the form of a semi-Socratic discussion, leading the kids through a process. But when I start to talk, the conversation has a direction and that directed conversation, to me, is the heart of teaching. One of my favorite memories of an ed school classmate came about as we were driving to our placement school.

“I’m really enjoying working on aspects of my teaching that I don’t like. For example, explanations. I hate doing that.”

“Um, what? You hate explanations?”

“Yeah. I’d rather never explain anything.”

Pause.

“What is teaching, if it’s not explaining things?”

I thought it was a rhetorical question. I was wrong. He went on and on about other aspects of teaching: curriculum, motivation, role modeling, assessing students, and so on. Huh. Interesting. Eye-opening. It’s not that I disagreed, but how can you be a teacher if you don’t like to explain things?

And as I began to develop, I realized that teaching is not synonymous with explaining. Still. It’s my go-to skill, it’s what I do best, it’s a big part of my success with low ability students, and it’s why I prioritize getting my students to shut up while I’m teaching up front.

Next, the story reveals that I adopt my students’ values and goals, rather than insist they adopt mine. The kids were shocked into silence when they realize that my most heartfelt goal was to pass everyone in the class.

I learned a key lesson I still use every time I meet a new class, and make it clear I want to help them achieve their goals, which usually involve surviving the class. I do not understand why so many teachers set out objectives based on the assumption that they will successfully re-align their students’ value systems.

And in a related revelation, you can see how I frame my task. In his TED talk, Dan Meyer asks the audience to imagine:

“you really loved something…and you recommended it wholeheartedly to someone you really liked…and the person hated it. By way of introduction, that is the exact same state in which I spent every working day of the last six years. I teach high school math. I sell a product to a market that doesn’t want it but is forced by law to buy it.”

All math teachers can relate to this statement; it’s clever, funny, and does a good job of introducing the fundamental dilemma of high school math teachers: most kids hate math and are required to take it. Many dedicated math teachers would not only relate, but agree with Dan’s framing of his task as a sales job, regardless of their teaching ideology. When I say I disagree, it’s not because Meyer is wrong but because we approach our jobs in fundamentally different ways. I don’t love math, and I’m not selling a product.

Victoria: I’m terrible. I know I’m terrible. I look at the mirror and I’m ashamed. Maybe I should quit. I just can’t seem to do anything right.

Joe Gideon: Listen. I can’t make you a great dancer. I don’t even know if I can make you a good dancer. But, if you keep trying and don’t quit, I know I can make you a better dancer. I’d like very much to do that. Stay?

Were it not for the unfortunate plot point about Joe Gideon’s motives for hiring Victoria for the show (he was a hounddog who had her in bed an hour after they first met), I suspect more math teachers would reveal that they can quote this scene from All That Jazz verbatim.

And those math teachers mostly would agree with me. Teaching math, for us, isn’t about creating mathematicians. It’s only occasionally about working with kids who want to be engineers, doctors, or architects. Mostly, it’s about giving kids enough math skills to pass a college placement test so they won’t end up spending a fortune on remedial math classes and never get any further—or at least enough skills so they’ll pass a remedial math class and move on. Or giving kids enough math so they look at a trade school placement test and think, “Hey, I can do this.” Or just giving kids the will to pass the class and keep them out of mindless credit recovery in alternative institutions, letting them feel part of the educational system, not a failure who couldn’t cut it at normal high school.

We don’t promise miracles. We do promise “better”.

Finally, though, the story indicates that I am acutely aware of all my students’ motivations, that not all my students just want to pass. I have bright kids in almost every class, I have highly motivated kids, I have kids with specific objectives, most of whom want to learn as much as they can. I never forget them, and if I can’t dedicate my entire teaching agenda to meeting their goals, it’s only because I owe allegiance to all my students. I never stop looking for better ways to give these kids what they need while still ensuring I meet my overall responsibility. Many other teachers say these kids should come first. I always worry they might be right. But as I said above, I do not overvalue any individual kid over the needs of the entire class.

This tale doesn’t tell much about how I teach, but that particular topic gets plenty of coverage in other essays.

Anyone who is familiar with reform math can probably infer not only my teaching values and priorities, but also a lot of reasons why I’m not crazy about reform math. But I’ll go into details in the next post.