Category Archives: philosophy

Graduating My Geometry Class

In the fall of 2012, I began my first year at this school. First block, first day, I met a group of 29 freshmen in their first high school math class: geometry.  From the beginning, we all clicked. A new school didn’t seem quite so intimidating because every day of that first semester started with camaraderie and good times–and some learning, too.

Three freshmen left the school mid-term. All but one of the rest passed. Eleven Asians (1 east, 3 south,4 south east, 3 mideast), nine whites, seven Hispanic , one black. Five Muslim. No long-term ELLs, one suffered from near-blindness. Ten athletes who played their entire high school careers,  including two who eventually got scholarships. The eventual senior prom queen. All those who passed made it through trigonometry, at least. Most made it to pre-calculus. Only a few made it to Calculus or AP Stats, although at least three talented students were derailed by an F from Mr. Singh , which I found frustrating. All of them are going to college. They reflected the school’s population writ large: diverse, athletic, not overly focused on academics, but smart enough to get it done.

One student I never saw again: the feckless, charming girl who failed all her classes by treating school as social hour continued to frustrate her father, who brought her away from the Philippines and her mother, hoping he could prevent a pregnancy before a high school diploma. Another student I just didn’t run into much.

Four others were likewise never in one of my classes again, but I saw them frequently; they’d always shout a greeting across the quad, identifying themselves because they know I never wear my glasses.

The remaining twenty saw me in at least one subsequent math class. Five saw me twice more. None seemed to mind.

In all our frequent chats, literally up through their June graduation, we’d regularly refer to “that first geometry class”.  Our touchstone memory, kept alive through four years of their education.

One of my “three-timers”, a sweet, tentative young man  who never had another math teacher until pre-calc, stopped by with his yearbook. As we thumbed through the senior pages, calling out familiar faces, he suddenly said,”Man, I bet you’ve taught most of the seniors at least once.”

We counted it together—of the 93 rows of four students each, I’d taught 288 of them, or roughly 75%. Many–at least fifty–more than once.

In the face of that percentage, I decided it was time to work around my dislike of crowds, speeches, and heat in order to represent on their big night. So at 4:30, I showed up to help assemble them for the procession.

At first, the seniors were gathered in informal groups outside the staging area, taking pictures, talking, dancing about impatiently. Many called me over or waved, shouting out their names because they know my sunglasses aren’t prescription.

As they moved into the cafeteria for the staging, I wandered around, touching base, asking about plans, saying goodbye. As I’d expected, they needed teachers to organize the alphabetized lines for the procession, so I took a list of twenty. Rounded them up, hollered them into line, while the fourteen students I’d taught before joked that in less than three hours they’d never have to listen to me again. “And that’s why you became a teacher!” a bunch of them chorused.

Finally, the graduation manager gave the sign for zero hour. Suddenly well-behaved and serious, they streamed out in order, paused for a few minutes at some inevitable delay, and then the music started. Their procession took them by the stadium’s fence along the security road; I stood about 15 feet away by a barrier and put on my prescription glasses, even in the sun, the better not to miss any face. Waved and cheered at brand new adults who waved and cheered back, glad I was there, happy to see me, happy that I was wearing my glasses and could see them.  And when the last student–one of mine–turned for one final smile, I decided that the graduation itself, the heat, the speeches, the names, would dull the joy I felt in this moment. Time to go.

As I walked back to the Starbucks where I’d parked my car, latecomers were hustling to the stadium, many holding signs and pictures. I saw pictures I knew, stopped to congratulate the parents and send them on their way. And suddenly:

“Hey, it’s my geometry teacher!”

I looked at the pretty, lively young woman holding a…toddler? infant? gurgling happily walking towards me, waving. Smiled, running through the names of the only other geometry class I taught and coming up blank.

“You don’t remember me? I’m Annie!” and I gasped.

“Oh, my god. Annie! I thought…I haven’t run into you for so long…you didn’t go back to live with your mom? I don’t think I’ve seen you in..three years? I didn’t recognize you. You’re all grown up!  How’s your dad? You look fantastic. And how’s this little guy? How old is he, fifteen months?”

“Nope, just nine months.”

“He’s gorgeous. How are you? Come to see the grad…well, duh, yes.”

She laughed, and hitched the baby to her other hip. “It’s great you came! I still think about that geometry class. It was so fun!”

“I wish I’d run into you more. Go, get going, you don’t want to be late. Take care of this adorable one. I’m happy to see you.”

“Me, too. Take care. Bye!” and off she went, striding confidently into her future. I watched her, thinking of all the questions I wanted to ask: did she graduate? Go to our excellent alternative high school? Is the baby’s dad in the picture? What are your plans? and being so very glad I didn’t.

I resist presenting Annie as a tragedy. I didn’t feel guilt, watching her walk away.  But I did feel…awareness, maybe? I’m good with unmotivated underachieving boys. Am I as good with girls? Could I be reach out more? Give them reasons to try, to play along?

“You should never be satisfied. You can always do better.”

I remember telling that ed school professor that the two sentiments don’t follow. I am satisfied. I can try to do better.

Goodbye, class of 2016.

Goodbye, geometry class. Next year is my first without my touchstone group. I’ll miss you.

I want you to go forth and live happy, productive lives. Please know that for the past four years, your presence has been a big part of mine.



What I Learned: Years 4-7

I was going to continue my year by  year  (by year) retrospective, but I decided that the last four years can be considered as a block. Which is good, because if I did a post per year I’d never catch up.

tl;dr Years 4-7 were all about happiness.

I began at this school in late August of Year 4, just a week or so before school began.  Utterly desperate for work, I would have accepted any offer, anywhere in a 35 mile radius and really, by late August, 50 mile drives weren’t out of the question.  That I got my first choice, a school that had actually offered for me the year before, seemed almost a miracle.

And really, I’ve been happy ever since. Teaching has always been a joy. The previous schools, with all the challenges, never dented my belief in my own abilities or the faith that kids were benefiting from my teaching. But at the other schools, the administrators didn’t agree. It’s not that they thought I was a bad teacher. I just wasn’t what they wanted–someone younger, ideally.  Here, for the first time since student teaching, my bosses also thought I was a darn good teacher. May this bliss last at least eight years more.

So in those four years, what changes and accomplishments can I point to?

Teaching Persona

As mentioned in Year 3 retrospective,  I’d begun to establish the same ambiance in my school classrooms that existed in my test prep and enrichment instruction classes. At this school, the process was complete and I never looked back. From day one, I was unpredictable, flexible, friendly, ruthlessly sarcastic, and damn funny, which is where I live the rest of the time. The second year there, I introduced a meme: I am the star of my classroom.  I get a guaranteed audience three or four times a day. It is in my contract. Students are the audience. Their job is to attend. If they’re lucky, they might get some lines. A walk on part. But mostly students are to watch. To listen. Eh…learning would be nice, but that’s up to them.

Someone somewhere is going to take this as a serious statement of priorities, rather than a mindset. Remember that I spend very little upfront time teaching. It’s more of an attitude. It allows me to be big, overblown, demanding attention, dammit, whether you learn or not. Students enjoy the spin on the usual pay attention because education is good for you. Hell with that, kids, your attention is good for me.

I count it as a good sign that I’m regularly in the Teacher Awards section of the yearbook, and for fun things: Storyteller, Unpredictable, Mostly Likely to Lose Whiteboard Eraser. May that, too, extend through the next eight years. I’m a geek; popularity is a nice change.

Building Curriculum–Never Be Satisfied

I vividly remember in the spring of year 4, my first year at this school, when I was looking ahead to linear inequalities. I was just about done with my new method of modeling linear equations which had now gone well twice in a row (remember, this school does a year in a semester and then repeats).

But at the time, I did little more than go through the procedures on linear inequalities, and felt a twinge of shame the first semester, as we moved from a unified modeling approach to…here’s how you test a value.  And suddenly, out of the blue, I remember my ed school professor saying “You should never be satisfied. You can always do better.”

At the time, I rolled my eyes. She was saying this in the context of our first year of teaching, to never feel satisfied. I think this is absurd. “Good enough” is fine a lot of the time. But at this moment, I realized it could apply to an entire career (and in fairness to the professor, that’s probably what she meant.)

So I challenged myself in that moment to come up with something different. How could I introduce  linear inequalities in such a way that would build on the linear equations, while showing their differences? I still use the methods I built that day, although I’ve developed them somewhat.

But from that point on, I always take that moment, that wince away from a piece of curriculum I don’t like. What can I rebuild? How can I make it better? I’m not a perfectionist, not a driving careerist, definitely not hard-charging in approach. (my affect and opinions, whole different deal.) Just one of many ways in which my pricey ed school degree has transformed me well after the fact.

I’ve written about many other curriculum improvements over time. All of these were done with that same spirit of yeah, the old way wasn’t working, let’s try this:

I’ve completely reworked quadratics and exponents as well, but haven’t written them up. It’s been fun.

I don’t have one approach to curriculum, but if I have a go-to process, it’s the “illustrating activity” or problem, which can be seen here in the Projectile Motion writeup, or this lesson on proving the pythagorean theorem and geometric mean activity. I began to write it up as part of this entry, but decided no, do a separate post. (I do apologize for my scarce blogging lately.)

Classroom Ambiance


This is the first time I had my students “work in the round”, which is how you’ll find my class at least 12-15 days a month since then. My current classroom has whiteboards all the way around. The walls have a 5 x wall-length strip of white board paint (which is really cool). I have small white boards with coordinate planes etched in. I also have a wonderful donor who sends me $100 worth of whiteboard pens every year, so the kids can always be working on a big surface, with plenty of room for mistakes.

There must be whiteboards.  Working constantly in class, moving around, reduces the risk of math zombies. Earphones are allowed to shut out the noise, provided I don’t see the student enjoying the music more than the work.

I sit my kids in groups, which has been true since my first year. I don’t do homework, which has been true for two years, but I never counted failure to do homework.

There must also be movies. Twice a semester in the fall, because Christmas means “It’s a Wonderful Life”. Always at the end of the semester.


The December of Year 5, I got a look at the new Common Core tests and laughed, again, at the ludicrous notion that the new mean achievement would be centered around these ridiculously difficult standards. Except…..

I noticed that many questions required more than one answer. They weren’t simple multiple choice questions. “Identify all the solutions.” “Select all the equivalent expressions.”

Hey, now. That’s interesting. And my first multiple assessment test was born a week later.

Thanks, Common Core! sez I. My kids, not so much.The tests are really helpful for lower ability kids to show what they know, but the strongest kids have to be on their game to do well.

Here’s my first post on the topic, but I’ve revisited it often. They allow flexibility way beyond the usual multiple choice–I can mix and match between freeform and formatted response, or include both in the same question. I can create one question with varied procedural tasks, or one question that dives deep into one situation. They also allow me to greater access to student thinking.

I’ve also had fun redoing my quizzes in the past year. Typically, my quizzes have been straightforward affairs that contain no surprises. But I’ve started to mix it up. helicopterquest

These are nice stylistic changes, even if the underlying question is still straightforward.

Meta Teaching
While I mentioned that my third year saw fundamental .changes in my approach to teaching, I completely forgot to mention that the year also gave  birth to this blog.  While I began blogging at my last school, all but eight months of it have been here. The blog itself is a constant insight into my teaching practice–among other things. I’ve kept it primarily on education, whether it be policy, practice, law, or the reality, which often violates all the others. And occasionally Trump, of course. But then, a good chunk of my Trump support is also related to teaching.

I was not terribly popular with the head of my ed school, but on at least two occasions, she mentioned my gift for writing about classroom experiences. My second year out, I was telling one of my ed school professors about my administration woes, and he told me that he wanted me to keep teaching so I could write about it.

“You’re a very good new teacher. But writing about teaching will be your unique contribution to the field.” I was immensely complimented, and said so–wondering how I could possibly get someone to ever be interested in publishing my thoughts, and how I could get my thoughts down to 750 word chunks.

Turned out I could do first part myself, making the second (ahem) unnecessary.

I try to avoid doing too much with clubs or other school activities that involve stipends.Mentoring credentialed and student teachers1on the other hand, fits in well with my temperament. I’ve spent most of my life being paid for opinions. Consulting new teachers carries on that piece of my past. I’ll be doing induction this year, and hope to find another student teacher soon.

And so, I move onto years 8 and beyond. Looking forward to it.


1My student teacher got at least two job offers from the district; I’m assuming he took one of them but haven’t talked to

Curriculum Development: Not Work for Hire

I chopped off part of my last piece to expand more on teacher intellectual property, a topic near and dear1.

The conventional wisdom (which Stephen Sawchuk nicely outlines in the last part of this piece) holds that teachers are district employees, so any curriculum, lessons, or tests are considered work for hire . The teacher is paid specifically to develop the curriculum by the district, so the district owns the copyright and any subsequent profits from all of their teachers’ work—tests, worksheets, lesson plans, sequencing, whatever. .

In theory, my district could force me to pull down my posted curriculum from this blog—since I don’t own the copyright, I don’t have the right to give it away for free. Sites like Teachers Paying Teachers are illegal in this view, since teachers are making profits off their district’s property.

Originally, a teacher’s work was exempted from the work to hire rule, but in 1978 Congress didn’t include the exemption. Teachers’ unions have been trying to get the exemption reinstated.

Not for the first time, I’d argue the unions are going about this in exactly the wrong way. The exemption is unnecessary. Teachers aren’t hired to write curriculum. We are hired to teach. I’ve now outlined three well-established, time-honored practices that support this interpretation.

  1. Teacher contracts spell out their time commitments, which are the time in the classroom, staff and department meetings, supervisories, and mandatory professional development. No contracts hold teachers responsible for developing their own curriculum. A teacher is welcome to teach day by day from a provided textbook, or eschew a textbook altogether. They are not evaluated on the strength of their curriculum development in any way, nor can they be required to improve performance on this point. (More about this here.)

  2. While districts have begun to claim copyright, districts have never paid each other for teacher-developed curriculum. I have been in three districts. Like all teachers, I have a directory of my own curriculum, and I’ve carried it from school to school without any district ever informing me I couldn’t–much less demanding payment from my new district for use of their copyrighted curriculum.

    This practice, which has gone on for generations, clearly demonstrates that districts don’t consider themselves owners of the teacher curriculum. So if they want to ban a teacher from selling it, they need to start seizing the curriculum from teachers who developed it. Good luck with that.

  3. As I recently wrote, teachers given the extra duty of a class are paid purely based on the class instruction time, not the additional time (or not) needed to develop curriculum for that class. I’ve written before that teacher preps, or number of subjects actually taught, impact teacher workload. Teaching three different classes would be considerably more work, for most teachers, than teaching the same class four (or six) times. Teaching large classes also impacts workload. The teacher with multiple preps but a free period could have a student load of 150, while the teacher who works the prep could have 120 students (6 classes of 20). Unlikely, but theoretically possible. Doesn’t matter. More preps, more students, more outside work: irrelevant. What earns teachers a significant premium is the number of scheduled classes they are responsible for.

No one ever listens to me, but I’d advise unions to look for a good test case to challenge the work-for-hire idea, rather than argue for a change to copyright law, on the grounds that existing practice has acknowledged teacher intellectual property for decades. Certainly, the district should never be required to pay for the teacher’s work product in later years, should receive automatic use of anything developed during the teacher’s term of employment. But any rights in the curriculum we develop is our own.

I’ve often seen reformers–and other teachers—bemoan the notion of teachers who go home right after school everyday, clearly implying that the extra work developing lesson plans and curriculum is an element of our salary. But this simply isn’t true.

Besides, we don’t have any real idea of what makes a good teacher. Some of us work hours after school, some leave right after. No teachers who spend hours crafting curriculum, be it handouts, lesson plans, or tests, have any guarantee that they are getting better results. What they do know is that they are creating, creating without pay, and what they create should be theirs.

Here, again, acting works well as an analogy. Two actors are cast in a play, given supporting roles with an equivalent number of lines. They are both paid “scale” (whatever that is). The first actor spends six hours a day outside of rehearsal, practicing and perfecting the role, trying out different readings. The second actor barely makes it to rehearsal because he’s busy auditioning for a movie, doesn’t put any time into preparation.

They both would be paid scale for rehearsal and performance hours. The first actor wouldn’t be paid for the additional hours. The second actor might, in an unfair world, receive more acclaim and audience approval despite his lackluster approach.

But neither of them would be precluded from re-using aspects of their performance in later roles. The studied wince. The knowing sneer. The warm beaming smile, the turn and rapid delivery. Their performances were the result of work-for-hire. The script, like the textbook, belongs to someone else. The manner and method they use to deliver the performance are entirely theirs.

I ran into our union rep, an excellent English teacher, in the copy room. We began by chatting about class size (I’m teaching three massive A2 classes, which has given me some sympathy for the limits) and for various reasons (no doubt because this was on my mind), we got around to curriculum development.

“I wonder why the union doesn’t realize that we aren’t paid to develop curriculum? They don’t really need to change the copyright act to give teachers ownership of their work.”

“Or to give everyone ownership,” she said instantly. “There’s good reason to believe that no one’s work is truly original, that everything is derivative.”

Oh, lord. A CopyLeft fan. If our conversation had been Twitter based, I would have been properly contemptuous, but she’s a colleague and really very smart (she knew about the 1978 Copyright Act!) and besides, on this issue, I am actually seeking to persuade so I bite back my first response.

“Yeah, I ‘ve never agreed on that. But can we agree, at least, that whether teachers own their work or everyone owns their work, that the district doesn’t own our work?”

“Oh, absolutely. In order to give it away, we need the rights to it.”

So to the many loopy committed Creative Commons, Open Source, everything is derivative folks, can I just ask that we put aside our differences long enough to get the union to argue our case?

1I’ve been writing about teacher IP and curriculum development for four years, as long as this blog’s been around–that’s in addition to many, many posts on my actual curriculum development. Here’s the primary pieces:

Teaching and Intellectual Property
Grant Wiggins
Developing Curriculum
Handling Teacher Preps
Math isn’t Aspirin. Neither is Teaching.

Assessing Math Understanding: Max, Homer, and Wesley

This is only tangentially a “math zombies” post, but I did come up with the idea because of the conversation.

I agree with Garelick and Beals that asking kids to “explain math” is most often a waste of time. Templates and diagrams and “flow maps” aren’t going to cut it, either. Assessing understanding is a complicated process that requires several different solutions methods and an interpretive dance. Plus a poster or three. No, not really.

As I mentioned earlier, I don’t usually ask kids to “explain their answer” because too many kids confuse “I wrote some words” with “I explained”. I grade their responses in the spirit given, a few points for effort. “Explain your answer” test questions are sometimes handy to see if top students are just going through the motions, or how much of my efforts have sunk through to the students. But I don’t rely on them much and apart from top students, don’t care much if the kids can’t articulate their thinking.

It’s still important to determine whether kids actually understand the math, and not just because some kids know the algorithm only. Other kids struggle with the algorithm but understand the concepts, Still others don’t understand the algorithm because they don’t grok the concepts. Finally, many kids get overwhelmed or can’t be bothered to work out the problem but will indicate their understanding if they can just read and answer true/false points.

If you are thinking “Good lord, you fail the kids who can’t be bothered or get overwhelmed by the algorithms!” then you do not understand the vast range of abilities many high school teachers face, and you don’t normally read this blog. These are easily remediable shortcomings. I’m not going to cover that ground again.

So how to ascertain understanding without the deadening “explain your answer” or the often insufficient “show your work”?

My task became much easier once I turned to multiple answer assessments. I can design questions that test algorithm knowledge, including interim steps, while also ascertaining conceptual knowledge.

I captured some student test results to illustrate, choosing two students for direct comparison, and one student for additional range. None of these students are my strongest. One of the comparison students, Max, would be doing much better if he were taught by Mr. Singh, a pure lecture & set teacher; the other, Homer, would be struggling to pass. The third, Wesley, would have quit attending class long ago with most other teachers.

To start: a pure factoring problem. The first is Max, the second Homer.


Both students got full credit for the factoring and for identifying all the correct responses. Max at first appears to be the superior math student; his work is neat, precise, efficient. He doesn’t need any factoring aids, doing it all in his head. Homer’s work is sloppier; he makes full use of my trinomial factoring technique. He factored out the 3 much lower on the page (out of sight), and only after I pointed out he’d have an easier time doing that first.

Now two questions that test conceptual knowledge:


Max guessed on the “product of two lines” question entirely, and has no idea how to convert a quadratic in vertex form to standard or factored. Yet he could expand the square in his head, which is why he knew that c=-8. He was unable to relate the questions to the needed algorithms.

Homer aced it. In that same big, slightly childish handwriting, he used the (h,k) parameters to determine the vertex. Then he carefully expanded the vertex form to standard form, which he factored. This after he correctly identified the fact that two lines always multiply to form a quadratic, no matter the orientation.

Here’s more of Homer’s work, although I can’t find (or didn’t take a picture of) Max’s test.


This question tests students’ understanding of the parameters of three forms of the quadratic: standard, vertex, factored. I graded this generously. Students got full credit if they correctly identified just one quadratic by parameter, even if they missed or misidentified another. Kids don’t intuitively think of shapes by their parameter attributes, so I wanted to reward any right answers. Full credit for this question was 18 points. A few kids scored 22 points; another ten scored between 15 and 18. A third got ten or fewer points.

Homer did pretty well. He was clearly guessing at times, but he was logical and consistent in his approach. Max got six points. He got a wrong, got b, c, & d correct, then left the rest blank. It wasn’t time; I pointed out the empty responses during the test, pointing out some common elements as a hint. He still left it blank.

On the same test, I returned to an earlier topic, linear inequalities. I give them a graph with several “true” points. Their task: identify the inequalities that would include all of these solutions.


(Ack: I just realized I flipped the order when building this image. Homer’s is the first.)

Note the typo that you can see both kids have corrected (My test typos are fewer each year, but they still happen.) I just told them to fix it; the kids had to figure out if the “fix” made the boundary true or false. (This question was designed to test their understanding of linear concepts–that is, I didn’t want them plugging in points but rather visualizing or drawing the boundary lines.)

Both Max and Homer aced the question, applying previous knowledge to an unfamiliar question. Max converted the standard form equation to linear form, while Homer just graphed the lines he wasn’t sure of. Homer also went through the effort of testing regions as “true”, as I teach them, while Max just visualized them (and probably would have been made a mistake had I been more aggressive on testing regions).

Here I threw something they should have learned in a previous year, but hadn’t covered in class:

Most students were confused or uncertain; I told them that when in doubt, given a point….and they all chorused “PLUG IT IN.”

This was all Max needed to work the problem correctly. Homer, who had been trying to solve for y, then started plugging it in, but not as fluently as Max. He has a health problem forcing him to leave slightly early for lunch, so didn’t finish. For the next four days, I reminded students in class that they could come in after school or during lunch to finish their tests, if they needed time. Homer didn’t bother.

So despite the fact that Homer had much stronger conceptual understanding of quadratics than Max, and roughly equal fluency in both lines and quadratics, he only got a C+ to Max’s C because Homer doesn’t really care about his grade so long as he’s passing.


I called in both boys for a brief chat.

For Max, I reiterated my concern that he’s not doing as well as he could be. He constantly stares off into space, not paying attention to class discussions. Then he finishes work, often very early, often not using the method discussed in class. It’s fine; he’s not required to use my method, but the fact that he has another method means he has an outside tutor, that he’s tuning me out because “he knows this already”. He rips through practice sheets if he’s familiar with the method, otherwise he zones out, trying to fake it when I stop by. I told him he’s absolutely got the ability to get an A in class, but at this point, he’s at a B and dropping.

Max asked for extra credit. He knew the answer, because he asks me almost weekly. I told him that if he wanted to spend more time improving his grade, he should pay attention in class and ask questions, particularly on tests.

We’ve had this conversation before. He hasn’t changed his behavior. I suspect he’s just going to take his B and hope he gets a different teacher next year who’ll make the tutor worth the trouble. At least he’s not trying to force a failing grade to get to summer school for an easy A.

Homer got yelled at. I expressed (snarled) my disappointment that he wouldn’t make the effort to be excellent, when he was so clearly capable of more. What was he doing that was so important he couldn’t take 20 minutes or so away to finish a test, given the gift of extra time? Homer stood looking a bit abashed. Next test, he came in during lunch to complete his work. And got an A.

Max got a B- on the same test, with no change in behavior.

I haven’t included any of the top students’ work because it’s rather boring; revelations only come with error patterns. But here, in a later test, is an actual “weak student”, who I shall dub Wesley.

Wesley had been forced into Algebra 2, against his wishes, since it took him five attempts to pass algebra I and geometry. He was furious and determined to fail. I told him all he had to do was work and I’d pass him. Didn’t help. I insisted he work. He’d often demand to get a referral instead. Finally, his mother emailed about his grade and I passed on our conversations. I don’t know how, but she convinced him to at least pick up a pencil. And, to Wesley’s astonishment, he actually did start to understand the material. Not all of it, not always.


This systems of equations question (on which many students did poorly) was also previous material. But look at Wesley! He creates a table! Just like I told him to do! It’s almost as if he listened to me!

He originally got the first equation as 20x + 2y = 210 (using table values); when I stopped by and saw his table, I reminded him to use it to find the slope–or, he could remember the tacos and burritos problem, which spurred his memory. You can’t really see the rest of the questions, but he did not get all the selections correct. He circled two correctly, but missed two, including one asking about the slope, which he could have found using his table. He also graphed a parabola almost correctly, above (you can see he’s marked the vertex point but then ignored it for the y-intercept).

He got a 69, a stupendous grade and effort, and actually grinned with amazement when I handed it back.

Clearly, I’m much better at motivating underachieving boys than I am “math zombies”. Unsurprising, since motivating the former is my peculiar expertise going back to my earliest days in test prep, and I’ve only recently had to contend with the latter. However, I’ve successfully reached out and intervened with similar students using this approach, so it’s not a complete failure. I will continue to work on my approach.

None of the boys have anything approaching a coherent, unified understanding of the math involved. In order to give them all credit for what they know and can do, while still challenging my strongest students, I have to test the subject from every angle. Assessing all students, scoring the range of abilities accurately, is difficult work.

As you can see, the challenges I face have little to do with Asperger’s kids who can’t explain what they think or frustrated parents dealing with number lines or boxes of 10. Nor is it anything solved by lectures or complex instruction. My task is complicated. But hell, it’s fun.

Understanding Math, and the Zombie Problem

I have been mulling this piece on the evils of explanations for a while. There’s many ways to approach this issue, and I highly recommend the extended discussion at Dan Meyer’s blog, as it captures experience-based teachers (mostly reform biased) with the traditionalists, who are primarily not teachers.

What struck me suddenly, as I was engaged in commenting, was the Atlantic’s clever juxtaposition.

All the buzz, all the sturm und drang about Common Core and overprocessed math has involved elementary school. The cute show your thinking pictures are from 8 year olds and first graders. Louis CK breaks our hearts with his third grader’s pain. The image in the Atlantic article has cute little pudgy second grade arms—with just the suggestion of race, maybe black, maybe Hispanic, probably male—writing a whole paragraph on math. The evocative image evokes protective feelings, outrage over the iniquities of modern math instruction, as a probably male student desperately struggles to obey meaningless demands from a probably female teacher who probably doesn’t understand math beyond an elementary level anyway. Hence another underprivileged child’s potential crushed, early and permanently, by the white matriarchal power structure unwilling to acknowledge its limitations.

And who could disagree? Arithmetic has, as John Derbyshire notes, “the peculiar characteristic that it easy to state problems in it that are ferociously difficult to solve.” Why force children to explain place value or the division algorithm? Let them get fluency first. Garelick and Beals (henceforth referred to as G&B) cite various studies finding that elementary school students gain competence by focusing on procedure first, conceptual understanding at some later point.

There’s just one problem. While the Atlantic’s framing targets elementary school, and the essay’s evidence base is entirely from elementary school, G&B’s focus is on middle school.

Percentages. Proportions. Historically, the bane of middle school math. Exhibit C on high school math teachers list of “things our students should know but don’t” (after negatives and fractions), and an oft-tested topic, both conceptually and procedurally, in college placement.

G&B make no bones about their focus. They aren’t the ones who chose the image. They start off with a middle school example, and speak of middle school students who “just want to do the math”.

But again, there’s that authoritatively cited research (linked in blue here):


Again, all cites to research on elementary school math. The researched students are at most fifth graders; the topics never move above arithmetic facts. G&B even make it clear that the claim of “procedure without understanding is rare” is limited to elementary school math, and in the comments, Garelick discusses the limitations of a child’s brain, acknowledging that explanations become more important in adolescence—aka, middle school, algebra, and beyond.

G&B aren’t arguing for 8 year olds to multiply integers in happy, ignorant fluency, but for 14 year olds to calculate percentages and simply “show their work”. And in the event, which they deem unlikely, that students are just going through the motions, that’s okay because “doing a procedure devoid of any understanding of what is being done is actually hard to accomplish with elementary math.” Oh. Wait.

Once you get past the Atlantic bait and switch and discuss the issue at the appropriate age level, everything about the article seems odd.

First, Beals and Garelick would–or should, at least–be delighted with math instruction in 8th grade and beyond. Reform math doesn’t get very far in high school. Not only do most high school teachers reject reform math, most research shows that the bulk of advanced math teachers have proven impervious to all efforts to move beyond “lecture and assign a problem set”. Most math teachers at the high school level accept a worked problem as evidence of understanding, even when it’s not. I’m not as familiar with middle school algebra and geometry teachers, but since NCLB required middle school teachers to be subject-certified, it’s more likely they profile like high school teachers.

G&B don’t even begin to make the case that “explaining math” dominates at the middle school level. They gave an anecdote suggesting that 10% of the week’s math instruction was spent on 2-3 problems, “explaining thinking”.

This is the basis for an interesting discussion. Is it worth spending 10% of the time that would, presumably, otherwise be spent on procedural fluency on making kids jump through hoops to add meaningless detail to correctly worked problems? And then some people would say well, hang on, how about meaningful detail? Or how about other methods of assessing for understanding? For example, how about asking students why they can’t just increase $160 by 20% to get the original coat price? And if 10% is too much time, how about 5%? How about just a few test questions?

But G&B present the case as utterly beyond question, because research and besides, Aspergers. And you know, ELL. We shouldn’t make sure they understand what’s going on, provided they they know the procedures! Isn’t that enough?

Except, as noted, the research they use is for younger kids. None of their research supports their assertion that procedural fluency leads to conceptual understanding for algebra and beyond. We don’t really know.

However, to the extent we do know, most of the research available in algebra suggests exactly the opposite–that students benefit from “sense-making”, conceptual approaches (which is not the same as discovery) as opposed to entirely procedural based instruction. But researching algebra instruction is far more difficult than evaluating the pedagogy of arithmetic operations—and forget about any research done beyond the algebra level. So G&B didn’t provide adequate basis for making their claims about the relative value of procedural vs conceptual fluency, and it’s doubtful the basis exists.

I’ll get to the rest in a minute, but let’s take a pause there. Imagine how different the article would be if G&B had acknowledged that, while elementary school research supports fact fluency over sense-making (and fact fluency seems to be helpful in advanced math), the research and practice at algebra and beyond is less well established. What if they’d argued for their preferences, as opposed to research-based practices, and made an effort to build a case for procedural fluency over comprehension in advanced math? It would have led to a much richer conversation, with everyone acknowledging the strengths and weaknesses of different strategies and choices.

Someday, I’d like to see that conversation take place. Not with G&B, though, since I’m not even sure they understand the big hole in their case. They aren’t experienced enough.

Then there’s the zombie quote, where Garelick and Beals most tellingly display their inexperience:

Yes, Virginia, there are “math zombies”.

In high school, math zombies are very common, particularly in schools with a diverse range of students and thus abilities. Experienced teachers commenting at Dan Meyer’s blog or the Atlantic article all confirm their existence. This piece is long enough without going into anecdotal proof of zombies. One can infer zombie existence by the ever-growing complaints of college math professors about students with strong math transcripts but limited math knowledge.

I’ve seen zombies in tutoring through calculus, in my own teaching through pre-calc. In lower level classes, I’ve stopped some zombies dead in their tracks, often devastating them and angering their parents. The zombies, obviously, are the younger students in my classes, since I don’t teach honors courses. Most of the zombies in my school don’t go through my courses.

Whether math zombies are a problem rather depends on one’s point of view.

There are many math teachers who agree with G&B, who rip through the material, explaining it both procedurally and conceptually but focus on procedural competence. They assign difficult math problems in class with lots of homework. Their tests are difficult but predictable. They value students who wrote the didactic contract with Dolores Umbridge’s nasty pen, etching it into their skin. They diligently memorize the cues and procedures, and obediently regurgitate the procedures, aping understanding without having a clue. There is no dawning moment of conceptual understanding. The students don’t care in the slightest. They are there for the A and, to varying degrees, play Clever Hans for math teachers interested only in correctly worked procedures and right answers. Left as an open issue is the degree to which zombies are also cheating (and if they cheat are they zombies? is also a question left for another day). For now, assume I’m referring to kids who simply go through the motions, stuffing procedures into episodic memory with nothing making it to semantic, all to be forgotten as soon as the test is over.

Math zombies enable our absurd national math expectations. Twenty or thirty years ago, top tier kids had less incentive to fake it through advanced math. But as AP Calculus or die drove our national policy (thanks, Jay Mathews!) and students were driven to start advanced math earlier each year, zombies were rewarded for rather frightening behavior.

G&B and those who operate from the presumption that math can easily be mastered by memorizing procedures, who believe that teachers who slow down or limit coverage are enablers, don’t see math zombies as a problem. They’re the solution. You can see this in G&B’s devotion and constant appeal to the test scores of China, Singapore, and Korea, the ur-Zombies and still the sublime practitioners of the art, if it is to be called that.

For those of us who disagree, zombies create two related problems. First, their behavior encourages math teachers and policy makers to raise expectations, increase covered material, accelerate instruction pace. They allow schools to pretend that half their students or more are capable of advanced, college level math in high school while simultaneously getting As in many other difficult topics. They lead to BC Calculus pass rates of 50% or more (because yes, the AP Calc tests reward zombie math). Arguably, they have created a distortion in our sense of what “college math” should be, by pretending that “college math” is easily doable by most high school students willing to put in some time.

But the related problem is even more of an issue, because the more math teachers and policies reward zombies, the more smart, intellectually curious non-zombies bow out of the game, decide they’ll go to a state school or community college. Which means zombie kids just aren’t numbered among the “smart” kids, they become the smart kids. They define what smart kids “are capable of”, because no one comes along later to measure what they’ve…well, not forgotten, but never really learned to start with. So people think it really is possible to take 10-12 AP courses and understand the material (as opposed to get a 5 on the AP), and that defines what they expect from all top rank students. Meanwhile, those kids–and I know many–are neither intellectually curious nor even “intelligent” as we’d define it.

The Garelick/Beals piece is just a symptom of this mindset, not a cause. They don’t even know enough to realize that most high school math is taught just the way they like it. They’d understand this better if they were teachers, but neither of them has spent any significant time in the classroom, despite their bio claims. Both have significant academic knowledge in related areas–Garelick in elementary math pedagogy, which he studied as a hobby, Beals as a language expert for Asperger’s—which someone at the Atlantic confused with relevant experience.

Such is the nature of discourse in education policy that some people will think I’m rebutting G&B. No. I don’t even disagree with them on everything. The push for elementary school explanation is misguided and wasteful. Many math teachers reward words, not valid explanations; that’s why I use multiple answer math tests to assess conceptual knowledge. I also would love–yea, love–to see my kids willing to work to acquire greater procedural fluency.

But G&B go far beyond their actual expertise and ultimately, their piece is just a sad reminder of how easy it is to be treated as an “expert” by major publications simply by having the right contacts and backers. Nice work if you can get it.

And the “zombie” allusion, further developed by Brett Gilland, is a keeper.

What I Learned: Year 3

I want to continue my teaching retrospective, if only for my own edification. Year 3 in particular led to major changes in my curriculum and pacing.

To recap: my first year was spent in a very progressive school, where I taught algebra, geometry, and humanities, both literature and history. I loved teaching, didn’t much care for the school, and definitely wasn’t sufficiently of the left to stay there. Years 2 and 3 were at a Title I school, 65% Hispanic/ELL. As I’ve said before, year 2’s all algebra all the time schedule was my toughest schedule ever as a teacher; I do not expect to see its like again. Which is good, because I still get flashbacks. I have, in fact, never officially taught algebra 1 since that time although most people would consider what I teach in Algebra 2 to be, in fact, Algebra 1.

Year 3 was at the same school, but I was assigned Algebra 2 and Geometry. And that made all the difference.

Establishing Classroom Ambiance

My 65 geometry students included twenty I’d taught the previous year in Algebra I, students who knew and liked me.

First day, I started one class a bit early when in walked Robbie, redheaded, pale, anxious, diagnosed with Asperger’s but almost certainly a high functioning autistic. I told him to have a seat, and didn’t immediately realize that the little freshman was utterly aghast at the idea that he was late to class. He was murmuring “class starts at 9:15, I was here at 9:12” over and over again, slowly working up to a meltdown by the time I noticed. Before I could react Augustin, a junior, first student I’d met at this school the year before, leaned over from a desk in the same group.

“Relax. Teacher started early. Never cares about time anyway. You’re good.”

Meltdown over. Robbie was awestruck that a junior had deigned to notice him. He also remembered all year that I “never cared about time”, which did much to keep him balanced and happy with a teacher incapable of a predictable routine. I have always remembered Augustin for his offhand kindness to an odd kid.

My geometry classes gave me the feeling of being a known quantity, a teacher with student cred, something I’d long easily established in my Asian enrichment classes, as well as my Kaplan test prep, but never felt in a public school before. I’d always been a loose disciplinarian, an easy classroom controller, and this isn’t as easy in test prep as you might think—it’s why I got so much work. I knew that teaching outside of private instruction would be different, but I found the change more challenging than I expected.

For my first two years in public school, I struggled to recreate the friendly “we’re all in this together” atmosphere I expected to achieve easily. My first year, only my humanities class ever achieved the ambiance I took for granted in private instruction. Only two of my 4 algebra classes (one was a double block) had that cheerful noisiness that is now a trademark of my public school classes. I wasn’t a failure as a teacher; in many ways, I was doing exactly what I anticipated and dealing with expected obstacles. But I had secretly mourned the loss of my standing as a popular teacher. And now, suddenly, I had my mojo again.

My algebra 2 classes were more like my algebra 1 classes from the year before; I didn’t have yet the same easy rapport that I had with my geometry students. This gave me a chance to study the difference. Would I always need to have repeat students, or was there something I could do to establish the environment of easy fun with hard work–or at least some effort?

Over time, I learned that some students find me harder to understand than others. They often don’t grok my ironic asides. They do not understand that I “blast” without malice. They assume I hold grudges, that I count misdemeanors in a black book somewhere. They don’t understand I am often somewhat ruthlessly focused on one objective. As I’ve said before, teaching is a performance art, and the act of engaging students to convince them to learn is often an arduous mental task.

And so I’ve learned to explain this up front. That I am often sarcastic, and think attempts to ban this essential classroom management tool are Against God. That I’m not often annoyed, and usually harmless. But when I am annoyed I yell first, ask questions later when I remember to, which I often don’t. That I am unlikely to remember what I was mad about 20 minutes later, much less hold a grudge. In fact, the only behaviors that I remember are cruelty and cheating. That I love teaching, and like all of them. Except Joe. I can’t stand Joe. And frankly, I’ve never been a big fan of Alison. But except them. And Mario. Don’t care for Mario much. But everyone else. Really. (Yeah, see that, kids? Mild irony. Get used to it.)

I’ve also learned to reach out on things that don’t matter as much to me but I’ve realized matter much more than I realized to students. I’ve always been one to say “Hi!” in the hallways and chitchat for a moment with past and present students but in truth honestly don’t care about football games or sporting events. Still, kids really do like it when you show up at the games, or ask about the outcomes, or call out a student who had a great game or ran a PR. I ban the singing of Happy Birthday because the noise is unbearable, but after they beg, I give them a count of three and we all shout the phrase at once. And all my classes delight in realizing how easy it is to drive me off-topic by asking about food or politics.

All my ability to deliberately set a classroom environment came from the lucky break of teaching geometry to some of the same students I’d just passed in algebra.

Coverage vs. Comprehension


I sure hope Bud Blake got credit for this 1974 classic, reproduced daily in ed school and professional development lessons everywhere.

I used to take state tests more seriously, and was quite proud that my first year out, I “hit the dinger” in geometry and algebra. I hadn’t rushed, and even back then had deemed many topics non-essential, or at least far less important than others. My students were doing reasonably well on tests, which were free-response that year.

But towards the end of the year, I realized with a shock that many of my mid-tier students had forgotten most of the content. Students who understood the Pythagorean Theorem were now marking up triangles with SOHCAHTOA when they had two sides and just needed the third. Algebra students were plugging linear equations into the quadratic formula. Cats were sleeping with dogs. All was not right. It was as if they’d never been taught.

Year two, I was primed to look for learning loss but pacing was so impossible with the wide ability range that I instituted four levels of differentiation. I succeeded in slowing down instruction and letting students absorb more information.

But year three saw my first attempts to help Stripe learn to whistle.

In geometry, the first sign of change came in October. I’d explained transversals of parallel lines. I’d done a great job. Brilliant, even. Not content to simply lecture, I asked questions, prompted discussion, ensured students saw the connection and sketched the familiar representation.

And the lesson didn’t thud. All the students obediently worked the problem set. They asked reasonable questions.

So I don’t know, really, what compelled me to double check.

“Am I picking up a weird vibe? You all are working, but I have this sense that you’re still confused.”

Murmurs of agreement.

“How about everyone close their eyes and we’ll do a thumb check?” (I rarely use such obvious CFUs these days, but they’re still a great tool for uncertain situations.)

Most of the thumbs came up sideways.

So I told the kids I’d think about this for a while, and came back with an activity, one that required about $70 in materials that I still use to this day.



It worked. The transversal angle relationships were easier to understand with the physical representation, the students could see the inevitability, see how the angles “fit”. And from that point, they could easily see that unless the transversal was perpendicular, each transversal over parallel lines formed only two distinct angle measurements: an obtuse and an acute.

A nifty transversal lesson wasn’t the important development, even though my geometry students still enjoy the activity almost as much as they enjoy creating madcap patterns with the boards and rubber bands.

Sensing confusion despite a generally successful lesson, I had developed an illustration on my own to develop a stronger understanding. I was beginning to spot the difference between teaching and learning.

I still struggle with this. It’s very easy to get sloppy, particularly in a large class with ability ranges of 4 to 5 years, with kids in the lower ranges happily sleeping through classes, stirring themselves only enough to beg me for a passing grade. But ultimately, I circle back with yet one more pass through, coming up with an illustration or series of problems to shine a light on confusion.

I’ve written extensively of Year 3’s other major development. Faced with the reality that I’d wasted a semester covering linear equations and quadratics that students didn’t remember in the slightest, I decided to start over, beginning with modeling linear equations. Not only did I completely change my approach to curriculum, I also flatly punted on coverage from that point on, focusing on the big five for every subject. As I improve at introducing and explaining concepts, my students become capable of taking on more challenging topics; the interaction between my curriculum and student understanding is very much a positive feedback loop.

Ironically, my decision to abandon coverage was driven in part because Algebra 2 was a terminal course, meaning it was to be offered only to remedial seniors, students were not expected or in fact allowed to take any other math course. For this reason, I felt free to craft my own course to focus purely on getting the students ready for college math. But at least half of my students were juniors, and most of them took pre-calc the next year. This was my first exposure to Algebra 2’s dual nature. More on that later.

Mentoring Colleagues

For my first two years, I had almost no contact with colleagues. Year 3, two new math teachers joined and we instantly hit it off. Went for coffee on late start mornings, beers after work. I was their resource; both of them found me far more helpful than their assigned mentors. I still meet up with both of them four or five times a year at least.

I left that year for my current school, and went over two years again without any real colleagues. I missed it. Having spent most of my professional life working without colleagues that liked lunch, beer, coffee, whatever, I can map out the exception eras, and treasure them. Last year I began mentoring, and now have lunch, coffee, whatever with them individually and together.

I’m not chummy enough, much less normal enough, to bond easily with other teachers. But I’m a good mentor, and that seems to be how I make friends as a teacher.

Finally, Year Three taught me how to cope with genuinely unfair treatment, which I haven’t often had to deal with. I never go into details about it, but while I wasn’t crazy about the school, I didn’t want to look for jobs again. Being a fifty year old teacher without a job is a Very Bad Thing—of course, take out the word “teacher” and it’s still true, probably more so.

On the other hand, while I wasn’t crazy about that school, I am very happy at this one. What do they call that, perspective?

On the Spring Valley High Incident

So the Spring Valley High School incident is yet another case of a teenager treating a cop like a teacher. This is, as always, a terrible idea.

I watch the video and wonder about the teacher. I wonder if he’s wondering what I’d wonder in his shoes. Teachers aren’t just focused on the recalcitrant girl who refuses to comply, who hits the police officer, who gets arrested. Teachers notice the girl directly behind the cop and the defiant kid, the one who wasn’t a troublemaker, was just sitting in class doing her work and nearly gets clobbered by the flipped over desk. Or the other kids trying not to watch–suggestion, I think, that the shocking events aren’t a common occurrence. Teachers notice that the kids are working with laptops and hope none of them fly off a desk into another student. (Teachers probably also notice the photographer’s test has many wrong answers. Occupational hazard.)

He’s got to be wondering, now and forever, if he could have prevented this. One time, a student in my class inexplicably left her $600 iPhone on her desk during a class activity that involved working at boards, and it disappeared, which required a call to the supervisors and a full class search. I told them who I suspected, then left because I didn’t want to know. When I came back, they’d detained the strongest student in the class–not for stealing the phone, which was never found. I have decided it’s better not to say why, but it was one of those things that lots of kids do in violation of policy because they’re unlikely to get caught. But if they get caught, it’s bad. (No, not drugs). He was suspended for the maximum time period and had to worry about more than that, although more was mostly scare talk.

The point is, I felt absolutely terrible. The student who left the phone out was careless and silly, the student who stole the phone was a criminal, the student who got suspended was knowingly in violation of a major school policy without the slightest thought for his long-term prospects. But if I’d just seen the damn phone on the desk, none of this would have happened.

So when I look at this video, like many if not most teachers, I’m not thinking about whether the girl deserved to be flipped about, because that’s the cop’s problem. I’m wondering was there anything that teacher could have done to avoid having the cop there in the first place.

Reports say that the student initiated the event by refusing to turn over a cell phone—also offered up is refusal to stop chewing gum, which I find unlikely. However, it’s clear the student was refusing several direct orders that began with the teacher and moved up through the administrator and the cop.

Defiance is a big deal in high school. It must not be tolerated. Tolerating open defiance is what leads to hopelessness, to out of control classrooms, to kids wandering around the halls, to screaming fights on a routine basis. Some teachers care about dress code, others about swearing, still others get bothered by tardies. But most teachers enforce, and most administrators support, a strong, absolute bulwark against outright defiance as an essential discipline element.

Let me put it this way: an angry student tells me to f*** off or worse, I’m likely to shrug it off if peace is restored. Get an apology later when things have settled. But if that student refuses to hand me a cell phone, or change seats, or put food away, I tell him he’ll be removed from class if he doesn’t comply. No compliance, I call the supervisor and have the kid removed. Instantly. Not something I spend more than 30 seconds of class time on, including writing up a referral.

At that point, the student will occasionally leave the classroom without waiting for the supervisor, which changes the charge from “defiance” to “leaving class without permission”. The rest of the time the supervisor comes, the kid leaves, comes back the next day, and next time I tell them to do something, they do it. Overwhelmingly, though, the kids just hand me the phone, put away the food, change seatswhen I ask, every so often pleading for a second chance which every so often I give. Otherwise, the incident is over. Just today I had three phones in my pocket for just one class, and four lunches on the table that had to wait until advisory was over because I don’t like eating in my classroom.

We have a school resource officer (SRO), but I’d call a supervisor for defiance, and I’ve never heard of a kid refusing to go with a supervisor. If there was a refusal, at a certain point the supervisor would call an administrator, and it’s conceivable, I guess, that the administrator could authorize the SRO to step in. So assuming I couldn’t have talked this student down, I would have done what the teacher did, and called for someone else to take over—and long after I did something that should have been no big deal, this catastrophe could conceivably have happened.

I ask you, readers, to consider the recalcitrance required to defy three or four levels of authority, to hold up a class for at least 10-15 minutes, to refuse even to leave the classroom to discuss whatever outrage the student feels warrants this level of disruption.

Then I ask you to consider what would happen if students constantly defied orders (couched as requests, of course) to turn over a cell phone, or change seats, or stop combing their hair, or put the food away. If every time a student defied an order, a long drawn-out battle going through three levels of authority ensued. School would rapidly become unmanageable.

So you have two choices at that point: let madness prevail, or be unflinching with open defiance. Students have to understand that defiance is worse than compliance, that once defiance has occurred, complying with a supervisor is a step up from being turned over to an administrator, which is way, way better than being turned over to a cop. (Note that all of this assumes that the parents aren’t a fear factor.)

Some schools can’t avoid the insanity. Their students simply don’t fear the outcomes enough, and unlike charters, they are bound by federal and state laws to educate all children. If the schools suspend too many kids, the feds will come in and force you into a voluntary agreement. This is when desperate times lead to desperate measures like restorative justice, where each incident leads to an endless yammer about feeeeeeeeelings as teachers play therapist and tell their kids to circle up.

Judge the cop as you will. I can see no excuse for putting other students in danger; the fight could have seriously injured the girl sitting directly behind the incident. He could have cleared the area first, making sure all students were safe. I believe that’s his responsibility.

However, once the administrator asked the SRO to take over, the student was dealing not with a school official, but with a cop. At that point, she was disobeying a police officer’s order. On government property. And she is clearly hitting him, in this video.

And, like I said, disobeying a cop is a bad idea.

So the question is not what should the cop have done, but why did the administrator call the cop? And what would you have had the administrator do instead? Don’t focus on that single incident, because teachers, administrators, and cops don’t have that luxury. They have to handle it in such a way so that defiance doesn’t become a regular routine, that students customarily obey their teachers, maybe with some backtalk, maybe with ample opportunities to walk a bad mistake back. Ultimately, though, students have to comply. If a school backs away from that line, defiance gets contagious. It’s one thing for new, inept teachers to have trouble controlling their students, quite another for an entire school to give up.

I recently had an exchange with David Leonhardt on his NAEP scores article, and he asked me “I assume you agree school quality should be linked to amount students learn, yes?”

Well, not the way we currently measure it, probably not. But I do think school quality should be linked to established order and by “order” I don’t mean an Eva Moskowitz gulag. Control freaks like Moskowitz fail to allow for normal mood swings and eruptions from kids who are, after all, engaged in an involuntary activity for eight hours a day.

Schools that fail to establish order are those like Normandy High School, with out of control violence, open defiance of teachers and administrators, and students in constant danger of assault. Students should have the opportunity to learn, even if they aren’t mastering material at the rate our policy wonks would allow. Schools that can’t enable that are genuine failures.

The Moskowitz contingent point to schools like Normandy as rationale for their despotic rules. Look, they say. Let “these kids” think they can act however they like, and you end up with screaming, chaotic classrooms, truancy, assaults and fights on and between students, ineffectual teachers, and worst of all, low test scores. Teach them to behave respectfully, five times more compliant than suburban white kids, and you’re doing them a favor, saving them from “those schools”. Better Animal Farm than Clockwork Orange

Any school with a solid percentage of kids who’d really rather be somewhere else has to find a balance. Make enough kids want to comply so there’s room to expel the kids who routinely don’t. This isn’t achieved by Eva Moskowitz tyranny, but nor will restorative justice get the job done. It’s hard. There has to be limits. There has to be balance. Administrators who think they have the perfect mix are probably kidding themselves.

In the meantime, if, like Martin O’Malley or Chris Hayes, you’d be “ripped ballistic” if a cop did this to your kid, familiarize yourself and your children with the dangers of disobeying a cop and resisting arrest.

Handling the Teacher Perks

Before turning teacher, I spent all but five years as a temp worker, self-employed or contract. Unemployment? A hassle I didn’t bother with the few times I was eligible. Retirement? My very own funded SEP_IRA, no employer matching. Paid vacation and sick leave? Outside of those five years, I never had any.

Going from that life to public school teaching was kind of like Neal Stephenson’s description (excerpted from In the Beginning was the Command Line) of the guy who was raised by carpenters from early childhood with only a Hole Hawg as a drill and then meeting up finally with a puny homeowner’s version.

What the hell. With so much free stuff, how can you call this work?

From Veteran’s Day to the first week of the New Year, over three weeks off, the bulk of them from mid-December to early January. Five plus days off at spring break, and two months off in the summer. Eleven days of sick leave that accrue, and two “use it or lose it” days. I get the same amount of pay every single month. Guaranteed pension, already vested comfortably, probably to retire with 30%—not bad for a late entry.

Plus, I hear it’s hard to get fired.

I clearly remember watching the perks of corporate employment slowly be stripped away back in my twenties, perks that few people under 50 can even imagine. So it’s bizarre to have entered a profession where it feels like the 80s again.

Now, I’m wondering if I’m getting used to it.

In the previous five years of teaching, my collective time out of the classroom was 3 sick days and 6 mandated professional development days. This year, I was out of class for nearly 10 days of professional obligations: three days for an honest to god, out of state, education conference, two-plus days for mentoring and induction responsibilities, and 4 days of Common Core testing.

I felt very guilty about all this time off, and without question the absences impacted instruction time and coverage. So much so that when I came down with a really severe case of with food poisoning (you know those rotisserie chickens? Used to love them. Hope I eventually trust them again) during testing week, I came in anyway because I knew it would wreak havoc both on testing schedules for administration and my carefully scheduled coverage plans (I was missing alternate classes during the week). I went four days munching crackers and chugging that weird chalky pink stuff, previously unknown to me.

In retrospect this struck me as idiotic, so I went to the principal’s secretary and asked how to request time off. That’s when I learned formally I had 13 days a year, including two use or lose–which I’ve been losing for the past five years. I took a whole day and a half just for a family graduation 10 hours away, when I normally would have left Friday afternoon and come back Sunday night.

More evidence: for the first time in eight summers, six of them as a teacher, I decided to forego employment (part-time and no benefits, of course) at my favorite hagwon, where I usually act as chief lunatic for book club, PSAT prep, and occasionally geometry.

Why? I wanted more time off.

This wasn’t a sudden decision. Last year it finally sunk in that despite the easy hours and students, the elapsed time of my hagwon day clocked in at 9 hours: three on, three off, three on, for eight weeks. While this hadn’t seemed punitive with a 5 minute commute, the schedule lost much of its charm when I moved 45 minutes away. Meanwhile, the eight week schedule left just eight uninterrupted days off at the end of summer.

Yes. The four weeks I am granted throughout the year is not enough. I want more of the eight uninterrupted weeks. It shames me.

But there’s hope. If eight days seemed too little, two months off seemed….excessive. Years of temp work leaves me never entirely comfortable not knowing where my next dollar would come from. Long vacations make me nervous. Back in my tutor/test prep instructor life, my son and I took a long road trip one summer that culminated in a 6 week stay in another city. I notified a local Kaplan branch, got some SAT classes, put ads in Craigslist and got some private tutoring, making enough to offset the fuel and food expenditures for the trip.

I am not yet ready to abandon summer work altogether. I wanted a summer job. Just a different one, with a shorter work day, a shorter employment term, and higher hourly pay so I’d get more time off but the same dollars’ pay.

Normal people are thinking “Hah! And a pony.” Teachers are thinking “Duh. Just teach summer school.” Public summer school, that is. Six weeks at most in my area, higher hourly pay, out at 1:30.

I have very strong feelings about summer school, none of them positive. But public summer school it is, this summer. More of that later, assuming I can push through and finish this absurdly non-essential piece because family fun time and work are coming perilously close to giving me writer’s block.

As a side note, a transition marked: I’ve now left all three legs of my previous income behind. Private tutoring mostly gone over the past two years, the hagwon this last year, Kaplan since ed school.

A job change to get a longer summer break. Another worrisome trend?

But then, just when I began to worry about having been slowly sucked in, I learned what my preps for the upcoming year would be and nearly had a meltdown.

Every year, teachers are given a form to list their preferences for subject assignments (aka, “preps”). Every year, my form says “I’m happy to teach any academic subject I’ve got a credential for–but please don’t limit me to one prep a semester. Two is better, three is best.” Then I list three classes I haven’t taught in a while, or would like to do a second time. This year, I’d asked to teach at least one session of history, to build on my last year, pre-calc, which I hadn’t taught in a year, and any lower level class, just to keep myself humble. Again, this is in the context of teaching any other class as well.

I went into school after summer started to work on one of the professional obligations above, and as a thank-you, the principal showed us the master schedule board.

Semester One: Algebra 2, Trig. Two blocks of each.
Semester Two: Algebra 2, Trig. Three blocks total, two blocks Trig.

This schedule would be, to most teachers, a perk. Just two preps I’m familiar with. An easy year, after an extraordinarily demanding one in which I had two brand new classes, one of which was in a completely different academic subject for the first time in five years. Some might view the schedule as a form of thank-you, or maybe an acknowledgement that I’ve got more professional responsibilities so require a schedule with less planning or curriculum development.

I looked at the board and thought Christ, I have to quit this school, that’s awful, I love this school, but I have to get out of here. I need some time for job-hunting. I can’t quit summer school, it starts Monday. But I can jobhunt in the afternoons, it’s a Friday so I have some time to update my resume. Maybe I won’t have to leave the district, so I could keep tenure, and maybe I can talk to the administrator at summer school, hey, it’s actually good that I’m not at the hagwon this year, I just need to update my resume….

So not a perk, to me.

I tend towards extreme reactions, as alert readers may have noticed. Self-knowledge has led to compensatory braking systems. In years past, I would have just turned in my resignation on the spot. But my braking system kicked in, I remembered that quitting is just a symptom of my temporary worker mindset. I reminded myself how good it felt to get tenure, that my administration team likes me. Before I quit, I should perhaps consider other alternatives.

I will cover those alternatives, and my fears, in a follow-up post. No really, I promise.

So no, I’m not yet sucked in by the teacher perks. But I do want more free time during my 10 weeks off. Call me ungrateful.


Note: I will always value intellectual challenge over predictability for my own job satisfaction. But many teachers do an outstanding job teaching just one subject or the same two preps for thirty years. Outsiders, particularly well-educated folks with elite pedigrees, champion intellectual curious teachers with cognitive ability to spare as an obvious advancement over what they see as the “factory model” teacher turning out the same widgets ever year. But little evidence suggests that intellectual chops produces better results, much less better teachers. So please don’t interpret my rejection of predictability and routine as evidence of anything other than a fear of boredom.

Math isn’t Aspirin. Neither is Teaching.

First, congrats to Dan Meyer, who finished his doctorate at Stanford and just hired on as CAO for Desmos, a tremendously useful online graphing calculator. He persisted in the face of threatened failure, and didn’t give up even when he had an easy out into a great job. (Presumably Dan and most of the Math Twitter Blogosphere are still annoyed at my jeremiad about the meaning of his meteoric rise, in which Dan played the part of illustration.)

Dan has asked math teachers for ways to create “headaches” for which math can be considered aspirin:


And this interested me because the request completely, perfectly, captures the difference between our two philosophies, which I also wrote about a couple years ago:


The comparison is an instructive one, I think. Both of us find it necessary to build our own curriculum, rejecting the one on offer, and both of us, I think, tremendously enjoy the creation process. Both of us reject the typical didactic contract described by Guy Brouseau, setting expectations very different from those of typical math teachers: explain, work a few examples, assign a set. Both of us largely eschew textbooks for instruction, although I consider them completely unnecessary save as reference books that often provide interesting problems I can steal, while Dan dreams of the perfect digital textbook.

And yet we couldn’t differ more in both teaching philosophy and curriculum approach.

Dan’s still selling curiosity and desire for knowledge, assuming capability will follow. I’m still selling capability because I see confidence follow.

Dan still believes that student engagement captures their curiosity which leads to academic success, that the Holy Grail of academic success in math lies in finding the perfect problems that universally stimulate interest in finding answers, which leads to understanding for all. I hold that student engagement leads to their willingness to attempt what they previously thought was impossible but that the Holy Grail doesn’t exist.

Meyer thinks teachers skeptical of his methods are resistant to change and the best interests of their students. I advise teachers and recommend curriculum; if they find my advice helpful, great. I encourage them to modify or even reject my advice, to continue to see an approach that works for them and their students.

Dan wants to be “less helpful”. I want to teach kids to use their own resources, but given a kid who wants to give up, I’m offering help every time.

Meyer’s methods would probably need tremendous readjustment if he worked in a low-income school with a wide range of abilities. I’d probably be much “less helpful” if I taught at a school with a high-achieving, homogenous population obsessed about grades.

Meyer rose quickly in the rarefied world of rock star teachers. I aspire to the role of and indie with cult status.

Dan’s query: “Why did mathematicians think this skill was worth even a little bit of our time? If the ability to factor that trinomial is aspirin for a mathematician, then how do we create the headache?

My answer: You can’t.

The commenters, mostly teachers, took the question seriously, understanding that it was another way of looking at the students’ demand, “When will we use this?”. Answering this question clearly troubles most of the commenters—or they have an affirmative answer they’re satisfied with.

My answer to the student demand: “Probably never. But the more willing you are to take on challenging tasks you learn from, the more opportunities you’ll have in life, both professional and personal. Call me crazy, but I see this as a good thing.”

Dan Meyer is wrong, I believe, in looking for the Holy Grail that makes math “aspirin”1. But that’s not the point of my running through the Dan vs. Ed showdown.

Instead, consider the comparison yet another data point in my slowly developing thesis that ed schools need more flexibility and even less prescription. Few people understand the vast scale of values, philosophies, management and curriculum found in the teaching population.

Two teachers developing uncommon curriculum who agree on very little—yet both of us are considered successful teachers. (one has much more success selling his ideas to people with money, I grant you.) Take ten more math teachers likewise who build their own curriculum, have their own takes on philosophy, discipline, and even grading and they’re unlikely to change to suit another model. Take 100 more–ditto. Voila! an expanding population of teachers who have successful teaching approaches and curriculum design that they’ve developed and modified. None of them are going to agree on much. They have come to widely varying conclusions that they will continue to develop and enhance on their timeline as they see fit. No one will have anything approaching a convincing argument that could possibly convince them otherwise.

The point: the current push to “fix” ed schools, a fond delusion of reformers, progressives and union leaders alike. People as diverse as Benjamin Riley, Paul Bruno, Rick Hess and others believe we can find (or already have) a teaching knowledge base that can be passed on to novices.

Teachers are never going to agree.

Agreement or even consensus is impossible. Teachers and students form infinite combinations of interests, values, incentives and unlike reformers, teachers are going to value their experience and unique circumstances over anything ed schools tried to pretend was the only way.

Teaching, like math, isn’t aspirin. It’s not medicine. It’s not a cure. It is an art enhanced by skills appropriate to the situation and medium, that will achieve all outcomes including success and failure based on complex interactions between the teachers and their audience. Treat it as a medicine, mandate a particular course of treatment, and hundreds of thousands of teachers will simply refuse to comply because it won’t cure the challenges and opportunities they face.

So when the status quo has prevailed for the next 30 years, don’t say you weren’t warned.

1which isn’t to say I don’t plan on writing up the how and why of my quadratic equations section.

Grant Wiggins

Curriculum is the least understood of the reform efforts, even though parents have more day to day contact with curriculum than choice or accountability. This is in large part because curriculum advocates don’t agree to the degree that accountability and choice reformers do, but also because teachers have far more control over curriculum than most understand. As Larry Cuban explains, curriculum has multiple layers: intended, tested, taught, and learned. Curriculum battles usually involve the intended curriculum, the one designed by the state, which usually creates the tested curriculum as a manageable subset. (Much of the Common Core controversy is caused by the overwhelming difficulty of the tested curriculum, but leave that for another time.)

But intended and tested curriculum are irrelevant once the doors close, and in this essay, I refer to the taught curriculum, the one that we teachers sculpt, whether we use “the book” (actually just pieces of the district approved book), use another book we like better, or build our own.

To the extent most non-educators know anything about curriculum advocacy, it begins and ends with E. D. Hirsch, otherwise known as “the guy who says what my nth grader should know”, author of a book series he eventually transformed into a curriculum for k-6, Core Knowledge. Hirsch offers one Big Idea: improving student background knowledge will improve their reading comprehension, because only with background knowledge can students learn from text. But, the Idea continues, schools ignore content knowledge in favor of teaching students “skills”. To improve reading comprehension and ongoing student academic outcomes, schools must shift from a skills approach to one dedicated to improving knowledge.

Then there’s Grant Wiggins, whose death last week occasioned this essay as an attempt to explain that we’ve lost a giant.

The media proper didn’t give Wiggins’ passing much notice. Valerie Strauss gave his last blog sequence a good sendoff and Edutopia brought back all their interviews with him. Education World and Education Week gave him obits. It doesn’t look as if Real Clear Education noted his passing, which is a bit shocking but perhaps I missed the mention.

Inside education schools, that world reformers hold in considerable contempt, Wiggins’ work is incredibly influential and his death sent off shockwaves. Since 1998, Understanding by Design has been an essential component in preparing teachers for the professional challenge of deciding what to teach and how to deliver the instruction.

Prospective teachers don’t always understand this preparation will have relevance to their lives until their first year in the classroom. Progressive ed schools would never say anything so directly as “You will be faced with 30 kids with an 8 year range in ability and the textbooks won’t work.” Their ideology demands they wrap this message up in hooha on how insensitive textbooks are to the diverse needs of the classroom. Then, their ideology influences the examples and tasks they choose for instruction. Teacher candidates with an instructivist bent thus often tune out curriculum development classes in ed school, rolling their eyes at the absurd examples and thinking keerist, just use the textbook. (Yeah. This was me.)

Usually, they figure out the relevance of curriculum instruction when they get into the classroom, when they realize how laughably inadequate the textbook is for the wide range of abilities and interests of their students. When they realize the book assumes kids will sit patiently and listen, then obediently practice. When they realize that most of the kids won’t bring their books, and that all the well-intended advice about giving consequences for unprepared students will alone result in failing half the class, never mind the problems with their ability. When they realize that many kids have checked out, either actively misbehaving or passively sitting. Worst of all the teachers experience the kids who are eager to learn, try hard, don’t get it, and don’t remember anyway. Then, even after they make a bunch of adjustments, these teachers realize that kids who do seem to be learning don’t remember much—that is, in Cuban’s paradigm, the learned curriculum is wildly different than the one taught (or in the Wiggins universe, “transferred”).

The teachers who don’t quit or move to charters or comprehensives with a higher SES may remember vaguely hey, there was something about this in ed school (hell, maybe that’s just me). So they go dig up their readers and textbooks and suddenly, all the twaddle about diversity and cultural imperialism fades away and the real message becomes legible, like developing invisible ink. How do you create a learning unit? What are your objectives? How will you assess student learning? And at that point, many roads lead to Wiggins.

Grant Wiggins was impossible to pigeonhole in a reform typology. In 1988, he made 10 proposals for high school reform that leaned progressive but that everyone could find some agreement with. He didn’t think much of lecturing, but he wrote a really terrific analysis of lectures that should be required reading for all teachers. (While I also liked Harry Webb’s rejoinder, I reread them in preparation for this essay and Grant’s is far superior.) He approved of Common Core’s ELA standards, but found the math ones weak. In the space of two weeks in 2013, he took on both Diane Ravitch and E. D. Hirsch, and this is after Ravitch flipped on Hirsch and other traditionalists.

Grant Wiggins was more than ready to mix it up. Both his essays on Hirsch and Ravitch might fairly be called broadsides, although backed with research and logic that made both compelling, (perhaps that’s because I largely agreed with them). His last two posts dissected Hirsch supporter Dan Willingham’s op-ed on reading strategies. While he listened and watched teachers intently, he would readily disagree with them and was rarely gentle in pointing it out. I found his insights on curriculum and instruction absolutely fascinating, but rolled my eyes hard at his more excessive plaints on behalf of students, like the nonsense on apartheid bathrooms and the shadowing experience that supposedly revealed the terrible lives of high school students—and if teachers were all denied the right to sarcasm, as he would have it, I’d quit. He didn’t hesitate to say I didn’t understand the lives that students lead, and I told him right back that he was wrong. More troubling to me was his conviction that most teachers were derelict in their duty and his belief that teachers are responsible for low test scores. But what made him so compelling, I think, is that he offered value to all teachers on a wide range of topics near to our needs, whether or not we shared all his opinions.

I knew him slightly. He once linked to my essay on math philosophies as an example of a “learned” teacher, and read my extended response (do I have any other kind?) and took the time to answer. Then, a few months later, I responded to his post on “teacher job descriptions” with a comment he found worthy of pulling out for a post on planning. He then privately emailed to let me know he’d used my comment and asked me to give feedback on his survey. That was a very big day. Like, I told my folks about it.

In the last week of his life, Grant had asked Robert Pondiscio to read his Willingham critique. Pondiscio, a passionate advocate of all things content knowledge, dismissed this overture and declared his posts on both Willingham and Hirsch “intemperate”. Benjamin Riley of Deans for Impact broke in, complimenting Grant and encouraging the idea of debate. The next day, Daniel Willingham responded to Grant on his site (I would be unsurprised to learn that Riley had something to do with that, and kudos to him if so). Grant was clearly pleased to be hashing the issues out directly and they exchanged a series of comments.

I had been retweeting the conversation and adding comments. Grant agreed with my observation that Core Knowledge advocates are (wrongly) treated as neutral experts.

On the last day of his life, Grant favorited a few of these tweets, I think because he realized I understood both his frustration at the silence and his delight at finally engaging Dan in debate.

And then Grant Wiggins died suddenly, shockingly. He’ll will never finish that conversation with Dan Willingham. Death, clearly, has no respect for the demands of social media discourse.

Dan Willingham tweeted his respect. Robert Pondiscio wrote an appreciation, expressing regret for his abruptness. If the general media ignored Grant’s passing, Twitter did not.

I didn’t know Grant well enough to provide personal insights. But I’m an educator, and so I will try to educate people, make them aware of who was lost, and what he had to offer.

Novices can find plenty of vidoes on his “backwards design” with a simple google. But his discussions on learning and assessment are probably more interesting to the general audience and teachers alike—and my favorites as well.

Reformers like Michael Petrilli are experiencing a significant backlash to their causes. Petrilli isn’t wrong about the need for parent buy-in, but as Rick Hess recently wrote, the talkers in education policy are simply uninterested in what the “doers” have to offer the conversation.

Amen to that. The best education policy advocates—Wiggins, Larry Cuban, Tom Loveless–have all spent significant time as teachers. Grant Wiggins set an example reformers could follow as someone who could criticize teachers, rightly or wrongly, and be heard because he listened. If he disagreed, he’d either cite evidence or argue values. So while he genuinely believed that most teachers were inadequate, teachers who engaged with him instantly knew this guy understood their world, and were more likely to listen.

And for the teachers that Grant found inadequate—well, I will always think him in error about the responsibility teachers own for academic outcomes. But teachers should stretch and challenge themselves. I encourage all teachers to look for ways to increase engagement, rigor, and learning, and I can think of no better starting point than Grant Wiggins’ blog.

I will honor his memory by reading his work regularly and looking for new insights to bring to both my teaching and writing.

If there’s an afterlife, I’m sure Grant is currently explaining to God how the world would have turned out better if he’d had started with the assessment and worked backwards. It would have taken longer than seven days, though.

My sincere condolences to his wife, four children, two grandsons, his long-time colleague Jay McTighe, his band the Hazbins, and the many people who were privileged to know him well. But even out here on the outskirts of Grant’s galaxy of influence, he’ll be sorely missed.