Test Gatekeeping

This was written sometime between March and April of 2009. As part of our practicum, we have to do an observation of a fellow student, write up an observation, and then write a reflective response to each other’s observation.

My fellow student observed me give an exam to my students and was surprised, but highly complimentary of my practice of “gatekeeping”. A student just doesn’t get to turn in a test. First I check the test, scan for unforced errors and blank responses. If the first, I underline some key term that should trigger a recognition, if the problem is just that they misread the question. If the second, I just hand it back to them and say “You know how to do this. Or you know how to start doing this. Go get it done.” Some students whine, some ask quiet questions, and some look at my underlined term and gasp out “Thank you!” as they run back to their seat and fix the problem.

My colleague asked if I would continue doing this throughout the semester. Would I always provide this support, or as the class progressed, would I let them go out on their own? I answered the question in this reflection.

Ten years later, this is one practice I haven’t changed even slightly. I make tough tests, and I make the students try hard, sending them back with advice, pointing out small mistakes, giving them a hint if they are lower level. And I wouldn’t change a thing. It’s amazing to see this again and be reminded of how consistent my philosophy has been–and that it does come from my years in test prep.

One change–when a student asks me to check it for them, I still give it a once over. I’m nice that way.

I decided to focus my reflection on your comments about my test “scaffolding”, my practice of reviewing a math test before the student hands it in.

I didn’t mention this earlier, but I have only actively reviewed every student’s test for the past two chapter tests–and even then, only done it both times for fourth period. This test, I actively scanned all students in both classes before they could submit.

I began doing it because I noticed so many struggling students leaving questions blank when I knew that they knew how to do the math. I have spent five years teaching kids to take tests and have seen emotional responses that defy all logic knock down performance considerably. Some examples:

  • “I don’t know how to do this problem. See? I KNEW I didn’t know how to do this problem. I TOLD myself I didn’t. I was right!”
  • “Should I try this? No, it couldn’t be that. If it were that, then it would mean I knew how to do the problem, and I know I don’t know how to do this problem.”
  • “Eh, I did enough work to pass. I’m done. I’m bored.”
  • “Oh, my god, I thought I knew how to do this problem but it doesn’t work! I know NOTHING.” (instead of seeing if, you know, maybe a minor algebra mistake happened somewhere.)
  • “God, I’m done. I’m done. Thank god. I’m done. I’m turning it in now. Thank god.”

None of these thoughts make it into the conscious brain to allow the student to see logically how goofy their responses are, how maybe they should calm down and try some other approaches, take their time and think through the math, check their work for mistakes, or, god forbid, remember what they learned in class. No, the responses all pass through the brain at light speed, leaving behind despair and antagonism, affecting students’ decisions without letting them know what’s happening.

As a math teacher giving an assessment, my primary responsibility is to determine how much math each student knows. If I have to make them hork it up like a fur ball or punch it out of them via Heimlich maneuver, so be it. But to the extent possible, I will not allow their emotional response to determine their grade and my knowledge of their performance.

Many math teachers believe that learning math involves a degree of emotional maturity. As students progress, the thinking goes, they must learn how to accept responsibility for their performance. Maturity involves taking responsibility for one’s learning.

I have parented a teenager, and this sort of thinking makes me laugh. If I allow these kids to turn in their lesser effort, I am doing them a favor. They aren’t punished by the lower grade. They are vindicated. See? They were RIGHT. They didn’t know the math. Stupid fool teacher, and more importantly, stupid fool parents for thinking otherwise.

By insisting they can do the work, I prove two things. First, I am the boss. I will not allow them to get away with a lesser effort, whether that effort is due to lack of interest, fear of failure, or total panic. Second, I am right. They can do the work. They will get a higher grade.

The struggling students aren’t the only ones who benefit from scrutiny. Strong and even mid-level students make unforced errors, and these students genuinely appreciate my checking. These are the ones that go “Ack!” when I point out the word “line” and they realize they’ve solved a linear function as an exponential one and say “Thanks!” with enthusiasm.

But struggling students see math as a war, and in their minds, their failure is a form of victory. Lecturing them about failure doesn’t work nearly as well as showing them that they already have the knowledge to avoid failure–or at least mitigate the disaster. I would far rather engage in a humorous tug of war with a student who wants to turn in a math test than I would lecture them about an F after the fact. For one thing, even the weakest students appreciate the reality of a higher grade. For another, I have proven conclusively that I was right and THEY WERE WRONG. This gives me the credibility advantage and gives us a shared reference point. “Yeah, yeah, sure you can’t do it. Didn’t we have this conversation last test? Sit back down and think. You can do it.” This is already happening with some students. Others are still in the argument mode, but we’ll get there.

So when do I get around to allowing them to go cold turkey? With the stronger students, of course, the task will be easier. Over time, I will talk to them privately, mention SAT scores and the downside of not having a teacher check their work. Their own motivation will do the trick.

But with the struggling students, so long as it affects their grades, I will continue to force math out of them no matter how long it takes. My primary objective as a teacher is to be sure that I am capturing their math knowledge. Independence and self-direction are nice to haves, but they come second, in my mind.

However, if my test prep experience has any relevance here, over time, the struggling students will start to realize they know more than they think they know. By having test productivity forced out of them kicking and screaming, they’ll begin to accept that by golly, they do know math and will start asking small questions to clarify and taking on more responsibility. That’s the plan. When the struggling students are at the point of handing their test to me and saying “Hey, could you check this for me? I want to be sure I got everything”, I’ll start telling them to check their own work and count it a happy day.


Why Did I Go To Stanford If I Disagreed With STEP’s Philosophy?

(Note: I just noticed that I failed to register an old domain of mine, so I’m copying my old pieces about my Stanford woes over here. This essay (a series, really) was first written in the summer of 2009, I think.)

This question always makes me laugh. Yeah, that’s it! I should just go to a different ed school!

Which school would that be, exactly?

Check out David Labaree’s book, The Trouble With Ed Schools, paying particular attention to Chapter 7, The Ed School’s Romance With Progressivism

[Education professors] do have a vision. Most of us are convinced that we know what is wrong with education and how to fix it, and we are eager to make our case to all of the parties who shape the schools: teachers, administrators, parents, policymakers, lawmakers, curriculum developers, textbook writers, test designers, and the media. The vision of education we propose has been around for the last hundred years; it’s usually called “progressive education.”

From the late nineteenth century to the present, two strikingly different visions of teaching and learning have been competing for primacy in American schools. They have gone by a variety of names, some familiar and some more obscure….The most common labels, however, which capture most of the sense of these various category systems, are teacher-centered vs. child-centered (or student-centered), traditional vs. progressive, and, in what is the most popular terminology in education schools, traditional vs. constructivist teaching. For reasons of simplicity, common usage, and historical resonance, I refer to these visions by the names traditional and progressive.

For American education schools during the twentieth century and continuing into the present, the progressive vision has become canonical, serving as the definition of good teaching. In these institutions, the purpose of teacher education programs (for prospective practitioners) and teacher professional-development programs (for existing practitioners) is framed as an effort to dissuade teachers from adopting the traditional appropach and to enlist them firmly within the progressive cause. There are people in ed schools, like Chall, who choose not to employ the rhetoric of progressivism and even speak against it, but they are a small minority and they know their position is heterodox.

This is not a point about which there is any serious disagreement….*

David Labaree had Eamonn Callan’s job as dean of student affairs at the school of before he went on sabbatical. I emailed him once or twice asking for help, because I’d read his book. He declined. I don’t carry a grudge.

Labaree’s excellent book does not blame ed schools for educational failures; rather, he astutely points out that ed schools have little influence over educational policy because they are held in such low esteem. I agree with him, but would also observe that researchers are not allowed to explore other methods because they’d never get into a doctoral program without buying into progressive ideology.

But I digress. The operative issue here is that David Labaree is a Stanford professor, and he’s pointing out as a given that ed schools are dominated by progressivism.

So where was I going to go?

I wasn’t choosing between Stanford and a school more tailored to my own educational philosophy. I was choosing between $50K or $20K in loans for a dunk in the progressive Koolaid tank. The Koolaid tank itself was a given.

I knew what I was getting into. I had explored all the alternatives to ed school–alternative credential, emergency credential, no credential at all, moving to another state to get a credential more quickly then move back. All of them required nearly as much time as ed school, fortuitous contacts, or a hell of a lot of luck.

Even after I decided on the traditional route, it took me a while to apply to ed school. I assumed I would go to San Jose State, until I discovered that CSU campuses require 45 hours of public school work before the program started. That annoyed me so much I dropped the entire notion for several months and then, on the next to the last day of 2007, I realized that my son’s school, UC Santa Cruz, had to have a credential program. Hey, Berkeley probably does, too. And from there it was a teeny step to well, as long as I’m frantically putting together applications with a week to deadline, why not give Stanford a shot?

I didn’t compare their programs. I knew they’d all be identical on the big issues, and as a tutor/teacher who lives an active life in online discussion forums, I was totally up to speed on ed school cant. The only issue I considered was cost.

Berkeley made it easy by rejecting me. (They’d had me once already for my Master’s in Information Systems. It wouldn’t surprise me if Cal’s ed school contacted the School of Information and said “Hey, what about her?” and SIM said “Are you suicidal?”) So the highly-ranked inexpensive school was out, leaving UC Santa Cruz, an excellent but not top-tier school on the other side of the hill, and Stanford, which has the first or second rated school in the country.

I gave serious thought to UC Santa Cruz. I liked the staff, who didn’t call me and imply that my decision to work through the year cast doubt on my fitness for candidacy. For half the Stanford price tag, I could rent a second apartment in Santa Cruz to crash in if I didn’t feel like making the drive home.

But Stanford. I’m the only college graduate in my immediate family (my little sister will be second, my son the third). My undergrad degree was from San Jose State. My first Master’s was from Berkeley. With Stanford, I’d have diplomas from all the Bay Area Division I schools, which had to be good for a set of steak knives or something. Plus. Stanford. Koolaid or not. Price tag aside. If I had to go back to school at my age one more time, wouldn’t it just feel better to be going to one of the best schools in the country?

Again, note that all my dithering was about the cost. I knew about ed schools. I knew I disagreed with the ideology. I knew it would be a frustrating year. The only question was how much I was going to pay for the experience.

The last straw in favor of Stanford tipped when (I am not making this up) I got a ticket the day after my first meeting with Rachel, right after breakfast with my son at Zacharys, a classic Santa Cruz joint. I was just about to make my call to David Rasch, the ombudsman, when I got pulled over by a cop for going 30 in a 25 zone.

Wham. Like Dory in Finding Nemo, the memories all flooded in. Two years at Berkeley had resulted in a Master’s, yes, but also four additional speeding tickets and easily 50 parking tickets which, of course, I always forget to pay, so went something like $200 a pop. My insurance had only just returned to something approaching reasonable after all those speeding tickets.  If I went to UC Santa Cruz, I’d be driving over the mountains every day. I’d always be late. There’d always be a cop looking for an easy ticket. UCSC’s parking is even worse than Cal’s. My loans might only be $20K, but I could count on close to $5K more in ticket and insurance costs alone. To say nothing of the aggravation.

Stanford wasn’t only elite. It was close by. In a suburb. With a suburb’s attitude towards parking. And speeding. Then, just minutes after the ticket, David Rasch tells me not to worry about retaliation; if I want to go to Stanford, I should go.

So don’t ask why I went to STEP when I disagreed with its philosophy. Ask, rather, why anyone should have to drink so much Koolaid just to be a teacher.

And while you’re at it, ask how come speeding tickets without accidents still hike up your rates.

*I stopped quoting there because Google books limited my page views and I loaned out my copy to someone at STEP. I can’t remember who. Fellow STEPpies, if you have it, could you look up page 133 and send me the text? Or tell me that you returned it already and I’m blaming you when it’s really my disastrous disorganization? And everyone else: look! I am a nice person who loans out books to colleagues.

Smarter Balance Tests: California’s Juniors Did Well

So the Smarter Balance results are out and everyone is certain all the news is bad. The LA Times called the results sobering, while the Chronicle said they “weren’t stellar”.

But in fact, California’s juniors did a good job.

They qualified as “college ready” or “a year from college ready” at the same or higher rate than prior years. We can’t do a pure comparison at this time in math, but I’m hoping that California will make the necessary data available. However, even in a broad comparison, junior math scores improved over 2014 and was on par with 2014. As for English, far more juniors are going to finish high school qualified for credit-bearing college courses than ever before.

California’s Early Assessment program (EAP) provides juniors with an assessment of their college readiness in math and English. Students are categorized as either Proficient (fully ready for college work) or Conditional (must get a C or higher in a qualifying course their senior year). While the state is admirably thorough in providing results data, reporters tend to boil all this complexity down to a single factoid–the percentage of students deemed ready for college math. And even this, they usually get….well, not so much wrong, but the information is portrayed in a misleading fashion.

Before last spring, the EAP assessments were not a single test. In English, juniors had to agree to sit for an essay test a few weeks before the California Standards Tests (CST). Then, during the CST, interested juniors took an augmentation packet of questions in additional to the standard test. ELA participation was relatively high, but rarely 100%.

The math EAP was more complicated, but at least took place in one sitting. Juniors taking Algebra 2 or higher took their usual CST end-of-year test as well as another augmentation packet. Unlike the ELA, math students taking the EAP did not all take the same CST test. Students in Algebra 2 took the Algebra 2 CST; students who had finished algebra 2 took the Summative CST. Both groups were then evaluated with select questions from these different tests and the total augmentation packet.

Juniors who hadn’t yet reached algebra 2 could not be assessed for college readiness in the CST years. A few years back I had some excellent geometry students who might have been able to test at conditional status if given the opportunity. I emailed a query and learned that simply taking the additional packet was not enough; the students had to take either the Algebra 2 or Summative test.

The EAP state results only provided passing percentages based on EAP testers. So it’s easy to look at the 2014 results, see that 49% of all testers “did not demonstrate readiness” in math, and wrongly conclude that 51% of all juniors did demonstrate readiness. The numbers to make the right conclusion are on the page, but easy for the novice to miss.

Since 2015, all juniors take the Smarter Balanced test, regardless of their math entry point, and so all juniors are assessed for college readiness. This affects the ELA numbers somewhat, and the math results dramatically, since in prior years around a third of all students weren’t allowed to take the test.

So how’d they do? The cleanest year to compare to is 2013, the last year we had both the CSTs and the old-style EAP. The next year, 2014, juniors took the CST purely for EAP purposes, but the state wasn’t as careful with the statistics, and it’s a bit hard to determine how many juniors didn’t take the EAP that could have. Here are 2013-15 results–the important numbers are in the last two columns, which show what percentage tested as proficient or “conditional” (a year away from proficient).

Year Total
Math %
2013 435,223 384,722 143,870 253,004 128,159 33% 29.5%
2014 464,534 332,065 130,153 209,584 112,468 28% 23%
2015 455,953 418,802 234,529 428,179 121,217 56% 29%

Unless I’ve made a boneheaded mistake, these numbers do not jibe with the reporting of the results. California’s juniors should be singled out as a substantial exception to the overall story of lower scores. They did far better on the ELA and held their ground in math, improving over the most recent year.

Is the test significantly easier? The best way to determine this requires information about the pass rates per course. How many algebra 2 students passed? How many geometry and algebra 1 students passed, if any? I’m hoping that the new results in October will include student passing rates by subject.

Should more than 30% of students be ready for math at an advanced level? That’s a question for another day. For now, let’s take note that California’s juniors did just fine and even improved on prior performance with a difficult new test in a new medium. Let’s take a moment to celebrate their achievement.

The Grand March in the Quad: Linear vs. Angular Velocity, Part II

So my students had done a magnificent job the previous day. And I hadn’t done too badly my own self. The original Sammy problem is, I submit, a masterpiece that integrates three different concepts without tipping its hand.

But the students’ skepticism came through loud and clear. They understood the math. They grasped the significance of the radius to the speed. But ain’t no way they bought the notion that Sammy was going faster than the bird.

I mulled this over the evening, and went back to youtube looking for videos. The Grand March? Too much time to wait for a very small demo.

But wait. What if I did my own Grand March? And in the words of the great Oracle Jones of the noted Western mockumentary The Hallelujah Trail:

THERE, now I see it!”

Alas, no whiskey to be found.

But I had the idea. And it all depended on George.
George, seen here in my algebra 2 class last year, is a top student and a fantastic young man. He also possesses a battery-operated wheelchair.

The next morning, before class, I went looking for him.George1

“George. I have a really cool idea, I think, but I need your help. Can you set your wheelchair to a particular speed?”

“Sure.” George doesn’t even ask why. He’s used to me.

“Okay, and this is a weird question–but can you, like, tip over? Do I have to worry if you go round and round on a 3-foot radius circle that it will….tilt?”

He’s kind, and doesn’t mock me.

“Ms. K, it weighs a lot. It can’t tilt over.”

“Phew. I was having nightmares.”

So before class started, I got some chalk from an old-school colleague and using a tape measure, marked out a circle around the courtyard drain, with a 3′ radius.

When the bell rang, I was ready.

“So. Yesterday I noticed skepticism about the bird’s speed. You understand the evidence, but you trust your lyin’ eyes more. I came up with a way to illustrate the proof so you won’t have to take math’s word for it.”

Then for the first time in my over five years as a teacher, I took my kids outside. Very unnerving. (Yes. I’m a big weenie.)

So the basic idea: George sets a speed and follows my traced circle at a very slow pace. The rest of the kids line up on opposite sides of the quad, and one by one they join in with George. Two kids go in on each of George’s rotation, one from each side.

The class was skeptical, but game.(In fact, this trigonometry class could not have been a better guinea pig for my first time teaching the subject. Every day, they jumped right in.)

On the first day, I just did proof of concept. I wasn’t sure how to get everyone to link together, so everyone held the edge of a tape measure.

The kids did a great job and the activity just exceeded my wildest expectations—and best of all, took less than 20 minutes from start to finish. I took pictures, and showed them to anyone walking by, including the entire admin team. This is my favorite shot from the first day:


The end of the tail really captures the movement. Austin the Action Figure!

We went back in and worked basic problems on angular and linear velocity for the rest of the day.

Then I realized that I really missed an opportunity. I was so worried my idea wouldn’t work that I didn’t take advantage of the obvious real-life problem at hand. What was our Grand March angular and linear velocity? How fast was George going? What about the speed of those at the end of the chain?

So the next day, we went out and did it again. But the kids had some changes. Nuff of those idiotic tape measures, Ms. Kerr. We are all comfortable with our sexuality, and will link arms. Football players and all.

Note–some of these pictures are taken by me with my tablet, which has a pretty low quality camera for a Samsung; other stills were taken from video that two of my students filmed.

trigferrislinkingarms trigferrislinkingarms2
trigferris5 trigferris8
trigferris9a trigferris10a
trigferris13 trigferris14
ferristrig14a trigferris15

I knew we’d added as many kids as we could when I saw Alexis nearly getting creamed by the quad wall.


So I yelled at them all to go full speed for the last half for the grand finale, the picture at the top. Here they are a couple seconds later.


You can see the “whip” effect in many of the pictures. It would work even better if we weren’t running into the quad wall towards the end.

The kids had a blast. Between the two days, almost all the kids participated in a “grand march”.

Then everyone went in and learned how fast they’d been going. I measured a bunch of them shoulder to shoulder and took an average of 36″, or 3 feet for every two students.



This lesson was a stunning success, and not just because of the fun and games. I had created memories and math that students would remember—and they did, all the way through to the final. I couldn’t wait to try it again with my two trig classes in the spring semester.

But while part 1, the Ferris wheel problem, went just as well both times, the outside activity was just a bit flat. Our German exchange student, Simon, was my TA this semester after having taken my trig class last fall (he’s the first one next to George, above). He played the anchor position, since I didn’t have George, and did it very well.

trigferrissemsd trigferrissem2e
trigferrissem2a trigferrissem2b

If you notice, two students in the last picture, above, have dropped out later:


This despite the fact that Simon was holding the same pace that George was (we had timers to confirm).

It wasn’t a disaster, and we had plenty of time to do it again. In both my spring classes, I had kids drop out, which simply hadn’t occurred the first time last fall. They seemed to have fun, but there wasn’t the same joy I saw in the fall. Simon agreed that the spring students didn’t seem to be as absolutely thrilled.

However, I had one of the best “told you so” comments in my third block class. I was explaining that the first student had to move very, very slowly—around 18 seconds per cycle–so that everyone could keep up.

“Um, keep up? Eighteen seconds around?” Braxton said. “That’s not going to be a problem.”

“Okay, everyone remember he said that!” I ordered. Which made a nice little teaching point when we got back to the room after the grand march.

Still, I wish I could have made the spring classes as absolutely perfect as the fall one was.

When I finally got around to writing this up, I suddenly had a revelation. Look at the top picture again. At least 10 of the 17 students in that picture are athletes—4 of them in two sports. I suddenly remembered all the students towards the end of the whip bouncing on their toes, warming up, waiting for the line to come around.

I mentally riffed through all my students in the two classes this time round, and yep–far fewer athletes. And here their trig teacher is demanding physical activity.

While I was always calling kids randomly, I had a much higher shot at getting an athlete in my fall class.

So same activity, same lack of warning–but not the same level of absolute ready-to-go spirit I had in the fall. I’m going to have to think about how to get them prepared to enjoy themselves, get some guidelines, maybe warn them ahead of time.

But even with less absolute magic, the kids understood and enjoyed the lesson.

I just need more space! Maybe I’ll try the football field in the fall.

When Schools Get Political, What Should Teachers Do?

Rick Hess: Politically, nothing is more potent or poignant than the picture of a child’s face at a hearing or protest. Which is why adults in the system must wield their influence with great care.

Hess’s cautionary tale of schools involving students in their political agendas reminded me of my own experience with this institutional practice. Five years ago, I refused to comply with a school-wide political action: the March 4th Day of Protests, a semi-organized demonstration against budget cuts to California public education. While universities saw the most action, Oceana High School stopped instruction and dedicated an entire day to protests and political propaganda.

As a teacher, I was troubled and conflicted by the entire exercise. Troubled, because public instruction time and the students themselves were being used for political objectives. Conflicted, because I was a first year teacher who really didn’t want to go job-hunting over the summer again. So, for a period of about 6 weeks, I was constantly faced with the choice: do I go along to get along? Or do I ensure my students are making informed decisions about their use in a political exercise?

In late January of 2010, two Oceana teachers proposed that the staff participate in the March 4th action. We were given a “fact sheet” in the staff meeting to read to our students and told to encourage them to volunteer for “student planning committees”. No opposition was expected or given. At the time, I assumed the action would be voluntary and brief—and even on that basis my concerns were non-trivial. But I said nothing.

The humanities teachers were coordinating the participation, as they met daily with their students instead of every other day in the school’s multi-block schedule. Each teacher also has a single grade advisory. I had 20 of the approximately 140 freshmen as both my advisory and humanities class, a unique situation. The rest of the students had one of two other teachers for humanities, and one of six other teachers as an adviser–all of whom were passionately committed to the activity. Had my humanities students been randomly distributed among the different advisories, the other teachers would have learned of my perfidy sooner, and the results might have been different.

I kept all emotion from my face as I read the fact sheet aloud. My students quickly translated my lack of expression as lack of enthusiasm.

“You don’t think we should do this?” someone asked.

“I think you should absolutely do this if you want to,” I responded.

“But you don’t think we should?”

“No, that’s not it. Crap,” I sighed. “Look, I am just uncomfortable with schools getting their students involved in their political objectives.”

“Can’t schools teach their kids about politics?”

“They aren’t teaching you about politics,” I said. “They are involving you in achieving a political goal.”

“Yeah,” said Isaiah. “The school expects me to care about the budget cuts, but I don’t.”

“There’s another point of view entirely,” I said, and waited.

Not a single student was able to identify the other point of view. That fact, more than anything, led me to carry on with my non-compliance. After they tried to identify another side to take for a few minutes, I broke in:

“You’ve only identified students who support the protest and students who don’t care. What about any student who thinks the tax cuts are a good idea?”


“You mean, like we could demonstrate supporting the budget cuts?”

“Can you even imagine someone doing that here?”

No, they could not.

“This school believes it’s acting in the best interest of you students,” I offered. “ I’m just…not comfortable with the schools giving so much time to a single point of view while not even considering the possibility of opposition. I encourage you to take part if you want to. I would never oppose that. But never feel you have to participate.”

I hoped that would be the end of it. Unfortunately, a few meetings later, I learned that the protest would include off-campus activities, with the kids handing out pamphlets in public spaces.

Then we got a mandatory survey. Did we want to participate in a “teach in”, to explain the budget cuts to our students?

Protest participation had evolved from “opt in” to “opt out”. I checked the box for “I plan to teach my usual curriculum”, and hoped for the best.

A week later, I learned that the entire day was going to be given over to “teach ins”. We humanities teachers were to distribute permission slips for off-campus activities and “push” for their quick return. Students who didn’t return permission slips would have to watch a movie: Walkout, about student political action in East LA. I distributed the forms, reminded everyone that participation was their choice, and didn’t mention it again.

In another curriculum meeting later that week, another humanities teacher said, “We’re not even going to be on the campus that morning, since we’ll all be at the beach” before classes start. Oh, by the way, she added casually, I was the only teacher who wasn’t going to do a “teach in”.

I emailed a counselor privately, telling her that none of my students were turning in slips, and that I wasn’t sure how I could legally require them to do so. The counselor reassured me: under no circumstance was I to require the students turn in slips.

Ultimately, only one of my students turned in a permission slip, saying he “didn’t want to be stuck watching a movie” (score one for activism!). The rest of my students went against the tide.

On March 1st, all the freshmen teachers were working on the logistics of having the entire freshman class forming a huge SOS on a Pacifica pier.

“So we have just 19 students who didn’t turn in permission slips in our two classes,” said Jen. “Michele, how many in your class aren’t participating?”


“No, that’s how many have turned one in, right?”

“Only one student turned in a slip.”

The entire meeting stopped cold. I was suddenly the target of many narrowed eyes in unhappy faces.

“Did you push them?” one of the teachers asked.

“I can’t make them participate,” I said.

“Yes, actually, you can,” insisted a science teacher. “It’s required.”

I said, very carefully, “Look, I’m pretty sure it’s not required. I am extremely uncomfortable forcing kids to participate in political action.”

A counselor (not the same one I’d asked earlier) said casually, no big deal, “Of course it’s not required.” and the conversation ended.

The news of my recalcitrance spread rapidly. An assistant vice principal towed a brand new humanities student to my classroom during geometry, asking me for a permission slip. This was a very public rebuke, since the office had plenty of blank permission slips. After the AVP left, a freshman from another humanities class said “I heard your kids don’t have to go?” Several other freshmen chimed in: they’d been told the only way they could get out of the event was for their parents to write a letter explaining why they didn’t care about the school budget cuts.

During the final March 3rd planning meeting, that AVP mentioned that I’d only turned in one permission slip, but she was “trying to make it two”. (She didn’t succeed; the new student didn’t attend the protest.)

The planning meeting was somewhat brutal. Imagine all the school’s teachers sitting in a huge circle of tables, facing each other. Each teacher doing a “teach in” is given a huge curriculum packet in an envelope. Except me. So everyone is in a big circle opening and examining the contents of huge packets. Except me.

The day of the protest, word had gotten out among the students. More than one student I’d never seen before asked me why I “didn’t care about schools”.

On the other hand, my non-conformers were pretty proud of themselves, while I reminded them constantly that non-participation didn’t mean opposition. One student was kept home by her dad to ensure she wasn’t part of the demonstration. Another mentioned that he’d written a letter of protest to the principal. I read it aloud to the class and encouraged him to send it into a newspaper. His passionate protest led me to document my experiences in an email to Debra Saunders, a well-known local columnist at the San Francisco Chronicle. I didn’t want to go public, but my student was more than willing to share his letter.

So the same week that the staff celebrated the mention of our school in coverage of the state-wide demonstrations, Saunders wrote critically of the March 4th event and included quotes from my student’s letter to the principal. Huge thrill for my humanities class, less so for the staff. Several wrote letters responding to Saunders’ criticism.

Then Jay Mathews of the Washington Post read Saunders’ column and wrote approvingly of my student’s letter. Another thrill! One of my other top students asked if she could respond to his column and I confess I actively encouraged it, since I know Jay Mathews pretty well (he wrote about my Stanford travails). Jay published Meg’s entire response.

So in the space of a week, two of my students’ essays were discussed by nationally known columnists in major media outlets. While this normally would be cause for celebration, it was understandably not mentioned much at the school.

Unsurprisingly, Oceana didn’t renew my contract. While my first year included the best moment I’ve had as a teacher–so far, anyway—I’d been convinced as early as September that the school wouldn’t ask me back. We weren’t a good fit. While I’m both certain of and troubled by the fact that the school considered my personal beliefs a factor in the decision, I can’t know if my actions with regard to the protests were a factor in my non-renewal.

While Oceana doesn’t seem very different from a typical high school, few comprehensive schools could engage in a similar school-wide political action. Oceana is designated as alternative, unbound by many public school restrictions. But while blatant politicking is rare, all schools—public, charter, private—engage in their fair share of ideological mandates, from anti-bullying week to extra credit for “going green”, that often don’t consider whether the students are giving informed consent to participation. Meanwhile, many students are confusing “I don’t care” with “I oppose”. Avoiding participation becomes their primary objective. If that’s impossible, they become practiced at just going through the motions, rather than finding the internal fortitude to resist.

Everyone has the best of intentions. The teachers and administrators at Oceana meant well. So do the schools and teachers Rick Hess refers to, from Eva Moskowitz and all the Success Academy teachers, to the teachers and schools busing Newark students to a protest in Washington DC. So do I. Without question, my actions at Oceana were an expression of values, just as the other teachers and schools were expressing theirs. The difference lies in what we each want our students to do. I want my students to share my values about open expression, and could care less whether they agree with me. Oceana High School and Eva Moskowitz, as well as many other schools and teachers, see no valid alternative to their opinions, and so consider any efforts at “hearing all sides” to be wasted. They see agreement as essential, conflicting opinions as harmful and—I believe as a consequence—don’t really think much about the need for open expression.

This is a problem. I’m not sure how we address it as a society in our polarized times. But all teachers should think carefully about their expectations, and whether their desire to create “enlightened” students conflicts with their responsibility to educate students to form their own opinions.

The Ferris Wheel, Sammy and the Bird: Linear vs. Angular Velocity, Part I

After eighteen months focusing on pre-calc, I was assigned three trigonometry classes for this year (again, over two semester cycles). In both cases, I got a single class at first, giving me a chance to get my feet wet, and then a bigger dose later, so I could really start to experiment.

I didn’t know much more than the basics of trigonometry when I began this class, and I’m not much of a planner. So I was often learning the math a few steps ahead of my students. For example, I had absolutely no idea what linear or angular velocity was until the late afternoon the day before I introduced the concept. But hey, I’m a quick study.

What the book said:

The math symbols just when whoosh over my head (figures often do) but the ice skaters, that made sense. Thanks, William McClure!

I instantly thought of John Ford’s classic Fort Apache, which may cause you to wonder if I actually understand the concept after all. Unless you’re a really big fan of the movie and also know some math, in which case you’re thinking “Oh, yeah, the Grand March”. Long ago, I’d observed that Shirley Temple had to hustle to keep up with her screen dad Henry Fonda in the Grand March (around the 57 second mark) and then saw the same catch up effect in all the subsequent quartets making the turn. At least a decade before I ever conceived of becoming a teacher, I thought “that makes sense. She has further to go around, so she has to go faster.”

I often kick off a section with a scenario that asks a question. Sometimes the question is a short, intuitively easy problem or activity that the students can do with little analysis. Other times it’s a long, extended dive into multiple concepts, drawing on a lot of previous knowledge. But the scenario is always designed to introduce the new concept. (I read about this idea in ed school, but as it was a good year or so before I began to incorporate the practice into my teaching, I can’t remember the reading or the author. Since I save everything, I hereby vow to go back into my readers and see if I can dig up the info.)

So I originally intended to do a short, intuitively easy demonstration on the different velocities, but I couldn’t find I couldn’t find any decent videos other than the Grand March itself, which was a little to subtle. Merry-go-rounds would be great, if I could just find a video of kids on this, with some standing easily in the middle and some holding on at the ends…but no luck. I tried skating videos of crack the whip, and much as I’d love to use a Winslow Homer painting, I knew I’d have to do all the explaining. I abandoned my initial idea of presenting the phenomenon and asking the kids to explain it.

Plan B: longer, more complex problem. After perusing the book and googling, at some point I found a Ferris wheel problem asking about velocity. I wish I could remember where, because I am certain I invented this problem almost entirely, and I’ve love to include the genesis. The question that sparked mine provided the total time to complete one revolution (15 minutes, I think), and the dimensions of the Ferris wheel. It then said that someone had traveled 6 minutes, or maybe 4, and asked what his linear velocity was. It gave too much away.

But from that question (or something close), I went WHOA and morphed my plan entirely. No more small illustration, but a long extended dive into–or onto–a Ferris wheel. Because, as any trig teacher can tell you, the Ferris wheel is the mother lode for application problems, a rich source of ideas that can be turned to a number of uses. My kids had already been through Ferris wheel problems calculating heights. So once I was pointed in the direction of Ferris wheels, a multi-faceted problem was an easy next step: one that combined right triangle trig, arc length, and linear velocity, the last in an intuitive way. Booyah.

So the next day, right off the bat, I projected part one of the problem:

And figure it out they did.

My students had just learned how to find the length of an arc, whereas I, who figured it out intuitively, just took the needed percentage of the circumference. I had spent no small amount of time over the past few days explaining that the algorithm for radians, which is the product of the “angle over 180” and the radius, is exactly the same thing as taking the corresponding fraction of the circumference. I was still a bit taken aback to see them multiplying 125 by three quarters pi. Oh, wait. Yeah. Okay.



I wasn’t taking pictures through the class, unfortunately, but grabbed these shots the next day. The one on the left is most complete, but for some reason they flipped the heights. The work on the right is also done well, but they did more of it on the calculator. I remember making them talk me through their thinking.

Meanwhile, a struggling group sketched aimlessly, hoping I wouldn’t notice that they weren’t working. I reminded them of the right triangle trig, helped them to find the angle measure, then asked them to think about what it meant. This group used the circumference instead of the algorithm and made progress although they didn’t finish the problem completely by the time I called everyone back together.


At forty minutes or so, all but one group had finished the entire problem. I had to help two of the eight groups significantly; the rest just needed mild reassurance. Outstanding work, a math teacher’s propaganda day.

At that point, I defined linear velocity, which they had intuitively understood as they worked the question. Once you associate arc length with the time to travel, it’s only natural to think about the speed.

Time for part 2:

The kids all began their calculations, using Sammy’s speed.

“Hold on,” I said, calling everyone’s attention. “Didn’t you use the radius to calculate Sammy’s velocity?”

“Sure, but they’re going the same speed, right?”

“Did you use the radius to calculate Sammy’s speed?”

And I had a bunch of kids looking at me like this:


“The bird and Sammy are going the same speed!”

“But did you use the….”

“Come on! They’re going the same speed! How can the bird be going a different speed? They’re both on the same Ferris wheel!!”

“What if I’d not mentioned Sammy and we started with this problem? What would you have done?”

With much skepticism, they worked the same method and realized that the bird was, indeed, going slower. (You can see some of the work on first picture of boardwork, above. That group had finished first and I gave them the problem verbally. Everyone else started it after I called everyone back together and explained linear velocity, so their work was on paper.

And so, I introduced angular velocity. Sammy and the bird were traveling a different distance in the same time, so their speeds were clearly different. Howevever, they were both completing one complete cycle, or circumference, in 16 minutes, so their angular velocity is the same. As we watch Sammy and the bird, we see them covering a circle in the same amount of time and this fools us into thinking they’re going the same speed.

I could tell they weren’t convinced.

“So how fast is the bird going?”

“The math says the bird is going 7.85 feet a minute, which is about .09 miles per hour.”

“Well, let’s be more precise: .0892 miles per hour, right? How fast is Sammy going?”

“Half a mile…”

“.5569 miles per hour.”

“How much faster is that?”

I won some breathing room from all that doubt when the kids determined that the speeds had the same ratio as the radii. But I could see doubt.

The math proved Sammy and the bird had different velocity. But how could I get them to accept the math?

I came up with an idea for the next day. Which I’ll cover in the next post.

Classroom Alchemy

“Hey, how was Philadelphia?” asked Darius*, as I checked his work (“Sketch a parabola in which b=0”).

“Pittsburgh,” I said, pleased and taken aback. It was Wednesday, first day back after our 4-day Veterans Day weekend. Sometime on the previous Thursday, I’d mentioned casually I was going back east for my uncle’s 70th birthday. Six days later, Darius remembered my plans.

“The family reunion, right?”

“Yeah. How nice of you to remember. I had a wonderful time.”

I moved back to the front, checking for universal understanding of the impact that b=0 had on the position of a parabola, and then told everyone to sketch a parabola in which c=0.

“Did a lot of people show up?” Darius asked across the room.

“They did! Over 90 people. All my uncles and aunts on my dad’s side, and several of their cousins. Eleven of my fourteen surviving cousins on that side. At least 9 of the next generation–my son’s. And even some tiny members of the generation after that—the great-great-grandchildren of my dad’s parents.”

“Wow. Did you know them all?”

“Some of them I’d never met before, because they hadn’t been born the last time I’d visited. Others I’ve known all my life, like some cousins, and my aunt and uncles. We even had someone from my grandfather’s generation. Aunt Ruth–my dad’s aunt–who is 94, looks fantastic, and just came back from a trip to Paris.”

“Was the food good?” from Harres.

“Outstanding. It was simple, nothing dramatic. They put the food on different tables throughout the room.”

“Oh, I don’t like that,” Darius again. “I always want everything, and can’t decide which table.”

“There was a table with two big haunches of meat. One roast beef, one ham, with really good bread rolls. I had no trouble deciding which table.”

After we finished up c=0 and they were figuring out the significance of a parabola with just one zero/solution, Darius waited again until I was checking on his work.

“Did you talk to people there?”

“Me? Oh, yes. Non-stop talking. There were so many people I hadn’t seen in years, and then others I wanted to get to know. I wish I’d had more time. I need to go back more often. If I wait as long again, I’ll be older than my uncle is now.”

“I went to a family reunion one time.”

“You did? How was it?”

“No one talked to me. I was like this.” and Darius humorously mimed standing all alone, silent, looking about for something to do.

So that’s why he remembered.

“Darius, I can tell you for certain that no one at my family reunion was sitting all by himself. I’m sorry. That probably wasn’t fun.”

“Yeah. It was weird. I didn’t know anyone there, and they were all talking to each other.”

“That would totally suck. I’m sorry. We’d have asked all about you.”

As they worked out the next task, I had a brief moment of introspection. Darius, who’s a cool cat in every sense, is far less likely to be the one sitting alone at a party than, say, me, a cranky introvert who has to brave up for crowds so she can exercise her natural garrulousness. I know that my uncles, or my dad, would have probably joked about a teenaged African American appearing at the party. Some or all of them, egged on by siblings and downstream kin, would one up each other with ribald wordplay and puns about where and who had done what when to add color to the family tree. But they’d have sought him out, gotten him some food, grilled him on his life story, likes and dislikes, found out his plans after high school. Looked for links and common interests, bring in others to get conversation going. But would I have done everything to reach out? Or would I have been too busy enjoying not being the one sitting alone?

As the bell rang, I was actually showing Darius and others some family pictures from the night, which sounds impossibly boring, but they seemed genuinely interested in seeing evidence of my stories.

“I’m really sorry you felt isolated at your own family reunion, Darius.”

“Yeah. It’s always the same. I’m like the whitest person when I’m with my black relatives, and the darkest person when I’m with my white relatives.”

“Well, you’d have been the darkest person at my family reunion, for sure. I don’t think our bloodline moves east of Aberdeen. Maybe London. We’re pretty thoroughly white folks. But even though you felt isolated because of your race, some of it could just be family dynamics. My family’s big, boisterous. Really loud.”

“Everyone here was loud. They just were loud to everyone else but me.”

Kameron* punched his arm lightly. “I hear ya.” At Darius’s look, he elaborated. “I’m half black. My mom’s white.”

“Oh, then you know.”

“Does your black family ask if you’re ‘all-black’?”

“You get that too? Isn’t that idiotic? Like they’re measuring?”

“Well, gee, I guess at least the white side of the family didn’t ask if you were ‘all-white’.” I pointed out, and they cracked up.

“There’s a lot of research and profiles on biracial kids, did you know?”

“Really?” Both Kameron and Darius looked interested.

“Yes, that feeling you both have of not being one nor the other, of being slightly separate, is not uncommon. It’s also not unique to kids with one black and one white parent. Biracial Asians have similar feelings, whether their other parent is black, white, or Hispanic.”

“Huh. Really.”

“Sure. There are some good books that you can read about other teens with the same background. You should check them out. In any case, I promise you, Darius, that you wouldn’t have been all by yourself at our family reunion.”

“So the next one you have, invite me!”

“It’s a deal. Have a good day, guys.”

Such exchanges are classroom alchemy, a magical transformation of mundane, random elements into golden moments. They spring from elixirs of personalities, events, spontaneous conversations, the incidental inspired nudge. They are occasionally unrelated to content knowledge and always irrelevant to test scores. They will never be found in MOOCs, nor in classrooms obsessed with tight transitions. They are criterion deficient; ed schools can, to a limited extent, prepare teachers for such moments only with open-ended assignments that are probably opinion-based.

I don’t confuse alchemy with the meat and potatoes of teaching. Darius and Kameron are both doing very well, improving their competency and fluency in quadratics, modeling real-life situations with algorithms and, importantly, taking on intellectual challenges that don’t immediately hold interest.

But teachers are responsible for more than content, whether we are aware of it or not. We are the first adults students interact with, the first engagement students have with the outside world. Independent of content, we can give students a feeling of competency, of capability, or of frustration and helplessness. We can communicate values both indirectly and directly. We can teach them that work is a serious business, or we can teach them that work can be fun and entertaining—or both. We teach them how to interact with a wide range of personalities, how to ask for help, how to give help. It doesn’t matter if a teacher is determined to convey nothing but content. Simply by the nature of our job, we create an environment that has its own entirely unmeasured learning outcomes.

I am a teacher who focuses primarily on conveying content, as all observers have noted over the years. Yet for a teacher who doesn’t see her job in terms of its emotional impact, I have my fair share of classroom alchemy, the moments of knowing my classroom has been a positive force in the universe, whether for one student, a group, or a class of thirty five.

I never plan these moments. As the great Terry Pratchett noted (with props to Neil Gaiman), you can’t second guess ineffability. It’s just going to come along on its own terms.

*Darius and Kameron both confirmed this exchange as written.