Teaching and the Art of the Possible

A couple years ago, an administrative vice principal (AVP) walked into my classroom and asked, “I’m checking up on previously ELL students who were reclassified English proficient (RFEPed) to be sure they are getting enough support. What can you tell me about Santino?”

“Santino? He’s doing well. He’s gotten either a high F or a solid D on every test so far, which is a big step up for him.”

“Really. I guess we have different notions of what ‘doing well’ is.” She raised her eyebrow, refrained from sneering, made a check on her clipboard form, and walked back out before I could respond, which was probably a good thing.

Santino, a junior in my geometry class, was passing all of his classes at that time. He had finished his sophomore year with a sub-2.0 GPA, still higher than his freshman year. Ultimately, that AVP would determine that Santino’s upward progression was evidence of a valid reclassification. She didn’t walk back into my classroom and apologize for her nasty bit of snark, though.

Santino had a shock of black hair, big black glasses, and a rail-thin physique, which he clothed daily in black tees, skinny black jeans, and a light black hoodie. Think Hispanic Emo without the makeup. He almost never smiled in school. He didn’t amble but stalked silently through the halls, eyes always on the ground, occasionally with an equally silent and dark-garbed friend. His English was surprisingly fluent, considering his qualification for the Migrant Education Program and two parents who spoke no English, and his rarely used voice unexpectedly mellifluous.

As a sophomore, he sat silently through almost the entire first semester of my algebra class, doing nothing. He didn’t goof around. He just sat. He turned in empty tests. I’d called his home a couple times and tried to get him to work in class to no avail. Finally, I made contact. I vividly remember our first nearly wordless exchange.

In an early November test, Santino was just sitting there again, blank test in front of him. I stopped at his desk and picked up his pencil. Problem: Alycia made five times as many pumpkin pies as apple pies. If she made 24 pies, how many apple pies did she make?

I drew five circles, marked each one with a “P”, then handed him the pencil. He reread the problem and drew one circle, labeling it with an “A”. I waited. He thought. Drew another five “P” circles. Then another “A”. I smiled, and walked away. When I came back, the entire problem space was filled with circles, and the words “4 apple pies” was scrawled down in the corner.

“So let’s try this next one.” Problem: Julio was at the beach, and noticed that the ratio of seagulls to blackbirds was 3:2. If he counted 30 birds, how many blackbirds were there?

I drew 3 Ss and handed him the pencil. He drew 2 Bs, then three more Ss. “There you go.”

For the first time, Santino turned in a non-blank test. He got all three ratio problems correct, with pictures and “guess and check”. Everything else was still blank.

For this particular ratio unit, I had taught students both the algorithm and the visual method I’d just used with Santino. I’d taught it not once, but several times. I’d given the students a number of different techniques to help conceptualize a ratio, concepts that they’d already been taught extensively their previous year, either in Algebra or pre-Algebra. I had already dramatically simplified and slowed instruction for the class.

Yet Santino’s response to my intervention demonstrated that I still had students for whom the gap between the content I was teaching and the support they needed proved much larger than I’d imagined.

And so, over Christmas break, I winnowed algebra down to the fundamentals, designing an “algebra lite” curriculum for these students. Through trial and error, I settled on a method: start the day with something they could do instantly, without needing explanation. Introduce new material twenty minutes into class with simple practice problems—and I mean simple. Take my initial notion of simple, cut the difficulty in half, and then again. Then take just half the problems I’d planned on and I’d be in the ballpark. They’d work on those problems the rest of the class. The next day, they’d start with a basic—again, really REALLY basic—problem in the new material, and move forward on that. Although this method meant more work (remember, I was still teaching the usual course in the same class), it gave my weakest students a chance to progress. Most of them responded eagerly, grateful for work they knew how to do.

Santino’s math skills didn’t improve dramatically, but his engagement inched up several notches. He worked in class, and his tests (easier ones for this group) were no longer blank. He was noticeably stronger at word problems, and best of all at word ratios, that first type we’d worked on together.

As a sophomore, he took the required California High School Exit Exam (CAHSEE) in March of that year. I assigned my strongest freshmen to coach a sophomore for eight class days, using a tutorial I’d designed to help both freshman and sophomore understand how the test was constructed . For Santino, I chose Carl, a shy, sweet, white kid who wore his NERD teeshirt once a week. I told Carl that any score above 330 (passing was 350) would make Satino feel ready for a rematch, instead of hopeless. Carl understood, and as I wandered the room during that prep fortnight, I would often hear him reminding Santino to “estimate and eliminate”. Santino was always hunched over his practice questions, thinking hard, not sitting passively; he even ventured a question now and again to the far less threatening Carl.

Just over half of my algebra sophomores passed the CAHSEE, which is as much as I could ask for. Santino, who passed the English section with a 356, stunned me with a 348. The day the scores came out, we had the longest conversation of our two year acquaintance.

“I didn’t pass.”

“You got a 348! That is AMAZING! One question from passing! I am so proud of you!”

“I almost did it. I think I will do better next time, because I didn’t know geometry. I need to study again in November. I will pass it then.”

“You make sure to come back and see me in November and I’ll give you the practice material.”

“Okay.”

Santino passed my “algebra lite” curriculum and I changed his first semester grade to reflect his new work. His junior year, he was assigned to my geometry class. Come November, even before I’d prompted him, he came up and said, “I will be taking the CAHSEE.”

“I know. Do you want a few days in class to practice?”

He worked independently and diligently. While he didn’t go so far as to ask me questions with, say, his voice, he had questions circled and would look up mutely when I stopped at his desk. I’d coach him on best methods for elimination; he’d nod and get back to work. He came to class the day of the test, a little less inscrutable than usual, just a bit anxious. When the announcement calling students to the testing room came over the speaker, I said, “Go get ‘em” and the class all cheered him and the others on.

He passed with a 356. His seatmates and I harassed him to look happy, until he finally turned the ends of his mouth up, reluctantly. But he did look pleased.

In geometry, Santino would still sit silently in front of a blank sheet if he was stuck, but he never turned in an empty test again. He’d peek up through his shock of hair as I walked by, and point to a problem when I stopped. Most importantly, he was passing the same course as the other students—passing with a D, but passing.

So you can see, perhaps, why I didn’t particularly appreciate the AVP’s snark. Santino was, indeed, “doing well”.

He did well enough in right triangle trigonometry, of all things, that I gave him either a D+ or C- for the second semester. Since he’d passed pre-algebra in summer school his freshman year, Santino had, at the end of junior year, the necessary three years of math to meet his graduation requirements. He was as quiet as ever. Despite our two years’ acquaintance, he never initiated a greeting when we passed by in the yard, although he would, if I waved, give me a “chin jut of recognition”, as Sheldon Cooper would call it.

I left the school that year, but often wondered if Santino would be able to “make the walk”. Would his credit gap force him to an alternative high school for senior year, or some online academy? He didn’t have the grades for the voc-ed program, so that wouldn’t be an option. I have beer or coffee with my ex-colleagues frequently, and would often nag them for any status about Santino. None of them could find his name in the system, but I kept hoping they’d just missed something.

One Tuesday in early August, I ran into another student from Santino’s school, and wished him luck in college. “Did you see my name in the paper? They had the whole graduating class!”

I went home and googled the Mercury News list of graduating seniors for the school. Santino’s name was on the list. He’d walked with his class.

A growing body of research suggests that non-cognitive factors—persistence, effort, motivation—are important in adult outcomes. Kirabo Jackson of Northwestern University analyzed the impact of teachers on both test scores and non-cognitive skills (as assessed by attendance, graduation rates, and so on). He found that “many teachers who are among the best at improving test scores may be among the worst at improving non-cognitive skills”. Moreover, “teacher effects on the non-cognitive factor explain significant variability in their effects on these longer-run outcomes that are not captured by their test score effects”.

In practice, valuing “non-cognitive skills” almost always means lowering academic standards. Many students struggle with advanced content but have no ability to choose easier courses, thanks to our well-meaning but misguided education policies. If teachers hold all our students to a strict reading of the course requirements, students who either don’t want to or can’t understand the rigorous material will fail. Obviously, reasonable standards would eliminate the need for that choice. Schools might provide a menu of classes of varying difficulty, allow students to choose course material they are capable of and interested in learning, rather than set a ferociously high bar and then make some teachers choose between failing most of their students or not covering the material with a rigor appropriate for the strongest kids. But in today’s world, fail or pass a student who can’t really do the work is our only choice.

On the other hand, Rishawn Biddle argues that teachers like me are the problem: “Behind all this gatekeeping is the view among many traditionalists that there are some kids who just aren’t capable of high-level work”, and that students of color are given a terrible foundation due to terrible teachers and weak curriculum.

Biddle’s assertions aren’t borne out by any reality I’ve ever seen. In Santino’s case, he had a solid grasp of math facts but struggled tremendously with abstractions. He attended the same K-8 schools that many of my strongest students, both Hispanic and white, attended. But while I’m no traditionalist, it’s certainly true that I thought Santino was incapable or uninterested, at that point in his life, of deep understanding of algebra and geometry. So I modified both his work and my expectations to give him passing grades. I would do it again. In fact, I have done it again.

While the education philanthropists like Whitney Tilson hold that “kids will live up – or live down – to whatever expectations are set for them”, reality plays out very differently. Many kids simply don’t try. Many kids try but simply can’t do the work. And quite a few kids fall somewhere in between. Fail the kids like Santino, and they either drop out, or settle for a GED, or go to some credit-recovery room, separate from their peers. Pass the kids like Santino, and they get to feel normal, even in an environment designed to make them feel inadequate. The Whitney Tilsons believe that failing a kid simply makes him work harder at an achievable task. But what if they’re wrong, as the majority of teachers who work with low ability, low incentive kids would argue? The data shows that, given the same level of academic achievement, kids are better off graduating than dropping out, or even getting a GED.

So, the question: Do you teach the course or teach the kids? Many math teachers hold that higher standards are essential, that the only way to ensure that our classes accurately reflect their descriptions is to fail those students who don’t perform with the expected rigor. I understand that argument but ultimately, I agree with a colleague who said once, “Look. If half your class is failing, blame the person you see in the mirror.” I simply can’t fail half my kids in classes they didn’t choose to take.

As for Santino, I know this: He almost certainly would not have passed algebra and geometry with a different teacher. This alone gave him a better shot at graduating normally. Without the need to repeat math classes, he had more slots on his schedule to repeat earlier failed classes and make up even more credits. The more he could see graduation becoming a possibility, the more he was willing to work to achieve it.

God speed, Santino. Go get ‘em.

This piece was originally written in 2013.