There is a very long article in Quanta about various schools in the New York City area and how teachers go about teaching science and math. The context of the article is the usual “The US has not done well in science and math”, and the not so subtle sub-text of “That’s because we’re teaching it wrong”. Per the article, “Wrong” means teaching by rote, by cookbook, by telling students formulas instead of having them derive it, by having them do experiments with predictable results. In short, the traditional model of science and math treats students as novices. The collective wisdom of the teachers featured in this article, however, treats students as if they are experts.
The emphasis is project-based/inquiry-based structures in which students are given an assignment or problem with some prior knowledge, and expected to make up what they don’t know on a just-in-time basis. Guidance is kept to a minimum, with the student expected to discover what they are supposed to learn–or, in the case of science experiments gone awry, to discover what was the cause, and correct it.
The article profiles several teachers who have used these various methods. If a teacher can have success using such techniques, that’s great. But in reading the article, I do have to wonder about such methods and their basic assumptions and mischaracterization of the conventional/traditional techniques which they hold as “not working”.
Too often, said Vice Principal Elizabeth Leebens, students “get the history of science rather than getting an opportunity to do it for themselves.” Still, Leebens was surprised when, after a group of science club students asked Comer for help with their ice-cream-making experiment, which had already failed seven sticky times, Comer told them, “Go back and check your process.” Off they went to the bathroom to dump the latest batch and start over.
“I call it productive struggle,” Comer said. “That’s where the growth happens.”
In meetings, Leebens said, Comer has “challenged me to stop doing the cognitive work for kids: ‘Let them do it themselves. They can do it; they can do it.’” For Comer, she added, it’s about “life lessons and also high expectations for kids in letting them see what they can do before the adult decides what they can do.”
The “struggle is good” philosophy prevails at these schools and among these teachers. I am guessing that because such approach has come under criticism in the past, that it is now called “productive struggle”. In any event, there are good ways and poor ways to make students struggle. One hears about “scaffolding” problems so that students stretch beyond initial worked examples or experiments but have enough prior knowledge to make the leap. But there are those who consider “scaffolding” as handing it to the student, giving the student too much information so they don’t get the “deep understanding” nor learn how to “problem solve” (to use the edu-trendy parlance that has gained popularity over the past few years).
The article talks about a math teacher and how she came to her particular philosophy of productive struggle.
Midha has always loved math — it came easily. She suffered some doubts about her abilities in 10th grade, thanks to an algebra teacher who did the standard “chalk and talk” at the blackboard. But during freshman year at Wesleyan University, she took calculus with a professor who considered mathematics to be an art. “Everything he said was so profound,” she recalled. “I was like, ‘Oh, my god. This is the coolest thing ever.’” And that was that. She became a math major — and also a music major; she plays classical guitar.
With this quote, the article then lays the groundwork that the standard “chalk and talk” doesn’t work (and making the general assumption that all teachers using traditional methods never ask questions of students, but just lectures in a boring and uninspiring manner). Rather, teachers are required to be inspiring and profound and math is to be taught as an art. Or something like that. I don’t know much else about her calculus professor or what he did in class, but I suspect that he relied just a little bit on “chalk and talk”.
The article goes on to describe a lesson the Midha gives her students in which they have to determine the heights of buildings outside their classroom using an iPhone app that served as an inclinometer, and using what they know about trigonometry. She calls this a “struggle problem”:
Using two iPhone apps, they measured the angle of elevation from point A to the top of the building and the distance the walker traveled from point A to point B, at the base of the building. These two measurements gave them crucial pieces of information about a right triangle, and from there — using what they’d learned so far in class about trigonometry — they are now charged with the task of calculating their building’s height. But first there are ponderous stares, frowns, diagrams drawn and redrawn amid plumes of eraser dust, and a collective buzz of puzzlement:
“I dunno, man. I really don’t know.”
But they won’t get much help from their teacher.
“I’m the teacher who stopped giving them the answer,” said the 30-something Midha. “In every unit that we do, I warn them: ‘I’m going to give you the tools that you need, but I’m never going to tell you how to do something. You have to figure out how to do it, you have to figure out the answer, and you have to prove to me why you think that answer is what it is.’” She also offers reassurance through an oft-repeated mantra: “The only way that you can fail is if you give up. If you continue to persevere, if you continue to try, if you continue to work through this, you will get this. But if you give up, you will fail.”
“Remember: Where was the angle of elevation measured from? The eye. So when you are drawing and calculating, remember that. Your job is to calculate the total height of the building. … Remember: There is a reason we measured the eye height. There is a reason we measured the eye height.” Repetition, and more repetition, is key for penetrating the adolescent brain.
Midha also provides a bonus hint of sorts, pointing out to her students that they measured the eye height in inches and the building distance in miles, and that the worksheet asks for the height of the building in feet. With that, she leaves her students to their own devices —“Good luck!”
She circles the room, surveying the progress, asking simply: “Does it make any sense? … Why doesn’t it make any sense?” Despite her hints, the relevance of the eye height is proving elusive, and the inch-feet-miles conversions are confusing. She reiterates her tips one-on-one with the groups, and then lets them loose again, declaring: “I’m going to walk away now … ”
Which raises the question of whether it would do any harm to just tell students what they need to know when after some grappling with the problem they are clearly in a receptive mode to receive and process such information. No, I guess not. Best to just let them struggle.
I will stick with the more controlled variety of struggle, and provide the scaffolding needed and when it appears fruitful, tell them what they are now ready to hear. And in so doing, it appears that many will brand me “old school”. I recall a professor I had in ed school saying to a student that such direct instruction may be good in the short term, with students scoring higher on tests than those using inquiry-based techniques. “But in the long term, those using inquiry have a deeper understanding.”
This appears to be the premise that guides the teachers described in the article, as well as an ever-growing body of teachers indoctrinated into this type of teaching.
I’ll risk being called old school–and other names.