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.
7 thoughts on “Oh, Really, Dept.”
Regular homework requires struggle even with chalk and talk, and it IS productive. It’s never rote or drill only for speed. All problem sets require application of the material learned and I’m sure I’ve seen some that require the student to figure out the height of a building, but without making it an outdoor time-wasting project.
“they are now charged with the task of calculating their building’s height”
“They.” Forget whether some kids dominate and have some sort of productive struggle and then directly teach the rest. There really is a LOT of discovery that goes on with individual student homework problems, and they can’t hide in the pack and let others do the work. Feeling good about being part of a group does not create discoverers and problem solvers. Individual homework does that. PBL wastes time and requires slower coverage of material.
PBL time wasting is a HUGE problem. Is the engagement of value? Perhaps, but not in place of regular individual homework problem sets. That’s the question. For equal amounts of time invested, where does the student get to? It’s not some better level of understanding. Besides, with many of my traditional math and science classes, we had plenty of “projects” that attempted to synthesize the learning out of context of unit material.
PBL defines projects as the main process of learning. I’ve never seen it described as something that is built on top of traditional and required individual nightly problem sets. They can’t say that traditional teaching never did or does this. They could argue that there should be more projects, but that’s not what they’re saying. In my son’s high school, his honors and AP classes rarely wasted that sort of time. However, the lower general and base college-prep classes often did this. Perhaps that engagement trade-off works better for some, but the breadth and depth of coverage is greatly reduced. If you slow down any process, you would expect to do a better job no matter how you do it.
The better question is whether PBL is the best use of that time. I say no and students and parents should be given that choice. That’s the real problem here, isn’t it. High schools have some choice, but there is no choice for students in K-6. High schools have different level classes and the highest ones have little time to waste on silly projects. The implication that PBL creates better students with more understanding is false. Slower coverage may work for some, but I’ll bet that I could come up with better methods than time-wasting projects.
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It is not that I don’t agree that PBL could be useful, but the point you make about how much time are you willing to give is spot on. Our high school has 80 minutes to teach math for a full year for algebra one knowing that kids need more time to develop the concepts. Our elementary has 70 minutes or more depending on how they structure their lessons for a full year. However, our middle school is only given 40 minutes. This idea of traditional method is way over used and assumes, like you said, that all we do is rote memorization. Please take me to a classroom where that is happening? Maybe when I first started 20 years ago, but that is not the case that I have seen anymore. I really appreciate you keeping this reformster movement grounded. We definitely need to continue to hone our craft, but like Steve said, there are better more efficient ways to do that with DOK questions and within our time restraints. If I read this correctly, this occurred over the course of three days?
“But in the long term, those using inquiry have a deeper understanding.” – I’m not aware of any actual evidence for this. Were you given any?
This was a comment overheard that she made to another student–after she raved to me about a presentation I gave in class about the effectiveness of scaffolding and direct instruction. I was tempted to ask your question but figured I wasn’t meant to overhear her comment. Plus she would have given the usual “Oh, yes, I’ll look it up and get back to you.” It would probably be the usual “studies” by Fennema, Hieber, or Carpenter who have been writing papers and taking in each other’s laundry for years.
I think the idea of inquiry is not quite as strongly propagated in the UK, although there is very often the implicit belief that “group work” is inherently better than individual work.
“… one variable that’s too often lost amid public hand wringing over test scores and new standards is arguably the most vital: the fallible humans charged with imparting an appetite and appreciation for learning. To shine a spotlight on this linchpin of America’s byzantine education system, Quanta Magazine followed four master science and math teachers into their classrooms. Here are their stories.”
Stop. I want to “argue” about that. “Most vital?” That is NOT the reason why the US ranking on PISA is so low. Besides, would everything be OK if the US ranked in the top 10? Is the goal in math to raise a median score on a simple international test or is it to provide the best individual educational opportunities?
Academic tracks start in 7th grade, but you’re on your own until then, and kids from affluent families get that help at home and with tutors. This gap is worsened by full academic inclusion. Many of us parents now make up the difference so that schools do not see the problem. They don’t even ask. One older teacher told me once that the new emphasis on minimal proficiency helps the lower end students, many parents help their own kids, but that there is a large and capable middle group that is left on their own. In math, it’s all over by 7th grade for many of them. This problem will never be solved with guess and check, especially when the “guess” is assumed to be “arguably the most vital.”
They see a poor score on PISA, make a bad guess that they assume is true, and then go to great lengths to show that it is true. That is supposed to be critical thinking: make an hypothesis and then write something to prove that it’s true. If I were to try to answer why the US PISA score is so low (I wouldn’t, because raising a low mean is NOT the problem), I would, like any good scientist, start by working backwards from the details on the test. Which problems did students get wrong? Why did they get them wrong? What skill or understanding does it reflect? What is the curriculum and what are the yearly individual expectations? You don’t find answers by looking for statistical means on “big data.” You have to look at individual students to see why some do well and some fail. Individual anecdotes have all of the data to answer that question. Big data will never do that. People will only find what they are looking for.
I distinctly remember when my son’s K-6 schools talked about how all kids will learn when they are ready and that we parents should model a love of learning, make sure we turn off the TV, and ensure that homework is done – like the typical five problems expected by Everyday math. Then we started to get notes telling us parents to work on “math facts” at home and encouraged us to go to “math nights” at schools so we could better help our kids!?!?! What does that imply? I distinctly remember wondering what, exactly, do schools now expect from parents – home help to allow them to increase the range of willingness and ability in academic classrooms because of full inclusion? Perhaps it was to help them out because differentiated instruction was a complete failure. They had NO PROBLEM with having us parents take a strong role in the process. My wife and I had our first grade son read chapter books at home and write book reports to hand in. The teacher gave them checks with no comments and then handed them back to us. Anecdote of one? I have lots of anecdotes that add up to the fact that differentiated instruction requires (!) help by parents. It’s the only way your kids will ever get into the leveled upper in-class academic grouping of kids – to have any chance at getting to the upper math track split in 7th grade.
CCSS officially defines K-6 as a NO-STEM zone and their only solution is to offer in-class leveled groups where the upper levels are filled with students getting their math facts ensured by parents and tutors. Meanwhile, schools “trust the spiral” and never ask the parents of their best students what, exactly, they had to do at home. They just look at simple PISA rankings and play guess and prove.
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