January 2010 Archives

Debunking the Cone of Learning Theory

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Will at Work Learning: "People remember 10%, 20%...Oh Really?"

I'm posting this as a kind of outboarding of my memory: this is the kind of thing I'd like to have on file somewhere, but since it concerns work that lives only on the periphery of my zones of attention, I'm likely to forget about it if I don't post it here. So here it is, without much comment --

. . . except for this: the article shows that a widely-circulated and -cited piece of data about learning styles and information retention is based on no actual research whatsoever, and has been passed around in the field of education in various forms for decades without any interrogation at all.

One of the lessons is that good, accurate citations are actually meaningful and important, and that responsible readers should pay attention to them and on occasion follow up with them. In the internet age, it is extremely easy to do so, so this kind of bunkum is less likely to be perpetuated now that in earlier eras, but for the growing problem of people's unwillingness to read carefully and interrogate what they read when they do read it.

Math in the Schools and in the Colleges

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High-School Calculus: The Elephant in the Classroom

This Chronicle of Higher Education opinion piece focuses on the decline of mathematics students in colleges, despite what seems to be far better preparation in high schools today. After giving some data about enrollments and the like, the author (David M. Bressoud) says:

But the majority of high-school calculus students earn a satisfactory grade by focusing on algorithms and procedures rather than understanding.

This statement confirms what several math-teacher friends of mine at different schools have told me about math in schools today. Students just want to know how to solve the problems on the test, and many of them don't make the leap from performing those techniques to understanding their mathematical underpinnings.

The pressure to get into top colleges these days is so great that students feel the need to have an AP-level math course on their transcript regardless of the grade: most of them figure that if they can do well enough in the first semester to pass the admissions committees, it doesn't matter what they earn on the actual AP exam or in the rest of the course. Many of my own students in AP English struggle on the AP Calculus AB exam, which is truly not an extensive preparation for college math.

Regarding another point in the Chronicle piece: I did find college teaching in mathematics to be opaque and unhelpful, as were the textbooks. This was many years ago, but I went to college intending to major in mathematics: I had always been the top math student at my high school (which is itself a top school), and I had earned a 5 on the Calculus BC exam, which qualified me for the honors track in linear algebra and vector calculus. Within the year, I decided not to pursue math as a major, primarily because the professors and the books were incomprehensible -- and not just to me, but to the majority of my classmates (we took a team approach to studying and trying to master the material). I recall one lecture when the professor, who had been filling the chalkboards, was stopped by a student and asked to go back to explain how he got from one point to another. The prof (who always seemed nervous in front of us) just looked back at his work for a moment, looked back at us over his shoulder and said hesitatingly, "Well . . . that's it, you see."

From this whole experience, I learned that it is one thing to understand a subject, and another thing entirely to be able to communicate it effectively to others. It's also one thing to earn a minimal pass on an exam, and other thing to be able to use one's prior experience to gain further mastery in a discipline. This might be one way that teachers could rethink their teaching strategies in math, and defend those practices to demanding students and parents who value only the bottom-line exam scores: to focus solely on skills and strategies (the algorithms and procedures of math) is to miss the other four of the five dimensions of learning: knowledge and understanding, the use of prior and emerging experience, confidence and independence, and critical reflection. I put it to my colleagues in math departments and to administrators in curriculum development to develop ways of fostering these other dimensions of learning in their mathematics instruction and to share them with others across the secondary/collegiate divide.
"What Makes a Great Teacher?" The Atlantic (January/February 2010)

This fascinating piece describes, in part, the results of a study conducted by Teach for America about what qualities in a teacher are most likely to make them effective in the classroom, as measured by some fairly rough tools. Then answers are not that surprising, but it is nice to see them verified somewhat objectively. Money quotes:

As Teach for America began to identify exceptional teachers using this data, [Steven] Farr began to watch them. He observed their classes, read their lesson plans, and talked to them about their teaching methods and beliefs. He and his colleagues surveyed Teach for America teachers at least four times a year to find out what they were doing and what kinds of training had helped them the most.

Right away, certain patterns emerged. First, great teachers tended to set big goals for their students. They were also perpetually looking for ways to improve their effectiveness. For example, when Farr called up teachers who were making remarkable gains and asked to visit their classrooms, he noticed he'd get a similar response from all of them: "They'd say, 'You're welcome to come, but I have to warn you -- I am in the middle of just blowing up my classroom structure and changing my reading workshop because I think it's not working as well as it could.' When you hear that over and over, and you don't hear that from other teachers, you start to form a hypothesis." Great teachers, he concluded, constantly reevaluate what they are doing.

Superstar teachers had four other tendencies in common: they avidly recruited students and their families into the process; they maintained focus, ensuring that everything they did contributed to student learning; they planned exhaustively and purposefully -- for the next day or the year ahead -- by working backward from the desired outcome; and they worked relentlessly, refusing to surrender to the combined menaces of poverty, bureaucracy, and budgetary shortfalls.

But when Farr took his findings to teachers, they wanted more. "They'd say, 'Yeah, yeah. Give me the concrete actions. What does this mean for a lesson plan?'" So Farr and his colleagues made lists of specific teacher actions that fell under the high-level principles they had identified. For example, one way that great teachers ensure that kids are learning is to frequently check for understanding: Are the kids -- all of the kids -- following what you are saying? Asking "Does anyone have any questions?" does not work, and it's a classic rookie mistake. Students are not always the best judges of their own learning. They might understand a line read aloud from a Shakespeare play, but have no idea what happened in the last act.

"Strong teachers insist that effective teaching is neither mysterious nor magical. It is neither a function of dynamic personality nor dramatic performance," Farr writes in Teaching as Leadership, a book coming out in February from Farr and his colleagues. The model the book lays out, Farr is careful to say, is not the only path to success. But he is convinced it can improve teaching -- and already has.

And still more:
For years, Teach for America also selected for something called "constant learning." As Farr and others had noticed, great teachers tended to reflect on their performance and adapt accordingly. So people who tend to be self-aware might be a good bet. "It's a perfectly reasonable hypothesis," Ayotte-Hoeltzel says.
But in 2003, the admissions staff looked at the data and discovered that reflectiveness did not seem to matter either. Or more accurately, trying to predict reflectiveness in the hiring process did not work.
What did predict success, interestingly, was a history of perseverance -- not just an attitude, but a track record. In the interview process, Teach for America now asks applicants to talk about overcoming challenges in their lives--and ranks their perseverance based on their answers. Angela Lee Duckworth, an assistant professor of psychology at the University of Pennsylvania, and her colleagues have actually quantified the value of perseverance. In a study published inThe Journal of Positive Psychology in November 2009, they evaluated 390 Teach for America instructors before and after a year of teaching. Those who initially scored high for "grit" -- defined as perseverance and a passion for long-term goals, and measured using a short multiple-choice test -- were 31 percent more likely than their less gritty peers to spur academic growth in their students. Gritty people, the theory goes, work harder and stay committed to their goals longer. (Grit also predicts retention of cadets at West Point, Duckworth has found.)
But another trait seemed to matter even more. Teachers who scored high in "life satisfaction" -- reporting that they were very content with their lives -- were 43 percent more likely to perform well in the classroom than their less satisfied colleagues. These teachers "may be more adept at engaging their pupils, and their zest and enthusiasm may spread to their students," the study suggested.
In general, though, Teach for America's staffers have discovered that past performance -- especially the kind you can measure -- is the best predictor of future performance. Recruits who have achieved big, measurable goals in college tend to do so as teachers. And the two best metrics of previous success tend to be grade-point average and "leadership achievement" -- a record of running something and showing tangible results. If you not only led a tutoring program but doubled its size, that's promising.
Knowledge matters, but not in every case. In studies of high-school math teachers, majoring in the subject seems to predict better results in the classroom. And more generally, people who attended a selective college are more likely to excel as teachers (although graduating from an Ivy League school does not unto itself predict significant gains in a Teach for America classroom). Meanwhile, a master's degree in education seems to have no impact on classroom effectiveness.

The most valuable educational credentials may be the ones that circle back to squishier traits like perseverance. Last summer, an internal Teach for America analysis found that an applicant's college GPA alone is not as good a predictor as the GPA in the final two years of college. If an applicant starts out with mediocre grades and improves, in other words, that curve appears to be more revealing than getting straight A's all along.

What a wonderful thing to have this data source available for this type of research. As the article suggests, most people cannot sustain the TFA workload and pace for long: the energy and time required prevent folks from living a reasonable lifestyle. Career teachers have to make compromises between the energy they put into their preparation and teaching work and the energy they devote to other aspects of their lives (families, community work, personal interests, etc.), so it's hard to say whether these findings can be usefully applied in other teaching venues. However, the article does raise one interesting point on this score:

But if school systems hired, trained, and rewarded teachers according to the principles Teach for America has identified, then teachers would not need to work so hard. They would be operating in a system designed in a radically different way -- designed, that is, for success.
Wouldn't that be great -- to improve the whole system and make being a teacher a more desirable pursuit? Better job satisfaction, better people entering the field, better salaries. Let's have more of this kind of discussion in the public realm.

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