kitchen table math, the sequel: sage on the stage

Friday, April 22, 2011

sage on the stage

“The sage on the stage” versus “the guide on the side” is how the debate is often framed. Proponents of the former ruled the education roost throughout the 19th century, but in the 20th century a child-centered doctrine, developed by John Dewey in the gardens surrounding the University of Chicago’s Laboratory School, then refined at Columbia University’s Teachers College, gained the high ground, as “inquiry-based” and “problem-solving” became the pedagogies of choice, certainly as propounded by education-school professors. In recent years, the earlier view has staged something of a comeback, as KIPP and other “No Excuses” charter schools have insisted on devoting hours of class time to direct instruction, even to drill and memorization.

Eighth-Grade Students Learn More Through Direct Instruction
by Paul Peterson
Education Next
Summer 2011 / Vol. 11, No. 3
On the question of sages on stages versus guides on sides, we critically need parent choice.

You shouldn't have to pay private or parochial school tuition to get a teacher-centered classroom for your kids.


cranberry said...

On the other hand, for the highly gifted, the guide on the side may be better.

The Davidson Academy:
Carmen Garcia, the academy’s director of curriculum, teacher training, and admission, told me this is a fairly typical class. The school uses few textbooks because classes move too quickly—“No textbook is going to fit the bill for more than two weeks,” she said—and because students prefer the variety of perspectives that come from reading original sources. “A history textbook; it’s doomed here,” she added.
Teachers told me they seldom lecture. “If we try to lecture, these kids are going to get bored,” said Darren Ripley, who has a 10-year-old in one of his calculus classes, a girl he refers to as “a big mind.” Instead, teachers seem to ride the wave of classroom discussion, now and then dipping in a navigational oar. “Sometimes you have to let go and see what’s working at the moment, then try to reel it back,” said Jessica Juriaan, who teaches British and American literature.

The method, as described, sounds like the Harkness Method, which Phillips Exeter Academy uses.

Exeter uses the Harkness Method for math:

Our intention is to have students assume responsibility for the mathematics they explore—to understand theorems that are developed, to be able to use techniques appropriately, to know how to test results for reasonability, to learn to use technology appropriately, and to welcome new challenges whose outcomes are unknown.

To implement this educational philosophy, members of the PEA Mathematics Department have composed problems for nearly every course that we offer. The problems require that students read carefully, as all pertinent information is contained within the text of the problems themselves—there is no external annotation. The resulting curriculum is problem-centered rather than topic-centered. The purpose of this format is to have students continually encounter mathematics set in meaningful contexts, enabling them to draw, and then verify, their own conclusions.

As in most Academy classes, mathematics is studied seminar-style, with students and instructor seated around a large table. This pedagogy demands that students be active contributors in class each day; they are expected to ask questions, to share their results with their classmates, and to be prime movers of each day’s investigations. The benefit of such participation in the students’ study of mathematics is an enhanced ability to ask effective questions, to answer fellow students’ inquiries, and to critically assess and present their own work. The goal is that the students, not the teacher or a textbook, be the source of mathematical knowledge.

Jo in OKC said...

I think that "Sage on the Stage" is easier to implement and more people are likely to succeed at it.

"Guide on the Side" takes a lot of work and reading of the students. It also takes buy-in from the class. A group of disinterested, disenfranchised students can doom the learning environment even if some students do want to work and learn.

SteveH said...

Like Phillips Exeter (where it started), we have a private school in our area that uses the "Harkness Table" method. I don't like its blanket use for all classes, but then, I don't have to send my son there. I also think it is workable only for self-motivated students.

Grace Nunez said...

A group of disinterested, disenfranchised students can doom the learning environment even if some students do want to work and learn.

I believe these types of students are well-represented in many schools.

You know what can make an inquiry-based classroom an absolute nightmare for many students? A combination of heterogeneous grouping and a teacher with poor class management and/or content skills.

LynnG said...

I've seen the Harkness method work absolutely beautifully. BUT. It takes an enormous amount of preparation by the teacher. You just can't do it well off-the-cuff. Classes have a tendency to wander in the discussions, it takes a skilled teacher to get the class to flesh out the important concepts without losing focus, engaging in pointless arguing, or fizzling out.

As a first step, the teacher has to know the material inside out. I've seen more bad than good.

Anonymous said...

Also, the Harkness method depends on the students reading the background/factual material ahead of time, religiously. Without that, the discussions just turn into opportunities to voice opinions unsupported by evidence.

Allison said...

And, is anyone suggesting the Harkness method is good for students below 9th grade? The maturity needed to handle the Harkness method is not some thing that translates into elementary or middle school students.

Catherine Johnson said...

I believe these types of students are well-represented in many schools.


Catherine Johnson said...

hey cranberry --

boy, I dunno

I taught gifted students myself (for Johns Hopkins), and the idea that a gifted student is not able to stick with a textbook doesn't describe the kids I knew at all.

I don't know what the relationship is between giftedness, focus, and self-discipline, but my impression of gifted students is that they have if anything higher tolerance for staying with a book or textbook intead of having to jump to the next thing.

As to gifted students getting 'bored' in lectures, I think we've completely lost sight of the fact that lectures can be brilliant, challenging, enrapturing, etc., etc.

There's a reason why The Teaching Company sells filmed lectures for hundreds of dollars.

Catherine Johnson said...

The other issue is that giftedness in the humanities and social sciences may be different from giftedness in math and physics.

In history and writing, etc., no one does his best work in his 20s.

The idea that a school would have students so gifted in the field of history that they need to read original sources at age 10 doesn't track.

(btw, I had a few conversations with Carolyn about this...I **think** her take was that the reasons math/physics professionals peak in their 20s had more to do with the demands of life as a mathematician than with the nature of mathematical knowledge and talent...)

In any event, a 10-year old, no matter how smart, doesn't have the life experience, the historical knowledge, or the understanding of historiography to make expert good use of original sources.

Catherine Johnson said...

I went to an Open House at the local private school here that uses the Harkness Method.

The head of the school (this was the middle school, btw) described the technique as being like an orchestra conductor. It's not a freewheeling discussion but rather the conductor is pulling certain 'notes' out of each student in the class.

The teacher pulls, sustains, and modulates 'notes' the students produce....

He actually used his arms, hands, and fingers the way an orchestra conductor would in order to show us what he meant.

Cranberry said...

Johns Hopkins' CTY allows nominations for students who test at the 95th percentile or higher on a nationally normed test. If the description of the Davidson Academy's admissions procedures is to be believed, they enroll the top .1%. I'm willing to believe that the top one tenth of one percent could differ from the top 5%.

I have heard teachers express doubts about textbooks which have been over-simplified. After reading Diane Ravich's book, The Language Police, I can understand the concern.

As far as I know, the Harkness method is not used in public schools, nor is it used in middle schools. It is not direct instruction, and it depends upon motivated and engaged students who prepare well for class every day.

Allison said...

But Cranberry, the article you were referring to WAS talking about "guide on the side" in grades below 9th.

All sorts of schools use modified forms of the Harkness method. In high school over 20 years ago, we were required to move our desks into an oval shape every day to discuss our political philosophy/social philosophy reading and our AP english reading. In the philosophy class, it didn't teach us much of anything, because no one held us accountable for actually *doing the reading*. We were allowed to spout garbage. In AP english, it didn't teach us much of anything because the teacher was a postmodernist who told us that Shakespeare was a feminist who'd written every play to highlight the social inequity of women, from Hamlet to Henry V.

I'm with Catherine--the teaching company lectures are an example of lectures that largely work, and provide orders of magnitude more content than I learned in any such discussion class. I'd have preferred a lecture with historical and literary background in each of them. Of course it's theoretically possible such a course could have taught me something, but how could someone evaluate that ahead of time?

Allison said...

--The idea that a school would have students so gifted in the field of history that they need to read original sources at age 10 doesn't track.

Ah, Catherine, you've hit on something here. I was a 12 yr old given the Federalist Papers and DeTocqueville's Democracy in America because the textbook was something I'd grokked in 10 minutes and I was bored to tears.

Guess how little I got out of reading those things on my own, with no one guiding me? Even those works aren't really primary sources, but you get the idea. (My mother is a retired librarian, so I'm quite familiar with actual primary sources.) Even if I'd had a phd level tutor working with me one on one, I wouldn't have been able to synthesize enough background information about, e.g. the difference between the role of the Montesquieu vs. Rousseau to see how they would have influenced the role of the state in the US vs. France to have gotten some incredible insight out of those two works.

But the teacher didn't have any idea what to do in the middle--for her, I was sophisticated enough to be considered a college student because her only entrance point into meaty content was college.

I think the Harkness method in general suffers from this idea, which we've seen everywhere else in education: to bring students up to the level of X, have them mimic X!

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SteveH said...

"It's not a freewheeling discussion but rather the conductor is pulling certain 'notes' out of each student in the class."

"Certain" notes? Is there no score, or is this improv? How do those notes sound? In a good youth orchestra, you better know your notes before coming to rehearsal. The same is true for a master class. If you're playing Debussy, you better know something about that period of music. But it's more than being prepared. What, exactly, are you prepared for; group-learning?

A conductor (maestro on the podium) is not a good analogy for a Harkness Table approach, where the assumption is that the students drive (create?) the learning and the teacher just keeps them on course. How would that work for math? If students say that they don't understand how something works, is it the job of other students to explain? Does the teacher offer nothing?

In the overall continuum of class control, I would much prefer one where the maestro had a good score and a lot to add to the conversation. Jazz improv only works if you are already very good at playing your instrument. Even if you are prepared, would you like to have a class with Dave Brubeck and have him sit there just trying to keep you on track?

I've had many sage on the stage classes where the teacher tried to steer students toward having the lightbulb go on by asking leading questions. It didn't always work, and when it did, not all "got it". However, the teacher was happy that some figured it out. I can't imagine an environment where this is the norm. I suspect that a lot of sage on the stage teaching happens around their oval tables. The oval table with laptops out just makes them feel better about it.

Bonnie said...

Then there are the sage on the stage classes where the teacher yaks at the class for 90 minutes, while the students sit in stony silence or surf their phones. Then they wait until the night before the exam, frantically cram all the material into their brains from the textbook (which is a far more efficient way of learning factual material than a lecture in any case), and spew it all back out on the multiple choice exam the next day. That accounted for about 75% of my courses as an undergrad, and I suspect it still accounts for the majority of courses today. I know it is typical for most of the courses at my university.
Honestly, for all the hype, guide on the side courses haven't made many inroads at large universities simply because the lectures are too big, the TAs too clueless, and the professors too overwhelmed writing grants. So no need to worry there...

SteveH said...

Any style of teaching can be done badly. That's not the issue. Also, teaching is never just one thing or another. Even Everyday Math sets aside time for teachers to introduce new material. It's easy to talk about variations of each approach that might work well. With a Harkness Table approach, however, I think there is a big danger for pedagogy to overrule common sense, especially if it is applied dogmatically to all classes.

cranberry said...

SteveH, I think one must observe the Harkness method before making statements such as "applied dogmatically to all classes."

The study the article cites does not constitute a slam dunk for teaching by lecturing. I'm surprised Education Next published it. In what universe is 3.6% of a standard deviation significant?

For both math and science, a shift of 10 percentage points of time from problem solving to lecture-style presentations (e.g., increasing the share of time spent lecturing from 20 to 30 percent) is associated with an increase in student test scores of 1 percent of a standard deviation.

I'll go out on a limb here and state that it's foolish to think that the 639 teachers were all estimating their use of class time to the same degree of precision. However precise they were, they certainly weren't universally precise to the same degree.

It could also be that the teachers who were confident enough to admit spending more time lecturing in class were also better teachers. It's interesting that they were more likely to be male and under 50:

Teachers who spent more time lecturing were more likely to be male and under age 50. Interestingly, they were also less likely to have the maximum number of years of teacher training registered by the background survey or to have taken pedagogical or content knowledge classes in the prior two years (see Figure 2).

In other words, teachers aren't interchangeable widgets. One teacher's estimation of the time spent "in a typical week" on one style of teacher-student interaction isn't necessarily accurate (no way to check with self-reported data), and even if accurate, there's no way to know to what degree the teachers diverged from each other in estimations. (i.e., the time spent on a task may be around 25%. One teacher will say 20%, another may estimate 30%, for the same length of time.)

I don't oppose lecture, but I don't think this is a useful study. It should not have been trumpeted as, "sage on the stage wins." It could have been more reliably reported as, "Younger, male teachers do slightly better than older, female teachers." After all, the teachers might vary in their (unverifiable) time use estimations, but they're probably right 100% of the time when asked for their gender and age.

Joseph Kaye said...

I would think, like most things, a good mix of the two is most appropriate. The problem with completely bypassing the "sage on the stage" thing is that eventually, as an adult in the professional world, has to deal with a sage who owns the stage, and it's a unique and valuable skill to be able to get along with them.

SteveH said...

I don't care about the study or which side wins. However, there is bigger dogmatic risk with the Harkness Table approach, even if a teacher is good. How much material can be covered when the teacher just guides the process? Is this a matter or trading depth for coverage, since process is more important than content? Nothing, pedagogically, stops a sage-on-the-stage from having students discuss when needed.

For an AP class at a good school with good students, the differences might be less, but I would bet that it's hard to keep the class discussions flowing continuously along with the timeline of the curriculum. When too many people talk, the pace slows way down. Are all topics discussed as they hope, or are they just happy covering a few topics in depth?

At our local Harkness Table prep school, the anecdotal feedback I have received is that some classes seem more like sage-on-the-stage around an oval table, and others have great in-depth discussions that don't keep up with the timeline of the curriculum. I expect that courses with specific content and goals, taught by good teachers, would sound alike, even if the geometry of the students and teacher is different. Still, there is a higher dogmatic risk with Harkness Table approach.

Bostonian said...

A few people mentioned Teaching Company videos. I bought two Teaching Company videos on astrophysics and probability for my 7yo boy -- they were on sale. The DVDs are accompanied by small 50-page booklets with lecture transcripts. My boy thought the lectures were boring and preferred to just read the booklets, and I agree with him, having watched parts of the videos.