kitchen table math, the sequel: Is this true?

Friday, October 5, 2012

Is this true?

Each school day, millions of students move in unison from classroom to classroom where they listen to 50- to 90-minute lectures. Despite there being anywhere from 20 to 300 humans in the room, there is little actual interaction. This model of education is so commonplace that we have accepted it as a given. For centuries, it has been the most economical way to “educate” a large number of students.
Why School Should Focus on Engagement Instead of Lectures by Salman Khan
I'm trying to think how long I talk at a stretch, with no word from my students.

Five minutes? (For passersby, I teach freshman composition in the context of an English class.)

I'll have to time myself.

It strikes me as unlikely in the extreme that "millions of students" are spending entire school days listening to 50- to 90-minute lectures 6 hours a day.

In fact, it strikes me as being at least somewhat unlikely you could force millions of students to listen to 50- to 90-minute lectures 6 hours a day even if you tried. But I could be wrong.

My impression (and again, I don't know) is that the only teachers using straight lecture as their predominant or exclusive method of conveying knowledge to students are college professors teaching lecture courses. And lecture courses in my experience typically have "recitation" or "discussion" sections where the content of the lecture is elaborated and questions answered.

Plus college students take four courses, or thereabouts, each of which meets typically 2 to 3 times a week, so college students aren't spending 6 hours a day listening to lecture even when they're taking 4 lecture courses.

Besides which, I object to the blanket assumption that lecture is somehow an intrinsically bad form. The lecture is a time-honored, efficient, and often inspiring means of organizing and communicating material from an expert to a novice -- or from an expert to a colleague.....

And with that, I see I've veered off-topic.

A school would play heck getting me to pay attention to 6 hours of lecture a day, that's for sure. I don't have the focus.

Good thing no school I attended ever tried it.

Back to K-12. My intended topic is not to ask: Do students listen to lecture? I'm sure they do.

My intended topic is to ask: Do students in K-12 spend 6 hours a day moving in unison from classroom to classroom where they listen to 50-to 90-minute lectures?

(And, if they do, my follow-up question is: how is that possible?)

People seem to think "explicit instruction" means lecture, which is not remotely the case.

See, e.g.:
Barak Rosenshine, Five Meanings of Direct Instruction and Principles of Instruction; and Doug Lemov, Teach Like a Champion.

Not only does "explicit instruction" not mean "lecture," it means almost the opposite. I recall watching a professional development video on direct instruction a few years back (no longer available online, it appears) in which the presenter gave teachers an explicit figure for the number of questions they were advised to ask per each 20 minute segment of class time.

It was a lot.


OK, here we go. The Use of Questions in Teaching, 1970:
Certainly teachers ask many questions during an average school day. A half-century ago, Stevens (1912) estimated that four-fifths of school time was occupied with question-and-answer recitations. Stevens found that a sample of high-school teachers asked a mean number of 395 questions per day. High frequencies of question use by teachers were also found in recent investigations: 10 primary-grade teachers asked an average of 348 questions each during a school day (Floyd, 1960); 12 elementary-school teachers asked an average of 180 questions each in a science lesson (Moyer, 1965); and 14 fifth-grade teachers asked an average of 64 questions each in a 30-minute social studies lesson (Schreiber, 1967). Furthermore, students are exposed to many questions in their textbooks and on examinations. [emphasis added] 
This is what everyone on the planet (our current planet, I mean) seems to have forgotten: old-time teaching wasn't about teachers standing on a stage delivering a lecture for 50 or 90 minutes.

How could it have been?

How would that work in a one-room schoolhouse?

Old-time teaching, as far as I can tell, was highly interactive and fundamentally social. Probably most effective teaching is fundamentally social; at least, I wouldn't be surprised to learn that it is.

And that's the problem with trying to learn math from a math video. It's lonely!

I'm pretty sure that reforms whose purpose is to topple straw men are the wrong reforms.


Anonymous said...

I think the position that you and Khan are coming from are different. Khan came from a Computer Science/Math background. In these subjects (at least at the college level) 50-90 nonstop lectures for hours a day are actually the norm. I experienced this in college science courses too. But my college humanities courses (my second major was in philosophy) was somewhat different. While I noticed that lecturing was also common in the humanities, questioning and discussion were MUCH more frequent in the liberal arts courses. I hope I'm not overgeneralizing here, but I think this experience applies broadly to technical and liberal arts subjects. To an extent, literature courses are flipped, hence your confusion from the TIME article. In fact, I've read Khan mention humanities seminars and case study pedagogy from Harvard Business School as models for instruction. This video from his collaboration with Stanford Medical School may help -

A related (Stanford) article from a journal here -

kcab said...

Like Anon above, I've found lectures to be common in technical subjects, though my experience was that classes were/are typically lectures + recitation, or lecture + labs.

Both my high school and middle school kids have math classes with a lot of lecturing this year. Doesn't work that well for either child, unfortunately. The middle schooler also has lectures in social studies, but not for the full class period and not every day.

Catherine Johnson said...

In these subjects (at least at the college level) 50-90 nonstop lectures for hours a day are actually the norm. I experienced this in college science courses too.

Right -- I was thinking that's probably the case in college-level science.

Is it the case in K-12?

That's what he's talking about.

Catherine Johnson said...

kcab - thanks -- interesting.

I have to say, part of me wonders whether Powerpoint and Smartboards actually encourage straight lecture ---- although a student last spring told me that the Smartboard in his high school had software for cold calling!

I would love that.

I use Pick Sticks for cold calling, and my **sense** is that students like it. It's funny, it's different, and it really does keep them on their toes --- everyone knows there's no hiding.

I recommend it.

Catherine Johnson said...

ence your confusion from the TIME article.

I don't believe I'm confused.

He's talking about K-12, right?

Catherine Johnson said...

While I noticed that lecturing was also common in the humanities, questioning and discussion were MUCH more frequent in the liberal arts courses.


Khan is overgeneralizing, it sounds like .....

Catherine Johnson said...

Straight math lecture to kids is crazy.

How does the teacher know if the kids are following?

Actually, I know the answer to that. The math chair here once told me, apropos of a teacher from whom C. was learning very, very little, a fact she acknowledged, that she knew the teacher in question was good because she herself, meaning the chair, could "see from students' faces that they understood."

I actually agree that you can get a lot of information from students' faces .... but it's certainly not enough, and it's not all that easy to get information about every student in a class when you're also delivering a lecture.

kcab said...

Well, in the case of my kids & math lectures at school, they aren't following. One feels that in order to keep up she has to write fast and not think, the other can't see the board (smallest child in the class, seated in the back...sigh) and ends up with misunderstandings as a result.

kcab said...

Since I'm commenting today...Catherine, did you ever end up posting about handwriting improvement using timed short periods writing x's and 0's or tally marks? I can't find it and would like to try to do something to help my 10 yo write faster and with greater legibility. I don't think he's horribly behind by age standards, but his math is with older kids and I have some concern that his writing speed/neatness is going to end up affecting his math grade.

James said...

It's a bit much for Khan to criticize teachers in classrooms for lack of interactivity, given that his prerecorded videos are, by definition, non-interactive.

allison said...

For centuries, it has been the most economical way to “educate” a large number of students.


that implies at least 2.

That's just false. Just the idea that there were large classrooms of kids being taught the same material for 2 centuries is false, never mind the claims about lecture.

If you speak this inexactlty when edited, how badly do you speak in your own videos?

Still, I'm flabbergasted at a guy who became a rock star with his NONENGAGING LECTURES is complaining about this.

Short answer: Khan Academy made waves because it had a guy sounding authoritative that THIS is how you should teach math. The thirst is so big and deep that anyone claiming confidently they have an answer is immediately an expert.

what i don't get is how he got co opted so easily. i get why the educationists want him to tell their sob story, but was their flattery enough? does he really think the parents using Khan had kids begging to watch because of his engaging videos?
quencing is any good.

Anonymous said...

Catherine Johnson said...
[h]ence your confusion from the TIME article.

I don't believe I'm confused.

He's talking about K-12, right?


Sort of. But from what I've read/watched of Khan, he talks about higher education as much as K-12. I'd say that (and I again feel like I'm simplifying matters somewhat) as students move from grade to grade during K-12, classes in general become less interactive. This is especially true in technical subjects. Perhaps this is due to larger class sizes. If that's the case, then it helps explain the even more passive lessons in colleges (characterized by very large classes with near total lecturing). This is why I linked to the video and article about Stanford Medical School's collaboration with Khan. Now, I don't want to sound as if I'm necessarily advocating a pro-KA position. More research is clearly needed, but Eric Mazur's flipped class experiments at Harvard are promising. See -

Anonymous said...

Lecture-only is pretty common in math, the sciences, and economics. At the college-level, if it's a "small lecture" (35-70 students) it won't necessarily have a discussion section. A large lecture (say, 140+ students) will have a weekly section where a TA does the homework problems.

You ask, "how does the teacher know if the kids are following?" With many subjects, it is very rare for anyone to understand the material in real time -- it takes a while to sink in. Thus, the teacher will usually assign homework due the next class period or will give weekly quizzes to determine whether the students are keeping up with the material -- after they've had some time to think about it.

Typically it takes about 120-170 hours of engagement to learn a semester's worth of material in a typical quantitative class. Some of that time happens inside the classroom and some of that time happens outside the classroom. Some of the time in the classroom is devoted to making it clear which parts of the current topic are the most important and to what extent the students are responsible for understanding the most sophisticated material.

It's hard to know what students are doing outside the classroom unless it involves producing some sort of artifact (like the responses to a homework assignment) or using classtime to perform an assessment.

SteveH said...

"With the Internet, lectures can in fact be divided up into shorter, sub-15 minute sessions, and be delivered outside the classroom."

This says that the issue is the length of the lecture, not the fact that lecturing is ineffective. So, instead of 90 minutes of lecture, the student will have to separate and pace up to six 15 minute online videos at home.

"So what do we do with that class time? Here we can take inspiration from the humanities seminar, where any “information delivery” happens outside the classroom through student reading, allowing class time to be entirely devoted to teacher-moderated discussion."

What happened to the regular homework? He is not talking about rearranging the chairs or flipping. He is talking about adding more homework.

"This also happens in many business schools, where students read a case study ahead of time and the teacher leads a conversation about the issues facing the company or executive described in the case."

These are classes set up specifically for that purpose. They are known to be a lot of work. Other business classes are not set up that way.

"With engineering or science, class time can be used for students to collaboratively tackle more challenging questions or projects."

Once again, he is ignoring what happened to the homework sets that ensure that students know how to do things like find the moment of inertia of a complex cross-section. OK, so students now have to get the lecture online and have to learn to do the problems on their own, but when do they get to ask questions about those basic skills? When do they go over homework? My engineering and math classes were anything but passive.

Engineering schools already have special projects classes. They have collaborative projects, like the Baja Racer and the concrete canoe competitions. Why would one want all classes to be follow a hands-on or Socratic teaching model? One can opt for a college that is geared that way, but why would anyone impose that philosophy on K-12 as some sort of "best practice"?

Flipping a classroom is usually a solution to the fact that may students don't do any kind of homework. Teachers can now pretend that the students actually watch the online video, but then try to make more progress by having students do supervised homework in class. However, flipping is being sold as something more, not something less. At worst, it eliminates traditional problem set homework in place of having few watch the videos at home and having ineffective "active learning" in class.

"The main point is that when humans get together to learn, we should replace passivity with interactivity."

Of course, the solution is not to have effective, non-passive lectures. There is a lot of money to be made in telling educators what they want to hear - that there is some magic way for them to have active learning environments, off-load all of the dirty work, and have it all magically work.

I don't think he is co-opted. I think he has a product that he is adapting to what the customer wants.

lgm said...

Lecturing only in math is what my sons rec'd in a few K-5 classes. Frankly those teachers didn't know what they were talking about and from what my kids were made to copy in their composition books, that fact was obvious. The rest of the teachers, who understood math, go with a 'Do Now' activity if the students have switched classrooms, check and discussion of hw problems (gr 3-12), app 10 min of explanation of new concept, worked examples, then class time to begin hw. They circulate and fix obvious errors. I have one child that struggles with this as he is not a strong auditory learner and he uses so much energy in copying that he can't focus on learning. He does much better with reading the explanations than with a worked example on the board & auditory explanations. He does fine in a tutoring situation, which is what his placement this year is...basically 40 kids who have a lot of holes, with a setup of very little new material and a lot of time for the teacher to circulate and patch. My son that succeeds in the "Do Now" etc setup does it by not following the teacher direction. He attends to the instruction, then works the first example on his own, compares his sol'n to the teachers, then copies the examples that he missed while working on the first one. He works those himself, compares soln's again, then asks any questions. He usually has the entire hw set done before he leaves and spends his time helping others that didn't 'get it' from the presentation and examples. He uses the 'go over the hw' time for hw in other classes. AoPS style works for him, because he can go off on the side, think through, then read and join back in with the class.

Effective teaching of math to me is AoPS style, but live. But, that requires students who want to engage, which is not what is going to happen in a Regent's classroom without changing the atmosphere and school culture. It also requires teachers who are math competent, and don't present the courses as a series of skills to memorize.

Re: 1 room school house. I went to a 4 room school house, about 15 students for each classroom which consisted of 2 grade levels. The teacher used small group instruction for math and LA; groups that weren't with teacher did seatwork. In 8th, they went to independent study for math as kids transferring in were all over the place and no group of more than 2 could be formed. That worked well - we all learned to read a text and ask intelligent questions of the teacher. The downside was that those who wanted to do the minimum couldn't be pushed to step up the pace.

Anonymous said...

Also it is easier for a student to get away with cutting corners in a humanities seminar. If you haven't read all the assigned reading, you skim until you find a particularly discussion-worthy section (ideally dealing with something controversial) and read it closely. Extra-good if this relates to an earlier reading in the class that you actually did. Closely related: the highly focused essay.

A similar technique is unlikely to garner a passing grade in a quantitative course.

kcab said...

The best math teachers my kids have had organize their class time much as Igm describes (starting with "Do Now" problem, etc). One difference is that their worked examples *are* done much like AOPS, by soliciting student input and making it clear which approaches are correct and which are not. Also, the short explanation of concepts generally followed the jointly worked problems. Class time was usually spent working problems on the board rather than starting on homework.

Thinking back oh-so-many years, the best teachers I had in quantitative subjects in college also solicited student input, whether in large lecture halls or 5-10 person classes, even if the class was primarily lecture.

ATechie said...

Thinking back to college in the 1980's, where I majored in math. I don't think I EVER was asked or answered a question in any class outside of French class in my 4 years at my university (a large, good, research oriented university). In fact, if a professor had ever cold called on me in class, I think I would have dropped the class immediately. It just wasn't DONE. We did have recitations, but those consisted of a TA dutifully working out solutions to homework at the board while we copied down the solutions. I never heard of questions being asked by students; in fact, most of the TAs didn't speak enough English to understand questions. Later, as a grad student, I TA'ed myself, and did pretty much the same thing in my recitation sections.

Crimson Wife said...

The middle and high school I attended had mostly lectures in math & science. 6th grade English when we did the semester on grammar was mostly lecture too. Sometimes a student would be asked to come up to the chalkboard to solve an equation in front of the class. But it definitely wasn't the kind of back-and-forth discussions we had in humanities classes.

Anonymous said...

It might be worth considering two things:

1. Khan's focus is global. He presents his website to a global audience, and he may be talking here about global rather than American education. The lecture format, in my limited experience (I've studied in three countries besides the US) is overwhelmingly favored overseas.

2. Khan is not suggesting that children sit in class and watch his videos. He is suggesting that class time be used for interactive work. He states this explicitly: "We could then consider having multiple teachers in the same room working with students of multiple skill levels and age groups. A bell would no longer need to be rung to artificially stop one subject and to start the next. Ironically, by removing lecture from class time, we can make classrooms more engaging and human."

It seems clear that some folks here have such an animus against Khan they can't even read straight.

SteveH said...

"may be"?

Khan is clearly going to conferences in the US and pushing his ideas. They are treating him as a rock star. His videos are not very good.

"Khan is not suggesting that children sit in class and watch his videos."

Nobody thinks this. He is clearly pushing flipping.

"We could then consider having multiple teachers in the same room working with students of multiple skill levels and age groups."

Flipping the classroom usually implies different things to different educators. In one scenario, class time is used for mixed ability, hands-on group projects. In another scenario, kids work individually at their own skill level as a way to get differentiated instruction to work. However, few address the problems of effective curricula and acceleration past grade level. And they gloss over the problem of permanently grouping equal ability kids. Another scenario is to use the class time to get everyone to do supervised homework because many just don't do homework. Unfortunately, these are the kids who won't watch the videos at home.

Animus can be an effect, not a cause, and Anonymous needs to read more carefully.

Khan is clearly adaptng his message to US educator market demand.

"... by removing lecture from class time, we can make classrooms more engaging and human."

Lectures are not engaging and human? Than what? Individual work at your own level? Group work where a few students dominate the discussion? Mixed ability group work where nobody gets what they need?

When the teacher comes around to an indivudual group in class, does she/he lecture or facilitate a discovery process. If a facilitate approach is used, how much time does she/he have for each group?

The general problem is that many educators want to get something for nothing. It doesn't happen. I questioned above what happens to the regular math problem sets that are usually done as homework. Do students have to watch the videos and do the problem sets as homework? If they now do the regular homework sets in class individually (at their own level of acceleration?), then how is this more "engaging and human"? If students at the same ability level do homework problems in class as a group, then what keeps individual students from just going along for the ride?

My animus stems from the inability to get past general ideas to the details of assumptions, teaching methods and curriculum.

Anonymous said...

Although targeted at university students, this may be of interest: "Our analysis showed that teachers think that their students feel more positive about their classroom learning experience if there are more interactive, discussion-oriented activities. In reality, engaging and stimulating lectures, regardless of how technologies are used, are what really predict students' appreciation of a given course."

(Researchers Venkatesh and Fusaro about their study on how learners and instructors perceive the effectiveness of ICT in the classroom, cited in Science Daily, Oct 5.)