- If I say it then they will learn it.
- If I don’t say it then they won’t learn it.
This seems germane to our (roiling) discussion of Khan Academy.
2011 June 6. Sam Critchlow, in the comments:
Lets not forget the contrapositives, which must also be false:
- If they’ve learned it, it’s because I’ve explained it well.
- If they haven’t learned it, then I just must not have explained it well.
cheesemonkeysfJune 5, 2011 - 12:34 pm -
I think these are both germane to how most educated non-professionals view math education as well.
DAvid HampsonJune 5, 2011 - 12:51 pm -
That is AWESOME. Very succinct, yet lots of wisdom.
Joshua SchmidtJune 5, 2011 - 1:18 pm -
In many ways I think that’s what we as teachers are trying to fix. We want students to be able to learn things without us saying. We are trying to create lifelong individual learners.
Mr. KJune 5, 2011 - 2:21 pm -
Not only is it germane, it encapsulates a huge part of what I’ve learned that teaching is since I went into the classroom.
Now I need to get myself some media exposure so that I can introduce it to the mainstream dialog.
RigginsJune 5, 2011 - 2:23 pm -
Profound and so true! Ashamedly, it took me several years of teaching before I realized any of them.
Metivier, chem engineering studentJune 5, 2011 - 2:25 pm -
I agree w/ Mr. Schmidt: I think that each student have to learn in your own way I mean the knowledge is particular and it starts out of classroom!
josh g.June 5, 2011 - 2:37 pm -
Wait, but in your original post you said that these were “The Two Lies of Teaching”. So is he saying this is true, or untrue? What are you saying?
(This may sound like sarcastic joke confusion, but it is real.)
josh g.June 5, 2011 - 2:42 pm -
Man, I should read the title of this post.
MsGajdaJune 5, 2011 - 3:10 pm -
Love it! I think that I will need to take those two lies into my next department meeting!
cbrownJune 5, 2011 - 3:22 pm -
he’s saying, i hope, that those two principles might seem like they’re true, that students won’t learn what you don’t say and learn only what you tell them. he’s implying that students learn mostly tacitly, perhaps by way of example, by way of an attitude the teacher displays, perhaps an attitude about knowledge, over and above the information per se a teacher disseminates. i think he’s write to a certain extent, but i also believe that what’s really true is that a student’s learning style depends on that student’s attitude toward the kind of teaching style he or she is presented w/. such that a student who’s very engaged *can* learn as much from a lecture than from a teacher’s style of teaching. it all depends on the student’s ability to be receptive to any particular teaching style. these two principles are indeed lies, *when* a student doesn’t have the skill and/or desire to listen engagingly. tom sallee is presuming the kind of student that is relatively common now, the skeptical post-modern, too-cool-for-school student. sure, telling is not going to be effective for that kind of student. but a student who *is* receptive to telling will find telling an effective method of learning.
Dan O.June 5, 2011 - 6:50 pm -
I think cbrown is right on. I was thinking about this as I read through the Khan Academy posts today. I teach some motivated, intelligent students in my AP Calculus course, and they take advantage of the recorded lectures we do. Of course, that doesn’t mean they work for everyone. i.e. one-size (or technique) doesn’t-fit all. as wrong as it is to assume a non-motivated student will simply learn by being told (or asked to watch a video) it is similarly wrong to dismis the entire concept if it works for certain students in certain situations (see Cheryl van Tilburg’s comment in the KA discussion.
I think some of us teachers are quick to criticize techniques that we don’t see working for OUR classroom or OUR students, but that doesn’t mean they won’t work for others. It depends on the context – right?
Don’t get me wrong. I think the debate is good, it makes me think, and I believe makes me a better teacher. However, our allegiance to methods we have used successfully doesn’t mean that everything else is terrible.
MBPJune 5, 2011 - 7:47 pm -
Lie #1 is, “If I say it then they will learn it.”
I often feel like a teaching moron–which is fine, I guess, since I’m new at this thing–but I would appreciate some help thinking this through.
I totally understand that just because you say it, doesn’t mean that they learn it. But, sometimes when you say it, they do learn it. So there are two ways to react to accepting these “lies.” First, I could try to get better at saying things. Second, I could try other things.
Q1: Does anyone deny that saying something sometimes leads to learning?
Let’s say I want to work on the latter. Then what are my other tools for helping 20-something students learn some math in a 40 minute window? Here’s what I can come up with:
* Problem solving
* Explaining to others
Q2: Is this list the sort of thing that Dan/others think about when they think about how learning happens in the classroom?
Let’s say that I want to work on the former, assuming that saying stuff sometimes works. What are my ways of getting better at saying/lecturing?
* Lecture as investigation
* Feedback/assessment loops
* Be brief
Q3: Is this list the sort of things that you think about when you think about how to be effective when you say things in the classroom?
Dan MeyerJune 5, 2011 - 7:53 pm -
Dan MeyerJune 5, 2011 - 8:02 pm -
No one you should take seriously.
Terms like “inquiry” and “problem solving” mean vastly different things to different, reasonable people, but in spirit I’m with you.
Also a good list. I’m sure other people will add to it, and I’m sure I don’t know what “lecture as investigation” means, but in spirit I’m with you. Also, as a quick nod to any lurking, conservative mathematicians, if you’re going to say something, make sure what you’re saying is correct.
cbrownJune 5, 2011 - 8:03 pm -
i think the spirit of the pronouncement that those two principles are lies is that it doesn’t really matter what you *say* in the classroom; rather, it’s the manner in which you say it and how you conduct yrself, how you treat the students and perhaps how you interact w/ knowledge, so to speak. the presumption is that there’s a kind of freudian man behind the curtain who’s inspiring the students, or not, and the man behind the curtain is the undefinable spirit of teacher (not spirit in the spiritual sense, but the person, the ethos of the person, his/her character). it’s that ethos that is essentially what gets transmitted over & above anything you say. the good teacher, according to this approach, essentially teaches students to want to learn, and then the learning begins to take care of itself; the student can then begin or continue carrying on the journey.
Aaron B.June 5, 2011 - 8:03 pm -
Seems like cbrown may be reading too much into Sallee’s comments. Dan would know – he was there, maybe he can speak to that…
I don’t know – for me, I have a hard time subscribing to telling as an effective way for anyone to really learn something. I guess though it depends on what learning is. If it’s repeating or copying, then I guess so, but in order to learn something, don’t you have to wrestle with it and struggle with it? Doesn’t there have to be some sort of conflict that challenges a misconception or causes you to question?
Things that I know really well are things that I have screwed up or made a mess of and had to resolve for myself. Andrew Wiles (who proved Fermat’s Theorem) described mathematics as sort of a bumping around in the dark until you find the light switch, then more bumping around until you find the next one. If someone is telling me where the light switches are, or worse yet flipping them on for me, then what have I gained?
Maybe I’m misrepresenting telling. I don’t know.
Dan MeyerJune 5, 2011 - 8:10 pm -
If I explain to you how to calculate the sale price of an item at the store, I shouldn’t assume you then know how to do that. If I don’t explain to you how to calculate the sale price of an item at the store, I shouldn’t assume you won’t learn how to do that.
cbrownJune 5, 2011 - 8:10 pm -
but i would also say that in order for the teacher to convey a love of learning he or she has to love a) the knowledge per se (and therefore has to simply know his subject very well) and b) love the transmission of the knowledge and how it and the love of learning can transport students and c) essentially love the students, even when they’re being pains in the ass, even when they write stupid shit on teacher evaluations b/c they think they know what or how they should be taught. you have to love them in spite of themselves.
PwolfJune 5, 2011 - 8:39 pm -
Last year I spent all Christmas break making lecture notes that were designed to show my Algebra 1 students why exponent rules worked they way they do (for integer exponents at least).
Low classroom assessment scores aside, the main reason I’ll never do it that way again is that when I would prod students as to why x^a*x^b=x^(a+b), they would say “because you told us so!”
MBPJune 5, 2011 - 8:42 pm -
Q4: Given that sometimes saying stuff leads to learning, and that there are ways to lecture well, when do you decide to lecture?
LauraJune 5, 2011 - 8:56 pm -
This Khan stuff has been interesting. Silly me for not checking Google Reader for a few days and then finding myself 80 comments behind. Yikes!
Recently in second grade I had a girl who, at seven years old, had already been infected with the notion that math is a wolverine. I have never met someone so terrified of math, so much so that when asked a question like “So how did you know what to do with the pennies?” in small group setting, she would stammer, “4?” or some other hapless, nonsensical answer. The poor thing was paralyzed with fear.
I agree with a commenter on this post (or the previous one…I’m a little muddled now) who said that we live in a culture that wants to know “how” (maybe), but can’t be bothered with “why” or the “when” or any deeper inquisitive move toward understanding. This little girl is a product of this culture.
MBP had some interesting things to say above. Looking to these factors to reach students is key, rather than watering down the content to step-by-step procedures that, to a struggling student, may as well look like a well-stocked aisle of knick-knacks at walmart. I understand the possibilities for Khan as remediation. But for my terrified student? Over my dead body.
cbrownJune 5, 2011 - 8:59 pm -
when it’s simply painfully obvious that they simply don’t know what’s what, and there’s some basic information you have to tell them. but i never ever lecture in a way as to imply that the knowledge is precious in any way. it’s really a matter of survival for me–if i go in thinking this knowledge is essential and important, and therefore precious, they’ll deflate it in the most humiliating way imaginable, not intentionally humiliating but just by their natural response to it. so i try to never be too attached to any of the knowledge i’m imparting to them, even though i let them see that i love it. the knowledge itself is analogous to the knowledge of how to tie their shoelaces. the knowledge is ultimately incidental–as far as my relationship to students is concerned–even though, like i say above, i let them see that i love it.
Mr. KJune 5, 2011 - 9:29 pm -
When I teach my kids this, I don’t give them the formula. I have them expand the exponentiations, and combine them. It takes fractions of a second for some smart kid to wave their hands wildly to tell me they found a shortcut. When I go to check their work, and tell them not to share their observation with anyone else, it spreads through the room like wildfire.
You will note that I never ever told them what I wanted them to learn.
I’m not sure if this fits rule 1, or rule 2.
Dan MeyerJune 5, 2011 - 10:26 pm -
Roughly speaking, when you can be sure that your audience has sufficient pretext to care and to understand. The moments are rare, though, when every student in the classroom is simultaneously eager for the lecture and ready for the lecture. It’s rarely the case that students all have the same or sufficient background knowledge preparing them for your lecture. It’s your job, in those cases, to determine what they know, what they don’t know, what they think they know but really don’t, and challenge each according to her abilities. That’s difficult to do, period. That’s impossible to do in a lecture, whether delivered on video or in person.
Which is the pretty much the bulk of my actual critique of the flipped classroom in general and Khan’s videos in particular. Don’t tell anybody I’m in here talking smack about Khan, though.
Joshua SchmidtJune 5, 2011 - 11:18 pm -
I feel like one of the best pieces of advice I ever received in teaching education fits with this concept.
Students learn by doing, and not by watching the teacher do anything.
I think it’s powerful to understand that every student, even the really good ones, doesn’t learn by being told something is true. Eventually every kid wants to find out if a statement works or not. Even if that statement is “can you do this?”
ObsidianCraneJune 5, 2011 - 11:56 pm -
Well I agree with the original sentiment, and I agree very much with cbrown: the best thing we can do is inspire the desire to learn. Part of doing that, in math, is getting them to see math as a tool beyond doing calculation, getting them to see math as good for solving problems. Today I had one of those moments in class: it was awesome.
Incidentally I recommend Khan Academy to my students, for those driven to learn it is a great resource for when the teacher isn’t there, but it doesn’t replace a good teacher.
Darren DraperJune 6, 2011 - 5:04 am -
I’m thankful I finally have a legit reason to look up the word ‘roiling.’
Questions I now have, resulting from these two posts:
1. Where and why do teachers learn that the two questions in this post are (supposed to be) true? Surely they’re not taught in teacher prep courses, but it seems that many in the profession eventually fall into the trap. Is this a cultural snafu or an unfortunate consequence of the teaching process and some strange wrinkle tied to human nature?
2. When do teachers finally realize the truth of your post? What must take place for them to come to the understanding naturally?
3. How is it that Khan and others are able to successfully pull the wool over over so many eyes? Something’s gotta give.
mdowsJune 6, 2011 - 6:24 am -
This is the first thing stated by dan in his Tom post: “Tom Sallee could read passages from a microwave repair manual and I’d enthuse wildly. ” This is why dan is ready to learn. I’ve followed this blog for a long time b/c I love to see how he’s thinking. (I teach Biology). And now I know why my school PD centers around a) Bill Daggett’s Rigor, Relevance, and Relationships, and b) Stephen Covey’s 7 habits. Reading dan’s words about Tom doesn’t make me want to learn what Tom said. Say it or don’t say it – both work. To go from good to great requires what KA will never have.
OwenJune 6, 2011 - 6:24 am -
Corollary 1: If a student can give a rule/answer/observation, it doesn’t mean they have learnt a concept.
Corollary 2: If a student can’t give a rule, it doesn’t mean they have learnt nothing about a concept.
This ties back to assessment – how do we determine what students can do? At what level do they understand a concept or in what contexts can they apply it?
OwenJune 6, 2011 - 6:24 am -
Corollary 1: If a student can give a rule/answer/observation, it doesn’t mean they have learnt a concept.
Corollary 2: If a student can’t give a rule/answer/observation, it doesn’t mean they have learnt nothing about a concept.
This ties back to assessment – how do we determine what students can do? At what level do they understand a concept or in what contexts can they apply it?
MBPJune 6, 2011 - 6:39 am -
I am not claiming that the following are GOOD reasons, but here are the reasons why I spend most of my time in the classroom lecturing:
(1) My administration/parents/students think that lecturing and answering questions is how a teacher helps people learn. When I don’t lecture, the interested parties think that I’m goofing around.
(2) My school tries to cover lots and lots of material over a short (~130 day) year, and I’m held responsible if I don’t cover all the material that’s part of NY’s Regents exams. Lecturing is the fastest way to discharge my responsibilities.
(3) It’s not like what I’m doing isn’t leading to learning. I give skill tests, and my kids do OK on them.
(4) I teach three curricula and lecturing is what requires the least amount of preparation.
(5) It’s not like I walk into class with a script and just say things to people. I do what a lot of teacher-centered teachers do. I walk in, and try to hook them with an interesting question. No, my questions are not often the everyday, wolverine-declawing kind, but I do my best with mathematical context. I’m constantly assessing, both formally and informally. I stop every 10-20 minutes and let kids solve problems using our ideas, and they usually help each other. I cold-call kids. I demand questions. People have questions. I ask questions. We wait and think about them.
(6) Other methods of teaching require skills that I don’t yet have.
There are probably more reasons, but this is a start. As I get better/if I stick around, I’ll lean less on lecturing. But the point is that it’s not that I magically think that saying things is super-learning. It’s just the best that I can pull off, daily.
Paul J. KarafiolJune 6, 2011 - 6:56 am -
What I like to say is: time I spend talking is time wasted.
SeanJune 6, 2011 - 7:23 am -
You’re killing this thread with really honest, well-constructed comments. Number 31 in particular. It kind of took me off the holy mountain of ‘what math education is supposed to be.’ Well done.
My small qualm is that what you’re describing doesn’t sound like ‘lecture’ in the sense that I understand it. It sounds more like whole-class discussion (and really effective whole-class discussion). Lecture is talking at, not with. I haven’t seen you teach, but what you’ve described – cold-calling, pair work, thoughtful questioning, practice problems, feedback – sounds like a fluid, well-run classroom.
The discussion about the relative merits of ‘talking’ got me thinking. Imagine someone (say Khan 2.0) comes out in 2012 with videos of staggering quality. Just perfect. Multiple strategies, engaging hooks, critical reasoning, interactive, differentiated, etc.
As a student, you want to learn how to add polynomial expressions. Would you rather have access to Khan 4.0 (with pause, rewind, and assessment with immediate feedback) or a typical class with access to your teacher and peers?
And does your answer change if the topic changes?
Dina StrasserJune 6, 2011 - 7:29 am -
So what IS this problematic pedagogy called “lecture”? Simply? Give it to us in one sentence.
Seems to me we need to get Socratic on this debate’s ass…umptions.
Nick MJune 6, 2011 - 9:00 am -
Wow- good to see the heated and rolling debate here. I’ve been thinking about Kahn’s implications on education ever since the TedTalk he gave, and one thing all you critics need to do before you keep bashing is learn more about what “flipping the classroom” really means. I recommend checking out this site here, as these chemistry teachers have been doing it for some time: http://mast.unco.edu/programs/vodcasting/
Flipping the classroom when done well actually allows MORE time for inquiry-based investigations and project-based learning. So unless you’re pretty radical and avoid lecture/direct instruction all together, video lectures like Kahn could benefit you.
I also agree with the good point that videos lectures are “one-size-fits-all” but not “one-time-fits-all”. I’ve made many video lecture clips for my science students that get watched repeatedly by the same student- and that certainly has more impact than saying it one time in the classroom.
As a side note- unfortunately I think there may be a tendency for our media-saturated students to actually pay better attention to a video lecturing than a teacher lecturing. I have no data to back this up- but somebody should do a study of this!
I understand Dan’s critique that video lectures used blindly ignore a need for differentiation- but then since videos are easy to make and save, there can also open up some truly innovative ways to utilize them in a differentiated way. Again, refer to the link above for a good example- there learning is paced by the students.
I guess my overall takeaway is that video (and other technologies as well) are still hugely underutilized or improperly applied. So before we knee-jerk against something like Kahn we need to keep a more open mind.
Sue VanHattumJune 6, 2011 - 9:07 am -
Darren asked: 1. Where and why do teachers learn that the two questions in this post are (supposed to be) true?
We imprinted on our 12+ years sitting in other teachers’ classrooms, taking notes on lectures. Schooling is a social system that is self-replicating. It’s pretty hard to change it.
And, as MBP mentions, students will complain if you don’t ‘teach’ them. They are used to being told, and have come to believe (by high school and college age) that listening is learning.
R. WrightJune 6, 2011 - 9:26 am -
If anyone has any more thoughts on what you see as the advantages of video presentations over textbook readings, feel free to let me know over at my blog (link above) to keep this thread clear of that tangential question.
Practically every teacher of math at any level above basic algebra is in this position. Again, I teach college, so I probably don’t feel your pain quite so acutely (I am evaluated mostly on my popularity, rather than some measure, however deeply flawed, of how much my students have learned), but I am still pressured to cover most of the soul-crushing meaninglessness that is squeezed into some math classes. This is why I’ll be experimenting with “flipping” a couple of my courses in the fall, roughly following Eric Mazur’s lead. I feel that this is the best I can do for my students, given the circumstances — though I honestly don’t expect to be rewarded for it in the student evaluations.
cheesemonkeysfJune 6, 2011 - 9:27 am -
Since I get nervous whenever we start drawing such stark lines in the sand as “lecture=ALWAYS BAD, collaborative work=ALWAYS GOOD,” let me toss in a word in favor of a more balanced perspective.
The best modality for a piece of instruction depends on the outcome I am trying to bring about.
If I want students to be able to DO something as a consequence of my practice, then yes, I really will need them to have a hands-on experience of DOING something themselves, with all that that entails.
But if I am doing a little mood-setting or context-switching or gear-shifting, then sometimes a bit of “lecture” cum storytelling can be a good and helpful way to change the pace and refresh students’ interest or pique their curiosity.
And speaking of pacing, nothing is more mind-numbing for students than a constant monotonous pace of ANY one modality. It’s just not humanly possible to remain rabidly interested in a steady drumbeat of ANY one modality of instruction over an extended block of time.
Dan MeyerJune 6, 2011 - 12:52 pm -
It’s the “apprenticeship of observation.” We teach as we were taught. See Sue’s comment below.
That’s a trick, innit. Bad lecture is easy so you’re always fighting the natural inclination to do what’s easy. Teachers also have the sense that “this is how it has been and has to be.” We can disrupt that sense by showing video cases of teachers managing classrooms well.
I asked for a definition in 140-characters on Twitter. Results?
Selected responses, fwiw.
dandersod: lecture: teacher talks and demonstrates, students listen and copy demonstrations.
sophgermain: delivering material in a teacher-centric way. mostly involving teacher talk-students listen/respond.
bwfrank: Unidirectional discourse from authority wherein modes of participation are regulated as to maintain that directionality & authority
kellyoshea: Lecture means that I get better at physics by solving problems or talking about concepts while my students watch.
garystager: Great lectures require a presenter with exceptional performance skills and expertise that exceeds that of most teachers.
rickhanlonii: The clarification and expansion of the topics currently studied.
chrisgoedde: is the introduction of new content through a (usually live) audio-visual presentation.
samjshah: someone explaining the subject matter at a board without any / much audience interaction/participation.
aresnick: lecture, n. :: performance art aiming to at best, guide me through the creation of a mental model, & at worst, transmit information
At this point it’s evident to me that proponents of Khan’s videos define “knee-jerk” as “any kind of criticism at all.” We’re pitching softballs in here. Nothing but softballs. You should see how we tear apart our own teaching.
@cheesemonkeysf, strong comment.
Sam CritchlowJune 6, 2011 - 12:54 pm -
Lets not forget the contrapositives, which must also be false:
1. “If they’ve learned it, it’s because I’ve explained it well.”
2. “If they haven’t learned it, then I just must not have explained it well.”
Denis RoartyJune 6, 2011 - 12:56 pm -
This and the Khan thread have been fascinating to follow. I loved Sean’s brief pitch (comment 33) for a future technology enabled Khan 4.0 approach (though I don’t think of Khan as the inventor of this, so how about Math 4.0)
Add rich media, assessment and an organizer for all this and the result would be that skill and concept acquisition can be partially farmed out to technology so that:
a) kids have more options that suit their learning style and pace
b) teachers have tools to manage a more individualized approach to skills and concepts acquisition.
c) teachers and students have more time to apply mathematics which always gets short shrift by most of us and should be a rich and wonderfully engaging class activity.
MBP’s frank post (comment 31) makes it abundantly clear that getting from lecture based instruction to Math 4.0 is going to be tricky business considering the current emphasis on ‘getting through the curriculum’ and the lack of organized Math 4.0 tools and training to make it happen… but blogs like this certainly have us pointed down the right path.
SeanJune 6, 2011 - 1:40 pm -
What fascinates me about the more appropriately named ‘Math 4.0’ is that it makes passive learning- call it ‘lecturing’- somewhat active.
The student cannot directly inquire or speculate, but they do have some degree of control, arguably more than in a typical classroom. If the delivery was really strong (like really, really strong), I could see students benefitting from it.
But I think there’s nuance here. I threw out adding polynomials because- arguably- there’s not a ton of damage that can be done there. But what about slope?
For a mathematics-as-imitation model, Math 4.0 has potential. For a mathematics-for-understanding model, I think technological innovation has to be paired with a skilled questioner.
I think Dan posted a while back about where teachers would best fit in this new paradigm. Using his three-act structure, I think it was act 2. This is where you elicit questions, where you evaluate whether current data is sufficient, where you fit the pieces from Act 1 into a coherent structure.
That part isn’t easy for students or teachers.
DinaJune 6, 2011 - 2:16 pm -
Right. So “lecture” is about as precise a term as “love,” apparently. Right up there along with “say”.
And I’m not saying that this is the whole problem, except that this is the whole problem.
If ever we are to coalesce our thought about best practice into some kind of cohesive whole, and debate education realities meaningfully and efficiently within it, we have to apply the same rigorous process of creating definitions for these terms as readers did with “pseudocontext.”
R. WrightJune 6, 2011 - 7:04 pm -
I don’t see how the word “lecture” is the slightest bit imprecise. Most of the definitions of “lecture” Dan quoted are either not broad enough, or too judgmental, perhaps because their authors had agendas. But to lecture is simply to tell, or demonstrate, or explain (demonstrating and explaining are just different kinds of telling).
Can you think of some specific classroom activity that does not clearly fall into, or out of, the “lecture” category?
Christopher DanielsonJune 8, 2011 - 6:55 am -
R Wright asks:
Sure. I’ve got a whole mess of ’em. KWL. Think-Pair-Share. Orchestrating Mathematical Discussions, seatwork…
Lecture puts the teacher at the center of attention. Anything else isn’t that.
R. WrightJune 8, 2011 - 10:42 am -
I’m confused. Are you saying that your examples are somewhere ambiguously between lecture and not-lecture?
Christopher DanielsonJune 8, 2011 - 1:19 pm -
Note to self: read the stuff between the commas. Sorry. I read the original as “…that does not clearly fall into…the lecture category”. I thought it seemed like too easy of a task!
Now that I have read more carefully, I would like to reframe your question. Dina isn’t arguing that the line is too fuzzy, but that we don’t all agree where it is.
So, R Wright, the challenge ought to be: Can you name a classroom activity that some would call lecture that others would not?
These I don’t have a whole mess of. But I’m optimistic that it exists.
When, for example, does Answering a student’s question turn into lecture? Is after a certain amount of time has elapsed? When the topic changes? Or was it lecture all along? Does it have to take place in a classroom (if so, then Khan is off the hook, right? Neither he nor his “students” are in the classroom).
Concrete example: Did I give my daughter a lecture on circles the other day?
R. WrightJune 8, 2011 - 9:24 pm -
Mmm. I think I had that in mind (to some extent) with the question I asked, but I didn’t phrase it as clearly as you have. I would suspect that most people would basically agree on what constitutes “lecture” and what does not, but maybe I am wrong in that.
Answering a question is always a form of lecture. Whether I directly tell the students something because I want to, or because the state asks me to, or because an administrator asks me to, or because a student asks me to, the action of telling is the same. I don’t think it makes sense to classify an act differently based on my motivations for doing it (nor the time or place at which I did it).
I enjoyed that post; it reminded me of my own daughter. Yes, when you stated the definition of a circle, you were lecturing (briefly). I’m getting the sense that you want the word “lecture” to carry a built-in negative connotation. Is this correct?
I should have noticed more carefully that Dina wrote about “this problematic pedagogy called ‘lecture.'” Lecture isn’t a pedagogy; it’s just one tool, among many others, that serves some limited purposes in good pedagogy.
Maybe what is needed isn’t a definition of “lecture,” which I think is already defined more than adequately, but a word for the all-too-common philosophy that lecture should be used whenever possible.
Darren DraperJune 8, 2011 - 11:09 pm -
Strong comment from R. Wright, the kind of comment that’s only generated by a math teacher who’s also taken the time to become familiar with the academic literature surrounding teaching. I think we need more of those in the k-12 arena, fwiw. Honest, instructional, and yet inviting.
Sure is a smart crowd around these parts.
R. WrightJune 9, 2011 - 7:20 am -
On the topic of Salman Khan, he has apparently been participating in a discussion thread the last couple of days with some people critical of his videos. To be honest, I think he comes across as shockingly condescending and snide in some of his replies. Until reading these, I had a pretty good impression of him on a personal level.
DinaJune 9, 2011 - 8:25 am -
Thanks for all your thoughtful responses surrounding my question.
First: I do believe “lecture” is both a pedagogy AND a technique to some teachers (as R. Wright insightfully points out). That being said, my goal was to clarify the exact meaning of the technique (as Christopher Danielson points out, equally insightfully.)
I still maintain, as the debate between Christopher and R. Wright amply and ironically suggests, that there is no shared concensus on what “lecture” actually means– particularly when we are still evolving our sense of how multimedia does and should play into lecture.
As a result, I think the debate suffers from circular thinking and missed connections. Easy fix, though, don’t you think? Do what is being done in this thread. Define your terms. No biggie. :)
Christopher DanielsonJune 9, 2011 - 9:44 am -
Quick reply to R Wright‘s link: That’s not Salman Khan. You are completely right about the contrast in tone and that’s not him writing there.
And, also quickly, on R questions about lecture. I submit that some would not define my response to Tabitha’s circle question as a lecture. I’m not sure whether I do or not. And I don’t wish to give lecture a negative spin anymore than I wish to give group work a positive one.
But I do think defining lecture with precision will be challenging.
I wonder what we do with the result, though. Where does the effort get us, Dina? What will we be able to do once we have that term defined that we cannot do now?
I doubt that it will help the field come to consensus on Sal Khan’s work (except that we’ll all have to agree that he is lecturing). What will it help us do?
RookJune 9, 2011 - 11:11 am -
This seems like the old Behaviorism vs Constructivism debate to me.
Why lectures are inefficient ?
Because students need to try before knowing.
The fact that a knowledge appears as a response to a question or a problem helps to build the understanding and the appropriation of this knowledge. It is why problem solving must hold an important place in any curriculum.
In order to teach any notion the model should be :
1 – Discovery : evaluation of the initial conceptions of the students through a problem situation
2 – Familiarization : emergence of the characteristics of the notion, pooling of the strategies and procedures used or tried against the problem
3 – Training : structuring the notion in the student’s mind through simultaneous systematization (understanding the system of the notion, how it function and reorganize anterior conceptions) and automation (not having to think when reusing the notion).
At some point in this stage the students need some reflexivity on their process of learning : Why is this hard ? What is hard ?
4 – Reinvestment in a more complex situation, evaluation
Jason DyerJune 9, 2011 - 11:24 am -
I doubt that it will help the field come to consensus on Sal Khan’s work (except that we’ll all have to agree that he is lecturing). What will it help us do?
Delineate the boundaries enough that we know in discussion what goes past lecture. Example: Is it possible for video to go past lecture? Or is it a waste of energy to attempt to take it any farther than Khan and others have? Does videotaping students doing an exploration turn it into a lecture?
cbrownJune 9, 2011 - 11:37 am -
first of all, i would think a proper definition of lecture would wrap it in the notion of an extended period of time. simply answering a question is not what we mean by lecturing. that’s silly. a student asks a question, you answer it in 15 or 30 seconds, check in w/ the student, and the question is answered. end of exchange. there’s been no lecturing. i would think a lecture is a prolonged monologue. okay, if it the answer takes longer we get into murky territory, but, still, as long as the answer focuses on a pointed answer to the question, it’s not a lecture. also, i would think a lecture is prolonged monologue primarily *generated* by the lecturer. when answering a question, in contrast, the answer is generated by the student. perhaps that’s an important distinction in the definition of lecture.
i like rook’s schema. reflection is essential, of course, as he/she says in #3. another essential ingredient that i try to include is history. i think it’s truly unfortunate that subjects are often taught (usually!) w/out a reference to the historical context of the knowledge that’s presented. i would even go so far as to say that knowledge w/out historical context is not knowledge–it’s something else, but it ain’t knowledge. of course we have to be talking about spectrum here. i can teach students how to write a personal essay, but w/out their knowing the circumstances surrounding the emergence of the modern personal essay in the 16th century, their knowledge of how to write one is … significantly limited. their understanding of how that form of expression came to be seen as important is crucial to their understanding of their own use of it.
Dan MeyerJune 9, 2011 - 11:45 am -
Great question. I’m not comfortable calling that a lecture, but it’s still way inside the genre of “exposition.”
louiseJune 9, 2011 - 4:18 pm -
Students need real experiences. Watching “Deadliest Catch” (as I am right now) does not give me even the remotest experience of the Alaskan fishing. I do not think I am qualified, even after 4 seasons. Watching someone else stack blocks/construct geometrically/scubadive/pace out a linear graph does not give me the experience of doing it myself. Anyone who thinks that has no memory of being a student.
My students’ biggest deprivation is the removal of actual experiences.
Despite their bad behavior, they need to make bicarb rockets/ barbie bungee/remote control car videos. Substituting a video does not do it.
I don’t even consider this to be constructivism, I consider it to be context. When I found out that a kid thought a question about cutting fudge into one-inch cubes was stupid and unanswerable because you can’t cut fudge ( it’s runny and you pour it on ice cream), I realized the problem they had was way beyond math.
While I like WCYDWT, I use them as cues for real experiences (which is why the mall with the escalators is hopping mad ).
I personally am grateful for every single thing that has been put up on the web for free to help students learn. Can’t hurt. Thanks to everyone.
R. WrightJune 9, 2011 - 7:44 pm -
I stand corrected; it is indeed difficult to come to a consensus on the meaning of the word “lecture.” For example, cbrown openly finds my understanding of the word to be silly, and to be honest, I find his to be arbitrary and unnecessary value-laden. We’ll have to agree to disagree. I wonder if we could overcome this issue simply by using the (hopefully) less ambiguous word “telling” instead of “lecturing.” Surely, directly answering a question is a form of telling. Telling is often necessary in mathematics education, but telling for extended periods of time (cbrown‘s conception of “lecture”) — or, worse, telling as a primary tool — is relatively bad pedagogy.
If I may ask, how do you know?
R. WrightJune 9, 2011 - 7:49 pm -
(For clarity, that should be “unnecessarily.”)
Joshua SchmidtJune 9, 2011 - 9:16 pm -
The semantics of “lecturing” are going to be different for each teacher; however, we each have a similar bag of tricks. For example:
One teacher could have a set of strategies like
2) Group work
3) Inquiry Based Learning
4) Discovery Based Learning
5) Project Based Learning
And some other stuff, it’s a made up example. Another could have
1) Classroom discovery
2) Partner Practice
4) Group Problems
5) Real World Applications
The problem i have with these types of comparisons, and when we try to nitpick “lecture” versus “talking” or “telling” aren’t we missing the valuable conversation? I feel like lets talk less about what lecture means and more about ways to make it better. That’s just my take.
R. WrightJune 10, 2011 - 9:43 am -
But this sentiment ignores opportunity costs (i.e. students’ time spent on something with no long-tem benefit, aside from helping them pass a test), and the hidden message I saw in the few Khan videos I’ve taken a look at (i.e. mathematics is an arbitrary set of definitions and procedures to be diligently memorized).
Christopher DanielsonJune 10, 2011 - 10:28 am -
R Wright rightly calls out my certainty about who wrote those Khan comments. I should have stated a firm disbelief that it can’t be him rather than implying knowledge that I really don’t have.
Consider the facts:
(1) He NEVER speaks this way in the attributed media. Not even close. He is gracious and self-effacing.
(2) On the Internet, no one knows you’re a dog. There is absolutely no barrier to leaving comments under an assumed name.
Finally, germane to this discussion (and to Joshua Schmidt‘s attempt to redirect), there is a lovely article from JRME worth seeking out. Sadly, it predates the online archive and must be obtained through library hard copies or databases. But the basic premise is that the “reform” movement needs to help teachers who get their sense of being successful math teachers by the quality of their lectures find new ways of feeling successful. And it introduces the term judicious telling. That is, telling when students are ready to hear. This is a much more productive idea, I think, than trying to come to consensus on whether lecture is bad.
Smith, J. P. (1996). Efficacy and teaching mathematics by telling: A challenge for reform. Journal for research in mathematics education, 27, (4), 387-402.
RookJune 10, 2011 - 11:05 am -
But lecture is bad :-) and telling might be pointless when students are ready to hear.
Arguing about a precise definition of lecture seems a bit pointless, I give my own after reading some comments nonetheless : lecturing is telling the discoveries of others.
I think that trying to define learning would be much meaningful (if not hectic)
In fact I postulate that there exist a definition of learning for which The Two Truth of Teaching are :
1 – If I say it they won’t learn it.
2 – If I don’t say it they’ll will learn it (when confronted to a proper situation and given enough time)
RookJune 10, 2011 - 11:17 am -
…for a mathophile, I seem to have a strange dislike for points …
re-reading the first sentence of my last comment I realise it might be a bit obscure : what I meant was that being ready to be taught is not something you want to aim for : try getting your students eager to learn by themselves and giving them the situations from which will emerge procedures and notions you want them to learn.
The conventions will then be presented as an historical choice after the students have build their own maths (or whatever knowledge).
Joshua SchmidtJune 10, 2011 - 12:09 pm -
I still feel like we look at lecture as one thing. Lecture in and of itself is not inherently bad; however, it is a larger picture of our entire learning strategy. The key is looking at the two lies and recognizing something very obvious. They both talk about saying something, and it’s very obvious that students need to “do” in order to learn. Therefore, we have to look at regardless on if, how, when, and why we lecture, students still have to learn by doing.
R. WrightJune 10, 2011 - 12:13 pm -
I love it.
I think more accurately, “If I say it, they are discouraged from learning it.”
RookJune 10, 2011 - 12:55 pm -
It does depend on how you define learning : if it goes along the lines of discovering by yourself or as a group something, saying it will prevent them from learning.
If it refers to being able to reproduce, then lectures and electroshocks are very sensible means to teach.
Joshua SchmidtJune 10, 2011 - 5:15 pm -
Rook! Great point, I think learning as a phrase really depends on what you are telling. Especially when we start to look at “reproducing”. Reproducing exactly is very different than being able to reproduce in context. For example, doing Math inside a classroom versus outside it, where I think WCYDWT is fantastic as a structure.
MBPJune 11, 2011 - 9:57 pm -
I’m coming late to this party, but I do think that some working definitions would be useful to advance this discussion. I think the issue is that we’re discussing the efficacy of various learning methods, but lecturing is not a learning method–it’s a way of combining several learning/teaching methods.
So, here’s my attempt to find vocabulary for a more fine-grained vocabulary for learning methods.
If you reflect on what you know about the world, a lot of our knowledge comes because an individual “explained” an idea to us. And so instead of focusing on lecturing, I’d like to focus on explaining. People certainly sometimes learn when a matter is explained to them, so it’s natural that teachers will spend some time explaining matters to students.
A teacher has options when it comes to explaining ideas in a classroom. A teacher can explain things to a student, one-on-one, or a teacher can explain things to all of the students in the class at once. Another degree of freedom is that a teacher can either allow for questions from students during her explanation, or the teacher can not take any questions from students during her explanation.
Of course, the teacher can use props and video and other sorts of aids in her attempt to explain something to her student(s). It’s still an explanation.
So that’s the vocabulary. A teacher can choose to teach through explanation, and in doing so the teacher can explain to individuals or to the class, allow questions or not allow questions, use demos or not use demos. I’m sure we can add more to the degrees of freedom within explaining. For instance, we could distinguish between teachers who explain for an hour at a time (I’m looking at you, Sophomore year philosophy professor) and those that explain for just 4 minutes at a time.
I like this vocabulary for two reasons:
(1) Now I might know what positions some of y’all are defending.
(2) I think this way of talking about teaching gets at the heart of the confusion from students/parents/etc. We got so much of what we need to know from explanations. Why wouldn’t explanations work in the math classroom? Others will only see the light if we explain why explaining things, which works so often, fails so often in the math classroom.
Sue VanHattumJune 12, 2011 - 6:51 am -
>a student asks a question, you answer it in 15 or 30 seconds, check in w/ the student, and the question is answered. end of exchange.
Or you don’t answer it. You say, “That’s a good question. I wonder how we could figure that out.”
TTmcdevJune 20, 2011 - 8:47 am -
I think we’re all missing the point. The major limit of lecture is language. Words. This is the medium of lecture. Children vary GREATLY in their ability to process is medium. Some children are expend less energy re-creating the meaning of words in their minds. That’s what has to occur, a complete re-creation of our thought process. We should focus much more on this BASIC fact. I’m not saying that we should dump down language. But we should be scientifically aware of the rate of information being disseminated in any given word or sentence and rate of speech. We need to focus on language as a perception
Lectures, because of their medium, many times muddle actities. Lecture should highlight, accentuate, a demonstration or interactive activity. They are quite convenient, and the results are many times qiute “average”. How many words out of every lecture are partially or completely discounted in a students “re-creation” of an idea. My guess, for many students is 85%. Do we have studies on this?
I teach children. I think sometimes many forget what the role accumulating knowledge as in done in school has in a child’s psyche. Math and any subject CAN be, and should be, a source of PRIDE for students. The lecture format has little is any room to nuture this very individual feeling of “I CAN”. That’s what students need. They crave it. Once again I believe the fault lies with the format of the lecture itself, NOT the teacher, although most certainly the lecturer. Every child participating in a lecture is covered by the same EXACT same BROADCAST. But children understand that they are all different YET they still can’t help judge their worth on their ability to understand and execute task X. So we have one broadcast, or word-stream, and many different children. Even when we don’t pick up on this unequalness, children do. It hurts them, plain and simple.
We need technology to augment a teacher’s ability to challenge individual students in an appropriate manner; that being any manner that leads to PRIDE, ACCOMPLISHMENT, and eventual success. Let your imagination run wild here. Its totally under-developed, practically non-existant arena for exploration. Its worth investing in.
J. EdwardsJune 20, 2011 - 11:40 am -
Cbrown makes a good point but I would add color by saying, I believe there is a spectrum within the classroom, where at one end there is a teacher speaking and students taking notes, with no interaction from students and no checks for understanding from the teacher (extreme lecturing), at the other end of the spectrum might be group work where they discover concepts themselves. I think there is a band within that spectrum that can be called a “lecture”, from the extreme end down to one where there is a back and forth between students and teacher. Which I believe is consistent with R. Write “Answering a question is always a form of lecture”. A lecture probably requires a teacher at the front of the room talking but the style will vary from teacher to teacher. So it seems obvious that Khan is lecturing but I feel when he says it’s not “one size fits all” I interpret that as content not form or method. A student can take whichever video he wants but he has to choose it as a video. I do feel that these videos can be a useful tool as a supplement, not as an introduction, to a topic. I don’t think there’s anything wrong with a student at home thinking “I’ve learned this but it’s escaping my mind at the moment, let me watch the video on factoring quadratics”, the student will then make the connection between that lecture and their initial classroom discovery. That is to say there may be a place for all forms of teaching, even lecturing.
TTmcdevJune 20, 2011 - 6:11 pm -
sorry for the other post I should read what I type before submitting. I think we’re all missing the point. The major limit of lecture is language. Words. This is the medium of lecture. Math is very hierarchal in its language, it seems that we use WORDS to EXPLAIN more words. Look at numbers themselves, they are words. That’s a pretty high level of abstraction right there!
Lectures, because of their medium, many times muddle activities. Lecture should highlight, accentuate a demonstration or interactive activity. They are quite convenient, and the results are many times quite “average”. How many words out of every lecture are partially or completely discounted in a students “re-creation” of an idea. My guess, for many students, is 85%. Why do I guess this? Because you ask them to explain something back to you and they say, “this goes there.” They are sure “it” goes there. They’re right, and that’s what counts, they themselves need to feel right. Knowing and understanding WHY it goes there is too often secondary to “knowing” that it goes there.
Children vary GREATLY in their ability to process language. Some children expend less energy re-creating the meaning of words in their minds. That’s what has to occur, a complete re-creation of our thought process. We should focus much more on this BASIC fact. I’m not saying that we should dumb down language. But we should be scientifically aware of the rate of information being disseminated in any given word or sentence and rate of speech. We need to focus on language as a perceptible sense. Especially with younger children, they have to articulate what they learn if they’re to have a continuous “narrative”, and therefore a good memory, of their knowledge.
I believe that younger children rely heavily on their operative memory and working memory to recreate the PROCESS of a mathematical task. Instilling a more declarative memory “teaching experience” would feel more concrete and obvious to build off of in the long run. But I don’t think we insist on it. How many students actually have the idea of a number line present when they are adding and subtracting?
Math and any subject CAN be, and should be, a source of PRIDE for students. There’s a lot of knowledge to accumulate. The lecture format has little if any room to nurture this very individual feeling of “I CAN”. That’s what students need. They crave it. Once again I believe the fault lies with the format of the lecture itself, NOT the teacher, although most certainly the lecturer. Every child participating in a lecture is covered by the EXACT same BROADCAST. But children understand that they are all different YET they judge their worth on their ability to understand and execute task X (they can’t help it).
So we have one broadcast, or word-stream, and many different children. What kind of tension does this create? It works much better for some then others. Even when we don’t pick up on this unequalness, children do. It hurts them, plain and simple.
Lecturing has been a acceptable solution to unavailability of individual attention. But NOW, we can not accept it any longer because we have technology that COULD help us keep our “finger on the pulse” of the learning. A thousand forms of instant feedback and monitoring is what technology can bring, especially in a small relatively stable environment of the classroom.
Yes it is true that EVERY student must learn the same facts. But this will never happen if we do not AFFIRM the individual in a HEALTHY logical sequence and order. We need technology to augment a teacher’s ability to challenge individual students -in an appropriate manner; that being a manner that leads to PRIDE, ACCOMPLISHMENT, and eventual success. Let your imagination run wild here. Its totally under-developed, practically non-existant arena for exploration. Its worth investing in.
Nigel NisbetAugust 19, 2011 - 8:56 am -
Great blog discussion. You should all really check out this 1910 French Lithograph of a vision of education in the year 2000
I think this perfectly captures the essence of the fallacy inherent in “I taught it therefore they will learn it” – i.e. Kahn Academy. The problem is basically the underlying assumption that education is purely a matter of transferring knowledge from the teacher to the student, during which time, if only the student can remain passive enough, they will obviously absorb what is being taught.
It’s not too difficult to realize that this mechanism (basically what we have traditionally called “teaching” is effective – in math anyway – for about 40% of the population).
I was remarkably struck by the post from TTmcdev above discussing the limitation of language as a teaching medium – couldn’t agree more, but there is in fact already a significant amount of very successful research/development done in this area and technology created that absolutely does what you want here, i.e. technology developed that augment’s a teacher’s ability to challenge individual students – in an appropriate manner that leads to PRIDE, ACCOMPLISHMENT, and eventual success.
For those of you familiar with ST Math (JiJi) at the Elementary level you will know exactly what I mean – for the rest check out this TEDx talk
As we’re all aware, there are far more innovative ways of using technology to help students learn mathematics than the Kahn academy!