**Note:** this is Part 3 of a 4 part blog series on Khan Academy and math education. This post is an imaginary Q&A about what I’ve said in Part 1 about *math myths and learning theories* and Part 2 about *algorithms, practice, and autonomy*. The following questions are made up from what I’ve heard people say about Khan Academy. I am solely to blame for the answers.

**Isn’t it best to offer a balance of all different kinds of learning opportunities for students?… Can’t we have open-ended problem-solving AND show the kids how to do the hard parts when they get in trouble?
**Now, I would never tell a teacher what to do, it’s too easy for me to type a bunch of words and I don’t have to be there every day. But I think you have to consider the unexpected consequences of striving for balance between two opposing theories of learning – instructionism and constructionism.

To illustrate this, let’s imagine a playground game of hide and seek. On Monday, when everyone has hidden and the seeker finishes the count, he or she looks up… and at that moment, the teacher steps in and points out where everyone is hiding. On Tuesday, the teacher stands back and says nothing. On Wednesday, the teacher helpfully points out the hiders, on Thursday, says nothing.

What do you think happens on Friday?

I’m pretty sure that the seeker would immediately look to the teacher and ask where everyone is hiding. Or maybe everyone would just refuse to play since there’s no point to it. On the previous days, the teacher has trained them how to get the answer. Even with the “balance” in game play, one outweighs the other. There is no balance possible, because the teacher’s authority causes the balance to permanently shift. It’s the very essence of disempowerment. Teacher power and authority is the 800 pound gorilla siting on the end of a see-saw.

I believe that for many of the same reasons, the attempt to explicitly show students how to solve problems becomes a roadblock when you suddenly turn around and demand that they figure things out for themselves. It just sounds like a trick, and if they wait long enough, you will give them the answers and move on. Children are pretty pragmatic about these things.

**I still think you need balance…**

I could almost go along with the “balance” argument if the world of U.S. school math weren’t so unbalanced. I would guess that 95% of all math taught in all classrooms across the US is direct instruction aimed at the “skill” level and memorizing the right algorithm to solve problems most likely to be found on standardized tests. So there’s no balance there to start with – the only way to achieve “balance” is to do more open-ended, student-led inquiry about math, solving real problems (not textbook or test prep problems), not telling students what the right answers are, etc. And do LOTS more of it. Then we can talk about balance.

**But at least the ability to stop and replay the video gives the student control – isn’t that what we always look for in student-centered learning?
**Here’s the tradeoff – is student control over the pace worth losing student control of the entire process? They get to choose how quickly they are force-fed someone else’s representation of a process instead of creating their own representation in their heads. Asking the student to give up control of their own thought process to absorb a one-size-fits-all delivery of information requires a large degree of compliance on the student’s part. In my book, the ability to control the pace pales in comparison. I think a teacher would have to weigh these very different kinds of control and whether the trade-off is worth it.

**Why shouldn’t we teach students a good way to solve a problem, what’s the point of letting them fumble around?**

When we tell a student the “right way” – we are really telling them that math ability is primarily about compliance. This is about power, and we lose a lot of students in these power struggles.

Margaret Mead said, “emphasis has shifted from learning to teaching, from the doing to the one who causes it to be done, from spontaneity to coercion, from freedom to power. With this shift has come… dry pedagogy, regimentation, indoctrination, manipulation, & propaganda”. (thanks to Ryan Bretag for this quote)

What we call “good students” are compliant students who don’t call this power structure into question. (By the way, this was me – even when I saw other ways to solve problems I knew not to say anything. I amused myself by solving problems in alternate ways, then would write down the answer the way I knew the teacher wanted.) If you don’t think students are acutely aware of the power structures in school, you are underestimating students.

Students “fumbling around” is actually where the learning happens – and there’s no shortcut for this process.

**Why waste time letting students “discover” everything. They aren’t going to re-invent the Pythagorean theorem by themselves.**

It’s a straw man argument about inquiry-based, constructivist education that it’s “illegal” to lecture. Whenever I hear this I imagine a scene where the constructivist police burst through a classroom door and wrestle a teacher to the floor who was just explaining to a student how to do something. The difference is that explanations should serve to naturally move a problem-solving process along, not be the whole lesson.

In this kind of classroom, the teacher’s role is crucial – by posing problems that lead to big ideas and steering a class as they solve problems. By “being less helpful” as Dan Meyer says. (He doesn’t say don’t help at all!) This is not wasting time, it’s letting the students build the knowledge in their heads and acknowledging the fact that this takes time. It also takes time to learn how to teach this way. It’s not the case that the teacher is off taking a smoke break while the kids do this on their own. The teacher’s role is crucial – it’s difficult work and takes years to master.

This exact question is discussed by Piaget as related in a brilliant essay by Alfie Kohn – What Works Better than Traditional Math Instruction from his book *The Schools Our Children Deserve. (I can’t improve on his explanation of why traditional math instruction is failing our children – please read this essay.)*

**So isn’t this the “flipped classroom” that Khan Academy proposes?**

People are associating Khan Academy with the “flipped classroom” – something I talked about in this post (‘Teach Naked’ and complacency natives). In a so-called flipped classroom, the lecture takes place outside the classroom and classroom time is spent on discussion and problem solving. Students might watch the video at home (or in the car, bus, or anywhere) and then there would be a lot of classroom time freed up for discussion, working on individual problems, or whatever else needs to be done. That’s the theory, anyway.

So, first off, do you believe:

- Students will actually watch the lecture?
- The percentage that do watch the lecture will be any different than those who currently do their homework?
- The percentage of kids who zone out, multi-task, or don’t understand will be any different than during a classroom lecture?

But I’m willing to let all these assumptions slide so we can move on. Let’s pretend that most of the students will listen/watch a math lecture on their own time.

Can you disconnect the lecture from the problem solving? Khan Academy videos have no context outside of class – other than that they match the standardized tests. As Derek Muller points out (see Part 1), these videos may have the unintended consequence of cementing incorrect models as students assume that they understand, thus making the teacher’s job that much harder.

Swapping the timing of certain teaching practices seems a minor logistics issue, at best. Moving the timing of the lecture doesn’t change the fact that it’s still a lecture, and not even a lecture about interesting stuff. Most of these “lectures” are simply worked out example problems. Do we think that a student who doesn’t “get it” in the classroom is more likely to “get it” on the bus? The main issue is the reliance on information delivery to trigger understanding.

This also assumes that you are replacing one lecture with no feedback with another lecture with no feedback. That’s pretty insulting to LOTS of teachers. I won’t assume that ALL teachers who lecture are bad, or that there aren’t a thousand ways to intersperse lecture with checks for understanding. There are no raised hands in the Khan Academy, no questions, no teachable moments, no interesting asides. You have one interaction, and one interaction only — the ability to play, stop, and rewind.

If I were a huge fan of making videos about how to solve problems, I’d certainly try to make it more student-centered by allowing students to make the videos. The process of figuring out how to clearly explain a concept would give a student time to reflect about the process in depth. They say teaching is the best way to learn, so why let Mr. Khan have all the fun!

But seriously, here’s a conundrum — the art of leading a productive learning discussion is much more difficult than lecturing. Are we to expect that the teacher who couldn’t even do the lecture part is suddenly going to be able to lead a productive discussion about math? It would seem to me that the teachers most likely to see Khan Academy videos as a good substitute for their own lectures are also the least likely to be able to take advantage of the classroom time for any substantive discussion that would help students.

Let’s not even talk about what happens if 3, 4 or 5 teachers each assign a 40 minute lecture to listen to every night – so if this model actually works… it’s impossible. Don’t you love models of teaching where successful adoption assures failure?

**Nothing like this has ever existed before, it’s so exciting!**

Really now? Didn’t you ever watch Donald Duck in MathMagic Land or Sunrise Semester? The amount of acclaim for Khan Academy is, in my view, way over the top and only reflects our acceptance of math myths as drivers for pedagogy and wishful thinking that there is a easy answer for learning.

**I’m just glad to see that technology is finally useful in education.
**I’ve seen Khan hyped as a transformative use of technology, but. I can’t even begin to understand how turning the computer into a VHS player is seen as transformative. I know, I know — he’s got quizzes too. Answer ten questions and you can resume playing the video.

*Brring*,

*brrring*…

*1988 called and they want their CAI (Computer Aided Instruction) back.*

**But the Khan Academy videos show students how to solve the math problems that will be on tests – don’t we want students to do better on tests?**

That is the heart of it – do we care about kids learning math or doing well on tests? They aren’t the same thing.

**These videos have millions of hits on YouTube – it proves that students need this help and are searching for it.**

Yes, it does. It shows that many students really do want to do well, and doing well is defined as passing tests. We have a nation where lots of students are working their hardest to do something that matters little. Imagine if we asked students to do math that was actually useful and interesting!

**My teacher is terrible and these videos help me.**

I’m sorry. I’m glad you’ve found something that helps. Nobody is trying to take away something that is helping you.

**Salman Khan is a master teacher and shouldn’t everyone get the best teacher?**

Salman Khan obviously has a gift for clearly explaining how he understands complex computations. Being a teacher, however, is more than explaining stuff. When a student has misconceptions, they often need to talk through them, and a teacher SHOULD be an expert in recognizing those misconceptions and steering students through those rough waters. There SHOULD be a lot of listening involved. I’m not excusing bad teaching practice – far from it.

**You’ve cherry-picked your research and sources.**

Absolutely true. I said at the beginning this wasn’t going to be a literature review. I’ve included a few quotes and references that influence my thinking. Kamii, Papert, and Kohn appear often. Between them they have decades of work, dozens of books, and research to support it all. If you disagree, I hope at least you’ll read further. Their ideas form a connective network with other great educators from Piaget to Dewey to Vygotsky to Freire and many more.

Just to pile on, I’m looking forward to Alfie Kohn’s new book,** Feel-Bad Education . . . And Other Contrarian Essays on Children & Schooling**. I’m also loving his recent column,

*What does education research really tell us?***He relates new research about how studies done in the short term often support the use of traditional teaching practices (like direct instruction and homework for practicing skills). However, as these studies are refined and the students followed for longer periods (months or years instead of weeks), these traditional practices have zero, or even negative results. Yup, I <3 Alfie.**

**I like teaching in a more open-ended way – but no one understands.**

Many teachers struggle with these math myths and the cultural expectations of how math should be taught. Even if they want to teach in more open-ended way, they are often alone, facing off with parents, colleagues and administrators. Any attempt to teach math as less skill-based is met with skepticism, if not outright hostility. Even research is met with a “… yes, but, I believe it’s important” as if it’s a matter of opinion. It’s almost impossible not to give into that pressure, and as a consequence many teachers give up.

I for one would never encourage a teacher to martyr themselves in a no-win situation, especially with the overemphasis on standardized testing and current punitive politicized atmosphere.

As far as parents go, though, I think that most parents really do want what’s best for their children and many can be convinced. Teachers may find allies among parents who are at their wits end with battles over math homework or with parents who watch their children go into school natural learners and come back hating it. Some parents are going to buy fraction flashcards for their kids no matter what you say or do, that won’t change. Try showing them this: Finland’s Educational Success? The Anti-Tiger Mother Approach

Find allies wherever you can. Teachers are doing amazing things all over the US and around the world. These days, it’s possible to develop colleagues who you may never meet in person, but might be your pedagogical soulmates.

**You must not know much about real schools – haven’t you seen the list of standards that math teachers have to meet? The expectations for the test? The 400 page textbook? We have to get the kids through this stuff and there’s just no time for exploring, discovery, or anything else. Hoping that things will change someday doesn’t help me or my kids today.**

You are right – the need for Khan Academy is completely fits the way we assume math has to be learned and taught. The “if it’s Tuesday it must be exponents” model is failing us. That has to change.

I’ll say a bit more about this Monday… Someday* *dilemma in my next (and last) post of this series.

Part 1 – Khan Academy and the mythical math cure

Part 2 – Khan Academy – algorithms and autonomy

Part 3 – *Don’t we need balance?* and other questions (this post)

Part 4 – Monday… Someday

Loving this series. Have you talked yet about how doing computations isn’t really doing math? I recommend that all 4 of your articles be published everywhere and anywhere that mathematics educators read.

David

Hi David,

Thanks!

I had a whole bunch of stuff about the difference between “arithmetic” and “math” and decided to cut it out. I wanted to focus on the Khan Academy and use the common terminology of the day instead of getting caught in syntax.

But it’s very important – maybe another post…

Syliva,

I commend you for taking on this subject. It worries me that projects like Khan are attracting interest and heavy funding from corporate powerhouses like Google and the super wealthy-elite in Bill Gates.

This series takes me back to my grade school teaching days in the Milwaukee Public Schools where I used a philosophy of learning math developed at the University of Wisconsin-Madison known as “Cognitively Guided Instruction.” CGI was all about having students solve problems of all forms-the role of the the teacher was to become an expert listener as students ‘fumbled’ and struggled their way through all sorts of word problems. The approach encouraged students to create and share their own algorithms (the majority of my students would add the large place values first), was full of rich 3D media/manipulatives, valued depth over breadth, and was anything but neat and tidy. For the life of me I can’t think how this approach would be replicated using video (however, I can see real value in having students share their invented algorithms and creative solutions via video in that Eric Marcos does with his students at http://mathtrain.tv).

I often times wonder if I did more harm than good knowing that students would go on to experience an instructivist dominant approach in their math classes–this is something I still negotiate to this day.

But speaking of assumptions, I meet the victims of “discovery learning” every day. Remember the video about the science videos, and how, since misconceptions weren’t addressed, they weren’t corrected? How will “let them discover it themselves” address this problem?

(I also meet the victims of procedural teaching, and it can be equally crippling, but I’m afraid that more of these students can get through math courses and get on with their lives.)

@Sue: You’re right that discovery learning is in no way a silver bullet that leads to understanding, happiness, and world peace. That said, discovery learning doesn’t mean that misconceptions have to go unaddressed by the teacher. It doesn’t have to be an all or nothing proposal. For me, the fundamental question is “who is taking the lead in terms of developing methods and skills?” When I see misconceptions arise and not be addressed, I develop questions of my own that will help guide students to question their current paradigm (well, and I also do this when their conceptions ARE correct).

Although I am now entering the realm of opinion, I see “get through math courses and get on with their lives” as being a greater failure than not learning any particular content. The idea that math is something “we just need to get through” is what I really really want to change.

@Sue, I agree with Avery – there are a lot of misconceptions about “discovery learning” – and there are people who do it in varying degrees. I think the point is that we are losing a lot of kids the way we do it, and the “get it over with” approach isn’t any better. In fact, some might argue that damaging people’s confidence about their own math ability is worse than doing nothing at all.

As a student that has used these videos, I have to say that I feel they help. Now, you’ll say that they’re helping me pass tests and not much else. But that’s not true. i’m actually learning the concepts. Sometimes, information just doesn’t “click” in class. Hearing Sal repeat it or even explain it differently can help a lot. I once had a teacher that believed we should ‘figure it out ourselves’. This method is stupid. Students aren’t psychics! If we don’t understand something from our teacher ( or they don’t explain it, for that matter ), outside resources like Khanacademy are invaluable.

@Ayesha, “figure it out” is only a command to become psychic if you assume there’s a single right answer (and the teacher knows it). Real problems frequently have many solutions, and no one (or at least no one honest) will be able to explain The Right Answer once you leave school.

@jsb16 —

If you don’t know how to figure it out, then it is a command to become psychic … or a declaration that anybody with half a brain could figure it out, so what does that make you?

And then the math professor wonders why people don’t like math and get the idea that they just can’t do it. It is so much fun to figure things out, after all!

Algebra and pre-algebra are– in a sense– the grammar of all subsequent mathematical and scientific inquiry. We wouldn’t ask students to begin substantive writing with no knowledge of grammar? But of course we now do, and that is why no one can write anymore. What if discovery learning is more than another disastrous educational experiment (new math, whole language). Suppose it does promote some sort of problem solving meta skill. How is it then that students are learning the algorithmic skills to express their insights. We accept a large amount of rote learning in the pursuit of music, but not math or languages. Why?

“Why shouldn’t we teach students a good way to solve a problem, what’s the point of letting them fumble around?

When we tell a student the “right way” – we are really telling them that math ability is primarily about compliance. This is about power, and we lose a lot of students in these power struggles.

When we tell a student the “right way” – we are really telling them that math ability is primarily about compliance. This is about power, and we lose a lot of students in these power struggles. ”

——————————————————

Good thread and responses.

First, problem-solving is about Navigation. Long cuts and dead-ends – in appropriate amounts – can be instructive. How will they later in life, recognize that their solution path has led to dead-end, if they don’t experience dead-ends, with a guide? There are mixtures, too. In one class of problems, the ‘Standard Solution’, expects students to make an unnatural starting move, which then has a natural finish. When you let students, they naturally take the natural start, but this leads to an unnatural finish. Now they have to weigh the two paths.

It’s not about overpowering, but (I hate to use this word) empowering. There are multiple solution paths, to most problems. This should be reassuring… liberating. Bloom’s tells us to teach Evaluation, so, teach them to evaluate the paths. When the texts’ methods are inferior, show them, and let that power struggle work for you!

I tell students “Look, you can do this in 4 hard steps or 10 easy ones. Which is better? Ans: Depends on the person. It’s a personal call, depending on individual strengths, talents, background, current conditions.” There is a persistent myth, that there is always one optimal ‘right’ way to get through math problems.