Tag Archives: khan

I get that there is no perfect lesson

I get that there is no perfect lesson. Really I do.

And I get that students leave my classes with wrong ideas. But the thing is, when I come across these wrong ideas, I try to do something about it.

A couple of tweets from the field last week (sender’s tweets are locked, sorry).

S came in today claiming to have used Khan academy last night to learn about decimal place value. Was adamant 0.63 > 0.7 cc @Trianglemancsd

Was also adamant that 0.4 < 0.40. Not feeling overly confident about Mr. Khan and his explaining abilities…

Now, people get fussy when I fault Khan Academy for bad decimal instruction.

If I don’t like the videos, I am told it’s not about the videos; it’s about the exercises.

If I don’t like the exercises, I am told there are new ones in the queue.

If I don’t like the trial versions of the new ones in the queue, I am told that the particular exercises don’t matter; it’s about the knowledge map.

When I say that the knowledge map is flawed, I am told that it doesn’t matter because students can move around in Khan Academy in any way that they like.

And then every day kids are going to Khan Academy for help with decimals. Some of these kids, such as the one in the tweets above, are going there independently. And some of them are going there because their entire state is piloting it as a primary instructional resource!

Whoa there! they say. Khan Academy isn’t meant to be a primary instructional resource. 

But then here is a video that Khan Academy produced…

At 20 seconds in, a student teacher in mathematics says this:

When I first [learned] about Khan Academy, it was mostly “my teacher said this, but I can’t remember what he said, so I’m going to go check it out on Khan Academy. So it was more of a personal resource.

That’s kind of where I was thinking it would be in my classroom down the line. “If you’re struggling with this, go check out Khan Academy.”

But now, after coming to this, it can be that first step. It can be the go-to. “Hey, go learn this. Go learn the foundations, and then we can take it to the next level in our classroom, and put in those hands-on activities.”

Just to be clear, Khan Academy produced this video. I am not misrepresenting KA here. They are proud to share that a math teacher at a training views Khan Academy as a good primary instructional resource.

Now, I have long been critical of textbooks that introduce decimals as though they were a logical extension of the whole number place value system (just ask my students!) I am no fan of what Hung-Hsi Wu calls Textbook School Mathematics.

But if you are going to get introduced by the publisher of The New York Times  [at about 3:00 in the linked video] as  “a true pioneer” who is “breaking down barriers” with “heart”, “guts” and “innovation”, I think you have a responsibility at least as great as that of the average textbook author. You have to strive to do better and you have to pay attention to what people already know.

If you are going to repeat that your mission is “a free world-class education for anyone anywhere,” you need to spend some time concentrating on the meaning of world-class, rather than imitating the bad textbooks that presently exist.

I have taught many crappy lessons, and I surely have many ahead of me. I do not fault Khan Academy for having a few crappy lessons.

But I seek feedback from my students on what they are learning.

I consult research on learning for the topics they are struggling with. I collaborate with colleagues near and far to improve my lessons.

I do not defend my crappy lessons by calling them unimportant. I own their crappiness.

And I strive to do better next time.

[Comments closed. Hit me on Twitter if you want to talk.]

Life’s dashboard [#NYTEdtech]


Think of something complicated that all of the competent adults in your life are equally good at.

Having trouble?

Consider the following possibilities.

  • Parallel parking
  • Reading maps
  • Folding maps
  • Making risotto
  • Growing tomatoes from seed
  • Doing laundry
  • Consoling friends

So what would your life’s dashboard look like?

Three stages of mastery in the new Khan Academy dashboard for teachers. Students are organized into rows; content in columns.

Three stages of mastery in the new Khan Academy dashboard for teachers. Students are organized into rows; content in columns.

Is your goal for every adult in your life to master each of these skills? Is it OK for the adults in your life to attain some familiarity with each and to improve throughout their lifetime? Or must the dashboard be solid blue?

Additional question: How would you behave differently if life’s dashboard were available on your mobile device or desktop computer?

Much of the rhetoric at the New York Times Schools for Tomorrow Conference this past week was based on individualization. The mantra here is alluring.

We have been treating time as fixed and mastery as variable. We need to flip that so that everyone attains mastery and the time they take to do it is variable.

This was a much retweeted component of Sal Khan’s keynote address (see it at 12:56 in this video).

Watch live streaming video from nytschoolsfortomorrow at livestream.com

Instead of holding fixed how long you have to learn something and the variable is how well you learn it, do it the other way around. What’s fixed is every student should learn; we should all get to 100%, or 99% on basic exponents before moving on to the negative. And the variable should be how long we have to learn it and when we learn it.

The larger idea of which this is a part is competency-based education.

Perhaps the principle here is too broad for meaningful debate, but I do think the assumption is worth questioning. My Life’s Dashboard thinking is one way of doing that.

Another would be to state some explicit areas for concern. One is equity. We can imagine students cycling endlessly through arithmetic content deemed foundational, and never being given access to (say) algebra.

Another area for concern is the power that is given to those who create the knowledge map. A careful look at the KA knowledge map, for instance, reveals that the prerequisite knowledge for adding decimals consists of addition and subtraction skills together with additive whole number and negative number relationships.

No knowledge of fractions is necessary; no knowledge of the multiplication and division relationships underlying place value, decimals and fractions is necessary.

These assumptions about how people learn decimals are flawed, and they are known to be flawed. But powerful people are creating flawed knowledge maps, which then form the basis of the appealing fixed mastery, flexible time meme.

I have written multiple times about Cathy Fosnot‘s idea of the landscape of learning. This is a useful metaphor that conflicts in some important ways with Khan Academy’s more linear knowledge map metaphor (and at 9:21 in the video).

So I get how appealing this flexible time/fixed mastery thing is. I understand its allure. And the idea that we can summarize this information for teachers in a tidy array? Also appealing.

But it just isn’t that simple.

Mindsets, research and talking math with kids [#NYTEdTech]

This conversation happened in New York yesterday.

A view of New York City from the Times Center on Tuesday.

A view of New York City from the Times Center on Tuesday.

During a coffee break, I sat down on a white pleather sofa next to an older man.

Me: How has your day been?

Him: Good. You?

Me: Pretty good. Interesting.

What do you do?

Him: Retired.

Me: From what?

Him: I was president of [small New England college]. How about yourself?

Me: I teach math at a community college in Minnesota.

But I’m also working on a project. I work with future elementary teachers, so I have studied the mathematical development of children.

Him: Uh huh.

Me: And I want to use that knowledge for something else, which is this: I am trying to understand what knowledge parents need in order to support the mathematical development of their children.

Him: That’s important.

Me: Right.

[Short pause]

Me: Do you have grandchildren?

Him: Yes. They are 8 and 10.

Me: Oh nice! So their parents—your kids—are my target market.

Him: Yes. Their father is really into that. They use Khan Academy and all that.


If the end of that conversation makes no sense to you, I ask that you please, please, please spend the next 15 minutes over at my website, Talking Math with Your Kids. You might be especially interested in the research summaries, which demonstrate that young children need to talk about number and shape with their parents rather than (or at least in addition to) being sent to website, iPad apps and decks of flash cards.

Kids need mathematical conversation. And they enjoy it.

Mr. Khan? You got some ‘splainin to do!

Oh dear.



No, no, no.


I know we went over this. I know we did.

Seriously, Mr. Khan. Gimme a ring next time, OK? I’ll talk you through it. I promise.

I’m easy to find.

(“Thanks” to Frank Noschese for alerting me.)

Further progress

This isn’t available on the Khan Academy site yet; just YouTube so far. But it responds to my original critique—that nowhere does Khan Academy help students to compare decimals with different numbers of places.

I initially observed that the my feedback was incorporated in an awfully literal fashion. Frank Noschese came to Mr. Khan’s defense:

Maybe Mr. Khan and I can have an extended conversation in New York in September? (Although I am suspicious that he may be telecommuting to that thing!)

This is better

Ben Alpert from Khan Academy responded to my open letter to Sal Khan and provided a link to an improved set of decimal exercises.

They are better.

You end up having to compare two-digit decimals to one-digit decimals.

Screen shot 2013-08-06 at 9.00.35 AM

My major objections now boil down to pedagogy, on which point I understand that I will make no progress with Khan Academy, so I won’t make the effort. I’ll leave that to Frank Noschese.

If you accept that people learn mathematics by doing lots of multiple choice exercises, then all I have left are technical details.

They are these:

  • In the U.S., money is a good enough model to get students through two-digit decimals. It is not uncommon for children to be able to reason about two-digit decimals, but not generalize to three- and four-digit decimals.
  • These are randomly generated, I assume. And the probability of getting two-digit decimal>one-digit decimal seems artificially low. As I ran through a bunch of these, I began to build a model in which I could (1) treat comparisons with same number of decimal places as whole numbers, and (2) claim that the one-digit decimal is larger. So I ran an experiment. Twenty exercises using my model. I got 90%. (See video of a repeat of this experiment; I don’t know that I did 20 this time, but I did a bunch and only got one wrong)
  • Related to this, there is no need to click through the hints. None of the decimals came out equally (i.e. no 0.1 v. 0.10). So when I got a wrong answer, I just chose the other inequality. Pattern matching and process of elimination allowed me to avoid instruction of any kind and to get an A.

See, here’s the thing. Teaching requires a mix of knowledge and assumptions on which to base decisions. When everything is pre-programmed, deeper knowledge is required in order to create meaningful instruction, not more analytic data.

Carnegie-Mellon is working on a deep model for diagnosing student misconceptions with decimals [pdf] (and presumably many other domains). Again there’s the pedagogy thing, but I am impressed with the effort to build a solid theoretical foundation for their work. Here is a sample of a taxonomy of decimal misconceptions they have developed.

Thanks to Frank Noschese for the find.

Without that deep knowledge base, all that’s left are assumptions. Which is fine, as long as the assumptions are not flawed.

Khan’s kindness

Say what you will about Sal Khan (and I have certainly said a lot), but he communicates a tremendous amount of patience with his students.

I watched his video on “Basic Addition” the other day.

He begins with the assumption that the viewer has absolutely no equipment for finding the sum 1+1.

This bears repeating. He assumes absolutely no knowledge of the meaning of the addition symbol in the expression 1+1. None.

As he does so, Khan is patient, supportive and encouraging. He does not condescend and he even apologizes for the word basic in the title of the video-worrying that his viewer may be put off by the term.

When I think of the culture of many math classrooms, in which students don’t ask questions out of fear of looking stupid, or in which instructors use words such as trivial and obvious without apology or concern for the effect these words can have on learners, I get a glimpse of what people find so appealing about Khan’s videos.

Khan gives permission to not know. He reassures the viewer that it’s OK to still be figuring things out. And of course he is happy to repeat what he just said as many times as the viewer likes. Just stop and rewind. The calm, patient demeanor never changes.

The field could learn from Khan’s kindness.