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.

 

You Khan learn more about me here

I expect a few folks will stop by this blog after reading my recent critique (together with Michael Paul Goldenberg) of Khan Academy. That critique was based on Sal Khan’s lack of knowledge of common student misconceptions, as evidenced in his videos. It was also based on the fact that he seems not to care.

Forthwith, some more reading on the topic, Teachers need to know about their students’ ideas.

Read and enjoy.

And feel free to argue with me (read the comments-you’ll see that you’re not the first!)

But before you do, please read my post on ground rules. I adhered to these in my Washington Post piece. You need to adhere to them here. It’s how we’ll learn together.

• Division of fractions. (Contrast with Khan’s treatment of the matter. Of course our work has different audiences; but I argue that his teaching ought to reflect having though about the issues I wrote about. Does it? Discuss.)

• Ways to think about the sum of the angle measures of a polygon. (Again, contrast with Khan’s treatment.)

• Some thoughts on designing tasks from which students can learn.

• More observations about concepts underlying decimals.

• Problem-solving and understanding; notes on their relative importance in teacher preparation.

• A post in which I predicted my own students’ struggles-only partially correctly-and discussed with commenters afterwards.

• A high-concept, mathematically sophisticated way of saying Holy crap! I get why my students struggle with logarithms!

You might also enjoy my ongoing series on Talking Math with Your Kids.

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A common theme in critiquing Khan’s critics is to ask, “Why don’t you go ahead and make your own videos?”

This has some merit. But it’s not the fact that Khan’s making videos that I find troublesome. A more apt retort would be, “Why don’t you go ahead and make your own multi-million dollar website?” The answer to that should be obvious.

For me, on the video front, I have. I am still pretty open-minded and curious about what video can do well. I think it can provoke (examples here, here and here). And I think it can provide decent explanations and demonstrations. I do not think it can be the primary instructional medium for a quality math course. And yet, I am ready to be persuaded.

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Finally, I noticed that Karim Kai took some heat for a perceived (but fully disclosed) conflict of interest, in that he founded Mathalicious. Concerns in his case are unwarranted in my view. But be that as it may, I want to make clear that while I have written for Connected Mathematics, I have zero financial interest in the venture and my formal relationship with the project has ended. I neither speak for, nor profit from Connected Mathematics.

I have, however, written extensively about the curriculum.

Help! My parent and my teacher are both apps

People outside of the education profession look at Khan Academy and they see brilliance because Khan conforms closely to American cultural scripts of teaching. Teaching is telling and Khan tells in a friendly, seemingly competent way (which is actually incompetent in some important and non-obvious ways, but more on that in the coming weeks).

This is the drill: Tell students some stuff; ask them some questions to see whether they remember what you told them. See those first two headings on the Khan Academy landing page?

With thanks to Michael Pershan (@mpershan) for noticing this on Khan Academy.

Watch and practice.

People outside of the education profession look at iPad apps and online schools and see efficiency because these-again-closely follow the script of teaching and learning in this country.

So powerful is this cultural script that minor tweaks are seen as revolutionary. (Rewind the video to hear the same explanation again! As many times as you like!) So powerful is this script that our roles as parents can be misconstrued as preparing our children to be this type of student. From the comments on this blog last month:

Around 6-7, I think it is important for children to first internalize basic arithmetic equations as memorized, right-brain pattern recall. Once they do this, their minds are free to think about other aspects of the math problem in front of them. Once basic one-digit equations have been internalized, the next pattern needed is the simple process of stepping through more complex problems.

This was in response to my description of something I had done that had gotten my five-year old daughter to think, rather to respond in a rote way.

A parent talking with his child about mathematics gets redirected to a fact-drilling app.

I’ll make the analogy to literacy again. The equivalent would be a parent writing about how turned on his kid was by a story, and how his kid applied the ideas of that story to thinking about her lived experience. And then got pushback about the importance of phonics instruction to prepare a child for reading in first grade.

But we know that a lifelong love of reading is fostered by reading aloud with parents. (Of course, there are exceptions, blah blah blah.) And if you love reading—barring disability—you’ll learn to read as long as you are provided competent reading instruction.

We need to similarly foster a lifelong love of numeracy. And that does not start with math-drilling apps (Of course, there are exceptions, blah blah blah.) It starts as all things do, through play, conversation and wonder.

Let’s keep the focus, shall we?

Further reading:

Alfie Kohn (of course) on summer learning loss.

Will Richardson on online learning and apps.

The Teaching Gap

The Teaching Gap is a funny book. Not funny “ha ha”. Funny in terms of how it has been perceived.

It was published in about 1999 and the professional conversation turned to “Japanese Lesson Study”. Initiatives were initiated. Presentations were made. Etc.

And in fact, Japanese Lesson Study comprises about the last third of the book. But it’s not what the book is about. The Teaching Gap is about how assumptions and values play out in classroom practice. And it’s about how things don’t have to be the way they are in math classrooms because they are quite different in other countries’ math classrooms.

But it’s not about lesson study. Here is why I care.

I frequently recommend The Teaching Gap to colleagues. If the message they take away is that I am recommending Japanese Lesson Study, then my mission is not accomplished. When I recommend the book, I am recommending an insightful study of classroom teaching that forces readers to think critically about their own classroom practice.

We are all ready for critical thinking about our classroom practice.

We are not all ready for Lesson Study.

In fact, as a group, American teachers are tremendously far from being ready for lesson study.

Consider the rhetoric around Khan Academy. According to a recent Time Magazine piece, Khan says “He doesn’t use a script. In fact, he admits, ‘I don’t know what I’m going to say half the time.’ But the low production values of Khan’s videos are part of what makes them so effective.”

How does Khan plan? Same article: “Khan begins by doing two minutes’ worth of research on Google, looking for graphs that affirm what he remembers from his econ class in college, then flips through a few pages in a 4-in.-thick economics textbook sitting on his desk and clicks a button to start recording.”

And simultaneously, Khan has received millions of dollars to do more of this. He is hailed as “brilliant” (Newsweek) and “The new Andrew Carnegie” (Time).

If we’re ready to use Khan Academy as a primary instructional medium, we are not ready for lesson study.

At about 1:50 in the video below, a math teacher extols Khan Academy for the diagnostic data it gives him on students.

I should go back and think about what I’m really asking my students to do. Whether that’s something that’s too high of a level for 80% of the class, or something that’s too low of a level for the class.

That reflection is nowhere close to what lesson study would produce. Lesson study would involve planning with other teachers, teaching (with others observing) and a discussion afterwards of how students’ ideas played out in the lesson. The teachers would discuss the lesson in minute detail. Conclusions would be drawn about how the examples used should be different, what questions should be asked next time, whether the context in the lesson supported student reasoning, etc.

The rhetoric in US schools tends to focus on the speed with which material is covered, not on nuanced details of lesson structure.

That teacher in the video? I’m sure he’s very good at what he does. But he’s not questioning whether a linear trajectory through a set of skills is the best description of what it means to learn mathematics. Instead, he seems to uncritically accept this proposition. And that’s where a lot of us are, frankly.

It’s why Khan Academy is hailed as such a revolution. Khan Academy is a friendly tool for doing something better. But that thing it does? It’s the wrong thing to do. So being better at it doesn’t matter very much.

That teacher needs to read the first two-thirds of The Teaching Gap. Like all of us, he needs to critically analyze his practice in light of the ideas presented there. He needs to talk with colleagues about what he concludes.

Then he can come back in a couple of years, read the last part of the book and form a lesson study group.

So I continue to recommend The Teaching Gap. We desperately need to know how things could be different. But when I recommend it, I will continue to point out that the main message of the book is in the first two-thirds. Because as a field, we’re not ready for lesson study.

Vi Hart goes to Khan Academy

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