Tag Archives: video

This is what not to do

Oh my, do I love this video.

But seriously. Don’t do this.

Please.

Thanks to Approximately Normal for the find.

Back in the saddle

It’s summertime here at OMT. After an initial flurry of posting back at beginning of June, things have slowed down. But only on the blog. Behind the scenes, we’ve been busy as beavers. The interns have been trained in, and we’re rarin’ to go.

In particular, I’ve had a number of really interesting (to me) conversations by email. You’ve heard of email right? Kind of like Twitter, only no character limit, so most people use full sentences and spell words correctly.

Except one colleague of mine who sends the following sort of crap to all faculty (he is referring to Rate My Professor, and I wish I were making this up):

I dfer 2 yor sensibilities in this matter as I’v not gone there in yrs b/c I feel that things lyk worrying about how ‘hot’ students find us contribute 2 grade inflation—wich is a horse I’ve ben riding 4 sum tym, now

I digress.

Email conversations. Right.

I’d like to tell you about a few of these over the next week or so. Like the one I had with Justin Yantho as we hashed out whether the following video represents good teaching (with thanks to Frank Noschese for alerting us to it).

In a sign of summer torpor (and of the OMT interns’ inexperience), the following is copied and pasted mostly verbatim from one of my replies in the conversation.

That video is “training”, not “teaching” in my view. Effective training. But training nonetheless. I think of this analogously to training dolphins to jump through hoops. Stimulus (hoop), response (jump), reward (fish). Self-contained system, disconnected from other behaviors.

I’ve only watched four minutes or so of video. But it’s offered as “exemplary”-both in the sense of being an example of what’s being promoted, and in the sense of being very good. And as an example of what teaching should look like? I’m opposed.

To be sure, I’m opposed to a lot of what I’ve seen in other sorts of classrooms (including all too frequently in my own!)

What bothers me the most here is related to my reaction to another video Frank Noschese sent around recently in which “Integers are important because they’re a state standard.”

In the former, teacher says, “Tell your neighbor about the four operations”. In the latter, the teacher says, “In a pair/share, talk about why is it important for you to understand integers?”

In both instances, we’re setting the standard that “talking about math” equates with “repeating previously stated information” rather than with “exploring ideas, wondering or processing”.

Now, I get that I’m drawing gross generalizations based on small sample size (short video snippets). But each of the videos is purporting to demonstrate an aspect of good practice. These people want us to learn from the teaching we are seeing; they want teachers to emulate the model. That makes it fair to pick the examples apart, I think. And I’m totally ready to eat my words if you find videos in either one of these sites that pushes kids to really think about mathematics.

But I’ve been in a lot of math classrooms over the years. Lessons rarely move from this sort of rote opening into a mode involving rich thinking and dialogue. Not never, but it’s rare.

This puts me in the mind of The Teaching Gap (a book I cannot recommend highly enough). The authors of that book draw on evidence from a well-designed international video study to outline important differences in classroom practice in three countries: the US, Japan and Germany.

The connection here is that the teaching we see in these videos is an extreme example of how US teachers spend their class time-recitation and practice, in stark contrast to how Japanese teachers spend their class time-problem solving and discussing ideas.

And I haven’t even addressed the error(s), right? Why does the set of “order of operations” have six elements if there are only four operations? Is exponentiation not an operation? Why does the opening example involve an operation about which she does not speak?

Thanks to Justin for giving me permission to reference our conversation. As you can see, I didn’t really let him get a word in edgewise. He did a fabulous job of arguing back, though. If you’re not following him on Twitter, do so now.

Showing v. Telling: Lattice Continued

That last post wasn’t really about the lattice algorithm. This one isn’t either. It’s about supporting claims with evidence. (The last one, in case you’re keeping score, was about crafting tasks that show instead of spiels that tell).

Another claim my future elementary teachers like to make is that the lattice is inefficient for problems with large numbers of digits. The idea is that you have to spend a lot of time making that lattice before you can multiply. This stands in contrast to the standard algorithm, which you can just get started with straight away.

They make the claim, but they don’t back it up with evidence. (This, after all, is part of what a college education is supposed to teach-how to build arguments-so I’m not complaining that they don’t. I understand that it is my job to teach them to do so.)

So I began to wonder whether the lattice-drawing really did set one back.

So I put it to the test. Ten digits by ten digits. On your mark, get set, GO!

By the way, I was going to do three algorithms head-to-head. I was going to do partial products in the middle of the board. But about a third of the way through, I got fed up and quit. That one really is inefficient for large numbers of digits.

The importance of the imagery of teaching

Breedeen Murray writes about the importance of having an image of the kind of teaching we are striving to be:

[…]I had seen video of this problem being taught at PCMI the summer before. And this was a HUGE thing for me. I had a template for how this lesson should be taught. I didn’t have to imagine how to transform it from the book to something better all on my own. I didn’t have to create something from scratch. I just did what the teacher did in the video. Which is exactly what I did with the exception that I had a document camera, so I had students come up and put their work under it, instead of writing on an overhead. And this too was amazing. I had students who had been giving me grief all year long produce such beautiful explanations that it hurt my heart. How could I have waited so long to let them be this awesome?

The models of teaching we carry around in our heads are so very, very powerful. Here are some resources for independent study:

  1. Connecting Mathematical Ideas by Jo Boaler and Cathy Humphreys (which I suspect was the source of the video she writes about)
  2. TIMSS videos, available online with free registration. If you dig into these, you really should pick up…
  3. The Teaching Gap by Jim Stigler and Jim Hiebert.

The pH of concentrate

introduction

I set this up and critiqued it in this blog before teaching it. The basic idea is that I needed a way into logarithms with my College Algebra students.

The questions

I have two question videos. I debated which to use in class and ultimately chose the first option below.

Option Number 1

In this option, we measure the pH of water and the pH of pure orange juice concentrate.

Option Number 2

In this option, we measure the pH of water and the pH of 100 ml of water mixed with 1 ml of orange juice concentrate.

I imagine that Option 1 will prompt questions such as, “What is the pH of regular orange juice?” and “What if we mix it 50-50?”

I imagine that Option 2 will also prompt the question, “What is the pH of the straight-up concentrate?”

In fact, this last question is the one that motivated this project. I was expecting (as will my students) that the difference between the pH of juice and the pH of concentrate will be quite large.

answers

Juice (20 ml)

This actually doesn’t demonstrate juice (see post where I regret this oversight in my data collection). But it’s pretty close. Real OJ should be 3:1 water to concentrate. This is 5:1.

50-50 (100 ml)

10 ml

1 ml

Pure concentrate