Non-expository video clips

How can video clips be used effectively in the teaching of mathematics? And I don't mean clips of someone explaining something...

If I do a Google search for "maths videos", I discover a tonne (258m hits) of short clips of mostly people explaining various bits of mathematics - with varying degrees of clarity and accuracy. I'm sure that some of these may have their uses, but they're not what I'm interested in in this blogpost. I assume that clips like those are rarely used in the classroom, if you have a live teacher who can do the explaining themselves in a more interactive fashion.

What I'm focused on in this blogpost are what I call 'non-expository' video clips. These are not trying to tell you something or explain something mathematical. They might not even be created with mathematics education in mind, although sometimes they are. But they are intriguing and engaging in their own right, and have obvious potential for mathematical discussions - whether it's to introduce a new concept or to apply some recently-taught ideas. They are just a minute or two at the most in length.

Lots of these I first found via Twitter, and I'd like to acknowledge whoever it might have been (now long forgotten) who forwarded them to me.

You don't need sound for any of these.

Here's the first one:

Cookie cutter

Cookie cutter making machine pic.twitter.com/XyGCn51N0V

— Tool Of The Day (@toolotheday) December 24, 2018

I think you could use this clip with pretty much any age of learner. You could just play the clip and let discussion emerge, or you could ask:

What do you notice? What do you wonder?

Getting students to describe as precisely as they can in words what they have seen can be helpful in getting them talking about it, and mathematical terms might find their way into what they say quite naturally.

If the discussion doesn't take a mathematical turn by itself, you can always ask:

Where is the mathematics here?

or

What do you think is mathematical about this?

For me, this particular clip triggers thoughts about area and perimeter. If you wanted to be more directive, you could ask explicitly:

What does this have to do with perimeter?

There is still lots of room for different comments to be made, even with this level of direction. Someone could start by saying what they understand by the word 'perimeter'. Someone else might say that the perimeter is getting smaller, and then someone else might disagree with that and say that the perimeter is constant, but the area enclosed is getting smaller.

Another way to use the clip would be to introduce the idea of a cookie cutter first, so that everyone knows what one is, bearing in mind that not all children may have had experiences of home baking.

Or you could begin one step back from that, by showing a picture like this:

You could ask what kitchen equipment would be needed to make these, and then how they think cookie cutters themselves are made. Students might have interesting ideas about that - and then you could ask, "Would you like to see a video clip of how they are made?"

Drawing a freehand circle

Here's another example of a clip that never fails to engage students:

Students could come to the board and see if they can do it. If you have an electronic whiteboard, you could record snapshots of their attempts (they could sign their name in the middle of their circle, so that you can tell which one is which). If you have a traditional board, you would need to take a photograph of the board after they have walked away (so that they aren't in the shot), before the board is wiped. Each student gets only one go. Then you can print out some of the best ones (you could get six onto one sheet of A4 paper) and ask:

How can we fairly decide which one is the best circle?

This can go in broadly two directions.

(i) Students think about what measurements they would need to make on the drawn circles. There is a lot of mathematics to consider, and this is not straightforward, because, for instance, shapes with constant width are not necessarily circular. They might suggest covering the drawn circle with accurate circles - maybe sandwiching it between the largest circle that will fit completely inside it and the smallest circle it will fit completely inside, and then finding the difference between the diameters of those two circles, a smaller value representing a 'more circular' circle.

(ii) Students treat it as a statistical project and ask everyone in the class to rank the 6 circles from best to worst. Then they have to think about what to do with these rankings to come up with an overall answer (there are several options here). If they take this approach, to avoid bias they might prefer to obscure the names written in the middle of the circles. Ideally, they might wish to use participants from a different class, who wouldn't have a chance of remembering who had drawn which circle.

Work based on drawing freehand circles could test hypotheses such as that it is easier to draw a large circle accurately than a small one, or that people improve at this the more they do it, or that doing it faster is better than doing it more slowly.

I think that lessons that use activities such as these can be very memorable. The idea that the perimeter could remain constant while the area changes might be referenced by saying, “Remember the cookie cutters?”

If you browse around https://www.youtube.com/ or a site such as https://free-images.com/ you can find all sorts of interesting images and videos that could support this kind of activity. Many years ago, I collected some together myself at http://www.mathematicalbeginnings.com/.

Questions to reflect on

1. Do you have examples of non-expository video clips that you often use?

2. Would you use clips like the ones mentioned here? Why / why not?

3. Which class(es) would you use them with, and how would you use them?