Video helpers in the mechanics classroom

This is the second post in a sequence about teaching the NSW (Australia) HSC Mathematics Extension 2 Mechanics topic. The first post looked at some initial challenges teaching mechanics and ways to use Felix Baumgartner's historic freefall jump in 2012.

How wonderful it is to be teaching in the age of the internet - being able to draw on the work of so many talented and inspirational teachers - and better yet, bring their insights and passion directly into your classroom to share with your students! Like hundreds of thousands of other people, I've been following the work of Derek Muller and his incredible Veritasium YouTube channel for some time, however it's only now that I'm planning lessons for a sequence on mechanics that I get to draw on his work for my mathematics classroom. As I designed my lesson sequence, I was stunned just how well the Veritasium videos fitted into my lesson design. Here are a few ways I think it's going to be a winner to have Derek in my classroom this term.

Misconceptions about falling objects

It's all too easy for students to agree with the statement that every object falls with acceleration g, but do they really believe it? The truth is they don't - not even some students who have studied physics at university. This engaging and challenging video will do the trick:

Introducing force concepts with an interesting problem : dropping a slinky

Choice: draw some boring static diagrams - or watch Derek's intriguing video about dropping a slinky?  No brainer! What I love about this sequence is the way it's designed for deeper teaching and learning: it's not just a passive "sit and watch" session - instead we are presented with an intriguing problem and challenged to decide on a response. I'm certain my students are going to respond enthusiastically - and provide me the perfect hook to introduce free body diagrams as a way to better understand the situation.

Then in the next video we get to watch what happens - and it is surprising!

And then extend the idea in several ways: What if we attached something to the slinky? What if we used a SUPER MASSIVE slinky?

As a side benefit, this video communicates positive messages to students about studying science at University. You'll get to do interesting work, and work with people like Rod Cross.

After the slinky videos, we'll take a look at this excellent discussion of reaction forces - which is also going to support understanding of how to work out free body diagrams:

The next video isn't Veritasium, but so powerful I have to share it. This high definition footage from a camera on the Space Shuttle booster rockets, tracking the rise and fall of the boosters is going to make for a exciting exploration of terminal velocity ( 2,900 mph at timestamp 5:15 down to 220 mph at 6:45)

Again - I want to inspire as well as educate. Maths and science is so much more than school work - it's an exciting and rewarding pursuit - with great career options.

So many videos to choose from. The challenge is to choose videos that serve both the needs of the teacher and the student - the video has to do much more than just entertain in order to justify taking time away from "the regular program". It has to serve the learning goals and promote specific outcomes - as well as being engaging and memorable - a gift that keeps on giving in the classroom.

What makes the Veritasium videos so good in the classroom? It's not just the sheer enthusiasm and fun of the presentations, or the fact they are short and sweet and fit nicely into a lesson segment, it's the fact Derek has grounded them in quality pedagogy. Presenting information in videos as a statement of facts turns out to have very little benefit - most definitely for science content, and quite possibly of limited value for mathematical understanding. If you're a fan of using video for teaching, definitely check out Derek's research work - you might be a little surprised at what he found:

Finally, back on topic, if you dare, this contradictory Veritasium video "Three Incorrect Laws of Motion" would be a wonderful basis for class discussion and perfectly demonstrates what makes a richer educational video - provided there is good support in the classroom (you better really understand the correct laws!).

So thanks Derek for your amazing work and generosity - and welcome into my classroom!

Bringing Marcus du Sautoy into your classroom

I've had a wonderful helper in my classroom during 2011 - although he's totally unaware of it. Whenever I needed a high quality video to explain or demonstrate concepts, or just wanted an entertaining break that was still directly relevant to the mathematics curriculum, it was time to bring Marcus du Sautoy's BBC program "The Code" into my class.  My students absolutely love the program. Without fail, even if I had a class that wasn't in the mood for a maths video, if I could get to them to watch just a few minutes (see teacher tips below), they were hooked.

So why would you want to bring Marcus into your classroom? Apart from his incredible enthusiasm (which students respond to well), he shows mathematical ideas in action, in the real world, in surprising and engaging ways.

Original image from The Code Episode 3 (c) BBC with annotations.
No copyright infringment intended.

Some of the segments show things we should already be aware of as mathematics teachers, but with his (and the BBC's resources) we can actually see them. Other things are so different and quirky you marvel at de Sautoy's ingenuity and inspiration to present the material this way. For teachers interested in making links between mathematics and science, as well as mathematics and critical thinking, The Code has an underlying message of rich and deep significance which at least some of your students will respond to.

Here are some of my favorite sequences:

• Marcus goes to the fish market, asks a very solid fisherman about his day's catch, then pulls out his iPhone to do some calculations and predicts the size of the biggest catch the fisherman ever made. "We call them doormats!" the fisherman beams back. And all with the purpose of showing the number π appears in places not necessarily related to circles!
• The amazing expert bubble blower (my students were thrilled there was such a profession!) who makes a dodecahedron out of bubbles - no kidding!
• An explanation of how Jackson Pollock's art links to fractals. It turns out my students were already making Pollock style pictures in art class, so I'm planning a joint lesson with our art teachers next year to combine the art and the maths.
• Marcus puts his life at risk sitting in the path of a 30kg metal ball. Now there is faith in the accuracy of your mathematics!
• Marcus debunks the myth of the suicidal lemmings. Someone at Disney Studios has some explaining to do!

and there are many more wonders to enjoy.

One challenge with using a program like The Code in a classroom is that it's three hours long - and I'm really not comfortable with students sitting in class passively watching even one full episode at a stretch (in normal circumstances). It's not very good pedagogy and we really don't have the time - the curriculum and teaching program waits for no-one (sadly).  So my approach was to show ten or fifteen minutes segments at appropriate times in the teaching sequence.

The next challenge is to remember which sequences and topics are covered by The Code, and where they appear in the three episodes. During the holiday break I've finally kept a promise to myself:  to catalogue, by syllabus topic (loosely) every segment in The Code, with time sequences so I can quickly get the pieces that I want.  If like me you're a fan of The Code, you might like to download this analysis and fit it into your planning documents.

The Code - Content Analysis

Teaching Tips

• Some classes (especially those who don't like mathematics) will really resist watching a maths video. Probably because they've been forced to watch some hideous videos in the past. For these classes, I make a promise at the start : "Let's watch the first five minutes - if you hate it after that, I'll turn it off". I've never had students turn down watching more of The Code. On the contrary - I have a hard time stoppping the video before the next segment starts - they are hungry for more. Usually I relent for at least one more segment (if I see it's a genuine interest and not a way to avoid work!).
• Does "end of the year" silliness happen at your school after reports are done and the official program is over? Where students end up watching "The Lion King" and "Kung Fu Panda"? No need to put up with that in your class - time to watch a whole episode of The Code. If they have only seen segments, they will enjoy seeing the whole picture. If not, go for it!

Getting The Code

• A Region 2 (UK) DVD is available from the BBC and Amazon UK.
  Excellent news : Region 4 DVD coming to Australia Feb 2012 (thank you SBS!)
• Some extracts are available on BBC You Tube site.
• BBC Online appears to allow UK based browsers access to the program online.  When I visit, I get a "Not available in your area" message . Hear the sound of my teeth gnashing.

If you like using maths documentarys in class, consider also Bronowski's Ascent of Man. I've written a content analysis of his Episode 5: Music of the Sphere in an earlier post.

Inspiration from Bronowski's Ascent of Man

The best ever Christmas present: the full set of Jacob Bronowksi's staggering 1973 BBC series "The Ascent of Man" - a triumphant presentation of science, mathematics and art, delivered with warmth and style by an amazing human being. Unlike some other contemporary BBC series, this series remains fresh and exciting. The only slightly jarring element is the repeated use of "man" rather than "people" - but that's an artifact of the age. 

Jacob Bronwski on the island of Samos, exploring right triangles.

In Episode 5, "The Music of the Spheres", Bronowski reveals the mathematical elephant in its full glory. There is enough material in this one episode to last a full high school mathematics curriculum. I'm hoping my students this year will take some pleasure in watching some of extracts of this episode - we shall see! At the end of this post is a breakdown of the content. If you don't own the DVD, many extracts are available on YouTube.  Here is a wonderful segment on Pythagoras which could easily be extended into a student activity - either using physical media, or with software.

Topics Bronowski covers in Episode 5
with duration and suggested school grade level (using NSW syllabus)

Chapter 1: Pythagoras discovers mathematical relationships of notes of vibrating strings  (7 mins - maths starts at 4 min mark; Year 7/8)
Chapter 2: The nature of right triangles - reflection, rotation and Pythagoras' Theorem (7 mins; Year 8)
Chapter 3: Ptolemy - astronomy and geometry (4 mins; Year 8)
Chapter 4: Rise of Islam and flourishing of mathematics in the middle east (6 mins; Year 8)
Chapter 5: Tesselations at the Alhambra - good exposition of rotations and symmetry (8 mins; Year 7/8)
Chapter 6: Crystals forms - geometric structures in nature - related to symmetry (3 mins; Year 7/8/9)
Chapter 7: East meets West at Toledo: Arabic mathematics and astronomy arrives in Europe (6 mins)
Chapter 8: Geometric perspective (some nudity),  the dimension of time, Kepler orbits, calculus mentioned (8 mins; Year 10)

There is a significant amount of positive coverage of Middle Eastern culture in this episode, which should resonate with some student demographics who might otherwise feel mathematics is always about the Western World.