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.

Building confidence in maths class with SET!

A few months ago, a friend asked me to look after her 9 year old daughter for an afternoon. I was scrambling for things to do - and rummaging through my cupboards found a deck of cards for the pattern matching game SET!  At the time the young girl was struggling with mathematics, so I wasn't sure how she would take to it, but to my surprise, we ended up playing the game for hours. I knew I was on a winner - I rushed out to the games store and bought three more decks with the intention of seeing what would happen if I tried SET! with a class of teenagers who really disliked being in math class.

SET! is a pattern matching game which initially really hurts your head. Find sets of three cards where for each attribute (shape, colour, quantity and fill),  that attribute is either all the same or all different. Try it online at the New York Times SET! puzzle page.

At first they didn't want to try the game. I didn't force it, but eventually one group of students decided it might be more fun than regular class work and were willing to give it a go.  Working out how to play SET! does take a little time and I wondered how patient they would be with it.  For a while it looked like it might not work, and then suddenly one of my least engaged students - who repeatedly told me she can't do maths - started finding all the patterns. Suddenly the competitive nature of the students kicked in.  Other students started asking to be taught the game.  Over the next few weeks, most of the class was lured into the game.  For higher achieving mathematics classes, you won't need any subtlety to introduce SET! - they will take to it like ducks to water - marvelling at the elegant simplicity of the game that manages to hide so much variation and complexity.

A key feature that makes SET! so engaging is there are many different types of sets (patterns) to find in the deck. Some are fairly easy to spot, others are quite complicated. This means that students at different skills levels of the game can play together - there is something for everyone. Once the weaker students start having success finding the easier patterns, they get more involved and before long most are finding the harder patterns.

Bringing SET! into the classroom gave some students for the first time (I think) a  tangible demonstration they could succeed at challenging mathematical tasks.  They knew it was a game that required skill, patience and some strategy to master, and some of them were absolutely fantastic at playing the game. As a teacher, I was amazed to see students who usually had an almost non-existant attention span, starting intently and silently at a set of cards for minutes at time.  Highly recommended - give it a try!

Teaching Ideas

• Start off by reducing the deck to cards of only one colour. This reduces the complexity of the game by one dimension. Warn the students it will get "much much" harder when you put in the rest of the deck (and it will) - but they will soon be begging for the harder version. When they do get the full deck it will hit them hard - but by now they are hooked :-).  And when they do master the full game - the pay off is sweet.
• Ask the students to describe and name the card attributes. Let them tell you. Ask the students to choose names for the shapes. Once they name the shapes with their names, it becomes their game - use their terminology as you play the game. I like to share the names my 9-year old friend gave them: diamonds, peanuts and airplane windows. And I find using slightly childish names for the counts ("onesies, twosies, threesies") adds to the fun and reduces any stress students may feel about a maths game.
• Have a 15 second time out rule : If one student in the group is finding all the sets, put them on a 15 second timeout to give others a chance to learn the game.
• Go gently. Don't over-emphasise the logic elements - allow students to develop the idea over time that logic and strategy will help them locate patterns more efficiently.  Some lower achieving mathematics students will be intimidated by the game - I found a gentle approach, and allowing them to watch others play worked well. Their friends will encourage them to play - you don't need to. It's wonderful to hear students who initially told you the game looked stupid now encouraging other students to learn it with them.
• Choose your time wisely to discuss pattern finding strategies. Don't rush it - wait until they are really hooked. It doesn't matter it they don't find all the patterns - deal out some more cards. When students are ready for it, I like to rearrange the face up cards into number groups while discuss pattern finding strategies.
• SET! makes a great activity to use a 'group rotation' style activity session where you have different activities at each table and students move around the classroom. You may find SET! takes longer than your other activity and counts for 2 time slots in the rotation (so make two tables).
• Put an interactive SET! game up on your Interactive Whiteboard. Once students have mastered the (physical) card game, try the online version. The New York Times offers 4 SET! puzzles each day, 2 basic and 2 advanced. Invite groups of students to come up to the board and solve them. Could also make a good reward for students who complete work early.
• The SET! website has some interesting mathematics teacher resources about SET!  There are many high quality investigations students of all levels could be encouraged to try out.

Purchasing SET!

• Amazon sells SET! at good prices - around US$12. Unfortunately they will not deliver this product to Australia. In Sydney, Games Paradise (Pitt St) sells them for around AUD$20 - and good to support this friendly and helpful specialist shop.
• One pack will keep around four students occupied. 3-4 packs for a classroom is enough as not all your students will be playing SET! at once.

The gravest sin : favouritism

"You're a great teacher, but you have one problem - you have favourites"

When I read this feedback in the anonymous survey forms from five students I was shocked and disturbed - favouritism is one of the worst things a teacher can do - it distorts and poisons the classroom. What surprised me was that a teacher could have favourites without really being conscious of it. But I knew it must be true when so many students had written this in their feedback. 

It didn't take me long to realise the root cause : as a new teacher with a great class, I've made the mistake of not imposing a strict 'hands-up' rule during whole class discussion - with the consequences that a group of (well intentioned) students have dominated these sessions by calling out. And so week after week, the quieter students at the back of the class have been watching silently, building up the idea I preferred the ones in the front. Did I have favourites? I may not have thought so, but it surely worked out that way.

There's nothing for it when you get feedback like this - an immediate apology is required. I shared with the class my distress at having made this teaching mistake and apologised.  I thanked them for their trust and openness with me - and how grateful I was that they helped me be aware of this problem with my teaching. I was careful to put the blame where it rested - on me - and not on those students thought to be the favourites. I made a committment on their behalf to do better with my classes next year.  By small way of recompense - and as a test for myself to see if I could do it -  I made up a set of thirty "Thank You" cards and wrote a personalised comment to each student, taking care to demonstrate through the comments that I had indeed noticed what they had contributed to the class during the year. 

I'm so grateful my students gave me this feedback, and I really do believe the only reason they told me was because I collected anonymous feedback from them several times throughout the year. Without this framework and trust, students would never have dared tell a teacher about this until it was too late. Without the feedback, I could have blissfully continued unaware making the same mistake for years - building up a reservoir of hurt and misunderstanding along the way.

Was it all bad feedback from this class? Not at all :-)  Overall, the students really enjoyed the year and gave lots of positive feedback and encouragement. But as always - the most valuable feedback is the one that helps you see what didn't see before - appreciate the positive feedback, but it's the uncomfortable feedback that pays the biggest dividend.

Reaching the end of term for 2011? Try some anonymous student feedback - you will be amazed what you discover! Take the plunge - you will never regret it. Every time something special  happens - for the teacher and for the students. See my post on getting student feedback for templates and some suggestions. 

So what can I do better next time to avoid favouritism?

• Use the "hands-down/paddle-pop stick" system for asking questions. I had actually done this for the first month with this class but as we got more comfortable dropped it. Bad decision.
• Enforce "hands-up" for when students want to ask questions. How silly I feel writing this down - it's Teaching 101. I thought I didn't need to do this for this class - they were such enthusiastic students and it felt too authoritarian. Wow did that idealism bite me back!
• Split up or move dominant groups to a less prominent position in the classroom.
• Ask myself : have I visited each group table during this period? Have I asked them questions? Have I given them some of my time today?

End of year maths classes: a precious opportunity

If you live in the Southern Hempisphere and your school is anything like mine, everyone is winding down as the holidays draw near. Final tests and reports are done, and the students have decided there is no more formal learning for the year. I'm sure the same effect happens in the Northern Hemisphere around July. For some teachers the response is to provide 'find-a-word' worksheets or watch an entertaining video. And while it is a struggle to get students in this frame of mind to do any work, I've come to realise this "winding down" period is a fantastic and precious opportunity to do some maths beyond the confines of the standard syllabus. Now is the perfect time to bring out your big gun 'fun' mathematics activities.  

Some ideas for end of year activities

Bring out your concrete maths objects and just let students play: this week my Year 7 students helped me unpack a recently arrived box of 250 GeoShapes.  Once they saw someone construct a dodecahedron, there was pandemonium in the class for the fifty minutes while groups traded, cajoled and bargained to obtain the required 12 pentagons from the surrounding tables: "I need more pentagons!" demanded a student who had never used that word before. Students who didn't have the required shapes tried to build them using other shapes. One group wanted to know why they couldn't make a 3D regular solid with hexagons. I think this class have a better understanding of prisms and polyhedra than when I was actually 'teaching' them the topic.  From what I observed, just letting students 'play' with my concrete object kits, without any overall objective, produced very interesting results. If you feel the students aren't challenging themselves enough mathematically, join a group and ask a few questions, or just quietly construct  something interesting and then walk away. I really think we don't give students enough time to 'play' and get a feel for these mathematical objects.  So this end-of-year 'winding down' time is the perfect opportunity to have some quality play time.  Play helps older students too - I found even my Year 11 students gained benefits from more hands-on time with the concrete objects. 

Don't watch "The Lion King" - share your favorites maths videos and digital interactives: choose the right material and the response can be surprising. I showed my Year 8 a section of Marcus du Sautoy's "The Code" on the mysterious places π turns up. Once the class got over groaning that were going to watch a maths video ("Can't we watch Harry Potter?"), they were quickly drawn into du Sautoy's 'spooky' presentation. "Is this going to be scary, sir?". And they were hooked! The students were riveted by the exploration of how strange and interesting the number π was and demanded to watch more of the video: looking at the mystery of negative numbers and I even let the video keep going into imaginary numbers ("This is Year 12 maths", I said,  but they insisted on watching it). We then zoomed in and out of an amazing digital π poster (π to around 350,000 decimal places) and looked at a Buffon's Needles simulation for generating π.  The questions and conversations this material produced was amazing. Students who previously were bored or disengaged were asking very deep questions about numbers: "How do you know the decimals go on forever without repeating?", "Why is the ratio always π?"  du Sautoy's presentation and the follow up material really had stimulated thinking and wonder about mathematics.

Bring out your maths games :  I'm a huge fan of SET. I never cease to be amazed how students who don't like maths, or say they can't do math problems, can get hooked on SET. The secret is how you introduce the game and ramping up the complexity carefully. (I will write some more about this in a later post).

So - use this precious time - bring out your favorite maths activities, 'toys', games and videos - and very soon you will be wondering why you don't do this through out the whole year!

Still have syllabus content to get through these last weeks? I do! So I'm blending these activities into the new content I still need to teach. I'm doing circumference and area of a circle with my Year 8, hence the selection of π materials.  I have a sense they are going to learn this topic better than many others I did this year because I'm using so much concrete material and interesting, challenging digital material.

At play in mathland

I recently started a separate blog At Play in Mathland to store and share maths problems I like.

Mathland is like Homer Simpson's Land of Chocolate - except with maths.

In words of Seymour Papert, "If we all learned mathematics in math land, we would all learn mathematics perfectly well".

With apologies to Matt Groening.

SBAR with light bulbs and spanners

So how has my experiment with Standards Based Assessment and Reporting been going? Here is the first in a series of reflections.

Half way into my first year using outcomes sheets with my students as the basis for Standards Based Assessment and Reporting, I realised the outcome lists I was making every few weeks were really just a list of skills I expected students to master. When the penny finally dropped that skills were only one part of Working Mathematically, I realised my outcomes sheets had to change.

Here is my first attempt to be different - which I've been doing now with my outcomes sheets for a few months:

Click on the image for a full sized image.

The key idea is to separate outcomes into the categories of the Working Mathematically proficiencies:

A light bulb icon indicates an outcome that requires some new understanding of an important idea.


A spanner icon indicates a skill to be acquired - 'fluency' in the Australian Curriculum description.

A balance scale indicates that a reasoning process is being used.

How has using light bulbs and spanners changed teaching and learning in my classroom?

• Clearly showing the understanding and reasoning outcomes forces me to focus on these important elements. If I find my outcomes sheet for a new topic is full of spanners and no light bulbs or balance scales, I know I've made an unbalanced teaching sequence.
• It sends a clear message to the students that understanding and reasoning are important - it's not enough to just be able to mechanically follow a process to get an answer to an exercise. I will be expecting them to be able to explain and reason.
• Any time during a lesson when I'm about to introduce or consolidate the development of an understanding outcome, I stop for a moment, and point to it on the outcomes sheet, making it very clear to students were are working on a "light bulb" outcome. I emphasise this means it's a time for quality intellectual engagement: thinking, listening and asking questions. While we can get the idea behind a skill outcome by reading a text book, or perhaps watching Salman Khan do it on YouTube, the understanding outcomes are much better learnt interacting with peers and the teacher.

Where is Problem Solving?
The big challenge I'm facing now is how to integrate the problem solving proficiency into a set of outcomes related to a content heavy topic.  What this really reflects is the fact that real problem solving (beyond just "harder skills questions") aren't yet integrated into my content heavy program. For now, I'm experimenting with specific Problem Solving lessons which stand outside the regular content sequence - and that's something I'm going to work on in 2012.

You may notice the outcome sheet above doesn't make provision for recording quiz results - which you would normally see on my sheets. That's because for this course I'm actually not permitted to use SBG, but have to follow a statewide assessment method and schedule. But this doesn't stop me using the idea of standards, or using them for formative assessment. More on this in the next few posts.

In my toolkit: JFileSync

Been a while between posts - school year is getting very busy and as usual I'm trying to do too many things. 

The problem: I have three Windows computers I use all the time, in conjunction with an array of USB portable disk drives. I want to be able to use which ever computer or disk drive I have at the time, while keeping everything in sync. To make thing harder, I don't have admin rights to some of those computers (read: school issued laptop *).

The solution. A free open-source Java application called JFileSync.

Some tips to make the data management painless:

• Nominate a portable USB disk drive as your master data repository. Give it a name - this gives it a distinct identity, helping you form a mental image of the data store as a distinct entity. I call mine 'wombat' - and I have stuck a label on it.
• Carry your portable USB disk drive in a protective case. They are robust, but still vulnerable.
• Don't use a USB memory stick as your master data store - while they are convenient, they are also fragile. I have seen several teachers lose their entire collection of vital documents when their USB memory stick died. Just too fragile - a zap and they are dead.
• Any time I sit in front of a computer, I plug in that drive and immediately run JFileSynch to resynch that computer to the current state of my USB disk drive.
• I work on the computer's local drive.
• When I'm about to leave that computer, I run JFileSyn again to get my USB disk drive up to date.

If I don't have my USB disk drive on me, or I forget the ocassional JFileSync, it's usually fine to just resynch the next time - JFileSync will 'do the right thing'. The only challenge is if I edit the same file on another device - because JFileSynch will not merge files - and then you have to think. Best not to do that.

I've been using JFileSync now for three years and couldn't recommend it highly enough. And as a side benefit, I have four copies of my data in several locations. If worst comes to worst, there should always be a place I can recover my data (barring an asteroid strike on Sydney - in which case I'm dead anyway).

* If you have a NSW DEC laptop: JFileSync is a java app - so you can just put the Java file somewhere on your laptop and run it any time - no install required.