Tuesday, November 11, 2014

The Pi Collection : 50 maths enrichment books for your school libary

A little project I've been working on for the last year with my school librarians: we call it "The Pi Collection".  

We've built a carefully selected collection of around 50 books with maths themes - fiction and non-fiction, in an effort to entice our students to engage with mathematics beyond their regular classroom work.

Officially our idea is to encourage students to read more widely and deepen connections between maths and other subjects, but in truth, we just love having these great books available to share with our students. So, when, for example, we're exploring extra dimensions, we can ask "What if someone built a house in four dimensions?" - and point at the classic Robert Heinlein short story "And he built a crooked house" which just happens to be the library waiting for you to read.  Or when we're talking about equations, and wondering if we could use them to describe everything - point students at the wonderful Isaac Asimov "Foundation" series - every thirteen-year old nerdy boy's dream of running the universe through maths.   Or perhaps someone thinks girls don't math? Well have we got several books in the Pi Collection to show you otherwise!

Along the journey of building the collection, we've discovered books about people who think differently ("Born on a Blue Day"), a terrific manga-style book questioning the inner truth of logic in mathematics ("Logicomix") and short stories about what could happen if you were allowed to divide by zero ("Stories of your life"). And who could forget that the answer to the meaning of life is 42 ("Hitchhikers Guide to the Galaxy") - a book which also has great fun exploring probability - remember the "Improbability Drive"?  Doing permutations and combinations? Well that's just begging for a reference to Arthur C. Clarke's short story "The Nine Billion Names of God".

Nothing however quite had the impact of "The Cold Equations" - this flew off the shelf as soon as we posted it up:

Maths tells our hero he needs to eject his stowaway into space.
His heart tells him otherwise. What decision will he make? 

I was a little worried about the unsubtle appeal  to baser instincts - but hey - anything to get the students reading! And it turns out our English faculty teaches Science Fiction in Year 7 and The Detective Novel in Year 8 - so we made sure to select books in these genres that also had a maths element.  As we expand the collection, we're finding more connections to Geography, History, Science and Art.

We've also included maths extension and enrichment books for curious students who want to go beyond the official high school curriculum. Collections of classic puzzle books, short articles on maths topics as well as some more challenging books. We even snuck in a few that might encourage some students to consider a teaching career (thank your Mr Lockhart!).

The full list is available here. Do you know of any books we should add?

Looking for more maths themed books?  An invaluable resource is Alex Kasman's collation of titles. Some care is required though, because not every book here is suitable for high school students.

Thursday, October 23, 2014

AB Quizzes in the mathematics classroom

Notes and resources for a presentation I gave to the North Sydney Region Maths Association this week:

PowerPoint template for an AB quiz

Author's copy of article in MANSW Reflections - 2013 Conference Issue

Thanks for the invite and feedback - some great ideas from the group to experiment further with the AB Quiz concept.

Saturday, May 10, 2014

Bringing "childishness" into the mathematics classroom

Why would you show a Sesame Street video to a senior Year 12 mathematics classroom? Is there any value is doing paper folding exercises with such a class?  Here's my thoughts on the value of bringing "childishness" into every mathematics classroom - no matter the age group or the current achievement level, presented at a recent conference.

Games played by children and mathematicians
April 23, 2014
University of Sydney, Mathematics Education Alumni 2014 Conference. 

Or just preview the presentation:
Click on the image for the Google Drive document

Sunday, March 9, 2014


It's been a very long time between posts ...

CC-BY-NC Gabriela Ruellan
A very big change has happened in my teaching career - I have become the head of a mathematics department. I have been extremely fortunate to move to a school with a terrific faculty, a very supportive executive team and the most amazing students you could ever hope to teach. 

However even in the most ideal environment, the time pressures on a new head teacher are unbelievable and there is a very steep learning curve. As such, I'm putting this blog into a dormancy period. 

Thank you for your readership in the last few years and hopefully I will be blogging again later in the year.

Monday, October 7, 2013

Fruit vectors: checking for understanding in the mechanics classroom

Here's a small idea I had while teaching mechanics that turned out to have very surprising and fruitful results in my classroom.

So our class has been working on mechanics for a few weeks now, we think we know the basics from a physical and a mathematical view. It's time to look at something harder now: circular motion.  But just before we do that, let's check we really understand.

Can you draw vectors, any sort you like, and tell a story about what is happening here?

.. and this one ....

How about this one?

It was surprising just how much discussion resulted from just these three diagrams, by asking students to draw velocity vectors, acceleration vectors and force vectors - and then tell a narrative in mathematical and in physical terms. Many misconceptions dealt with!

And now for the reward, setting things up for circular motion. What are the acceleration vectors (and hence the force vectors) for this picture?

By the time you have finished working out the vectors it's very clear what is required to move in a circle, even at a constant speed. What I love about this activity is that the students have developed an intuitive mathematical sense for what the result should be even before we start doing the detailed analysis to get the acceleration and force equations.

Resource: Here's a version of the diagrams I gave to students to scribble on:

or get this from Google drive: Thinking about motion (free download)

Sunday, September 15, 2013

MANSW 2013 Presentation

A quick post for those wanting to see a copy of my presentation this morning at MANSW. Thanks to all who attended and gave such enthusiastic support - all the more so given it was 9AM on Sunday morning after a very late night conference dinner!

Three tools: The ABQuiz, the Tracking Sheet, the Feedback Form
September 15, 2013
MANSW 2013 Conference, Terrigal.

Google docs - free download:

Links to the Feedback Form tools:
Feedback Form template (Word doc)
Feedback Form analysis (Excel spreadsheet)

Read it now in Scribd:

Friday, July 12, 2013

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!