Wormholes and Tesseracts in the Classroom - Part 2

In Part A I looked at some inspiring ideas about teaching in the movie Interstellar. Here are some ideas for using some Interstellar content in the classroom.

Exploring Dimensions: whether you're doing lessons on 2D and 3D solids, or just having a discussion why we say "x-squared" and "x-cubed" but "x-to-the-fourth", it's time to bring out The Tesseract.  In the Interstellar version, it's an object that has spatial and time dimensions: as the main character Cooper moves through space, he's moving into different time "rooms".

"Time is represented here as a physical dimension"
Warning: SPOILER for the film!

My Year 7 students liked this, and were very fast on their internet devices to find more traditional mathematical representations of the tesseract (the hypercube) which made for a good discussion.

Permutations and Combinations: I haven't worked it out yet, but there's definitely a perms and combs activity to do with the CASE and TARS robots! Might link in well with a Quadrilaterals exploration too.

Watch CASE at work on Miller's Planet: 

Some good resources:

http://www.wired.com/2014/11/interstellar-droids/

http://www.businessinsider.com.au/interstellar-how-tars-was-built-2015-3

An exciting way to introduce circular motion:

A nice adjunct to the more classic and sedate circular motion sequences in my other all time favourite movie, "2001: A Space Odyssey".

And for something different, you may like to point your music teacher friends at this mini documentary about the making of the soundtrack:

Wormholes and Tesseracts in the Classroom - Part 1

"You have to go see the film Interstellar", I told my Year 12 class recently, "Maths saves the human race!"  They corrected me immediately:  "No Sir - that's not true, LOVE saved the human race".  Yeah - we have a lot of science fiction movie buffs in our school...

But quibbling aside, what a wonderful resource Christopher Nolan has given with this film. Here are a few highlights that inspired both my teaching and enriched the conversations in class.

Interstellar: Inspiration for Teachers

Need to describe the projection of 4 dimensions into 3 dimensions in under 30 seconds? This explanation of why a wormhole should be a sphere is astoundingly concise (start at 03:00)

Wow! Imagine if we could teach complex content this easily.

Probably the scariest conversation a maths/science teacher could ever hear takes place early in the film - a wake up call to all us! In a four minute sequence, Nolan describes the futility of assigning a single number to measure student success, text book wars and the battle we have on our hands to defend the scientific world view:

So why do I teach? In an astounding sequence, Cooper mumbles muses:

"We used to look up in the sky and wonder at our place in the stars. Now we just look down and worry about our place in the dirt."  

(sequence starts at 3:00)

We need more star gazing. If I can get even one student a year to decide to look at the stars, it's all been worth it.


Part 2: Curriculum links : ways to use Interstellar in your classroom.

(The videos are probably not going to be around for long ... watch them while you can!).

Just change one word

Ever found yourself describing a student or a class to another colleague as "low ability"? It's a shortcut we use more frequently than we may realise, even if said in the most caring, well-intentioned way. Early in my teacher education at Sydney University, I was very fortunate to be given a very simple and powerful idea: change one word.  Replace the word "ability" with "achievement". 

The result may surprise you. Here's my favorite example: next time you hear yourself saying: "Let's save that (interesting, challenging) activity for the high ability class", change it to: "Let's save that (interesting, challenging) activity for the high achieving class". Wow! Would you really want to do that? Changing one word isn't about being politically correct - it's about altering our mindset from a fixed mindset to a growth mindset. When done with awareness, changing one word can make a real impact in your classroom and your school.

It's approaching five years now since I graduated from Sydney University, and this simple idea continues to pay dividends in my teaching. So it seemed only fitting to make it the topic for my presentation at our alumni conference, SUSMAC 2015. 

Presentation slides on Google Drive

With thanks to Judy Anderson and Maria Quigley for organising the conference, and to Eddy Woo for his work to make the conference available on the internet.

For a full set of videos and notes from SUSMAC 2105, featuring a keynote from Andrew Martin, and over 20 short presentations from teachers and preservice teachers, see:

SUSMAC 2015

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.

Updated: 2015 Semester 1 Pi Collection

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.

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

https://drive.google.com/file/d/0ByVkChxwrC4DQ1V3cGJVUEN1UXc/

Changes

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.