Monday, 27 August 2012

Thoughts on 3Act Maths - FOLLOWUP

Last week I posted about a great TED talk on effective story telling and decided to analyse it from the perspective of 3Act maths, so here it is.

The first act:

"It's making a promise to you that this story will lead somewhere that's worth your time."
This is probably what I first liked about the 3Act idea. The first act hooks the students in and it can be extremely effective for engaging them to the end. 101 questions is a really good place to make sure your first act poses the questions you want it to or for finding good first acts.

"A well told promise is like a pebble being pulled back in a slingshot and propels you forward through the story to the end."
This is still something I am trying to master. My 1st acts are still pretty hit and miss at the moment.
To me the perplexity score on 101 questions is a more a measure of how obvious the questions are rather than how intriguing is that first act. I believe the website could be improved by having some sort of way to rate how much you want to know the answer to the question.

"That's your job as a storyteller, is to hide the fact that you're making them work for their meal."
This is particularly true of lower ability sets; pupils' engagement and confidence seems to inversely correlate with the amount of maths you can see in the first act (measurements, formulae, grids, etc.).

The second act:

"It's this well-organised absence of information that draws us in...We can't stop ourselves from wanting to complete the sentence and fill it in."
"The elements you provide and the order you place them in is crucial to whether you succeed or fail at engaging the audience."
This is a really interesting idea to me because it fits in very well with the idea of building up layers of abstraction on to the initial hook. For example, in Act 1 you might start with this image and ask whether pupils think it will go in:

In Act 2 you give them the information and tools they need to work it out mathematically (angles, tangents, power, etc.). My gut instinct says that I should hand out the information as pupils realise they need it, as it feels organic and you're rewarding that pupil for their thought process. There are definitely some questions though, where giving out certain information straight away would turn a rich problem in to a series of calculations, so its definitely something to watch out for.

Here are some tentative thoughts on giving out information:
  • Try to keep pupils at that perfect difficulty level so that pupils feel empowered.
  • Hold off the point where pupils are doing trivial calculations as much as possible.
  • Give pupils the opportunity to work out what they need, even if that doesn't change how the information is given out.
  • Make sure pupils fully understand the problems they've completed before giving out extension tasks.

On the central theme:

"A strong theme is always running through a well-told story."
"Al Pacino's character in "The Godfather,"...his spine was to please his father. And it's something that always drove all his choices."
This is something that I feel is more of a problem in the English system than the U.S. system. In the U.S. (as far as I know) maths is split in to geometry, algebra, pre-calc, etc. classes. In England we just have 'Maths' and when you're jumping from topic to topic I think that students often get lost. I think trying to keep a constant theme, at least for the length of a term, that underlies everything done in class could really help anchor pupils in the point of each lesson.

The problem is that I'm not sure what theme I want to drive my classes forward. I want it to be some central facet of maths or mathematical thinking, rather than 'this term we will look at the maths relating to sport', and I want it to be something that we can refer back to in lessons.

Here are some ideas so far:

"An example would be in "Finding Nemo," in the short tension, you were always worried, would Dory's short-term memory make her forget whatever she was being told by Marlin. But under that was this global tension of will we ever find Nemo in this huge, vast ocean?"
 This idea of having a central theme (I hope) may help keep interest from previous lessons so that pupils come to class ready to be engaged again. At this point its only a theory though.

Other thoughts:

 "And that's what I think the magic ingredient is, the secret sauce, is can you invoke wonder."
 To me, this is the difference between this:
and this:

Its the same question of scale, but the possibility of a 'big' cat spotting in England trumps (for me) working out the size of sombody's shoe (although it can be sold as a CSI technique).