The World Is Maths

Adventures in Mastery 2: Writing a Scheme of Work

This is post 2 in a series.  In post 1 I discussed why we’re beginning a mastery scheme of work, some of my initial objections, and a brief description of “mastery” in its current incarnation.

In this post I will describe the process that produced my scheme of work, and share the working draft of the scheme itself. Continue reading “Adventures in Mastery 2: Writing a Scheme of Work”

Adventures in Mastery 1: Starting Our Journey

When you’ve been in education a while you see plenty of fads come and go and you become carefully cynical about the latest big pronouncement or the new product that’s going to “transform” your practice.  And so it was that I responded (in my mind) when everyone started to talk about mastery. Continue reading “Adventures in Mastery 1: Starting Our Journey”

A Plague On Both Your Houses! (Or ‘Why I Don’t Like Observations and Lesson Plans’)

Over the last [insert large number here] years, the lesson observation and associated lesson plan have been the status symbol of the excellent teacher.  Schools living in dread of the next Ofsted inspection elevated them to their position at the top of the individual’s evidence pile.  For any observation, objectives were set out, detailing what ALL must learn, what MOST should learn and what SOME were lucky enough to learn, the minutiae of every activity and its purpose were described, every instance of cross-curricular/social/moral/cultural learning was noted and, in all probability, everything was colour-coded (ok, I made that last bit up, but it wouldn’t surprise me).

The thing is, this doesn’t really help anybody: Continue reading “A Plague On Both Your Houses! (Or ‘Why I Don’t Like Observations and Lesson Plans’)”

Cognitive Load and Problem Solving

I was asked recently to deliver a training session for two maths departments on the topic of problem solving.  After internally balking (problem solving as a discrete entity is something that gets on my nerves, “problem solving lessons” even more so) I decided it was the perfect opportunity to talk about cognitive load and relate it to the requested topic. Continue reading “Cognitive Load and Problem Solving”

researchED Maths and Science 2016

When Tom Bennett announced researchED Maths and Science I was more than a little bit excited: a subject-specific conference informed by strong academic research?  Yes please!  The programme for the day was packed full of sessions I wanted to see, so selecting which ones was very difficult.  Here’s what happened on my day, a mixture of what I heard with my own thoughts. Continue reading “researchED Maths and Science 2016”

Disillusionment in Schools

This week’s “Most read” top ten on the TES homepage contains the following headlines:

“Teachers work more overtime than any other professionals, analysis finds”
“‘My heart sank when my husband said he wanted to retrain and join me in teaching'”
“‘I dread GCSE and A-level results day because I know my pupils’ results are likely to be flawed’”
“‘This is why running a school has become the impossible job…'”

It occurred to me that it’s very hard to go a day on Twitter without seeing a negative headline.  In truth there are a lot of very disillusioned teachers who like to read about others’ disillusionment.  I meet many such teachers when I do support work in schools and run courses.  I wonder what the main causes of disillusionment and frustration are?  Here’s my first draft list, there’s nothing surprising on here: Continue reading “Disillusionment in Schools”

Relevance Is Not the Goal

Experience has shown, and a true philosophy will always show, that a vast, perhaps the larger portion of the truth arises from the seemingly irrelevant.

Edgar Allan Poe
The Mystery Of Marie Rogêt

In my last post, about the history of mathematics,  I mentioned briefly the mathematician GH Hardy, who was based in Cambridge in the early twentieth century and who was the mentor of Srinivasa Ramanujan, the subject of Hollywood’s latest foray into the world of mathematical genius.  Hardy wrote a wonderful book called A Mathematician’s Apology, in which he discusses the beauty of mathematics and expounds the importance of mathematics for its own sake, rather than for its applications.  Hardy was vociferous in his belief that the most beautiful mathematics was pure mathematics, that which had no applications. It wasn’t that Hardy was against applying mathematics per se, more that true elegance existed in a discipline that was pursued chiefly as a matter of intellectual curiosity, or in the act of creating or discovering something truly new, without the ulterior motive of improving the material lot of humankind. Continue reading “Relevance Is Not the Goal”

Mathematical Stories

Everyone loves a good story. Stories transport us to another time or place and make us think outside of ourselves, question our status quo. The mathematics classroom is not one of the more predictable places to find a good story, but that doesn’t mean there aren’t any.  One of my favourites goes something like this:

The Pythagoreans were an ancient mystical sect, a group of men who wore white robes and spent their days measuring and wondering; wondering at the beauty of nature and the expanse of the cosmos, resolute in their belief that the universe could be explained and deciphered using mathematics. They were masters of geometry and sought to understand the workings of the world by analysing numbers and shapes and the intersection of the two. One of the Pythagoreans’ core beliefs was that any number could be written as the ratio of two others in the way that 6 is 12/2, or 2.333333… is 7/3. This was the gift of the gods, that any number could be expressed through any other. It felt complete, it felt perfect. But for the Pythagoreans, perfection was about to be shattered. Continue reading “Mathematical Stories”

Junk Knowledge

Multiplying fractions is junk knowledge, so the TES told me this week.

That’s junk knowledge that enables someone to work adeptly with number.

That’s adeptly working with number that enables someone to abstract with algebra.

That’s algebraic abstraction that enables someone to understand calculus.

That’s understanding calculus that allows someone to become, say, an engineer.

That’s becoming an engineer that enables someone to design the building (and model and analyse its perfect conditions) that houses the servers on which the TES is located.

All so someone on the TES can call multiplying fractions ‘junk knowledge’.

I thought of lots of loops through mathematical knowledge with this same start and finish. It was quite good fun.

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