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Thoughts on the order of operations

I’ve had a small number of discussions lately about the order of operations. I wrote about it a little in my book on subject knowledge, but, as with everything, there is always more depth to go to (indeed, that’s one of the main messages of the book – if you think you know it all, you need to think again.)

The two questions that prompted the discussion were the following: Continue reading “Thoughts on the order of operations”

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‘Learning Scientists’ Talk and Scheme of Work

Back in June 2017 I wrote an article for the Learning Scientists on how I had started to try to incorporate their Six Strategies for Effective Learning into a maths curriculum and lessons.

A year has passed since then and the work has been continuing. I’ve spoken at two conferences recently on this theme – MathsConf14 in Kettering and researchED Rugby – and have shared a few more practical ideas, including resources we have found useful along the way. Continue reading “‘Learning Scientists’ Talk and Scheme of Work”

The Problem with Education in England

Did you know England tops the world’s league table in rote memorisation? This is, most certainly and without equivocation, a bad thing. There are three main reasons this is a bad thing: Continue reading “The Problem with Education in England”

To talk or not to talk? That is the question.

People have been talking about silence and dialogue lately.

Is silence golden?

Do talking and collaboration improve learning?

Does it matter whether or not pupils talk?

What type of talk is good talk?

This is probably one of those edu-topics that gets people all partisan, so I’m going to nail my colours to the mast and see what happens. Continue reading “To talk or not to talk? That is the question.”

Guest Post for the Learning Scientists

I was very excited to have written a post for the Learning Scientists last month, whose work is fabulous in spreading the word about effective (and ineffective) strategies throughout the teaching community.

I wrote for them about how I created a mathematics scheme of work trying to embed effective learning strategies from the outset.

You can read the post on their blog.

Algebra: you use the letter ‘x’ more than you ever have done in your whole life!

I started my first algebra unit with Year 7 on Monday.  It’s the essentials of algebraic manipulation: adding, subtracting, multiplying and dividing terms, including those with indices, as well as expanding and factorising single brackets, all pretty standard beginnings in algebra.  In the past I think my first lesson on algebra would consist of a brief introduction then some simple collecting like terms.  From what I’ve seen, that’s generally what comes up first in most schemes of work.  This time, though, I’ve tried to be more deliberate and more pedantic over the details.  Really, really pedantic, because it’s insecurity with the small details that causes so many mistakes for the rest of our students’ experience.  I’m starting out by assuming they have done no algebra.  Many of them have done a little but I’m not prepared to risk that all their different primary experiences were the same, or solid.  (This is a not a criticism of primary teachers, more that I want to take sole responsibility for something so important). Continue reading “Algebra: you use the letter ‘x’ more than you ever have done in your whole life!”

Please, no more rubbish about times tables!

The human adult spine has 33 vertebrae, the bones that support the rest of the body.  The lumbar vertebrae, in the lower back, bear the weight of the upper body and are very flexible.  If you have lower back problems, it’s often your lumbar vertebrae that are struggling under the weight they have to bear.

Multiplication is a lumbar vertebra in the spinal column of mathematics.  Multiplication supports the weight of, amongst other things: Continue reading “Please, no more rubbish about times tables!”

Adventures in Mastery 5: Making Connections

I taught my year 7 class today and had the most wonderful time.  I really love my year 7s, they’re so enthusiastic.  So far this year we’ve done place value, rounding, four operations (with natural numbers and decimals), powers, roots and primes, negative numbers, order of operations, fractions (including four operations) and are early into our unit on percentages.  Today it was common FDP conversions (quarters, eighths, fifths, thirds, ninths, etc).

We looked at 1/3 and 2/3, which led us to the fact that 0.999999….. = 3/3, which is, of course, 1.  I love teaching this fact, I tell them I’m about to blow their minds, and when I show them the initial reaction is always something like, “but it can’t be 1, it’s less than 1″.   Continue reading “Adventures in Mastery 5: Making Connections”

Adventures in Mastery 4: Lesson Sequences

In my maths department we are starting on a journey of building a new curriculum based on the principles of mastery.  To find out what mastery is, read Mark McCourt.  Implementing something different comes with all sorts of challenges but, if it’s a good thing to do, it brings benefits too.  One of the benefits I am finding this year is the liberation from the compulsion to produce a three- (or four- or five-) part lesson with objectives and mini-plenaries and some kind of forced activity to (falsely) demonstrate the “progress” my students have made over the course of an hour.  By having a curriculum with clear aims and (hopefully) coherent thinking underpinning every aspect I feel more confident to teach the way I feel will be most effective rather than making my lessons a conflation of lots of “best practice” techniques in order to satisfy a checklist. Continue reading “Adventures in Mastery 4: Lesson Sequences”

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