# Euclid and Sherwood – Anne Watson

When Euclid wrote about ratios of lengths and areas and similarity, without algebra, theorems were dependent on spatial representations. Five diagrams, all related to each other, appear in his text in various places, so I designed a ‘Match the theorem’ task in the manner of Malcolm Swan’s tasks.  There isn’t a one-to-one correspondence and you […]

# Exponentiation by Anne Watson

Exponentiation I was prompted by a recent tweet to think more about exponentiation. The problem being posed was how to convince students that the laws of indices apply even when the exponent is not a whole positive number. There is a deep issue lurking here, which is that the more abstract the mathematics, the less […]

# Deep Mastery

Like almost everyone else in Maths education, I have recently decided to broach the ‘mastery’ word.  It does feel a bit odd to do so, given that it’s been around at least since at least the 60’s, and I’ve never felt a need to use it before – despite having been an advocate of the […]

# Barred for life: Some thoughts about exercise books, rose gardens and bar modelling

Lines, squares or plain? The pages of maths exercise books, I mean. For years I have insisted that pages have to have squares. Without vertical lines as well as horizontal ones how could my students possibly draw all the right-angled triangles and bearing North lines and coordinate axes and so on that I would tell […]

# Building the Maths house: Singapore’s curriculum framework

I thought I’d write today about the framework of Singapore’s School Mathematics Curriculum.  The framework is captured in a well-known diagram that I’ve attached above, and it provoked a lot of interest among teachers when I was last in the UK in November.  This was great to see, because this diagram really is at the […]

# Collaborative Working – the Singapore Approach to Teaching Maths

In November I was in the UK delivering talks on the Singapore approach to teaching secondary mathematics.  While I’ve been delighted to share some of the details of our system during these talks, the real pleasure for me has been to interact with UK teachers and to learn how things are done over here. From […]

# What do students know about functions?

First, a bit of theory about learning.  In 1980, Shlomo Vinner, an Israeli mathematics educator, coined the terms ‘concept image’ and ‘concept definition’ to highlight the difference between what students actually know about a concept and the formal meaning of the concept. David Tall, an English mathematician and educator, is credited with promulgating the term […]

# Starting secondary school: Learning and homework

With the summer term well underway, you might be making plans to welcome September’s new Year 7 cohort to school on induction day. With this in mind, we asked former Leader of English (and parent) Jill Carter what advice she’d give to parents whose children are about to start secondary school for the first time. […]

# Starting secondary school: Pastoral care

With the summer term well underway, you might be making plans to welcome September’s new Year 7 cohort to school on induction day. With this in mind, we asked former Leader of English (and parent) Jill Carter what advice she’d give to parents whose children are about to start secondary school for the first time. […]

# Original Tangents

I want to offer an example of a mathematical exploration which is likely to enrich learners’ appreciation of an apparently unrelated aspect of graphs of functions. Imagine the graph of . Is there a point on the curve at which the tangent passes through the origin? One thing that emerged when I used this with […]