Here is part of a standard number line. I might call this a “unitised” number line, showing how many ones I have. One use of this number line might be to assist in the teaching of addition and subtraction of whole numbers. I could also use it to teach multiplication, say by two. For this … Continue reading More Thoughts (and Some Pictures) on Working With Fractions (and Other Numbers). →

In what follows I aim to set down a broad overview of some of my current thinking about fractions. The ideas expressed here are just that: ideas and wonderings that are purely personal and not intended as judgements or pronouncements about other people's views or practice. I don't pretend to speak with any authority and … Continue reading Some Thoughts on Working with Fractions →

I’ve recently been working to develop, among other things, my approach to introducing addition and subtraction of fractions with different denominators. In what follows, I shall outline my current thinking based on work I have done with two different secondary school classes and with a student teacher, Luke Ito, at certain points during the past … Continue reading Adding & Subtracting Fractions: A Learning Sequence →

Recently I’ve come across some posts on Twitter that have led me off in unexpected directions. In short, they have served as prompts for me to ask and pursue answers to questions, processes that have given me both enjoyment and insight into some mathematical ideas and truths. I thought I would share one here. It … Continue reading A series of not unfortunate events: Peaches, pairs, primes and squares →

This article is about some lessons that haven’t happened yet, inspired by a serendipitous realisation during a lesson that has. In a previous post, “No Teachers Are Really Young”, I described some other lessons on graphs of quadratic equations with the same class. That post provides some context for this one and I would recommend … Continue reading You’re Always Realising New Things: Graphs of Quadratic Functions (Part 2) →

I recently began teaching my S1 class (12-year-olds) about volume. This is a topic most of them had met at primary school - they were keen to tell me they knew that Volume = length x breadth x height. In addition, since joining my class, they have learned to find the areas of rectangles and … Continue reading Cuboids: a context for learning →

This is the third instalment of a record of some of my thoughts and actions in response to the #beingmathematical event on November 22 2018, part of series of fortnightly tasks and discussions for maths educators hosted on Twitter by ATM. I will continue to explore the relationships between how both novice and experienced learners … Continue reading My Back Pages – part 3: two triangles make a triangle →

In Part 1 of this article I described my thoughts and actions before and during a recent #beingmathematical session provided by @ATMMathematics on Twitter. In this, Part 2, I shall share some thoughts I had afterwards in response to contributions from other participants in the event. I continue to explore the links between how children … Continue reading My Back Pages – Part 2: two triangles make a square (but not necessarily one with four sides!) →

  Once again I find myself writing about the Association of Teachers of Mathematics and their fortnightly Twitter sessions (@ATMMathematics, #beingmathematical. See my earlier blog entitled "Working with place-value: an increasing constraints activity"). A recent one came on the back of the second meeting of the Glasgow Branch of ATM, organised and hosted by Chris … Continue reading My Back Pages – Part 1: on #beingmathematical and being young (again!). →