Blog Articles

Thoughts on Mathematics Education

Task Design Considerations

I have turned some of my attention back towards task design.  I started my website in September 2018 thinking I’d have a few hundred tasks by now.  I hadn’t anticipate leaving the classroom later that year!  It’s difficult to find the need to write new tasks when there are no pupils to try them with.  However, I’ve maintained an […]

A Deep Dive: Implementing Mastery Learning

I first heard of mastery learning around 2014.  Back then I thought it was something interesting to do with CPA approaches – it isn’t.  It also seemed to be something which was exclusively to do with countries in South East Asia.  I was surprised to learn that it is an Anglo-American construct, to do with […]

Mastery, Setting & Mixed Attainment

I posted the image above on Twitter recently.  This was a result of my thinking around the practical issues of implementing the curriculum in real schools. The views I express in this article are not popular or fashionable.  I do attempt to be balanced in this blog, although I clearly have a bias.   In this […]

A Progression from Long Multiplication to Algebraic Long Division

I’ve not been teaching (much) over the past 5 months. Instead I’ve been doing copious amounts of reading and a heck of a lot of thinking.  In having the opportunity to step back and think deeply about we do, I’ve found myself questioning teaching and thinking more of the nature of mathematics.  Or should I […]

A Learning Episode: Straight Line

Background I’ve been introducing the idea of straight line to my third year class recently.  This is a topic where I feel that the “just tell them” approach comes crumbling down.  After having taught this topic a dozen or more times, I’ve come to be of the opinion that direct instruction, no-matter how clear and […]

Summative Exams as Formative Devices with Implications

Let’s begin with what I mean by the following:  Summative assessment – is normally based upon a sample of a domain.  This is used for looking at the distribution of pupil attainment at a point in time. Formative assessment – is normally used for identifying what do next.  I’ve previously written at length about the […]

Short Reflection: Decimals, Division and Place Value

I’ve shared a couple of lessons in recent blog posts that went well.  The following is a lesson which I’m much less sure about. With my S2 class who, historically, would be likely borderline National 5 candidates in S5 I’ve been trying to develop their “sense” and “feel” for mathematics.  Much of their appreciation of […]

Revelations in Right Angle Trig – A Learning Episode

The normal introduction I’ve been introducing right angled trig to my S3 class this week.  I think it’s important that pupils realise that sin, cos and tan are not simply buttons on their calculator.  I want them to have a sense of these trig functions as ratios.  I don’t spend a lot of time trying […]

Mastery, rates of learning and closing the gap

In this blogpost I summarise some reading  on mastery learning and make some conjectures about the implications on how our teaching and curricula are planned.  This is not a manifesto for mastery learning and neither is it a rigorous piece of academic writing.  However, I felt that the papers I read had some interesting points […]

Reflections on Using Learner Generated Examples

I use mini whiteboards frequently in my lessons.  I do this to gauge pupil performance in the execution of whatever procedure I am teaching.   As learning takes place in the long term it is impossible to gauge this in any particular lesson, however, if the pupil is unable to execute the procedure correctly then I […]

Some things I’ve come to appreciate…

A weekend of enlightening conversation with John Mason, Anne Watson, Danny Brown and Tom Carson has drawn me to attend to these ideas which, to some extent have been on my mind for the past 6-12 months.  My understanding of pedagogy and mathematics is always evolving Disagreeing with some things I believed in the past is […]

A Mastery Curriculum in Scotland – A review of year 2

A Mastery Curriculum in Scotland – A review of year 2 This is the latest article in a series of blog posts on our implementation of a mastery curriculum from Third Level to Higher mathematics.  Previous installments can be found at: Part 1 – What and why Mastery? Part 2 – Pedagogical Principles Part 3 […]


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