Written by Dan Draper Friday, 07 June 2019
Edited and compiled by Robert J Smith @RJS2212
'Similarity: Clay Tablets, Trigonometry and Pyramids’ ' is a blog preview of Dan Draper's #MathsConf19 session/workshop being run at #MathsConf19.
Proportional reasoning is integral to lots of concepts in number, but are we making the most of this in our geometry teaching? Similarity can often feel like a dry add-on and separate from a lot of the more challenging maths that it underpins; but not only is similarity one of the most powerful concepts in geometry, it’s also one of the most interesting! This session will take you through an introduction to trigonometry by looking at similar triangles and ratios, building on learners’ capacity for proportional reasoning as well as helping you bring the history of maths into your curriculum offer. Beginning with demonstrating different approaches to assessing pupils’ prior knowledge and potential misconceptions of similarity, this session will then look to ancient examples of mathematics with practical ideas and resources to implement in lessons.
Some further thoughts from Dan:
Proportionality. A threshold concept when thinking about number, but how much do we utilise this when teaching shape and space? How many pupils are confident that trigonometric ratios are in fact ratios? How do we anchor trigonometry in something tangible and real without discussing trivial contexts like ladders up walls?In this session we’ll be looking at how the order in which we present questions as teachers provides a narrative for students, and how we can structure the maths we’re presenting to link concepts in maths together in a deep and robust way, but also to expose maths for what it really is: a human endeavour with a rich history of ideas.
In the first part of the session, delegates will categorise and order a series of questions to assess students prior understanding and discuss some thorny questions from students about seemingly simple definitions.
Following this, we’ll go through introducing trigonometry through similar triangles using historical examples of ancient pyramids, and unravelling cuneiform tablets and their place value systems, looking at angles not as a measure of turn against a scale, but as the measure of a turn created when two sides of a right-angled triangle are in a given ratio.
We’ll be look at some of the history of maths, discover some of the stories surrounding the evidence we have for these approaches and try some ancient mathematics ourselves. This session is designed to be a whistle-stop tour through lots of ideas as a starting point for delegates reflections going forward, and all resources will be shared for attendees to use in their schools after the session. I’m always on the lookout for feedback and suggestions for different approaches too.
This session aims to give practitioners time to reflect and discuss a notorious topic for pupils’ conceptual understanding, while giving a concrete example of how to use the history of maths to make the curriculum less relevant to pupils daily lives, but to share with them key developments in the history of civilisation.
You can see Dan Draper speak about "Similarity: Clay Tablets, Trigonometry and Pyramids" during #MathsConf19 at the Penistone Grammar School on Saturday 22nd June
Don't forget in July we also have our 'FREE' Maths Teacher Network events in association with Oxford University Press and AQA.
We look forward to seeing you at our next La Salle Education Event if you don't already, follow us on Twitter @LaSalleEd