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 […]

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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 […]

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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 […]

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Exit Cards

Sometimes we are unsure how well a topic has been received or understood by the class.  We don’t want to wait until they can’t do their homework, which you don’t find out about until they come into your next lesson, to do something about this. Collecting a quick snapshot from every student about their level […]

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Subbing zero

Consider x + y = 5 How do you know what this will look like plotted on equal aspect axes?  How do your students know? Some possible ways include: using a graphical calculator display rearranging the equation and plotting three points (including one to ‘make sure’) using one intercept and the gradient of –1 recognising […]

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