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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