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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With the summer term well underway, you might be making plans to welcome September’s new Year 7 cohort to school on induction day. With this in mind, we asked former Leader of English (and parent) Jill Carter what advice she’d give to parents whose children are about to start secondary school for the first time. […]
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With the summer term well underway, you might be making plans to welcome September’s new Year 7 cohort to school on induction day. With this in mind, we asked former Leader of English (and parent) Jill Carter what advice she’d give to parents whose children are about to start secondary school for the first time. […]
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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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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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Having a vision of mathematics, of what is possible in the way of appreciating and comprehending mathematics (distinct from simply gaining facility with arithmetic), is surely an important part of teaching people to think mathematically. One important aspect of mathematical vision is being aware of ubiquitous themes, and one theme that has been impressing itself […]
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In a previous blog post I outlined a very basic memory technique which works by creating a story out of to-be-remembered information. This makes the information more memorable than recalling a list of unrelated words and the technique itself requires no real groundwork, after all, you are just making up a story. Whilst impressive results […]
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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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I am able to commit a huge amount of information to memory in a very short space of time. I can memorise the order of a shuffled deck of playing cards in less than 2 minutes, a list of 240 random words within a 15-minute time limit and, given an hour, I can memorise the […]
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One of my favourite lessons on graphs is when I use the floor of my classroom as the x–y plane. I fix an origin in the middle of the floor (in order to make sure negative coordinates are included). I use masking tape to represent the axes along the floor, with masking tape dashes marked […]
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