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![Page 1: Charlie Gilderdale University of Cambridge December2014 Mathematics Workshop 2: Teachers as creative, reflective professionals Inspiring teaching, Inspiring.](https://reader036.fdocuments.us/reader036/viewer/2022081506/56649ec65503460f94bd1e3e/html5/thumbnails/1.jpg)
Charlie Gilderdale
University of Cambridge
December2014
Mathematics Workshop 2:Teachers as creative, reflective professionals
Inspiring teaching,Inspiring learning
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Build a community of mathematicians
By:
Creating a safe environment for learners to ask questions
Providing opportunities for collaborative work
Valuing a variety of approaches
Encouraging critical and logical reasoning
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Opposite vertices
If I give you a line, can you tell me straight away if that line could be:
• the side of a square?
• the diagonal of a square?
If such squares CAN be drawn, can you find an efficient method for drawing them?
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Triangles in a Square
Here is a triangle drawn on a 5 by 5 dotty grid square by joining the top-right-hand dot to one dot on the left hand side of the square, and one dot on the bottom side of the square
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What questions can we ask?
Triangles in a Square
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Mind Reader?
http://www.flashlightcreative.net/swf/mindreader/
Choose any two digit number, add together both digits and then subtract the total from your original number…
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Now look up your answer on the chart and find the relevant symbol.
Now concentrate on the symbol…
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Mind Reader?
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Mind Reader?
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How do we follow this up?
Always a Multiple?http://nrich.maths.org/7208
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What’s Possible?
Give me a whole number…
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Why might a teacher choose to use these activities?
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Alan Wigley’s Challenging Model (an alternative to the path-smoothing model)
• Leads to better learning – learning is an active process
• Engages the learner – learners have to make sense of what is offered
• Pupils see each other as a first resort for help and support
• Scope for pupil choice and opportunities for creative responses provide motivation
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Tilted Squares
Can you find a quick and easy method to
work out the areas of tilted squares?
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What can we offer learners?
• Low threshold, high ceiling tasks
• Opportunities to exhibit their thinking and refine their understanding
• A conjecturing culture where it is OK to make mistakes
• A careful use of guiding questions and prompts
• Opportunities to practice skills in an engaging way: HOTS not MOTS
• Frequent opportunities for talk (about maths)
• Teachers who model mathematical behaviour
• Teachers who emphasise mathematical behaviours that they wish to promote
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Enriching mathematics websitewww.nrich.maths.org
The NRICH Project aims to enrich the mathematical experiences of all learners by providing free resources designed to develop subject knowledge and problem-solving skills.
Enriching the Secondary curriculum
http://nrich.maths.org/11244
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Think of a topic you’ve just taught,or are about to teach,
and look for opportunities to
• reverse the questions
• look at/for alternative methods
• seek all possibilities
• greater generality (what if…?)
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The next steps
Two weeks with the students or it’s lost……
Think big, start small
Think far, start near to home
A challenge shared is more fun
What, how, when, with whom?
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Learn more!Getting in touch with Cambridge is easy
Email us at
or telephone +44 (0) 1223 553554
www.cie.org.uk