Charlie Gilderdale
University of Cambridge
December2014
Mathematics Workshop 2:Teachers as creative, reflective professionals
Inspiring teaching,Inspiring learning
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
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?
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
What questions can we ask?
Triangles in a Square
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…
Now look up your answer on the chart and find the relevant symbol.
Now concentrate on the symbol…
Mind Reader?
Mind Reader?
How do we follow this up?
Always a Multiple?http://nrich.maths.org/7208
What’s Possible?
Give me a whole number…
Why might a teacher choose to use these activities?
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
Tilted Squares
Can you find a quick and easy method to
work out the areas of tilted squares?
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
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
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…?)
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?
Learn more!Getting in touch with Cambridge is easy
Email us at
or telephone +44 (0) 1223 553554
www.cie.org.uk