Inspiring teaching,
Inspiring learning
Mathematics Workshop 2:
Teachers as creative,
reflective professionals
Charlie Gilderdale
University of Cambridge
December2014
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?
Choose any two digit number, add together both digits
and then subtract the total from your original number…
http://www.flashlightcreative.net/swf/mindreader/
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 website
www.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
info@cie.org.uk
or telephone
+44 (0) 1223 553554
www.cie.org.uk