Transcript Engaging Mathematics For All Learners

Embedding Problem Solving in
Our Classrooms: Engaging All
Learners
Lynne McClure, Jennie Pennant, Bernard Bagnall
and Liz Woodham
NRICH Project
Developing Excellence in Problem
Solving with Young Learners
Jennie Pennant’s article suggests we can support
children in becoming competent and confident
problem solvers in three main ways:
• Through choice of task
• Through structuring the problem-solving
process
• Through explicitly and repeatedly providing
children with opportunities to develop key
problem-solving skills
http://nrich.maths.org/10865
EYFS: Tidying
http://nrich.maths.org/early-years
That Number Square!
http://nrich.maths.org/8169
What is the mathematical knowledge
needed to tackle this activity?
What problem-solving skills did you use?
Who would it be for?
Hundred Square
http://nrich.maths.org/2397
What is the mathematical knowledge
needed to tackle this activity?
What problem-solving skills did you use?
Who would it be for?
Rich Tasks
• Have a relatively closed start but offer
different responses and different
approaches
• Invite own questions
• Combine fluency and reasoning
• Reveal/provoke generalisations
• Encourage collaboration and discussion
• Are intriguing
• May be accessible to all (LTHC)
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Low Threshold High Ceiling
• Suitable for whole range
• Low entry point
• Lots of choices in
• method
• response
• recording
• Learners can show what they CAN do,
not what they can’t
• High ‘finish’ possible
Problem-solving Skills
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Trial and improvement
Working systematically
Logical reasoning
Spotting patterns
Visualising
Working backwards
Conjecturing
Mystery Matrix
http://nrich.maths.org/1070
Numbers 212.
Only one
number
used exactly
twice
The Problem-solving Process
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Stage 1:
Stage 2:
Stage 3:
Stage 4:
Getting started
Working on the problem
Going further
Concluding
1. Getting started
try a simpler case
draw a diagram
represent with model
act it out
2. Working on the problem
visualise
work backwards
reason logically
conjecture
work systematically
look for a pattern
trial and improvement
3. Going further
generalise
verify
prove
4. Concluding
communicate findings
evaluate
Coded Hundred Square
http://nrich.maths.org/6554
To Summarise …
We can support children in becoming competent
and confident problem solvers in three main
ways:
• Through choice of task
• Through structuring the problem-solving
process
• Through explicitly and repeatedly providing
children with opportunities to develop key
problem-solving skills
http://nrich.maths.org/10865