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Preparing lifelong learners for a world of Mathematics . Dr Stephen Sproule Penryn College. Delivery routing. Investment banker. Data Mining. Sports analyst. Encryption. F1 racing. Logistics. Industrial design. Medical research. Fun fair design. Meteorologist. Airline scheduling.
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Preparing lifelong learners for a world of Mathematics Dr Stephen Sproule Penryn College
Delivery routing Investment banker Data Mining Sports analyst Encryption F1 racing Logistics Industrial design Medical research Fun fair design Meteorologist Airline scheduling Computer algorithms Cell phone technologies Astronomer Actuary Prosthetic design Engineers Economist Operations Research Forensics
Why do we need lifelong learners? When in primary school, 25 year olds didn’t have … • iPods: October 2001 • Surgical robots • ‘Friendster’ • GPS for individual use • Kindle • Smart phone frenzy starts • 3-D printing
The all too common story … • Maths was fine until grade 11 • “I don’t know where to start” the question • Primary School and Junior High School • Achieved 80% plus • Obedient • Completed work diligently, following the teacher’s procedures • …. learned in silos, and not how to choose a strategy
Preparing lifelong mathematics learners • Managing the curriculum • Nature of your questions • What? Why? When? • Nature of your classroom • Setting the culture • Building reasoning • Motivating the pupils
Managing the curriculum • Adapt • Deepen • Extend
Wide and shallow curriculum LARGE CONTENT COVERAGE Topic 1 Topic 2 Topic 3 . . . . . Topic 40 One day we go deeper ? ? SHALLOW LEARNING
Deep and narrower curriculum LESS CONTENT COVERAGE Topic 2 Topic 1 Topic 3 . . . . . Topic 18 One day we go deeper ? ? Lifelong learner DEEP LEARNING
Practise what? • Many people say maths involves practise. • Practise a procedure and you get better at it. • Practise reasoning and you get better at it. • You get better at what you practise. • Learning how to start a question is the biggest challenge of all.
Nature of your questions • What? • Knowledge of methods and procedures • Why? • A conceptual grasp of why it works • When? • Deciding when to use a particular strategy • “Stop before you start”
Arithmetic Why? When? What? Calculate: 7 + 0 = 0 + 8 = 8 – 0 = 5 – 0 = Calculate: 7 + 3 = 4 + 8 = 8 – 5 = Calculate: 2 + = 7 m + m = 8 8 – 3 = – 8
Fractions Why? When? What? Why does this statement work? Calculate: Calculate:
Proportion Why? When? What? A baker uses 1800 grams of flour to make 3 loaves of bread. How much flour will he need to make: • 2 loaves? • 7 loaves? Which of the following formulae are direct, inverse proportion or neither? Worksheet …
Number patterns Why? When? What? Determine the sum of the digits in Determine the 40th term in the pattern: 4, 7, 10, 13, …
Geometry Why? When? What? Determine the area of the shaded region Calculate the area of the triangle
It’s about you, teacher! • It’s what you do everyday • Require reasoning: • Select an appropriate question • Let them try it first • Everyday some questions should require decision making • Believe they can, and show it Boy: Um, oh here’s one. 5 take away 5 911 Operator: 5 take away 5. How much do you think that is? Boy: 5
Believe • Believe that your pupils can • Study psychology – my students say so • Expect your pupils to explore and reason • … but this approach is unsettling. • Your encouragement will see them through the tough times. • Their little successes will keep them trying.
