Post on 05-Dec-2014
description
‘Developing primary teachers’ maths skills… educating not training - a sample of the Primary Maths Programmes funded by the London Schools Excellence Fund
Ruth Williams, Lampton School’
What is number sense?
What is number sense?The term "number sense" is a relativelynew one in mathematics education.
It is difficult to define precisely, but broadly speaking, it refers to
"a well organised conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms"
(Bobis, 1996).
1. Dot arrangementConsider each of the following arrangements of dots.What mental strategies are likely to be prompted by each card?
What order would you place them in according to level of difficulty?
1.5 10 24670
2 327 6
2. My Numbers
Number of miles on my odometerNumber of sisters I haveHow old my car isNumber of cats I’d like to haveMy door numberNumber of years I lived in my house
Arithmetic ProficiencyArithmetic Proficiency: achieving fluency in calculating with understanding
An appreciation of number and number operations, which enables mental calculations and written procedures to be performed efficiently, fluently and accurately.
Arithmetic ProficiencyArithmetic Proficiency: achieving fluency in calculating with understanding
Public perceptions of arithmetic often relate to the ability to calculate quickly and accurately – to add, subtract, multiply and divide, both mentally and using traditional written methods.
But arithmetic taught well gives children so much more than this. Understanding about number, its structures and relationships, underpins progression from counting in nursery rhymes to calculating with and reasoning about numbers of all sizes, to working with measures, and establishing the foundations for algebraic thinking.
Ofsted report – Good practice in primary mathematics
Developing mathematical skills
MISCONCEPTIONS
STRATEGIES
RESOURCES
INCREASED TEACHER CONFIDENCE
IMPROVED PRACTICE
IMPROVED PUPIL OUTCOMES
PROBLEM SOLVING
INCREASED MOTIVATION AND ENGAGEMENT
RESILIENCE & PERSEVERANCE
Mathematics in action
How would you do 672 – 364?
How would you expect to see it being taught?
Would you expect to see the same strategy every time?
Mathematics in action
BALANCE
Procedural Fluency
Conceptual Understanding
INTEGRATION
How would you do 672 – 364?How would you expect to see it being taught? Would you expect to see the same strategy every time?
Developing mathematical skills
NUMBER SENSE AND SKILLS
FLUENCY
STRATEGIES
CONCEPTUAL UNDERSTANDING
TYPICALLY SUCCESSFUL MATHEMATICIAN
Mathematics in action
672 – 364 what next?
Mathematics in action
672 – 364 what next?
How would you extend the more able?
Mathematics in action
672 – 364 what next?
How would you extend the more able?
How can you deepen understanding rather than just increasing procedural fluency?
Mathematics in action
672 – 364 what next?
How would you extend the more able?
How can you deepen understanding rather than just increasing procedural fluency?
What about estimation and justification?
Mathematics in action
What about estimation and justification?
Improving teaching and learning by deepening understanding
Situations seen:
Theme of lesson: Calculate squares, cubes and roots
Extending the most able: Use the 6 laws of indices
Final Thought:
“Asking a student to understand something means asking a teacher to assess whether the student has understood it.
But what does mathematical understanding look like?
One hallmark of mathematical understanding is the ability to justify,
in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from.”