The document discusses developing primary teachers' math skills through professional development programs. It addresses the concept of number sense, which refers to a well-organized conceptual understanding of numbers that allows one to solve problems beyond basic algorithms. Examples are provided for dot arrangements and personal numbers to illustrate number sense strategies. Arithmetic proficiency is defined as achieving fluency through calculation with understanding. The benefits of improved teacher math skills are outlined as developing students' number sense, fluency, conceptual understanding, problem solving and engagement. Examples are given for teaching subtraction and extending students. The importance of understanding over procedural fluency alone is emphasized.
1. ‘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’
3. What is number sense?
The term "number sense" is a relatively
new 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).
4. 1. Dot arrangement
Consider 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?
5. 1.5 10 24670
2 327 6
2. My Numbers
Number of miles on my odometer
Number of sisters I have
How old my car is
Number of cats I’d like to have
My door number
Number of years I lived in my house
6. Arithmetic Proficiency
Arithmetic 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.
7. Arithmetic Proficiency
Arithmetic 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
9. 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?
14. 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?
15. 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?
16. Mathematics in action
What about estimation and justification?
Improving teaching and learning by deepening
understanding
17. Situations seen:
Theme of lesson: Calculate
squares, cubes and roots
Extending the most able: Use
the 6 laws of indices
18.
19. 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.”
