seamus barry david webster paula grimley. “mathematics has changed the shape of history. just as...

Mathematics Presentation

Seamus Barry

David Webster

Paula Grimley

“Mathematics has changed the shape of history. Just as literature cannot function without words, so science has no meaning without numbers and mathematical skill.” (Carol Vorderman)

“Pure mathematics is, in its way, the poetry of logical ideas.” (Albert

Einstein)

AimsBuild confidence and understanding for

under confident teachers in mathematics.

Show of hands -“Who is confident in teaching maths?”

Maths is like marmite.

Where to start?

The Basics - Maths is a lot clearer when you have sound knowledge of the basics.

Secure knowledge of number facts, number bonds and counting. Use ITPs and models i.e. number line.

..\..\Desktop\Maths Framework\ITP\ITP\NumberFacts_1_4.exe

“Counting is a pre-requisite for many other mathematical activities.” (Maclelian, E,1993)

Using a known fact a child gives a rapid response based on facts known by heart.

20- 5=15 20- 6=14

Using a derived fact – a child uses a known fact to work out a new one.

Four Key OperationsAddition, Subtraction, Multiplication and

Division.

Underpin all mathematical understanding.

Misconception is to teach these operations as separate entities. All operations are interlinked and knowledge of one can aid acquisition of another.

Interrelationship between operations

Inverse

Addition Subtraction

Repeated Repeated

Multiplication Division

Inverse

Instrumental vs. Relational Richard Skemp suggests two types of learning in

mathematics and these prove the underlying methods of teaching and understanding mathematics; instrumental and relational. Instrumental learning focuses on repetition, reinforcement and revisiting. Relational learning focuses on the links and relationships with real life which gives structure to mathematics. There is an interrelationship between the four operations and the comprehension of the laws of arithmetic.

Addition• Instrumental • 28 + 35 = 63 ----- vertical method• Number line – relational (possibly use £ (pennies).

Counting on.• Which do we advocate?• Commutative Law- the principle that the order of two

numbers in an addition calculation makes no difference to their sum.

• Associative Law – the principal that if there 3 numbers to be added it makes no difference whether you start by adding the first and second or by adding the second and third.

SubtractionSubtraction should be taught alongside addition so thatInstrumental – vertical method Problems- misconception communative law.

9-5 does not equal 5-9Also traditional method is hard to follow. Use number line again. Counting back.

MultiplicationKS1 - Can be seen as repeated addition.7x3=7+7+7Show this on number line.

This works ok with smaller calculations. For KS2- need a method to follow for larger calculations. 345x 52. Grid Method- relational

Distributative – does not matter which order

DivisionKS1 – repeated subtractionNumber line? Or Real life example – cake at a party.

VAK.

KS2 – we advocate chunking method. 250/5 . Number knowledge 5x10=50

Mental Calculation Strategies

Progression. Start with experience and exploration of number, then number facts, then mental strategies with jottings, informal methods to formal/written methods.

“Mental calculation encourages children to use and develop computational shortcuts, and in doing so, they gain a deeper insight into the workings of the number system” (McIntosh, A. 1999)

Practise of mental maths will assist understanding and development of written methods.

ReservationsIs relational learning always better than instrumental.

Example – Timestables – rote learning. Póla & Séamus.

Time constraints, practicality and longevity.Is it boring? Effective T&L – engagement. Competition KS1- Percy ParkerKS2 – Bang Bang Game

Investigation

Conclusion• The aims of this presentation were to build confidence

in mathematical understanding for an under confident teacher.

• 4 operations – simplified methods and ideas for delivery. Highlighted the benefits of a relational approach but also the merits of traditional methods.

• Successful mathematical teaching should integrate both aspects through enthusiasm, engaging and interactive delivery. If you’re not confident and enthusiastic about maths the this will be apparent to and rub off on the children.

“The essence of mathematics is not to make simple things

complicated, but to make complicated things simple.” (S.

Gudder)