Mathematical Ability

1
Mathematical Ability

• Jane Russell

2

• Where does our ability for mathematics come from?
• How does this affect our learning of mathematics?
• What causes differences in mathematical ability?

3

• Numbers are the language of science, and yet
  thinking about the world in terms of numbers is
  as natural and as human as talking. To understand
  the world, and our place in it, we need to
  understand our innate gift for numbers.

4
Piaget

• Babies born into world with no understanding of
  number or quantity.
• Concept of number thought to develop around 4-5
  years
• Studies have since shown that Piaget was wrong

5
Innate sense of numerosity

• ability to categorise world in terms of the
  number of things in a collection
• automatic cant help but do so
• even babies can process the number of items in a
  collection, and even have a rudimentary
  understanding of basic laws of arithmetic

6

• Babies shown two puppets, one after the other
  going behind a screen.
• Sometimes, one of the puppets would be removed
  without the baby seeing.
• Screen was removed, and more time was spent
  looking when the number of puppets left behind
  the screen was unexpected.

7
(No Transcript)
8
¼ pie
Whole pie
¼ glass of milk
Whole glass of milk
9

• mathematics as we know it today, has emerged in
  only a few thousand yearswithout requiring any
  modification of the mathematicians genetic
  material!

10
What makes more complex mathematical thinking
possible?

• Our ability for abstract thought
• E.g being able to conceptualise ideas such as the
  past, present and future
• Essentially, language ability has allowed
  mathematics to develop

11
How does this explain why some parts of maths
are more difficult than others?

• Negative numbers

12
Number Line
6 5 4 3 2 1 0 1 2 3 4
5 6
13
You may put a mark before a number, which it
will obey it submits to being taken away from
another number greater than itself, but to
attempt to take it away from a number less than
itself is ridiculous... William Fredn, in his
book, The Principles of Algebra (1796)
14
How does this explain why some parts of maths
are more difficult than others?

• Negative numbers
• Fractions

15
2 3

16
2 3

4 3

17
How does this explain why some parts of maths
are more difficult than others?

• Negative numbers
• Fractions
• Infinity

18
Set of natural numbers paired with the set of
primes
1 2 3 4 5 6 7
2 3 5 7 11 13 17
19
the problem arises because perfectly
comprehensible finite procedures, like adding
one, give rise to infinite collections
20
What is the cause of differences in ability?
21
Which is larger?

• 9 or 8?
• 9 or 2?

22
Impairment to Number Module

• People are slower when answering 9 gt 2 than 9gt8
• Time it takes for a response correlates with the
  time it would take for them to count between the
  numbers out loud
• Use fingers to count

23
Developmental Dyscalculia

• As common as dyslexia amongst school children
• Affects the ability to acquire mathematical
  skills
• Deficit of basic capacity for understanding
  numbers

24
Pupils with dyscalculia

• Have poor number sense
• Fail to see numbers as entities with patterns e.g
  that 8 8x1, and 8 2x4
• Struggle to grasp concept of base ten number
  system