Mathematics and the IB an International Perspective'

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Mathematics and the IB an International
Perspective.

• Overview of IB
• IB and Mathematics
• Portfolio Tasks
• Extended Essay
• TOK
• South East Asia Maths Competition SEAMC
• Helen Adams

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Overview of IB

• Founded in Geneva in 1968
• 2125 schools in 125 countries
• 568,000 students over the three programmes

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The IB Hexagon
Theory of Knowledge (TOK) Extended
Essay (EE) Creativity, Action and Service (CAS)

• Language A1
  Foreign Languages
• Individuals
• and Societies
  Sciences
• Mathematics
  Arts/Electives

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Subjects offered Group 5

• Mathematics Studies Standard Level.
• Mathematics Standard Level.
• Mathematics Higher Level.

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Course Content- Higher Level

• Functions and Equations
• Matrices
• Sequences and Series
• Circular Functions and Trigonometry
• Vectors
• Calculus
• Statistics and Probability
• Complex Numbers
• Option Statistics and Probability Sets and
  Groups Series and Differential Equations

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Course Content Studies Standard Level

• Number, Mensuration
• Sets
• Statistics and Probability
• Algebra
• Co-ordinate Geometry
• Functions
• Trigonometry
• Sequences and Series
• Financial Mathematics
• Logic
• Calculus

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Portfolio Tasks

• Type I Tasks Investigational
• Type II Tasks Modelling

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Portfolio Tasks Criteria

• Notation and Terminology (2)
• Communication (3)
• Mathematical Process (5)
• Results (5)
• Use of Technology (3)
• Quality of Work (2)

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Extended Essay

• How many convex polygons can be made from the
  seven tangram pieces?
• Is there a link between the Golden Ratio and how
  we perceive beauty in nature, with special
  emphasis on the human face and form?
• Theory of probability in Casinos
• Is there a correlation between SAT results and
  school test scores?
• Investigating a model for an optimum lighting
  system

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Theory of Knowledge (TOK)

• Ways of Knowing

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How Do You Know This?

• I know that if the sum of two of the internal
  angles of a triangle equals 110 degrees then the
  third internal angle will be 70 degrees.
• LOGICALLY

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How Do You Know This?

• A candle flame will be extinguished if you cover
  it with a glass jar.
• EMPIRICALLY by observation/use of senses

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How Do You Know This?

• America became independent in 1776
• AUTHORITY

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How Do You Know This?

• The Olympic Games were held in Atlanta in 1996.
• MEMORY

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How Do You Know This?

• When you die you go to heaven
• FAITH

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How Do You Know This?

• How to ride a bicycle?
• PRACTICE

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How Do You Know This?

• The moods of your friends
• ACQUAINTANCE

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How Do You Know This?

• The manufacture of land mines should be
  forbidden.
• MORAL BELIEF

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How Do You Know This?

• What it feels like to be in love?
• INTROSPECTION examination of own feelings

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How Do You Know This?

• That the presenter of this maths workshop feels
  nervous!
• EMPATHY

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How Do You Know This?

• It is wrong to steal.
• CONSCIENCE

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How Do You Know This?

• How to breathe
• INSTINCTIVELY

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TOK and Mathematics

• What is TRUTH in Mathematics?
• Axioms are facts that are assumed to be true a
  statement accepted without proof. Eg if y a and
  x a then y x
• Proof an argument that has no doubt at all
• Theorems

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Paradox

• Let x 1
• Then x² - 1 x 1
• Try substituting x 1 to check this line
• Factorising using the difference of two squares
• (x 1)(x 1) x 1
• Dividing both sides by x - 1
• x 1 1
• Substituting x 1
• 2 1

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Whats Wrong?

• Dividing both sides by x 1 and then using a
  value of x 1 making it a division by zero.

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The Elevator Paradox Gardner (1982)

• Why does it seem that when we are waiting for an
  elevator near the bottom of a tall building and
  wanting to go up, the first elevator to arrive is
  always going down? Also, when we want to go back
  down, why is it the first elevator to arrive is
  always going up?

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Further Information

• www.ibo.org

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South East Asia Maths Competition

• Once a year
• Two teams of three students year 9 or 10
• Three days

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What Happens

• Long-term Questions
• Maths Trail
• Individual Event
• Team Event
• Maths Circus collaborative
• Guest speaker