Mathematics in Australia and the International Baccalaureate

1. Mathematics in Australia and the International Baccalaureate Roger Brown Head of Research Support and Development, International Baccalaureate Organization.

2. Outline of presentation • Australian Education • 14 to 16 mathematics education • End of high school (18 to 19) mathematics education • International Baccalaureate • Middle Years Programme (MYP) • Diploma Programme

3. Australian Education • Each state responsible for education, governed by National Goals for schooling. • No national curriculum, but K to 10 Curriculum framework • University entrance determined by rank within entire Australian cohort • Integrated mathematics courses Queensland New South Wales Victoria

4. Overview of 14 to 16 education

5. Summary of age 14 to 16 • Secondary school commences at either years 7 (age 12/13) or 8 (age 13/14) • All curriculum follow structure of Key learning Areas • Victoria and Queensland: No end of Year 10 examinations • External examination at end of year 10 (age 16/17) in New South Wales

6. Benefits Breadth of content coverage Encourages wide participation in mathematics School testing can emulate 18/19 award Difficulties Lacking academic rigour Lack of setting of classes of concern to some Comparability between systems Issues for 14 to16

7. Overview of Certification and Assessment at age 18 to 19

8. Summary of age 18 to 19 • Three mathematics subjects in each state • No external written examinations in Queensland • Most popular subject in Victoria; Further Mathematics (Discrete mathematics subject) • Technology requirements in examinations vary between states

9. Benefits Wide participation Statistics based subject of equal value to pure mathematics Moderated coursework important Difficulties Lacking academic rigour University entrance requirements can be problematic Authenticity of moderated course work of some concern Issues for 18/19

10. International Baccalaureate • Three programmes • Primary Years Programme (PYP) • Middle Years Programme (MYP) • Diploma Programme (IBDP)

11. International Baccalaureate Middle Years Programme (age:11 - 16) • Offered in more than 230 schools in over 53 countries (3 in UK) • Approximately 25 000 students world wide • Moderated assessment

12. IB Middle Years Curriculum Model

13. Overview of MYP mathematics education

14. Benefits A curriculum framework not a specification Breadth of content coverage allows for different national systems Not examination driven Criterion referenced Difficulties Academic rigour Dependent on school for assessment Criterion referenced No end of programme examination Issues for MYP

15. International Baccalaureate Diploma • Offered in more than 1300 schools in over 110 countries (44 in UK of which 21 are state schools) • Approximately 100 000 students world wide • Two examination session, May and November

16. IB Diploma Curriculum Model

17. Mathematics in the IB Diploma • Mathematical Studies SL 150 hours over 2 years • Mathematical Methods SL 150 hours over 2 years • Mathematics Higher Level 240 hours over 2 years • Further Mathematics SL (extension for Mathematics HL) 150 hours over 2 years

18. Overview of assessment

19. Benefits Criterion referenced Three languages Caters for all academic levels Not subject to government intervention Designed by teachers Difficulties Elitism and western centric Does not match well with some national systems Criterion referenced Cultural impact on examinations Issues for IB Diploma

20. Further questions and details • Board of Studies New South Wales • http://www.boardofstudies.nsw.edu.au/ • Department of Education Science and Training, Australia • http://www.dest.gov.au/noosr/cep/australia/index.htm • Education Queensland • http://education.qld.gov.au/ • International Baccalaureate Organization • www.ibo.org • Victorian Curriculum and Assessment Authority • http://www.vcaa.vic.edu.au/ • Email: rgbrown@onetel.net.uk

21. NSW School Certificate

22. Sample MYP test questions 1. Let the functions f, g, h, and k be defined by the following rules Give the rules of the functions corresponding to: 2.Using a system of rectangular coordinates illustrate the solution of

23. NSW HSC Mathematics

24. VCE Further Mathematics • Question 3 A serious illness affects the island’s dragon population. The number, Tn, of sick dragons in week n obeys the difference equation Tn+1 = 2 Tn– 11, for n = 1, 2, . . . , where T1 = k. a. If the number of sick dragons in week 2 is 27, find the value of k, the number of sick dragons in week 1. b. How many dragons are sick in week 6? c. Is the sequence generated by the rule for Tnarithmetic, geometric or neither of these? Justify your answer. (November, 2002)

25. Mathematical Studies

26. Mathematical Methods SL

27. Mathematical Methods SL

28. Mathematics Higher Level

29. Further Mathematics SL

30. VCE Mathematical Methods 3. a. Write down an equation in x, the solutions of which give the x-coordinates of the stationary points of the curve whose equation is The diagram shows the curve whose equation is and the normal to the curve at A, where x = 1. b. i. Show that the equation of this normal is y = x – 1.5. ii. Show that this normal is a tangent to the curve at B. Find the exact values of the coordinates of B. c. i. Write down a definite integral, the value of which is the area of the shaded region. ii. Find the area of the shaded region, correct to two decimal places.