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b. The enrichment courses for Secondary School pupils include preparing the higher achieving pupils to handle higher order thinking (HOT) problems, e.g. Mathematical Olympiad problems. Activitity-based learning of Mathematics include allowing pupils to “play” and explore mathematics by giving them more time for hands-on and exploring at their own time own target.

The courses are described below.

1) Enrichment for Primary and Secondary School Pupils

a) Problem Solving Heuristics (Maths Olympiad Training)

b) Activity-based Learning of Mathematics

2) NIE – MOE Workshop for Teachers

a) Teaching of Vectors and Relative Velocity

b) Teaching of Permutations and Combinations

c) Algebra in Elementary Mathematics

d) Algebra in Additional Mathematics

e) Teaching of Additional Mathematics Algebra

f) A-Level Problem Solving Course

g) Calculus in Additional Mathematics

h) Teaching of Calculus in Additional Mathematics

i) Calculus at A-Levels

3) Cluster Workshops on Additional mathematics topics and other topics

a) On Vectors and Relative Velocity

b) On Permutation and Combination

c) General Problem Solving Heuristics (Maths Olympiad Training)

d) New Additional mathematics topics for 2007 Syllabus

e) General Trends for the new Mathematics Curriculum

f) Mathematical Logical Thinking for Teachers on Primary School Mathematical Olympiad

g) How to prepare your students for Mathematics Olympiad

4) Mathematics Professional Development Workshop for Teachers, Sampoerna Foundation, Indonesia

Exploratory Files on GSP

a. Relation between the circumference and radius of a circle. Click here.

GSP Task 1 : click here.

GSP Task 2 : click here.

GSP Task 3(A): click here.

GSP Task 3(B): click here.

GSP Task 3(C): click here.

Activity for the second part of the third day workshop:

This activity only makes sense in relation to the worksheet provided during the lesson.

Refer to the worksheets provided during the lesson. Click here.

5) Teachers’ Workshop at Conferences

a) Problem Solving in A-Levels, during Mathematics Teachers’ Conference 2005 at National Institute of Education

b) Problem Solving in A-Levels, during Asian Mathematics Conference 2005 at National University of Singapore

c) Mathematical Reasoning in Algebra, during Mathematics Teachers’ Conference 2006 at National Institute of Education

d) Using Mathematics to make Decisions, during Mathematics Teachers’ Conference 2008 at National Institute of Education

6) Curriculum Update and Pedagogy Workshop for private tutors from People Association

a) Curriculum Update on Primary School Mathematics Curriculum

b) Pedagogy issues in Teaching Primary School Mathematics

7) Pedagogy for Private Tuition Teachers from SINDA

a) Techniques of Small Group Teaching in Mathematics, 2009

8) Professional Development Courses for Army Officers and Specialists

a) Curriculum Development and Design: Theory and Practice

b) Small Group Teaching

c) Introduction to the Assessment of Learning

PEDAGOGICAL COURSE

These are the courses in NIE offered to the undergraduate students (pre-service teachers) regarding the teaching of Mathematics at both the primary and the Secondary School level.

The courses are described below:

9) PCM513 / PCM 514 : Teaching and Learning of Secondary School Mathematics

QCM520 / QCM521 : Teaching and Learning of Secondary School Mathematics

10) QCM 530 / 531: Teaching and Learning of Secondary School Mathematics at Lower Secondary Level

11) CCM201: Teaching and Learning of Primary School Mathematics

Lecture Notes on Lesson Planning, please click here

Lecture Notes on Learning Theory, please click here

12) QCM540: Teaching and Learning of A-Level Mathematics

MATHEMATICS CONTENT COURSE

These are the mathematics content courses meant for undergraduate Mathematics students.

13) ETM101: Curriculum Content in Mathematics

14) BAM 321 : Mathematical Methods I

15) CAM 334: Analysis I

16) CAM330 / AAM331: Mathematical Methods I

(Semester I in 2006/2007). To download lecture notes, please click here. Password is needed, so please check with me.

Current Research Interest:

The following are my current areas of research.

1) Generalized Riemann integration and its applications to Stochastic Integrals

2) Teaching of Problem Solving at Advanced Level Mathematics

3) In-service Mathematics Teachers’ Content Knowledge

4) Pupils’ Mathematics Self-Concept and Social Climate of Classroom

Members of Professional Bodies

1. Exco member of Association of Mathematics Educators (AME), 2006 - present

2. Assistant Editor, Singapore Mathematics Society (SMS), 2005 – present

Activities associated with the Professional Bodies

a. Judge of the SMS Project Festivals for Secondary Schools, 2004 – 2006

b. Member of SMO (Singapore Mathematical Olympiad) subcommittee, 2005 & 2006

c. Judge of the Sudoku Competitions jointly organized by SMS and PA, 2006

Speaking at Conferences

1. Toh T.L., Henstock-Kurzweil integration and Stochastic Differential Equations, Stochastic Processes and Applications 31, Paris, 2006.

2. Toh T.L., Mathematical Reasoning from O-Levels to A-Levels, Mathematics Teachers’ Conference 2006, National Institute of Education, 2006. (Keynote Address)

3. Toh T.L., On Henstock’s version of Multiple Stochastic Integral, Asian Mathematics Conference, 2005, National University of Singapore.

4. Toh T.L., Use of Geometer’s Sketchpad to teach Mechanics Concepts in Advanced Level Mathematics, ACTM 2004.

5. Toh T.L., Henstock approach to Multiple Wiener Integral, Paper presented at the Symposium on Latest Advances in the Theory of Integration in honour of Professor Lee Peng Yee on his 65^th birthday, 2004.

6. Toh T.L., On Henstock-Kurzweil integration and Integration-by-Parts Formula for Stochastic Integral, Stochastic Processes and Applications 28, Melbourne, 2002.

7. Dong F.M., Lee T.Y., Tay E.G., Toh T.L., Performance of Singapore Junior College Students on Some Nonroutine Problem, Proceedings of EARCOME, 2002

8. Toh T.L., Chew T.S., A Variational Approach to Ito’s Integral, Proceedings of the SAP’s 98, Taiwan, P291-2999, World Scientific, Singapore, 1999.

Some of my Publications (incomplete list):

Refereed Journal Articles

9. Toh T.L., Contextual Approach in Teaching Mathematics: An Example using the sum of series of Positive Integers, International Journal of Mathematics Education in Science and Technology, (accepted for publication)

10. Toh T.L., Chew T.S., On Belated Differentiation and a Characterization of Henstock-Kurzweil-Ito Integrable Processes, Mathematical Bohemica, Vol 130, 2005, P63-73.

11. Toh T.L., On in-service Mathematics teachers' content knowledge on kinematics, Asia-Pacific Forum on Science Learning and Teaching, Vol 6(2), 2005.

12. Toh T.L., Chew T.S., On Henstock’s Multiple Wiener Integral and Henstock’s Version of Hu-Meyer Theorem, Journal of Mathematical and Computer Modeling, Vol 42, 2005, P139 – 149.

13. Toh T.L., Chew T.S., On Ito-Kurzweil-Henstock integral and integration-by-part formula, Czechoslovak Mathematical Journal, Vol 55 (103), 2005, P653 – 663.

14. Toh T.L., Chew T.S., ON Henstock-Fubini’s Theorem for Multiple Stochastic Integral, Real Analysis Exchange, Vol 30, 2004/2005, P295 – 310.

15. Toh T.L., On Application of Vectors to Relative Velocity, International Journal of Mathematics Education in Science and Technology, Vol 35(6), 2004, P906 – 911.

16. Dong F.M., Lee T.Y., Leong Y.H., Tay E.G., Toh T.L., E Wood, Generalization of a Geometry problem, Mathematical Medley, 2004.

17. Toh T.L., Chew T.S., The Riemann approach to Multiple Wiener Integral, Real Analysis Exchange, Vol 29(1), 2003/2004, PP 275-289.

18. Toh T.L., On Using Geometer’s Sketchpad to Teach Relative Velocity, Asia-Pacific Forum on Science Learning and Teaching, Vol 4(2), 2003.

19. Lee T.Y., Tay E.G., Toh T.L., Dong F.M., Multi-proofs of a Geometric Problem, Mathematical Medley, Vol 30(1), 2003, Pp 43-53.

20. Tay E.G., Toh T.L., Dong F.M., Lee T.Y., The Convergence of a Linear Recursive Sequence, International Journal of Mathematics Education in Science and Technology, Vol 35(1), P51-63, 2004.

21. Toh T.L., On Teaching Binomial Series: More Meaning and Less Drill, International Journal of Mathematics Education in Science and Technology, 2002.

22. Toh T.L., Chew T.S., The Riemann Approach to Stochastic Integration using Non-Uniform Meshes, Mathematical Analysis and Applications, 2002.

23. Toh T.L., Chew T.S., Tay J.Y., The Non-Uniform Riemann Approach to Ito’s Integral, Real Analysis Exchange, Vol 27(2), 2001/2002, Pp 495-514.

24. Toh T.L., What is spoken in a Junior College Mathematics Lecture?, Mathematics Educator, Vol 6 No. 2, P113 – 119, 2002.

25. Toh T.L., Chew T.S., On Functional Differential Equations with Unbounded Delay and Henstock-Kurzweil Integrals, New Zealand Journal of Mathematics, Vol 28(1999), P111-123.

Non-refereed Journal Articles related to Mathematics Education

26. Toh T.L., Some issues on Partial Fractions, MathsBuzz, National Institute of Education, May 2006.

27. Toh T.L., Distinguishable and Indistinguishable objects: from combinatorics to Probability, MathsBuzz, National Institute of Education, October 2005.

28. Toh T.L., On Teaching of Vectors and Relative Velocity, MathsBuzz, National Institute of Education, October 2004.

29. Toh T.L., On Permutation and Combination, MathsBuzz, National Institute of Education, May 2004.

Books related to the in-service courses

30. Toh T.L., Algebra Resources for Secondary School Teachers, McGraw-Hill Education (Asia), Singapore, 2006.

31. Toh T.L., Useful Mathematics for Secondary School Teachers, McGraw-Hill Education (Asia), Singapore, 2005.

32. Toh T.L., Teaching of Vectors and Relative Velocity, McGraw-Hill Education (Asia), Singapore, 2004.