Wrapping up the course

In this four-week course we covered the following topics.

In week 1, we focused on how certain countries in Asia does well from an international perspective, and presented some possible reasons why this may be the case. We explained how this second course would focus on teaching practice, by presenting concrete tasks and materials from textbook resources, and how to model them as teachers.

In weeks 2 and 3, we focused on two very effective Singapore mathematics teaching methods. In international comparisons, Singapore performs very well. Education experts suggest several reasons for this. As well as strong structures in place for continuing professional development, there also is something special in the way the mathematics is taught.

In week 2 we looked at concrete tasks using the Concrete-Pictorial-Abstract (CPA) approach. This approach builds on ideas from the psychologist Jerome Bruner and describes how mathematical skills and concepts can be taught effectively. This is achieved by starting off with something concrete, then using visualisations and imagery, and finally working towards abstract notations.

In week 3 we then looked at a specific pictorial method, the so-called Bar Model method. This is a visual approach, and the way it is used is itself an example of CPA. It can aid understanding of fractions, ratios and percentages. By modelling and presenting several (sequences of) tasks, and asking you to try them yourself as well, we hope you have managed to create a mental picture of how these techniques could be used in your classroom. The last activity in particular, where you created a task yourself, should have been insightful.

In week 4 we focused on one final Asian maths principle, Variation theory. This shows how tasks can be varied and sequenced in such a way that it further supports learning. You completed several tasks and we then demonstrated how you could explain them in the classroom.

We hope you have enjoyed the course. If you would like to know some more of the research underpinnings these principles, and you haven’t yet done World Class Maths: Asian teaching methods, you could try that course. We would appreciate it if in the next and final step you could give examples where this course has impacted (or you think it will impact in the future) your views and daily practice of mathematics teaching.