Firstly, in Singapore it is just called mathematics: not Singapore math or Singaporean style mathematics. Whether you call it Singapore math, math mastery, or something else doesn’t matter. What matters is that Singapore did something with math that made everyone stand up and take notice. Singapore went from obtaining mediocre math scores to the best in the world in a very short period of time — and they’ve maintained that momentum.
Singapore math is three things
- The methods used to teach pupils mathematics in Singapore.
- The books used to teach children in Singapore.
- The professional development that supports teachers.
Methods – Stop Torturing Children and Work With Them Instead
Singapore maths is a method of teaching mathematics which emphasises problem solving. It works with people’s ability to visualise things, recognise patterns and make decisions. It does not resort to rote learning, memorisation or other tedious tactics that put most people off mathematics at a very early age. The goal is to make sure people understand what is going on and that they are not performing procedures that don’t make any sense to them. There is very little reliance on tedious calculations, memorisation and meaningless repetition as those things don’t help anyone to become a thinker; and creating thinkers is the goal.
Books – Didactics Matter
What you learn, how deep you go into the topic and in what order you learn it are all important. Free lessons downloaded from the internet cannot offer this: there is no guarantee that one lesson will lead meaningfully to another. Many schools and teachers rely on freely available lessons from the internet, or cobble together resources from a variety of sources. This approach, because of the lack of continuity from lesson to lesson or from year to year, means that mathematics is reduced to a series of unrelated facts. Meanwhile, Singapore has been producing and refining amazing books (yes, real books!) for 30 years. These books carefully take students through a journey that ensures they are having the right learning experience at the right time, enabling them to make the necessary connections between the different things they have learned. The books are highly scrutinized by the authors, publishers, consultants and the Ministry of Education. This peer review process is a very effective quality control system. People are amazed when I tell them that Singapore schools prefer books over interactive whiteboards in the classroom. The results speak for themselves.
The teacher plays a crucial role in bringing the well-thought-out and well-planned material to life. In order to do so, they should be fully trained in methodologies such as the concrete, pictorial, abstract approach. Knowing how to assess progress continuously and to use that information to vary how lessons are taught is a skill teachers must master. There are many learning theories that have gone into the development of Singapore maths that teachers need to be aware of.
It’s not Just a Trick or Some Gimmick
Some people think it’s all about ‘tricks’. The bar model, the number bond diagrams or using egg boxes or numicon or … Don’t kid yourself, none of these on their own will generate spectacular results. Concrete activities using real objects, loads of drawing pictures and models as well as lots of good-quality discussion is all part of it. Research has proven that this is how people learn new concepts. How these things are presented is just as important. Teaching the bar model to pupils in Year 7 will help them, no doubt, but not nearly as much as if they had benefited from the whole programme from the beginning.
There is very little about the ideas in Singapore maths that are Singaporean. In actual fact most of the ideas come from research undertaken from around the world. Internationally there is no lack of good ideas on how to teach mathematics. There are also countless well-intentioned educators and politicians, many of whom have strong views on how things should be done. Unfortunately, opinions differ or conflict with each other and are heatedly debated — often at the ballot poll.
One of the reasons Singapore has succeeded in turning its education system around is because it put all the politics and egos aside and took a practical approach to making real change.
This is my summary on the key points, which will explain what Singapore mathematics actually are.
Step 1 — Start with the Best Ideas
Two research papers written in the 1980s were the catalyst for change for Singapore in 1983. A UK paper called the Cockcroft report and a US paper called an Agenda for Action both argued that problem solving had to be the emphasis in mathematics education. Experts in education Jerome Bruner, Zoltan Diennes, Howard Gartner and of Richard Skemp all did extensive research on how people learn and this research is the basis for the methods that are used to teach mathematics, no tricks no gimmicks.
Step 2 — Create the Necessary Things to Make it Work
The necessary things are good books and good teacher training. Teacher training is at the heart of the success, with good-quality professional development always high on the agenda. Aspirations, goals and expectations of the learning are clearly laid out and continuously discussed. Carefully crafted books that take all of the above research-based ideas into account are there to ensure that, when teachers perform, the material is there to support them.
Step 3 — Continuous Improvement
Keep improving the material and the methods by measuring the progress and effectiveness of what you are doing, scrutinise the results of any changes and then persistently refine based on the facts you have collected, all the time being vigilant about what others are doing and what works for them.
Singapore’s results in TIMSS and PISA clearly show us that this approach works. Singapore amazed the world in 1995 when they became first in mathematics in the first TIMSS study. Nine years previously they were 16th out of 26 in the 1986 SIS study. How did they do it, and how have they maintain that outstanding performance ever since?