But there still remains plenty of confusion. How are the approaches in Singapore and Shanghai different? How are they similar? And where does the UK sit in all of this?
As our Mathematics Mastery programme is based on international practice (and initially inspired by Singapore), we’re asked these questions a lot. This blog is our attempt at a brief overview of the key similarities and differences, broken down into three key areas.
Anyone can become an excellent mathematician. This is the strong belief in both Singapore and Shanghai, which is finally beginning to take hold here in the UK.
Teachers reinforce the attitude that all pupils can achieve high standards, and pupils progress through the curriculum at the same pace.
In Shanghai, the expectation for all students to succeed is so high that setting and streaming do not exist. Tim Oates has discussed how the Shanghai model of differentiation and ability is entirely different to the UK. “All children are assumed to be capable of understanding, and ideas are elaborated in different ways in order to encourage individual understanding.”
In Singapore, pupils are ‘set’ by prior attainment but this is still done very differently to the UK. At secondary, 60% of students follow an ‘Express’ course (high expectations again!) and take the GCE ‘O’ level after four years. A further 25% follow the normal (Academic) course, with the option of spending an additional year then taking the ‘O’ level. Around 15% of students spend five years in secondary education, and take the GCE Normal (Technical).
Note the key difference with current practice here in the UK. In Singapore, the lower attaining students are not prepped for the test at 16, only to experience failure and spend another year preparing for resits. Instead, they take more time to prepare for the exams in the first place.
What’s most fascinating, however, is how the curriculum content for the first two or three years of secondary school is the same – regardless of the student’s set. They study the same mathematics.
In Shanghai, mathematics at both primary and secondary is taught by mathematics specialists who teach one to three 35 minute lessons daily.
Teachers spend the rest of the day planning collaboratively, marking pupils’ work and engaging in teaching research. For pupils who need extra support, teachers also hold regular interventions in small groups to address areas of difficulty and provide pupils with extra practise on the same day.
Teachers are also expected to complete 240 hours of further training every five years.
In Singapore, specialist mathematics teaching is only the norm in upper primary and secondary. Teachers are entitled to 100 hours of professional development every year.
These are both in stark contrast to the UK, where professional development is often ad hoc, and varies widely from school to school.
In Shanghai and Singapore, the curriculum allows significant time to learn each concept or skill. Teaching is underpinned by methodical curriculum design and supported by carefully crafted lessons and resources.
The curricula are designed in a way that promotes mathematical thinking. Enough time can be spent every lesson to go deep into the concepts. In Shanghai, intelligent practice and consolidation play a central role. Carefully designed variation in exercises encourages pupils to look for patterns, to specialise and to generalise.
Procedural fluency and understanding of underlying mathematical concepts are developed in tandem. Again this is in contrast to many UK schools, where a spiral curriculum repeatedly gives surface coverage to many more topics each year
In both Shanghai and Singapore, discussion is valued in the mathematics classroom. In Shanghai, desks are most likely to be arranged in pairs, facing the front. However, the teaching practice is far from the ‘chalk and talk’ style that such a set-up suggests.
The teacher may be mostly stood at the front, but much of the lesson involves the teacher posing a challenging question and asking pupils to discuss it in pairs.
The focus on talk is more obvious in Singapore, where tables and chairs are often arranged to facilitate pupils working in groups. Contrary to popular myth, lessons are varied and engaging.
We spent one memorable afternoon in a secondary school in Singapore walking between eight S3 mathematics classes (Year 10, roughly), all studying trigonometry. Across all eight classes we saw: students at the board explaining their method; students making their own notes; a quiz in teams; a video projected onto the whiteboard; students creating their own questions and students measuring the classroom and calculating to find the length of a diagonal.
All this activity was aimed at deepening students’ understanding, whatever their starting point. It really was impossible to tell (until we spoke individually to students) which set was which.
The most effective representations of abstract mathematical concepts have been carefully considered in both Singapore and Shanghai.
Mathematics teachers in Shanghai use a very visual approach. For each concept, they use a wide variety of visual representations, each with a carefully considered connection to the abstract. In addition to number lines and fraction diagrams (both used fairly often in the UK) Shanghai teachers use diagrams such as arrays and 3-D fraction diagrams.
Singapore’s ‘Concrete, Pictorial, Abstract’ approach takes representation one step further. At primary, dienes blocks and unifix cubes are often used, and sometimes cuisenaire rods. By the start of secondary school, students already have such a strong understanding of the number system that they tend to focus on working in the abstract.
In both Shanghai and Singapore, pupils have access to textbooks in every lesson – but this is rarely the main focus of a lesson. As all teachers follow the same curriculum structure, pupils of the same age are taught the same content at the same time, and the textbooks provide vital guidance for teachers. Teachers in both Singapore and Shanghai look to the textbooks, and the teachers’ guides, to inform their planning.
Students in both Shanghai and Singapore are set mathematics homework. In Shanghai, this typically involves a few daily exercises (as few as five quick questions). In Singapore, teachers set one or two pieces of maths homework each week, much like in the UK.
In the briefest of answers, perhaps it’s not the precise details of one particular approach that makes the difference.
Instead, perhaps it’s the key underpinning belief – a belief in every child, and their potential to succeed in mathematics – combined with a commitment to the professional development of teachers, that makes these countries so successful at mathematics teaching.Back to news list Next article