Behind Singapore Maths - Mastery, Whole Class and Kiasu Spirit
Since 2000, PISA’s educational benchmark assessments have provided an insight into how well curriculums are preparing students to apply learnt knowledge in real-life contexts¹.
In an effort to improve outcomes, it’s not uncommon for countries to turn to high-performing nations, borrowing teaching and learning techniques in the quest to further boost their place on the scoreboard.
This is particularly true in the case of Singapore’s success, with the nation’s educational prowess becoming somewhat of a talking point in the education sector. Whilst Singapore’s maths education has been highly revered since the 1990’s², it’s the nation’s more recent PISA success that has put the spotlight back on their education system.
Taking Inspiration From Singapore’s Mathematics Curriculum
On the surface, Singapore’s mathematics curriculum is comparable to those of lower-ranking nations. So what exactly sets their education system apart from the rest?
Unlike countries who still favour traditional rote learning methods of teaching, Singapore has long subscribed to a mathematical freedom model. Creativity is encouraged, generating flexible thinkers with adaptable, transferable and 21st-century applicable skills.
It’s no wonder then, that when faced with the real-world problems of PISA tests, Singaporean students excel. With an education behind them that instils thinking like a mathematician², learners are able to flex their mathematical knowledge and skills, applying them to a variety of contextual problems.
To be able to use mathematics outside of school, it appears critical thinking is, well...critical.
A quick scan down the rankings highlights how larger nations are falling behind when it comes to preparing their pupils for the mathematical demands of modern-day, and future, life. In the case of Australia for example, some critics argue that basic maths is prioritised, but students aren’t being encouraged enough to think critically & deeply³.
Conversely, Singapore’s mathematics isn’t about how much knowledge a student has, but about how they can apply that knowledge. Mathematical mastery is born out of a true understanding of the reasoning behind concepts and methods and this leading nation fosters this through the use of cognitive learning methods and powerful visuals².
In a bid to make an often abstract subject more tangible, Singapore maths prioritises physical objects and visuals ahead of introducing symbols and notation. Objects, such as blocks, allow students to really get to grips with mathematical concepts², with these visuals working to strengthen brain connections⁴.
Singapore’s mathematical success has, not surprisingly, caught the attention of other countries hoping to recreate their results. By utilising the nation’s popular textbooks and implementing comparable teaching techniques, improvements in student outcomes are impressive. From huge leaps in attainments to reclaiming falling averages, Singapore maths continues to be endorsed via the successes of other nations². However, these high expectations are placing strain on parents and, more notably, students.
How Kiasu Culture Negatively Impacts Upon Singapore’s Education System
Kiasu roughly translates to a fear of losing out⁵. It defines the competitive spirits born out of the survival instincts of a small nation. And sometimes more selfish acts exhibited in everyday social transactions such as reserving a table, speaking stereotypically, with a packet of tissues whilst you order. Whilst the nation doesn’t universally subscribe to the notion, kiasu culture is a way of life for many⁵.
Parents are known to exhibit kiasu-like behaviour to ensure their children excel educationally, from spending hours queuing to enrol at prestigious schools, to signing children up to a whole host of after school activities. Extracurriculars centred around learning are common, regularly extending well past school hours⁶. These often eye-wateringly expensive⁷ efforts may well give children an academic edge, but the negative effects on wellbeing are a cause for concern.
Singaporean children’s jam-packed schedules are often born out of the fear of the school segregation system. The country’s academic streams aim to filter students along a learning path suited to their abilities⁶. But with segregation effectively deciding the future fate of children as young as 11, it’s no wonder nervous parents are quick to subscribe their children to intensive after-school study sessions. However, piling on the workload leaves little downtime for children, potentially limiting the development of important social skills⁶.
The truth is, the pressure to succeed academically is felt from a young age. Concerns around mental health are well-founded. A startling number of suicides in Singapore’s youth population, some directly linked to fear of academic failure⁶, has motivated some to speak out about the impact of kiasu culture. The organisation ‘Life Beyond Grades’ is just one example of parents taking a stand against the undue pressures faced by Singapore’s children⁵.
There’s often more than meets the eye when it comes to academic success. Whilst Singapore may be flying high on the league tables, their educational system carries an emotional cost. With all considered, should policymakers turn to a single country’s approach to learning in order to generate maths success themselves?
Looking Beyond PISA Rankings to Reform Mathematics Education
Time and time again, the focus to drive up performance based on PISA rankings fails to consider the bigger picture; that many countries are failing to deliver an appropriate mathematics education for the digital age. Whilst we can learn from high-ranking countries, educational reform is more nuanced than classroom practices alone.
PISA’s 2018 ‘Insights and Interpretations’ report highlights various factors that impact upon student outcomes⁸. By looking through a curriculum-focused lens we run the risk of overlooking the system as a whole. The same is true when poor educational performance is blamed on one specific cause; an approach that often leads to arguments around reform⁸. Instead, a more holistic approach considers how the wellbeing of both students and teachers, as well as access to and implementation of resources and socioeconomic status, impacts education.
For example, Singapore’s success in mathematics is not only due to its approach to learning. The country also works to close gaps in attainment, carefully thinking about how they utilise the resources they have. By sending the best teachers to work with the students who need the most help, Singapore continues to secure its reputation. China, another high-ranking country, has also shown that socioeconomic status does not have to correlate with poorer outcomes, with their most disadvantaged students meeting, or exceeding, OECD averages⁹.
In fact, PISA has found that directing efforts to more disadvantaged learners does not detract from the successes of already high-achieving students⁹. Therefore it’s important to look at gaps in data and implement strategies that address specific populations, rather than applying a whole blanket approach and expecting all outcomes to improve.
Throwing more money at the problem also doesn’t guarantee solutions. PISA noted that there is a threshold to improving outcomes through financial investment⁹. This only goes to further emphasise the intricate nature of education, but this is good news for most. Even where resources are scarce, the collaboration between high and low performing schools and a sharing of resources are factors that will create positive change⁹.
Whilst many people in the education industry are on-board with PISA, the organisation still faces opposition. Whilst non-supporters are acknowledged, PISA continues to drive home the importance of educating students to modern-day standards and demands.
“Some people argued that the PISA tests are unfair, because they may confront students with problems they have not encountered in school. But then life is unfair, because the real test in life is not whether we can remember what we learned at school, but whether we will be able to solve problems that we can’t possibly anticipate today⁹.”
The backlash highlights how some educators are still not considering the nature in which mathematical skills will be applied by students later in life. It’s because of this that PISA has put forward a 21st-century mathematical framework comprising four main focal areas that are pertinent to the maths that exists in today’s society and workplace¹⁰.
A Mathematical Freedom Learning Model
PISA’s framework considers the essential mathematical skills of a 21st-century prepared mathematician. Mapping existing skills to this framework serves as a starting point to upgrade mathematics education to better prepare students for the demands they will face in the future.
Analysing existing curricula against PISA’s benchmark framework highlights key areas to address in order to bring up the standard of all schools. To show this, we’ve taken the end of primary learning expectations of four countries - the UK (England)¹¹, USA¹², Singapore¹³ & Australia¹⁴ - and mapped them to a content matrix based off of the PISA framework’s four content areas.
Whilst the age of which primary level education terminates varies amongst these nations, this transition phase signifies an important benchmark. However, PISA expectations provide a guide to whether policymakers are closing the gap between classroom mathematics and real-world mathematics.
Content Knowledge Matrix: Primary Completion at Age 11+
Whole numbers, fractions, mixed numbers decimals, percentages and ratios
An understanding of place value for both whole numbers as well as fractions and decimals.
Prime numbers, composite numbers, square, cube and triangular numbers
Using number sense, rounding & estimation to find accurate and approximate solutions, which can include decimals
Making connections between equivalent fractions, decimals and percentages
Relationship between fractions and ratios; simplifying & equivalent ratios, using ratio notation & dividing into a given ratio
Recognise units, using correct notation and symbols
Arithmetic four operations with whole numbers, fractions, mixed numbers and decimals with an understanding of the role of brackets.
Understanding percentage increase/decrease; factors and multiples
Exploring relationships between distance, time and speed; changing speed
Expressing relationships using variables and simple equations; finding unknowns by solving simple linear equations and using substitution to further evaluate
Recognise the relationships between numbers and fractions in a sequence; compare & order numbers; understand and use the inverse of operations to check solutions
An understanding of rate in contextual situations & calculating rate
2D Shapes and Patterns: areas, perimeters and other properties of triangles, rectangles, different quadrilaterals and 2D shapes (including circles & composite shapes)
3D Shapes and Patterns: understanding shape properties, finding volume of a cube/cuboid; building different solids from unit cubes and finding volume
Length, Volume, Weight: measuring, comparing and converting to different units using decimals
Space, Position and Direction: translations, enlargements, reflections and rotations of two-dimensional shapes; line and rotational symmetries; angles; four-quadrant coordinate-grid; simple map interpretation
Identify, compare & measure angles; use basic angle properties to find unknown angles; use understanding of angles to recognise regular and irregular polygons
Recognise perpendicular and parallel lines
Data Collection, Display and Interpretation: identify and carry out data collection methods; compare and interpret data using bar charts, pie charts, area charts and line graphs, including interpreting different scales on axes
Data Analysis: explore the concept of variability in a dataset and how that relates to concepts of mean, median and range
Chance: Describe probabilities using fractions, decimals and percentages and recognise mutually exclusive & non-mutually exclusive scenarios.
Chance: Explore chance experiments with both small and large numbers of trials and compare observed frequencies with expected frequencies.
The difference between curriculums, whilst not startling, provides some interesting food for thought. All four countries provide adequate coverage of ‘quantity’ related topics, however, ‘data and uncertainty’ is where most fall short (and why the matrix is lacking in this quadrant).
Reviewing the different curriculums shows that it’s Australia that does the best job at introducing this content area at the primary level. So whilst Singapore and the UK typically rank higher on the PISA scoreboard, we can still look to lower-performing countries who are ensuring to include skills that are important for today’s digital economy.
High achieving Singapore places a greater focus on covering traditional algorithms and geometry compared to the other three nations. It also stands out when it comes to its approach to financial related topics. Whilst all four nations recognise the importance of learning about money, Singapore understands how physical representations of money and play-based learning are integral to solidifying understanding in this area. This is one way in which the country’s curriculum stands out; highlighting ways to introduce concepts, rather than just stating desired outcomes.
Our mapped matrix also shows that the gap between a radically transformed mathematics education and the current status of it isn’t too caught up in the content itself. When mapped out we can see that these four curriculums are hitting on all four key areas. So it appears that bridging the gap lies in the delivery of the above concepts.
A curriculum alone is not enough to tick all the boxes of the requirements of a 21st-century mathematical skillset. In fact, PISA itself stresses the importance of skill development and the use of challenging and context-rich problems in the implementation of its framework¹⁰. Teaching methods and the application of resources, particularly technology, are crucial to aligning with the mathematical freedom model of teaching; where students are encouraged to be creative and think flexibly.
Looking Ahead to Demystify Education Rankings
There’s no doubt that we can learn from top-ranking countries, such as Singapore, however, there’s more to improving outcomes than simply applying the strategies of others. By considering future mathematical demands, we are better able to pave an educational pathway that best serves students.
Innovation is changing the way we use and engage with mathematics, which is why flexible thinking and an adaptable skillset is essential for the 21st-century. PISA recognise this with their framework, hence, policymakers need to review how curriculums, alongside teaching methods and resources, are currently impacting outcomes.
However, student wellbeing is an important part of the puzzle. Strategies to create positive change should also be conducive to student satisfaction and encourage social development, whilst reducing the pressures of academia.
By unpacking the myriad of factors that play a role in education, we can begin to demystify rankings. Educational reform becomes less of a guessing game and more about using proven strategies to instil the skills that truly count.
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