Numeracy and the Needs of Society:
The case of Singapore
Lim-Teo Suat Khoh
National Institute of Education
Nanyang Technological UniversitySingapore

Organisation of Talk
1. Introduction: Working definition ofNumeracy
2. Numeracy and living in the 21st Century(special reference to Singapore)
3. Balancing basic skills and knowledge withproblem solving
4. Conclusion

What is Numeracy?
Edge (2001)
 Ability to use “mathematics facts, skills, processes

and applications essential to daily living and working”
 Numeracy does not seem to include geometry norstatistics
 Mathematical Literacy
 Mathematical Proficiency – competence inknowledge of mathematics and in thinking
mathematicallyNumeracy vs Mathematics“Numeracy is not the same as mathematics, noris it an alternative to mathematics.”“Students need to have quantitative literacy(numeracy) . . . . They also need to masterthe established discipline of mathematics.”(Steen, (2001), Mathematics and Numeracy:
Two literacies, One language)

Comparison between
Mathematics and Numeracy
Discipline ofMathematics

Numeracy orquantitative literacy

 Absolute Messy

 Ideal Contextual Abstract Concrete Pure Practical

School Mathematics
Classical
categorisations
such asarithmetic,algebra,geometry,trigonometry
and calculus

Progression is from
simple to advanced
Builds on previous
concepts
Keeps pace withstudents’ readiness

Acquisition of Numeracy
 Assumption: Learning school mathematics up tocertain level allows the citizen to use schoolmathematics in his daily living.
 Basic arithmetic skills are very necessary and often
learnt at primary schools.
 Secondary school mathematics (arithmetic, algebra,geometry and some statistics) is often meant to
prepare students for further education, to be
grounded in the concepts and processes ofmathematics
 Does numeracy only refer to arithmetic at primarylevel?
 Is such numeracy enough for the modern world?

Numeracy in the 21st Century
 Survival, daily living (basic arithmetic,measurement of space, weight, etc.)
 Understanding data (percentages, rates,data organisation and inferences) Decision making and risk taking (rates vschanges in rates, systematic organisationand processing skills, combinatorics,probability)

Example: Number senseExample: Simple Financial
Transactions and Percentages

Example: Rates and changes in rates

Example: Spatial Skills
Spatial skills are needed for:
 Designing
 Planning furniture arrangements
 Reading maps
 Understanding networks for commuting

Example: Data Inference
Which headline
is correct?
More donations go toreligious groupsorMore people donate toreligious groups

Example: Data Inference A report used highscores achieved bypupils of Gifted
Education Programme
to argue that theprogramme was a greatsuccess.
 This letter to the forum
argues that thecomparisons wereflawed.

The case of Singapore

 A small island nation
 Land area: 690 sq km
 One city
 Population: 4.17 million
 No natural resources

The case of Singapore- Industries andServices Port and shipping Airport
 Oil Refining
 Banking Tourism Electronics
 Telecommunications

Need for educatedpopulation with highlevel of numeracy

The case of Singapore – an efficientand organised defence force Singapore’s defence

force was set up after
independence in 1965
 In recent Tsunami
disaster, SAF organised
relief action to Sumatra.

The case of Singapore

The case for survival: Water Singapore imports mostof its water.
 Water technology isthus extremelyimportant.
 Singapore was inposition to assist theTsunami-disaster areas
with desalination plants
and water dispensers
which takes water fromthe air.

Need for numeracy in daily living even recreation

Better understanding ofchance and probability

Balancing Basic Skills and Knowledge
with Problem Solving and Creativity
Misconception (about 10 years ago)
 East Asian schoolmathematics
emphasised rotelearning and drills inmechanicalcomputation

 Western schoolmathematics
emphasised conceptual
understanding andconstructivist
approaches

Some argue that East Asian nations did well in TIMSS because TIMSS
tested computations rather than creativity and problem solving.

Balancing Basic Skills and Knowledge
with Problem Solving and Creativity
 True: Confucian Heritage cultures (Japan,China, Korea, Singapore) accept that theability to perform routine computations andprocedures is a necessary condition forunderstanding and doing mathematics.
 This ability is also regarded as important
foundation for mathematical problem solving.
 Not true: East Asian countries concentrateon computation drills.

Case 1: Japan TIMSS video study showed that in Japan,

highest amount of engagement inmathematical problem solving wasundertaken.
 Japanese mathematics lessons had students
doing extended problem-solving (openproblems) and learning new concepts throughproblem-solving.
 Level of mathematics expected of students
was very high.

Case 2: China
 The two basics (basic knowledge and basic skills)

provide the foundation.
 Four dimensions are:(a) Calculation speed (leading to efficiency)(b) Memorisation of procedures (even if there is nounderstanding initially)(c) Accuracy in expression (based on logical analysis)(d) Practising with variations (exposure to different
variations of the same concept or process)Zhang & Dai, 2004, ICME-10

Case 2: China
 In China, students are expected to be highly

proficient in computation and manipulation
skills.
 In the 1990s, following Japan’s example,
more and more open-ended problems wereused in mathematics teaching Students were encouraged to find many
acceptable and justifiable answers – thus
developing creativity.

Case 3: Singapore
 Singapore has a centrally controlled education

system.
 All schools follow common syllabus set by theMinistry of Education
 There are nation-wide common examinations at endof primary school (6 years), secondary schools (4years) and junior college (2 years) before university
entrance Since 1990s, mathematical problem solving has
been the central theme of the mathematics syllabus

Framework of Singapore Mathematics Curriculum
Monitoring one’s
own thinking

cognu
itiot
itnAt
MathematicalProblem
SolvingsdeProcesses

Estimation &approximation
Communication
Use of math tools
Arithmetic
manipulationAlgebraic
manipulation
Handling data

MetalslikS

Appreciation
Interest
Confidence
Perseverance

Concepts
Numerical
Geometrical
Algebraic
StatisticalThinking skills
Heuristics

Case 3: Singapore
 Concepts and procedures/skills are

considered basic and very important.
 Students are expected to practice many
variation of the same processes withincreasing levels of difficulties and they are
regularly tested on these.

Case 3: Singapore
 Singapore students are also taught problem-

solving heuristics and thinking skills explicitly
at primary levels.
 Students are exposed to problems which
need combination of maths concepts such as
ratios and percentages.
 High stakes exam at end of primary schools –families put great stress on children to dosuch types of problems intensively throughoutthat year.

Example 1
 Father gave Jason 50 stamps. 16% of themwere from Australia. After Mary gave Jason
more stamps from Australia, the percentage
of his stamps which were from Australia
increased to 30%. How many stamps did
Mary give Jason?

Example 2
 The figure is made up

of overlapping
squares A, B and C.
The ratio of the areasof A to that of B tothat of C is 2 : 4 : 7. If
3/8 of B is shaded,
what percentage ofthe figure is notshaded?

CBASingapore: Contributing Factors forHigh TIMSS Performance One of the contributing factors of Singapore’shigh performance in TIMSS is that Singapore
students regarded doing well in studies asimportant. They had high aspirations “tofinish university”.
 Private tuition and tuition schools (juku) are alarge (unofficial) education industry.
 Schools and homes are well-resourced.
Singapore had the highest Index of Availibilityof School Resources (86 – 88%) compared toInternational Average of (26 – 33%)

Seeking a balance Both China and Singapore are seeking abalance between developing basic skills/knowledge and developing deeper thinking
skills/processes.
 Both are necessary for effective problem
solving.

Seeking a balance Using the idea of foundation may imply that we develop

basic skills and knowledge first and leave the understanding
and real life problem solving processes to later on.
 However, to have better connections to the real world, weneed to move on to encourage real problem solving throughthe processes soon after we teach various computation andmanipulative skills.
 Using the analogy of a pair of chopsticks, we need bothchopsticks to be balanced for our society to have goodproblem-solvers.

Concluding Point 1
 In TIMSS 1995, although East Asiancountries (Japan, Hong Kong, Chinese
Taipei, Korea and Singapore) topped themathematics performance, the students did
not enjoy mathematics as much as thestudents from the western countries.
 Is enjoyment and achievement correlated?
 Do students have to be encouraged to do“hard” mathematics?

Concluding Point 1
 Is the East Asian

culture of giving priority
to common goodagainst individual rights
means that society caninfluence students towork at their studies.
But this is slowly changing.
Students will not learn if thelessons are not motivating.

Concluding Point 1¾ Again a balance¾ Learning must be meaningful and in context
and enjoyable if possible. In TIMSS 2003,
Singapore students’ enjoyment ofmathematics improved significantly overTIMSS 1995 and 1999.
¾ But learning to sacrifice and to work hard andpersevere to learn difficult concepts and solve
difficult problems is also good value tocultivate.

Concluding Point 2
 In Japan and China, the problems used inopen problem-solving could be open insolution methods or answers.
 Generally, they are strong in use ofmathematics and emphasis may not be in“real-life” problem solving.
 Singapore uses a mixture, not with such highmathematics content as China and Japan.
There is move towards using moremathematics in “real-life” situations.

Concluding Point 3
 In East Asian countries, the exam culture isvery well established.
 Students are pragmatic and will work towards
what counts in high stakes exams.
 Since assessment influences teachingapproaches, assessments should movetowards being more “real” and influence theteaching approaches towards nurturing thenumeracy needed for living in today’s world.

Concluding Point 4
 How should we nurture numeracy (number sense,logical thinking, data interpretation, etc)?
 Should we learn mathematics through traditional
topics and in order of difficulty or through the uses ofmathematics as in numeracy for living in an informedmanner in the 21st century? (Steen, 2001)
 Schools teach mathematics as a discipline throughtraditional topics and leave it to higher levels (tertiarycourses) to use the mathematics concepts in usefulapplications.
 Is this too late?

Thank You