Mathematics Curriculum Framework of Singapore SEAMEO-RECSAM and University of Tsubuka Joint Seminar 15-18 Feb 2016 1 Copyright Ministry of Education, Singapore. Section 1 Background Copyright Ministry of Education, Singapore. Background The national mathematics curriculum comprises a set of
documents (called syllabuses) covering the teaching, learning and assessment of mathematics from Grade 1 to 12. There is no separate standards document. Copyright Ministry of Education, Singapore. Background There are 3 broad levels Primary (Grade 1 to 6) Secondary (Grade 7 to 10) Pre-University (Grade 11 to 12) Copyright Ministry of Education, Singapore. Background
At each level, there are different syllabuses, reflecting the choices available in the system. For example, at the secondary levels, there are: Express Normal (Academic) Normal (Technical) Copyright Ministry of Education, Singapore. Background SOURCE: Ministry of Education, Singapore. (2015). Bringing out the best in every child: Education in Singapore. Design Branch, Communications. Retrieved on 11 Feb 2016 from http://www.moe.gov.sg/about/files/moe-corporate-brochure.pdf. Ministry of Education, Singapore Copyright Ministry of Education, Singapore.
Background The syllabuses are reviewed by MOE regularly. Past cycles have been 6 years. The review involves consultations with key stakeholders and partners like teachers, academics, examiners, teacher-trainers. Copyright Ministry of Education, Singapore. Background MOE supports schools in the implementation of the syllabuses. This support includes communication, professional development, approval of textbooks and the development of other
supporting materials. Copyright Ministry of Education, Singapore. Background Each revision is accompanied by a new set of textbooks. MOE invites commercial publishers to produce textbooks and submit them for review. Schools choose textbooks from an approved textbooks list. Most schools use textbooks. Copyright Ministry of Education, Singapore. Background Textbook authors are selected by the publishers. They could be
academics, teachers or former teachers. Generally, students pay for the textbooks, with financial assistance given to those who need help. MOE helps to manage the pricing as part of the review process. Copyright Ministry of Education, Singapore. Background MOE monitors the implementation of the syllabuses through regular contacts with schools, e.g. annual head of department seminars, school visits, focused-group discussion and workshops, and through data available e.g. TIMSS and national examinations.
Copyright Ministry of Education, Singapore. Background Schools conduct both formative and summative assessments to support learning, inform teaching and make decision about progression. Typically, there is an year-end examination for every level from P2. Other modes of assessment beyond pen-and-paper tests are also used. Copyright Ministry of Education, Singapore. Background The national examinations at the end of primary, secondary and preuniversity are based on the national
curriculum. MOE works closely with the Singapore Examinations and Assessment Board (SEAB) to design and develop the national examinations. This follows from every syllabus review. Copyright Ministry of Education, Singapore. Background The strong alignment between the intended curriculum and the national examinations is key to strengthen the fidelity of implementation even as schools have the autonomy to customize and innovate. Copyright Ministry of Education, Singapore.
Section 2 Format of National Curriculum https://www.moe.gov.sg/education/syllabuses/ sciences Copyright Ministry of Education, Singapore. Format of National Curriculum The writing of the national curriculum is largely influenced by the need to communicate the thinking behind the curriculum arising from the review and guided by practical considerations to support teachers so that they can do a good job.
Copyright Ministry of Education, Singapore. Format of National Curriculum The syllabuses have common sections giving an overview of the entire mathematics curriculum, the goals and aims of each syllabus to give teachers to big picture of the curriculum. (p.7) Copyright Ministry of Education, Singapore. Format of National Curriculum The spiral design is used to build the content up from one level to
another. Such an approach also allows for connections to be made across strands. Copyright Ministry of Education, Singapore. 0 3/ 0 3/ 2 0 2 0 Format of National Curriculum The mathematics
curriculum framework is explained in every syllabus to promote a shared understanding of central focus of mathematics education (i.e. problem solving) and the components and broad description of the approaches 19 Copyright Ministry of Education, Singapore. Format of National Curriculum Each syllabus details the content to be taught and learned (year-by-year,
except from grade 9 onwards) and the learning experiences that teachers should create for the target group of students offering the syllabus. Copyright Ministry of Education, Singapore. Format of National Curriculum The inclusion of statements of learning experiences and a process strand is new and is intended to influence the way teachers teach and students learn and to give attention to the development of mathematical processes.
Copyright Ministry of Education, Singapore. Format of National Curriculum General guidance on teaching, learning and assessment is given in the documents. This includes the principles of teaching and learning, the phases of learning, role and practice of assessment. Copyright Ministry of Education, Singapore. Format of National Curriculum The current version evolves and builds on from previous version. This is an important point, because
teachers have tacit understanding and assumptions about the scope based on the description of the content. Copyright Ministry of Education, Singapore. Format of National Curriculum Levels A-level Math (Optional) Content Strands Functions, Graphs, Sequences and Series, Vectors and Complex Numbers
Statistics and Probability Calculus Secondary (Add Math) (Optional) Algebra Geometry and Trigonometry X Calculus
Secondary Number and Algebra Measurement and Geometry Statistics and Probability x Primary Number and Algebra
Measurement and Geometry Statistics x Copyright Ministry of Education, Singapore. Format of National Curriculum The development of content follows a spiral approach, facilitating connections and inter-relationships. An example is the use of algebra in measurement problems. Each strand is revisited and taught with increasing depth.
Copyright Ministry of Education, Singapore. Format of National Curriculum The process strand highlights the important mathematical processes that students should develop in the course of learning. Of particular emphasis is mathematical modelling. Copyright Ministry of Education, Singapore. Format of National Curriculum A Walk Through Secondary Math Syllabus
Adobe Acrobat Document Copyright Ministry of Education, Singapore. Section 3 Direction of Reforms Copyright Ministry of Education, Singapore. Challenges Two big questions in every review Staying relevant Improving learning Copyright Ministry of Education, Singapore.
Direction of Reforms We need to support those who need more help to learn mathematics We need to go beyond knowing to being able to apply mathematics meaningfully We need to support the development of other important 21st century competencies Copyright Ministry of Education, Singapore. Section 4 Recommendations Copyright Ministry of Education, Singapore. Recommendations
To engage different learners To focus on how students learn To develop the capacity to learn on their own Copyright Ministry of Education, Singapore. Key Facts and Figures Half a million students 32,000 teachers 356 schools 173 Primary 155 Secondary and others 33
Copyright Ministry of Education, Singapore. Primary English Mother Tongue Mathematics Science (from P3) Arts Music Civic and Moral Education Social Studies Physical Education Co-curricular activities English, Mother Tongue, Mathematics and Science offered at Standard or Foundation level from P5
Literacy and numeracy Common curriculum to P4 Subject-based banding at P5 Primary School Leaving Examination 34 Copyright Ministry of Education, Singapore. Secondary English Mother Tongue Mathematics Science Visual Arts Music Civic and Moral Education
History, Geography, Literature Home Economics, Design & Tech Physical Education Co-curricular activities Upper Sec Electives All students continue to study English, Mother Tongue, Mathematics, at least one science and one humanities subject Express (4 years to O-level) Normal(Academic) (4 years to N(A) level; +1 year to Olevel) Normal(Technical) (4 years to N(T) level) Flexibility & transfers
35 Copyright Ministry of Education, Singapore. PreUniversity Knowledge Skills & Life Skills General Paper Project Work Co-curricular Activities Civics Physical Education Languages Mother Tongue, Third Language Mathematics & Sciences Mathematics, Physics, Chemistry & Biology, Computing Arts and Humanities
Arts, Economics, Geography, History, Literature, Music Academic subjects offered at H1, H2 and H3 levels Contrasting subject requirement 2-3 years to A-level 36 Copyright Ministry of Education, Singapore. Others Integrated Programme Schools -Started in 2004 NUS High School of Mathematics and Science -Set up in 2005 School of the Arts
-Set up in 2007 School of Science and Technology -Set up in 2010 Integrated Programmes 6 years direct to A-level or IB Enriched programme Specialised Independent Schools Niche programme Customised programme 37 Copyright Ministry of Education, Singapore. Importance of Mathematics
Compulsory up to the end of Secondary education Centrally planned, flexible implementation Options and electives at higher grades Curriculum Levels Per Week %
Primary 3 to 5.5 h 15-27% Secondary 2 to 4 h 12.5-25% PreUniversity 2 to 6 h
6.4-12% Depends on electives and levels 38 Copyright Ministry of Education, Singapore. Mathematics Curriculum Framework Beliefs Interest Appreciation Confidence Perseverance Numerical calculation Algebraic manipulation
Spatial visualisation Data analysis Measurement Use of mathematical tools Estimation Monitoring of ones own thinking Self-regulation of learning Reasoning, communication and connections Applications and modelling Thinking skills and heuristics
Numerical, Algebraic Geometric, Statistical Probabilistic Analytical 39 Copyright Ministry of Education, Singapore. General Aims of Mathematics Education Acquire and apply mathematical concepts and skills; Develop cognitive and metacognitive skills through a mathematical approach to problem solving; and Develop positive attitudes towards mathematics
40 Copyright Ministry of Education, Singapore. Laying a Strong Foundation PRIMARY MATHEMATICS 41 Copyright Ministry of Education, Singapore. Aims Acquire mathematical concepts and skills for everyday use and continuous learning in mathematics; Develop thinking, reasoning, communication,
application and metacognitive skills through a mathematical approach to problemsolving; Build confidence and foster interest in mathematics 42 Copyright Ministry of Education, Singapore. Primary Whole numbers Fractions Decimals Four operations Rate, Ratio, Proportion
Time Money Length, Area, Volume and Mass Basic shapes and properties Direction Symmetry Spatial visualisation Reading from picture graphs, bar graphs, line graphs, pie charts Three strands Number and algebra Measurement and geometry Statistics Word problems
Algebra without symbol 43 Copyright Ministry of Education, Singapore. Differentiation at Upper Primary Primary 5 & 6 Standard Mathematics Percentage, Ratio and Speed Area and Volume Data and graph Geometry Algebra Primary 5 & 6 Foundation Mathematics
Re-visit some of Primary 14 content Percentage Area and Volume Data and graph Geometry Primary 14 Number concepts and operations Measurements (length, mass, time, angle, area, volume etc.) Basic shapes Data and graphs 44 Copyright Ministry of Education, Singapore. Building up strengths
SECONDARY MATHEMATICS 45 Copyright Ministry of Education, Singapore. Different Syllabuses 3 syllabuses O-Level N(A)-Level N(T)-Level N(A) O N(T) N(A) Electives at upper secondary 46 Copyright Ministry of Education, Singapore.
Aims O and N(A) Math Acquire mathematical concepts and skills for continuous learning in mathematics and to support learning in other subjects; Develop thinking, reasoning, communication, application and metacognitive skills through a
mathematical approach to problem solving; Connect ideas within mathematics and between mathematics and other subjects through applications of mathematics; and Build confidence and foster interest in mathematics. N(T) Math For students who are bound for postsecondary vocational education to: Acquire mathematical concepts and skills for real life, to support learning in other subjects, and to prepare for vocational education; Develop thinking, reasoning, communication, application and
metacognitive skills through a mathematical approach to problem solving; and Build confidence in using mathematics and appreciate its value in making informed decisions in real life. 47 Copyright Ministry of Education, Singapore. O and N(A) Math Numbers and their operations Ratio and proportion Percentage, Rate and speed Algebraic expressions and formulae Functions and graphs
Equations and inequalities Set language and notation Matrices Angles, triangles and polygons Congruence and similarity Properties of circles Pythagoras theorem and trigonometry Mensuration Coordinate geometry Vectors in two dimensions Data Analysis Three Strands Numbers and Algebra Measurement and Geometry Statistics and
Probability Problems in real-world contexts 48 Copyright Ministry of Education, Singapore. N(T) Math Numbers and their operations Ratio and proportion Percentage, Rate and speed Algebraic expressions and formulae Functions and graphs Solutions of equations Angles, triangles and polygons Symmetry, congruence and similarity
Pythagoras theorem and trigonometry Mensuration Data Analysis Probability Problems derived from realworld contexts Three Strands Numbers and Algebra Measurement and Geometry Statistics and Probability Real-world contexts Geared towards vocational training 49
Copyright Ministry of Education, Singapore. Elective for Math O & N(A) Additional Math For students who have an aptitude and interest in mathematics to: Acquire mathematical concepts and skills for higher studies in mathematics and to support learning in the other subjects, in particular, the sciences; Develop thinking, reasoning and metacognitive skills through a mathematical approach to problem solving; Connect ideas within mathematics
and between mathematics and the sciences through applications of mathematics; and Appreciate the abstract nature and power of mathematics 50 Copyright Ministry of Education, Singapore. O and N(A) Add Math Algebra Equations and inequalities Indices and surds Polynomials and Partial Fractions Binomial expansions Power, Exponential,
Logarithmic Modulus Functions Geometry & Trigonometry Trigonometric functions, identities and equations Coordinate geometry in two dimensions Proofs in plane geometry Calculus Differentiation and integration Upper secondary elective Extension of algebra and trigonometry Introduction of calculus
Valued by preuniversity and polytechnics 51 Copyright Ministry of Education, Singapore. Gearing for University Education PRE-UNIVERSITY MATHEMATICS 52 Copyright Ministry of Education, Singapore. Aims H2 for Math, Science & Engineering H1 for Business & Social
Sciences H3 for those with passion and aptitude for Math 53 Copyright Ministry of Education, Singapore. A-level Math H1 and H2 Functions and graphs Sequence and Series Differentiation and Integration Inferential Statistics hypothesis testing, correlation Probability Combinatorics
H3 MOE-Combinatorics, Differential Equations, Functions and Graphs NUS-Linear Algebra NTU-Numbers and Matrices H1 2h per week H2 4h per week H3 can be taken with H2 Common element of H3 Proof, modelling & applications Graphing calculators High participation
54 Copyright Ministry of Education, Singapore. 2013 Mathematics Curriculum, Thinking Behind REVIEW OF MATH CURRICULUM 55 Copyright Ministry of Education, Singapore. 2013 Curriculum Centrally driven Extensive consultation One steering committee Six working committees
> Primary > O and N(A) > N(T) > O and N(A) Additional Math > H1 and H2 > H3 Six Consultative groups Engaging teachers in pre- and post-draft discussion Environmental scan TIMSS Findings Examination and impact on learning Part of scheduled review Improve teaching and learning
Support the development of 21st Century Competencies Other curriculum-wide initiatives 56 Copyright Ministry of Education, Singapore. 2013 Curriculum Learning to learn 21st century skills Real understanding, not just examination preparation More opportunities for students
to reason, communicate, make connections and apply Experience mathematical modelling Be a critical and creative user of mathematics Explicit listing of learning experiences Students should have the opportunities to ... Strengthen mathematical processes Learning outcomes and experiences Little change in content Influence teaching
and learning 57 Copyright Ministry of Education, Singapore. Textbooks and Resources Tap on creativity of publishing industry Quality and variety Textbook authorisation process > Invitation to publish > Briefing to publishers > Feedback on conceptual framework > Forming review panel > Provisional approval or rejection
> Final approval > Listing of textbooks Whole process takes about 12 months for each level submission Textbooks influence teaching and learning Best form of support for teachers Align with curriculum changes Other resources from MOE 58 Copyright Ministry of Education, Singapore. National
Examinatio ns PSLE by Singapore Examinations and Assessment Board (SEAB) O, N(A), N(T) and A-levels by SEAB and Cambridge International Examinations (CIE) SEAB part of review committee Joint development of specimen paper Approximate 12 months to complete High stake examinations at P6, S4/5 and Pre-U
Examinations influence practices Close consultations with examinations authority Specimen papers 59 Copyright Ministry of Education, Singapore. Thank You 60 Copyright Ministry of Education, Singapore.
