Singapore Math framework guide for families and teachers outside Singapore: what MOE’s Mathematics Curriculum Framework says and how it shapes learning from Primary 1 to Secondary 4.
Every topic in Singapore Mathematics sits inside one framework.
It has a single centre, and that centre is problem solving.
The current primary syllabus (2021) and secondary syllabus (2020) both use this framework. Problem solving sits at the centre, supported by five components: concepts, skills, processes, metacognition and attitudes.
The framework adds no topics of its own. It describes what a student should be able to do with every topic they learn, from counting in Primary 1 to algebra and geometry in secondary school.
This guide is useful for families and teachers who want to:
- understand the thinking behind Singapore Math materials;
- see what Singapore expects beyond correct answers;
- prepare a child who is moving into a Singapore school; or
- plan lessons around the framework, not only the textbook.
Quick facts
Level: Primary 1 to Secondary 4 (one framework for both stages)
Strand: All strands. The framework sits above the content.
Official source: MOE Primary Mathematics Syllabus (2021) and MOE Mathematics Syllabuses, Secondary One to Four (2020)
Comes after: What Is Singapore Math?
Leads to: Mathematical Processes and Metacognition
What the Framework Means in Singapore Mathematics
The framework is MOE’s summary of what Mathematics education is for.
The 2021 primary syllabus states its centre plainly: “The central focus of the mathematics curriculum is the development of mathematical problem-solving competency.”
It continues: “Supporting this focus are five inter-related components – concepts, skills, processes, metacognition and attitudes.”
The framework diagram gives each component a short label.
| Component | Label on the 2021 primary framework diagram |
|---|---|
| Concepts | Understanding of the properties and relationships, operations and algorithms |
| Skills | Proficiency in carrying out operations and algorithms, visualising space, handling data and using mathematical tools |
| Processes | Competencies in abstracting and reasoning, representing and communicating, applying and modelling |
| Metacognition | Awareness, monitoring and regulation of thought processes |
| Attitudes | Belief, appreciation, confidence, motivation, interest and perseverance |
The word “inter-related” matters. A child who understands a concept but cannot carry out the calculation, or who can do both but gives up after one attempt, has not yet reached the centre.
The problems themselves can come from everyday life or future work, from other subjects, or from within Mathematics. They range from routine tasks to non-routine ones.
Where the Framework Appears in the Syllabus
The framework appears near the start of both current MOE syllabuses, before any content is listed.
- Primary (2021 syllabus, P1 to P6). Problem-solving competency at the centre, with the five components above. This syllabus reached Primary 6 in 2026, and the 2026 PSLE cohort is the first to sit the PSLE on it.
- Secondary (2020 syllabus, Sec 1 to Sec 4). The same five components. The secondary wording reads: “The central focus of the mathematics curriculum is the development of mathematical problem solving competency.”
- Processes in both. “These include abstracting, reasoning, representing and communicating, applying and modelling.”
- Problem-solving strategies in both. Both syllabuses name Pólya’s 4 steps to problem solving and the use of heuristics as general strategies. The 2021 primary syllabus gives no list of heuristics.
Each syllabus surrounds the framework with a few related ideas.
| Feature | Primary | Secondary |
|---|---|---|
| Content strands | Number and Algebra; Measurement and Geometry; Statistics | Number and Algebra; Geometry and Measurement; Statistics and Probability |
| Big ideas | Six clusters: Equivalence, Diagrams, Invariance, Measures, Notations, Proportionality | Eight: Diagrams, Equivalence, Functions, Invariance, Measures, Models, Notations, Proportionality |
| In the exams | PSLE AO3: “reason mathematically; analyse information and make inferences; select appropriate strategies to solve problems” | G3 Mathematics AO3: “Reason and communicate mathematically” (15% of the marks) |
The secondary strand names are those used in SEAB’s G3 Mathematics syllabus.
The primary syllabus also states three aims. It “aims to enable all students to” acquire concepts and skills “for everyday use and continuous learning in mathematics”, to “develop thinking, reasoning, communication, application and metacognitive skills through a mathematical approach to problem solving”, and to “build confidence and foster interest in mathematics”.
Each aim maps onto the framework: first concepts and skills, then processes and metacognition, then attitudes.
How Singapore Uses the Framework in Teaching
1. Start from a problem
The framework points every lesson at problem solving, so a good lesson gives students something to solve, not only something to copy.
2. Build the concept
Students learn what an operation means before they practise it at speed. Multiplication starts as equal groups, not as a table to recite.
3. Practise the skill
Fluent calculation frees attention for harder thinking. Practice is planned and regular.
4. Make the processes visible
Students reason, draw, explain and apply. A teacher asks “How do you know?” as often as “What is the answer?”
5. Teach students to watch their own thinking
Metacognition is planned into lessons: estimating, checking, and choosing a different strategy when the first one fails.
6. Look after attitudes
Confidence and perseverance are part of the framework, so effort and recovery from mistakes are noticed, not only correct answers.
The 2021 primary syllabus describes three phases of learning. Readiness comes first. Engagement follows, through activity-based learning, inquiry-based learning and direct instruction. Mastery comes last, through motivated practice, reflective review and extended learning.
Teachers are also asked to “teach towards big ideas”, helping students connect ideas within a topic and across topics.
An Example in Practice
One problem, five components
Question: There are 4 boxes with 6 pencils in each box. 5 pencils are lost. How many pencils are left?
Step 1. Concepts. The child recognises equal groups, which means multiplication, and a loss, which means subtraction.
Step 2. Skills. 4 × 6 = 24, then 24 − 5 = 19.
Step 3. Processes. The child sketches the four boxes and explains why the multiplication comes first.
Step 4. Metacognition. The child asks: does 19 make sense? It is less than 24, and pencils were lost, so yes.
Step 5. Attitudes. If the first attempt goes wrong, the child checks and tries again instead of guessing.
Check: 19 + 5 = 24, and 24 ÷ 4 = 6 pencils in each box.
A worksheet that records only “19” sees one component. The framework asks the adult to notice all five.
Routine and non-routine
Routine: Work out 4 × 6.
Non-routine: Find two whole numbers that multiply to make 24 and add to make 10.
The second question uses the same fact, but the child must try pairs, reason and check. The pairs 1 and 24, 2 and 12, and 3 and 8 do not work. Only 4 and 6 do.
Both kinds of question belong in Singapore Mathematics. The framework is a reminder that the second kind should not be left out.
Common Misunderstandings
- “The framework is a teaching method.” It describes goals, not a lesson script. Fix: use the five components as a checklist for what a child can do, then choose methods that fit.
- “Singapore Math means the bar model.” The bar model is one widely used representation. The framework is much wider. Fix: treat drawing as one part of the processes, alongside reasoning and communicating.
- “The current syllabus prescribes CPA.” The 2021 primary syllabus does not mention the Concrete-Pictorial-Abstract approach. CPA is widely associated with Singapore Math and was named in MOE’s earlier 2013 syllabus. Fix: use concrete materials and pictures because they help, not because the current syllabus requires them.
- Using the older process headings. “Reasoning, communication and connections”, “Applications and modelling” and “Thinking skills and heuristics” are 2013 headings. Fix: use the current wording: abstracting, reasoning, representing and communicating, applying and modelling.
- “Problem solving means word problems.” Problems can also come from within Mathematics itself. Fix: include number puzzles and pattern questions, not only stories.
- Treating attitudes as an extra. A child who fears Mathematics stops early and so practises less. Fix: notice persistence and careful checking, not only speed.
Using the Framework Outside Singapore
The framework travels well because it describes learning, not a particular textbook.
- Terminology. A “strand” is a broad content area, such as Number and Algebra. A “heuristic” is a general problem-solving strategy. MOE’s 2013 syllabus listed examples such as drawing a diagram and working backwards; the 2021 syllabus gives no list.
- Materials. Not every Singapore Math programme sold abroad is written to the current syllabus. Check the edition, and see the Singapore Math textbook programmes guide before choosing.
- Timing. The same framework runs from Primary 1 to Secondary 4. Local grade names differ, and the Singapore Math Grade Levels guide explains why direct conversions are unreliable.
- Assessment. In Singapore, the framework shows in exam objectives. Both the PSLE and G3 Mathematics include an objective on reasoning, so explanations and working matter, not only answers.
- Spelling. MOE writes “modelling” and “visualising”, the British spellings. American materials usually write “modeling”.
How to Use the Framework at Home
A short daily conversation does more than a long worksheet.
- Choose one problem a day instead of a page of similar sums.
- Before calculating, ask the child what the problem is about.
- Let them calculate without interruption.
- Ask them to show the answer another way: a drawing, a table or a number sentence.
- Ask “How do you know it is right?” and wait for a reason.
- Praise careful checking and persistence, not only speed.
Ten to fifteen minutes is enough when the conversation is focused.
Try These
These are short tasks for the adult as well as the child.
- Name the five components that support problem solving in the Singapore framework.
- A child writes 24 − 5 = 19 correctly but cannot say why they subtracted. Which component needs attention?
- Which phrase is current process wording: “thinking skills and heuristics” or “representing and communicating”?
- A child stops after one failed attempt and says, “I can’t do this.” Which component does this show?
Answers
- Concepts, skills, processes, metacognition and attitudes.
- Processes, especially reasoning and communicating. The skill is secure, but the explanation is missing.
- “Representing and communicating”. “Thinking skills and heuristics” is a 2013 heading.
- Attitudes, especially perseverance. A metacognitive prompt such as “What else could you try?” also helps.
What Comes Next
The next pages look at the framework’s parts one at a time.
- Mathematical Processes explains abstracting, reasoning, representing and communicating, applying and modelling.
- Metacognition explains “thinking about thinking” and how to build it.
- Mathematical Modelling shows how real-world problems are handled, mainly in secondary school.
- Calculators explains when Singapore students may use one.
Once the framework is clear, every topic page in this series reads as one part of the same design.
Frequently Asked Questions
When do Singapore students learn the framework?
They do not study it as a topic. It shapes lessons at every level from Primary 1 to Secondary 4.
Is the framework the same at primary and secondary level?
Yes in structure. Both have problem solving at the centre and the same five components. The lists of big ideas differ: six clusters at primary and eight at secondary.
Does the framework require the bar model?
No. The framework does not name a single diagram. Diagrams are one of the big ideas, and the bar model is one widely used example.
Does the 2021 syllabus list heuristics?
No. It mentions “Pólya’s 4 steps to problem solving and the use of heuristics” but gives no list. The well-known lists come from the 2013 syllabus.
Is the framework examined?
Not directly. Its effect shows in exam objectives: the PSLE asks students to “reason mathematically”, and G3 Mathematics gives 15% of the marks to reasoning and communication.
Is CPA part of the current framework?
No. The 2021 primary syllabus does not mention CPA. It was named in the 2013 syllabus and is still widely associated with Singapore Math.
Helpful Reading
- Singapore Mathematics | International Edition: Mathematical Processes
- Singapore Mathematics | International Edition: Metacognition
- Singapore Mathematics | International Edition: Mathematical Modelling
- What Is Singapore Math? | Curriculum, Methods, Models and Problem Solving
- Singapore Math Heuristics | Problem-Solving Strategies Without Memorising Tricks
- How AO1, AO2 and AO3 Work in PSLE Mathematics
- MOE Primary Mathematics Syllabus
- MOE Mathematics Syllabuses, Secondary One to Four (2020)
The Framework in Singapore Mathematics
Problem solving at the centre.
Concepts to understand.
Skills to carry out.
Processes to reason, explain and apply.
Metacognition to watch the thinking.
Attitudes to keep going.
Seen whole, the framework is less a diagram than a description of a capable learner.
That description holds from the first lesson in Primary 1 to the last examination in Secondary 4.
Ask Bukit Timah Tutor
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If your child is learning Singapore Mathematics at home, in an international school or in a Singapore school, and you are unsure where to begin with this topic, send us a short message with the student’s level and one example of the work.
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Singapore Mathematics | International Edition is a Bukit Timah Tutor guide series for families and teachers outside Singapore. It is not a textbook and is not affiliated with MOE, SEAB or any publisher. Syllabus details were checked against MOE and SEAB documents in October 2026. Always confirm current requirements with your school.
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