Lesson 1: Introduction to Singapore Math

In this session, Dawn Swartz introduces Singapore Math by sharing its background, effectiveness, overall approach and pedagogy, and its harmony with the classical tradition of education.

Recommended Reading

See Dr. Christopher Perrin’s blog articles on principles of pedagogy on InsideClassicalEd.com.

Outline of Session

An Introduction to Singapore Math


  • Singapore Math fits well within the context of classical education 
  • It is important to make a good transition to Singapore Math (SM) by preparing well
  • This course is designed for you whether you are brand new to SM or have been teaching it for a while.
  • The favorite part of Dawn’s day: teaching Singapore Math!


  • In 1965 Singapore become independent. In the 1980s the Ministry of Education started the primary mathematics project. Combined effective teacher strategies with teacher training and development.
  • Team was started to address students who struggled with mathematics word problems; created the math model approach
  • In the 1990s it was noted that Singapore students were scoring in the highest tier in the international TIMSS test (Trends in International Mathematics and Science) for fourth and eighth graders. 2015: students were at the very top. 
  • Questions people began to ask: How do we get students to master math the way students in Singapore are?
  • This course will present the distinctive aspects of Singapore Math and strategies for teaching it
  • Amount of topics per year in SM is only 10-15 rather than the conventional 30 topics.
  • Each topic in SM should be taught to mastery. 
  • It is important for each teacher to know what mathematics was taught in the previous grade.
  • Basic pedagogical movement in Singapore Math is from CONCRETE to PICTORIAL to ABSTRACT.
  • Concepts taught first with manipulatives and movement. If we move to fast to the abstract we sacrifice conceptual understanding for procedural proficiency. Example; It important to teach place value concretely in preparation for teaching long division.


THE SM MATHEMATICAL FRAMEWORK: A Mathematical Problem-Solving Framework


Review this mathematical framework throughout the course and let it guide you through your study and teaching of SM


  • CONCEPTS: Varied learning experiences teach understanding of concepts (concrete-pictorial-abstract)
  • SKILLS: Concepts developed through skills; skills as procedures that are part of conceptual understanding.
  • ATTITUDES: These are shaped and influenced by learning experiences. The story of James: James tells Dawn “I don’t like math.” Dawn takes this as a challenge…after several months his attitude about math changed and improved until he liked math.  Approach students with a growth mindset.
  • METACOGNITION: How to think about thinking?
  • PROCESS: How to construct arguments to get to the answer. Heuristics: ways of approaching a problem when the solution is not obvious–experienced-based techniques for learning and discovery. Examples: make a representation, diagram, or list for the material; calculated guess (guess and check); act out the problem or story; change the problem altogether.


  • Language-based program
  • Filled with constant guided and purposeful questions; how? why? different strategy possible? Explain your strategy; constant conversation.
  • It keeps problem-solving central to mathematical learning
  • It teaches thinking skills and heuristics
  • One piece missing: the beauty and order of math that is inherent because of our Creator. This should come out in your math lessons.

Scott Buchanan quotation:

“The structures with which mathematics deal are more like lace, the leaves of trees and the play of the light and the shadow on a human face then they are like buildings and machines, the least of their representatives.”

Teaching SM will help us develop lifelong learners…of mathematics.


  • The rest of the course session will address the questions each math teacher will have: What do I do and why?
  • Coming sessions will follow these topics (in order): Number sense, place value, and model drawing
  • Dawn encourages each teacher-learner to create and use a three-ring binder.
  • Be ready to “work along” with Dawn during the rest of the course
  • Print out the accompanying sheets (see the downloadable PDF) to put in your binder and work along with Dawn.


Image: The Singapore Math Problem-Solving Framework

Here is the Singapore Math Problem-Solving Framework used by Dawn in her presentation:



Viewer: Slides for Presentation

Here are some slides to print and place in your Singapore Math binder:



Discussion Questions
  • In what ways does Singapore Math fit well with the classical model of education?
  • Why does Singapore Math feature a pedagogy that moves from the concrete to the pictorial to the abstract?
  • Why is it important to teach each mathematical concept to mastery?
  • Discuss the educational value of using heuristics teaching Singapore Math.

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