Centers & Institutes

  • Singapore Math Implementation Project

    Singapore Mathematics refers to the math textbooks from the small Asian country of Singapore. Since 1995, it has been one of the top performing countries in mathematics in the TIMSS study. Their success is not just due to the quality of the books, but to the strong mathematical preparation of their elementary teachers. Worcester State University Professor of Mathematics Richard Bisk, Ph.D., has provided content-based professional development for teachers using these books since 2000. His work focuses on improving the mathematical understanding of teachers and is valuable regardless of the textbook series that the teachers are using.

    Characteristics of Singapore Math

    • Greater Depth/Less Breadth: More time is spent on each topic. Fewer topics are covered in a year. There is greater emphasis on mastery.
    • Problem-Solving Emphasis: Model drawing diagrams are used to promote understanding of word problems and provide a bridge to algebraic thinking.
    • More Multi-Step Problems: Problems often require the use of several concepts.
    • Mental Math: Techniques encourage understanding of mathematical properties and promote numerical fluency.
    • Absence of Clutter and Distraction: Presentation is clean and clear, and uses simple, concise explanations.
    • Coherent Development: Topics are introduced with simple examples and then incrementally developed until more difficult problems are addressed.
    • Teacher- and Parent-Friendly: Since mathematical content is clear, it is often easier for teachers to plan lessons. Parents can read the books and help their children.
    • Concepts in the Curriculum: Review of concepts is not explicitly incorporated into the curriculum. Students are expected to have mastered a concept once it has been taught.
    • High Expectations: A high level of expectation is implicit in the curriculum.
    • Stress on Developing Conceptual Understanding: Students and teachers learn to focus on “why,” not just “how.”
  • Why Singapore Math
    A few comments from a mathematician:

    When I teach, at any level, the key question is always why?

    I started using Singapore Math in professional development courses in 2000 as a vehicle to connect teacher knowledge of mathematical content with elementary and middle school student work. The biggest challenge we face in improving K-8 mathematics instruction is teacher content knowledge of the subject. We would never be satisfied if our third grade teachers read at the sixth grade level. But we have accepted that many operate mathematically at the sixth grade level. This is not meant to be a criticism of teachers, but rather of some of our teacher training programs and state departments that license teachers. Many elementary school teachers will readily admit that they don’t feel comfortable with mathematics. I believe that teacher content knowledge is critical and see the Singapore Math books as a vehicle for improving it. I also suspect that it’s the best elementary textbook series around.

    How do you teach a mathematical subject when you aren’t proficient in it? You focus on rules, procedures and memorization; or on manipulatives, games, and activities that you can’t readily connect to concepts. (I should note that none of these things are bad if done appropriately.) When I work with teachers or students, the overriding point that I want to get across is the importance of understanding whatever mathematics you are doing. When you resort to teaching or learning by memorization only, nothing is being taught or learned. The focus on understanding is implicit in the Singapore Math books.

    In the current Math Wars, we often see two positions about elementary mathematics: reform and traditional. Many see these positions as diametrically opposed: traditional focuses on basic skills, while reform emphasizes conceptual understanding. But a student who understands place value should have no difficulty multiplying 2 digits numbers. I want students to memorize their times tables, but to do the memorization with understanding. Then, when they can’t remember what 6x8 equals, they might think: “I know that 5x8=40. So one more 8 is 48.” Or they might think: “I know that 3x8=24. To get 6x8, I need to double that result.” These are just 2 of the many areas where basic skills and conceptual understanding support each other.

    The Singapore Math books do an excellent job of teaching for understanding and emphasizing the importance of basic skills.

    Richard Bisk