At Avenues, we have adopted Math in Focus, a Singapore approach, as our math curriculum in the Lower School*. So what is Singapore Math? The math we are teaching is not different math. Two plus two is still four; ten times ten is still one hundred. What is unique about the Singapore approach is the style of teaching and the student goals.
The classroom lessons begin with concrete experience. A kindergartener may use four blue blocks and three red blocks to add 4 + 3. A third grader may use groups of tens and ones counters to make four groups of fifteen in order to multiply 4 x 15. This concrete step engages students and builds deeper understanding of mathematical concepts. From the concrete stage, lessons move toward a pictorial focus. In this stage students use pictures, symbols, diagrams and other two-dimensional representations. Students learn to visualize math concepts and create representations based on the pictures in their minds.
In the early years of Singapore Math, students learn to use number bonds—diagrams that help students represent a whole number and the parts that make up the whole. For example, the whole number 10 could be made up of the parts 3 and 7. In second grade, students begin representing parts and whole numbers using bar models—pictorial representations that show relationships between numbers in a problem. Long bars represent larger numbers and short bars represent smaller numbers. Both number bonds and bar models aid in problem solving. After the pictorial stage, lessons progress toward abstract mathematics. This is the numeric representation: 12 + 3, 18 x 2, etc. This stage includes traditional and non-traditional manipulations of numbers.
Many traditional American approaches to mathematics focus on the development of skills such as calculation, estimation and algebraic manipulation. These skills are developed through drills and memorization. While skill development is a part of the Singapore approach, it is not the only focus. Other goals include strong conceptual understanding, increased mathematical reasoning and communication, metacognitive skills and improving student beliefs and attitudes about math. Mastery of topics is measured through many goals rather than simply through skill development. Classroom lessons often involve collaborative problem solving work and an emphasis on math communication. Students need to arrive at a correct answer; but they also need to understand why their answer is correct.
We encourage parents to be open-minded about this approach. Students may be working on topics they have previously studied in order to deepen conceptual understanding and improve their problem solving skills. They may also utilize strategies and techniques that are unfamiliar to parents. Rather than discounting these strategies in favor of more traditional methods, we encourage parents to engage in mathematical dialogue with students. Ask your student to explain what she is practicing and how she learned that concept. This is an excellent way to develop children’s reasoning and vocabulary.
*Please note that beginning in the 2016–17 school year, Avenues moved from a four-division school structure with an Early Learning Center (N–Pre-K), Lower School, (K–4), Middle School (5–8) and Upper School (9–12) to a three-division structure with an Early Learning Center (N–K), Lower Division (1–5) and Upper Division (6–12). The Upper Division is further divided into two programs—the middle grades program (6–8) and the upper grades program (9–12).