THREE GUIDELINES FOR CHANGE
1. Concrete −> Pictorial −> Abstract. This is perhaps Singapore’s greatest contribution to math pedagogy. Based on research that goes back over a hundred years (Dewey, Bruner, Piaget, Vygotsky, Montessori, and others), Singapore validated the strength of this approach by using it to achieve top scores internationally.
According to constructivist theory, children learn best through active participation in the learning process. In math, they use manipulatives like base-10 blocks (Concrete Phase) to explore each new math concept, and build their own understanding of that concept. They then transfer their understanding to drawings of those same blocks (Pictorial Phase). Finally, they begin to solve mathematical problems with increasingly abstract tools: tick marks, numbers and symbols. The slow, incremental scope of this pedagogy cannot be exaggerated, especially for students who traditionally struggled with math. These students are often visual learners who do not memorize well at the abstract level. Building meaning incrementally provides math access to all students.
2. “Ask, Don’t Tell”. The role of the teacher in Singapore is a huge shift from what we teachers are used to. Our new job is to ask good questions, and let children figure out answers in multiple ways, using base-10 blocks. Our job is not even to talk them through the use of the blocks, but to respect their ability to derive relational understanding by figuring it out themselves. This approach is time-consuming but efficient! Students retain their learning and develop strong number sense.
3. Slow D-o-w-n. This approach requires teachers to concentrate on longer units with more depth. Students who need to spend more time at the concrete/pictorial levels get that time. Students who progress to the abstract level more quickly get challenging problems that take that same unit into greater depth.