Many educators are impressed with the curriculum and materials from Singapore that have enabled Singapore’s students to be so successful in mathematics. Two of its key features are the emphasis on problem solving and the concrete to pictorial to abstract approach first described by Jerome Bruner. What is sometimes overlooked in this is the importance of visualization in developing both conceptual understanding and procedural fluency. You can’t carry around ten frames or base ten materials, or fraction strips in your pocket—people will laugh—but you can carry them in your “mind’s eye.” In other words, the visual and pictorial models used in the Singapore material enable students to visualize number, operations, and word problems.
The ability to visualize quantitative relationships is critical to learning basic facts, to understanding complex operations with fractions and ratio, to solving routine and non-routine problems and even solving variable equations
In first grade, students learn to “make ten” on a ten frames to learn facts to 20. To learn how much 8 + 6 is, students think moving two from the 6 to the 8, 8 + 6 = 10 + 4 = 14
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