![]() Singapore Math® is a trademark owned by Singapore Math Inc. Math in Focus® is a registered trademark of Times Publishing Limited. Read more of Andy Clark’s posts on Singapore Math here. Interested in learning more about Singapore Math, Math in Focus, and meeting Andy Clark on April 26–28 at NCTM? See our complete line-up of thought leader events and presentations here. ![]() Visualization enables students to see relationships, to simplify problems, and to change problems into a mathematical form. Visualizing that of all the rectangles with a common area, the square has the smallest perimeter.Recognizing that an equal sign means the amounts on either side are equivalent amounts and resemble a balance, even when variables are on both sides.Understanding multiplication of fractions as an area problem.Identifying equivalent fractions on a number line or on the multiplication chart.Recognizing that 8 x 7 is just double 4 x 7.Finding the difference of 198 and 89 on a number line.Just think of all the important concepts that are made easier by visualization: To learn how much 8 + 6 is, students think moving two from the 6 to the 8, 8 + 6 = 10 + 4 = 14 In first grade, students learn to “make ten” on a ten frames to learn facts to 20. 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 This system is rooted in allowing children to use. 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. At LEH, we use the concrete, pictorial, abstract (CPA) model in our teaching of mathematical concepts. What is sometimes overlooked in this is the importance of visualization in developing both conceptual understanding and procedural fluency. It begins at the concrete level when students physically act out a math problem, or use manipulatives such as blocks, toothpicks, fraction pieces, or other three-dimensional objects to model a mathematical relationship. Two of its key features are the emphasis on problem solving and the concrete to pictorial to abstract approach first described by Jerome Bruner. Research on the Concrete-Pictorial-Abstract (CPA) Sequence Conceptual understanding of quantity follows a developmental sequence. Many educators are impressed with the curriculum and materials from Singapore that have enabled Singapore’s students to be so successful in mathematics. Students may count up from 3 to solve, or they could use their fingers as representations of the numbers. ICLE (International Center for Leadership in Education)Ĭustomer Service & Technical Support Portal Thinking Abstractly When students understand how to draw pictures to represent mathematical equations, they can begin to think abstractly by using numbers. Into Algebra 1, Geometry, Algebra 2, 8-12 Science & Engineering Leveled Readers, K-5
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |