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## How Students Learn: History, Mathematics, and Science in the Classroom (2005) Board on Behavioral, Cognitive, and Sensory Sciences (BBCSS)

### Citation Manager

. "6 Fostering the Development of Whole-Number Sense: Teaching Mathematics in the Primary Grades." How Students Learn: History, Mathematics, and Science in the Classroom. Washington, DC: The National Academies Press, 2005.

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How Students Learn: History, Mathematics, and Science in the Classroom

FIGURE 6-5 Skating Party game board—a Circle Land activity used to provide a hands-on representation for children to explore the relationship between movement and increases and decreases in quantity.

game play by placing their pawns at the starting gate. They then take turns rolling a die, counting the dots, and moving their pawns that many spaces around the dial. Each time they complete a revolution around the dial, they collect an Award card. At the end of the game, children count and compare their Award cards, and the child with the most cards is the first winner, followed by the child with the second most, who is the second winner, and so on. In one variation of this game, the Award cards collected by each group of four children are computed and compared, and a group winner is declared.

Questions are posed at several points in game play, and the sorts of questions that are put to individual children are most productive if they are finely tuned to each child’s current level of understanding (learning principle 1). For example, when all children have their pawns on the board, they can be asked, “Who is farther around? Who has gone the least distance? How much farther do you need to go to win an Award card?” These questions are always followed by “How do you know?” or “How did you figure that out?” Plenty of time needs to be allowed for children to come up with answers that make sense to them and for them to share their answers with each other. When children are counting their Award cards, they can be asked, “How many times did you go around the rink? Who has the most Award cards? How come that child went around the rink more times than this child if everyone had the same number of turns?” The last question is the most challenging of this set, and beginning players often attribute going

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 Front Matter (R1-R16) 1 Introduction (1-28) Part I HISTORY - 2 Putting Principles into Practice: Understanding History (29-78) 3 Putting Principles into Practice: Teaching and Planning (79-178) 4 They Thought the World Was Flat? Applying the Principles of How People Learn in Teaching High School History (179-214) Part II MATHEMATICS- 5 Mathematical Understanding: An Introduction (215-256) 6 Fostering the Development of Whole-Number Sense: Teaching Mathematics in the Primary Grades (257-308) 7 Pipes, Tubes, and Beakers: New Approaches to Teaching the Rational-Number System (309-350) 8 Teaching and Learning Functions (351-396) Part III SCIENCE - 9 Scientific Inquiry and How People Learn (397-420) 10 Teaching to Promote the Development of Scientific Knowledge and Reasoning About Light at the Elementary School Level (421-474) 11 Guided Inquiry in the Science Classroom (475-514) 12 Developing Understanding Through Model-Based Inquiry (515-566) A FINAL SYNTHESIS: REVISITING THE THREE LEARNING PRINCIPLES - 13 Pulling Threads (567-590) Biographical Sketches of Committee Members and Contributors (591-596) Index (597-616)