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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 6-7 Neighborhood Number Line game board—used to help children understand the base-ten number system.

or farther away from it? How do you know?” By answering and discussing these questions and by confirming or disconfirming their thoughts and predictions with real actions, children gradually build up a solid intuitive understanding of the links among the world of quantity (in spatial contexts), the world of counting numbers, and the world of formal symbols.

###### Rosemary’s Magic Shoes

This game provides an illustration of a spatial context developed for Line Land in the second-grade program to help children build an understanding of the base-ten number system. The prop itself—the Neighborhood Number Line—comprises 10 blocks of houses, each containing 10 houses that attach with Velcro to create a linear neighborhood of 100 houses that is 15 feet long when fully assembled (see Figure 6-7). This prop is used extensively in the first-grade program as well, to teach several concepts implicit in the 1–100 number sequence. The character created for this game, a professional monster-tracker called Rosemary, has a pair of magic shoes that allows her to leap over 10 houses in a single bound. For Rosemary’s shoes to work, however, she first must tell them how many times to jump 10 houses and how many times to walk past 1 house.

To play this game, children take turns picking a number tile that indicates a house where the presence of a monster has been suspected. Using Rosemary’s magic shoes, they then move to the house as quickly and efficiently as possible; check for monsters (by drawing a card from a face-down deck that indicates the monsters’ presence or absence); and, if indicated, place a sticker on the house to show that it is a “monster-free zone.” In later

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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)