Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

The MARS approach is to integrate instruction on area and volume into the science curriculum and to offer recurring encounters with both concepts throughout the curriculum. Even in the absence of integrated curriculum materials, there is a need for coordination of topics in mathematics and science instruction and for cooperation among teachers to provide complementary learning experiences. Such an approach might help students and teachers alike appreciate how mathematics is so admirably adapted to reality.


ACKNOWLEDGMENTS

Development of this curriculum was sponsored by the Andrew W. Mellon Foundation as part of the Varieties of Reasoning in the Social and Natural Sciences program at the Learning Research and Development Center of the University of Pittsburgh. Thanks to Ann Davidson for help with data collection and to Bill Moore for help in software development. We are extremely appreciative of our partners in education Dr. Alice Hirsch (curriculum coordinator), Al Herrle (science teacher), and Judy Kielman (mathematics teacher) of the Montour School District for their support in implementing the curriculum. This is LRDC Research Report No. MARS-004.


REFERENCES

Berlin, D. F., & White, A. L. ( 1991). A network for integrated science and mathematics teaching and learning (Monograph Series No. 2). Columbus, OH: National Center for Science Teaching and Learning.

Brainerd, C. J. ( 1971). "The development of the proportionality scheme in children and adolescents". Developmental Psychology, 5, 171-197.

Brainerd, C. J., & Allen, T. W. ( 1971). "Training and generalization of density conservation: Effects of feedback and consecutive similar stimuli". Child Development, 42, 693-704.

Burger, W. F, & Shaughnessy, J. M. ( 1986). "Characterizing the van Hiele levels of development in geometry". Journal for Research in Mathematics Education, 17( 1), 31-48.

Carpenter, T. P. ( 1976). "Analysis and synthesis of existing research on measurement". In R. A. Lesh & D. A. Bradbard (Eds.), Number and measurement: Papers from a research workshop (pp. 47-83). Athens, GA: Georgia Center for the Study of Learning and Teaching Mathematics.

Chi, M. T. H., Feltovich, P. J., & Glaser, R. ( 1981). "Categorization and representation of physics problems by experts and novices". Cognitive Science, 5( 2), 121-152.

Clements, D. H., & Battista, M. T. ( 1992). "Geometry and spatial reasoning". In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). New York: Macmillan.

Fuys, D., Geddes, D., & Tischler, R. ( 1988). "The van Hiele model of thinking in geometry among adolescents". Journal for Research in Mathematics Education, Monograph No. 3.

Gallagher, J. ( 1979). "Basic skills common to science and mathematics". School Science and Mathematics, 79, 555-565.

Halford, G. S., Brown, C. A., & Thompson, R. M. ( 1986). "Children's concepts of volume and flotation". Developmental Psychology, 22( 2), 218-222.

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