Designing Learning Environments for Developing Understanding of Geometry and Space

By Richard Lehrer; Daniel Chazan | Go to book overview

Subject Index
A
Additivity (of area), 156
Adventures of Jasper Woodbury, The,see Jasper series
Algebra, 302-303, 307-317
Analytic geometry, 297-298
Anchored instruction, 440-442
Angle, 60-61, 145-152, 164
Area measure, 164-165, 268-270
assessment task examples involving, 153-154, 197-199
classroom examples involving, 185-194
student learning outcomes on, 154-159
visualization of, 11-12
Argumentation, 334-335, 341-346
Art, 183-184, 401-402
Axioms, 69
B
BBN Function Machines, 359-361
Buoyancy, 278-281, 284-292
C
Cabri software, 75-76
CAD (computer-aided design) software, 82n, see also KidCAD
Ceva's theorem, 381-382
CGI, see Cognitively Guided Instruction (CGI)
Chaos, 91
Chaos game, the, 92-96, 100-104
Classroom discourse, 84-85, 177, 194-195
Cognitive development, see SOLO taxonomy, Spatial reasoning; van Hiele theory
Cognitively Guided Instruction (CGI), 172-173
Congruence, 9-10, 191
Conic sections, 409-411
Conjecture, 84-85, 319, 344-346
cognitive model of, 328-335
modeling and, 330-331, 332-333, 336-339
software for, 339-341
student learning outcomes on, 321-328
task analysis for, 320-321
Construction
approaches to, 72-77, 331, 336-339
iterated, 26-29
student learning outcomes involving, 325-326
Construction programs, 71-77, 81-83, see also Dynamic geometry; specific software programs
Contour lines, 35-37
Counterexamples, 334-335, 384-386, 399
Crossed configurations, 356-357, 364-365, 384-388, 389
Cube arrays
classroom examples involving, 237-247
student strategies for visualization of, 228-235
tasks developed for, 235-237
Curriculum, see also Euclidean geometry; Geometry education; Realistic Mathematics Education (RME); Task development
development of, 38-43, 53-54, 221-223, 262-264
reform of (need for), 85-88, 165, 344-346
traditional, 72-73, 77, 465-466
visual approaches to, 6, 314-317
Curve-drawing devices, 298-301
generation of equations using, 308-314
student exploration of, 301-308, 315-317
D
Deductive reasoning, see Proof
Density, 283-292
Diagrams, 336-339

-501-

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