FIGURE 5.10 Specify locations and describe spatial relationships using coordinate geometry and other representational systems. SOURCE: NCTM, 2000. Reprinted with permission from Principles and Standards for School Mathematics, copyright 2000 by the National Council of Teachers of Mathematics. All rights reserved.

spatial thinking and reasoning in the early years is, in the mathematics standards, aided by computer-based support systems. Third, this close coupling is not present during the grades 9–12 experience. Specifically, the science standards continue to presume, but do not make explicit, the use of spatial thinking and reasoning. Further, the presumed spatial thinking skills are more sophisticated than those being emphasized in the mathematics standards. Fourth, higher-level ability for spatial thinking is central to many key science education outcomes such as the analysis of situations in rotating frames of reference. Finally, the science standards seem to presume a very sophisticated skill set in spatial thinking, reasoning, and representation, and it is unclear where in the education system that skill set has been developed. To the extent that spatial thinking skills are explicitly taught, the process occurs under the rubric of geometry, which is only one of ten standards that are to be met by mathematics teaching and learning. Therefore, there is currently no significant, systematic treatment of spatial thinking as part of standards-based instruction in the United States.