Look At The Physical Science Standard
As part of the grades 9-12 experience, the physical science standard involves developing an understanding of the geometry of molecules. An examination of the geometry standard for the corresponding grade grouping does not yield any material that is closely connected to the kind of thinking required for understanding the examples of molecules. However the geometry standards for pre-K-2 and grades 3-5 do contain material useful in developing thinking skills that could be used to understand three-dimensional molecular structures. Specifi. ally, the visualization standard for grades 3-5 has a focus on building up three. dimensional structures from blocks. In the pre-K-2 standards, students are asked to apply transfor. mations and to use symmetry to analyze mathematical situations, skills that could again be useful in describing molecular structures. However, in sharp contrast to the strong links between K-4 math. ematics and science, the necessary concepts in geometry are not introduced concurrently with science content that might use them. Therefore, the light coordination of simple spatial concepts in the early years is not retained through high school.
The lack of connection takes two forms. In the first case, that of grades 9-12 chemistry, the way of thinking concepts that would allow the student to grasp the structure of atoms and molecules are introduced well ahead of need; therefore both students and teachers may not recall the relevant material from earlier grades. In the second case, that of the Earth and space science standard, other than the discussion of coordinate geometry, the committee could not find anything in the mathemat- ics standards that supported the complex spatial thinking process associated with the description of the motion of fluids (wind and ocean currents) on a rotating sphere. It is interesting to note that the examples and explicit ties from the mathematics to the science standards that were so noticeable for early education have largely disappeared.
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There are several conclusions about the coupling of the use of spatial thinking and reasoning in the mathematics and science standards. First, there is a close connection between the mathematics (pre-K-2 and 3-5) and the science standards (K-4) in early education. Second, the development of spatial thinking and reasoning in the early years is, in the mathematics standards, aided by com. puter-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 sophis. ticated 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 thinking as part of standards-based instruction in the United States.
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