Several questions arise from this overview of the national standards for mathematics and science. Where exactly in the course of K-12 standards-based education are the fundamental concepts of space, representation, and spatial reasoning taught, exercised, and developed? Who as in teachers of which school subject(s) is responsible for ensuring that studentsdevelop increasing mastery of these ideas? Is this mastery available for transfer across the curriculum? As noted above, the mathematics standards are constructivist, building to higher levels of abstraction as the student progresses through the grades to the level of understanding and competency expected of a graduating senior. Chapter 3 of the Principles and Standards for School Mathematics provides an integrated view of the progression of understanding and competency for all ten mathematics standards. Figures 5.1 and 5.2 are excerpts from two parts of the geometry standard: (I) specify locations and describe spatial relationships using coordinate geometry and other representational systems, and (2) use visualization, spatial reasoning, and geometric modeling to solve problems. These two parts are closely tied to concepts of space, representation, and spatial reasoning. Each of these parts has clearly stated outcomes with respect to mathematical understanding and contains clear examples of their application to real-world problems.

This article through 7 of the mathematics standards describe how the goals are accomplished in bur developmental levels (pre-K-2, 3-5, 6-8, and 9-12). The progression for the geometry standard starts with the identification of points and coordinate systems, clearly oriented toward maps and other graphic representations, and the visualization of two. and three-dimensional objects. These basic concepts are developed in the corresponding sections of grade levels K-2 and 3-5 standards. In Figure 5.3 the idea of placing things in space begins a process of constructing the ability to deal with more complicated spatial concepts that grows to ideas of distance and direction, part of a progression of increasingly complicated spatial concepts.

There are these concepts developed further, enabling navigation for example, but also basic computer technology is used to support and enhance the learning process. In Figure 5.5 the focus is on developing spatial thinking as a skill in young learners, explicitly in terms of navigation and visualization. By the time students are in grades 3-5, the geometry standard calls not only for the building of additional spatial thinking skills (Figure 5.6), but also for the teacher to explicitly tie those skills to other areas of mathematics and to other disciplines such as science.

How well is the mathematicians’ call for making ties to other disciplines reflected in and supported by the science standards? The simple concepts of position and shape are nicely mirrored in the science standards. The science standards provide a guide to the specific science content at each grade level (K-4,5-8, and 9-12) for each area of science covered (physical, life, Earth, and space). The content guide for the physical science standard for grades K-4 is shown. The sections on the physical properties of objects and materialsand the position and motion of objects both use the spatial concepts being developed in the mathematics standard. Objects have position and shape in the science standard. In the geometry standard the concepts of position and shape am explicitly taught and reinforced. Similarly there are connections to other parts of the mathematics standards, and therefore the connection between the mathematics and science standards seems clear. At these early grades, the assumptions on the part of the writers of the science standards that mathematics will provide a prerequisite basis of knowledge that can be drawn on by science teachers and students seems appropriate.

Learning things is not limited to the scentific area. Instead it also has relations with some other things like speaking a language or using software, including Rosetta Stone Russian and Rosetta Stone Spanish. If you have a creative mind, you will make all your own differences in the end!

Related Role Of Computers In Science And Technology Articles