The role of spatial thinking in the coupling between the mathematics and Science standards

Several questions of this overview of the national standards for mathematics and sciences. Where exactly in K-12, based on the standards of education are the basic concepts of space, representation, and spatial reasoning taught, exercised and developed? As in subjects teachers of the school is responsible for ensuring that studentsdevelop increasing control of these ideas? This control is available for transfer across the curriculum? As indicated above, the standards of mathematics are constructivist, building higher levels of abstraction as a student through the ranks to the level of understanding and skills that it expected a higher degree. Chapter 3 of the principles and standards for school mathematics provides an overview of the progression of understanding and skills for all 10 mathematics standards. Figures 5.1 and 5.2 are extracted from the two parts of the standard geometry: (I) specify the locations and describe spatial relationships using the coordinated geometry and other representative systems and (2) the use visualization, spatial reasoning, and geometric modeling to solve problems. These two parts are closely linked to the concepts of space, spatial reasoning and representation. Each of these parties stated clearly the results for mathematical understanding and contains clear examples of their application to real-world problems.

Article 7 of the standards of mathematics to describe how objectives are accomplished in the levels of development bur (pre-K-2, 3 - 5, 6 - 8 and 9-12). The progression of standard geometry begins by identifying points and systems of coordinates, clearly oriented to maps and other graphic representations and visualization of two. and objects in three dimensions. These concepts are developed in the corresponding sections of the K-2 levels and 3-5 standards. Figure 5.3 the idea of placing things in space begins a process of building the capacity to deal with space concepts more complexes that pushes to the ideas of distance and space management, part of a progression in more complicated concepts.

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

How much appeal for mathematicians to links with other disciplines is reflected in and supported by the standards of science? The simple concepts of the position and shape are beautifully mirrored in the science standards. Science standards provide a guide to the scientific content specific to each level (K-4, 5-8 and 9-12) for each domain covered Science (physical, life, Earth and space). Guide content for standard physical science for grades K-4 is shown. The sections on the physical properties of objects and materialsand position and movement of objects that both use the spatial concepts under development in the standard of mathematics. Objects have the position and shape in standard science. In the standard geometry concepts of the position and shape am explicitly taught and reinforced. Similarly, there are connections to other parts of mathematics standards, and therefore the relationship between mathematics and science standards seems obvious. In these early years, the assumptions on the part of the authors of the scientific standards that mathematics will provide a prior knowledge base that can be drawn by students and professors of science seems appropriate.

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