Science and Technology/Engineering
Science and technology/engineering are inegrally related to mathematic
Mathematics is an essential tool for scientists and engineers because it specifies in precise and abstract (general) terms many attributes of natural phenomena and manmade objects and the nature of relationships among them. Mathematics facilitates precise analysis and prediction.
Take, for example, the equation for one of Newton's Laws: F = ma (force equals mass times acceleration). This remarkably succinct description states the invariable relationship among three fundamental features of our known universe. Its mathematical form permits all kinds of analysis and predictions.
Other insights come from simple geometric analysis applied to the living world. For example, volume increases by the cube of an object's fundamental dimension while area increases by the square. Thus, in an effort to maintain constant body temperature, most small mammals metabolize at much higher rates than larger ones. It is hard to imagine a more compelling and simple explanation than this for the relatively high heart rate of rodents versus antelopes.
Even more simple is the quantification of dimensions. How small is a bacterium, how large is a star, how dense is lead, how fast is sound, how hard is a diamond, how sturdy is the bridge, how safe is the plane? These questions can all be answered mathematically. And with these analyses, all kinds of intellectual and practical questions can be posed and solved.
Because of the importance of mathematics to science and technology/engineering, all teachers, curriculum coordinators, and others who help implement this framework must be aware of the level of mathematical knowledge needed for each science course at the high school level and ensure that the appropriate mathematical knowledge has already been taught or, at the least, is being taught concurrently.