The development of mathematics, from its very beginnings, has been about problem solving. Whether it has been commerce, trade or navigation we have always used early mathematical explorations of our world for very practical purposes.
The study of the heavens, in addition to the quest for knowledge about the world around us, was required in order for human beings to be able to better navigate, and map, the vast world around them. It is in this context, a practical applications approach, in which I would like to teach this unit.
Metropolitan Business Academy is an inter-district magnet high school in New Haven. The students have primarily chosen to pursue careers in business. Historically these students have done better on the verbal portion of standardized tests such as the CAPT. It is the intent of this unit to draw upon these superior verbal skills to teach about conic sections.
Rather than focus on the abstract and procedural nature of the subject we will attempt to put a human face on what is a very human endeavor. Additionally, we will emphasize the problem solving and practical aspects of the whole enterprise. By having students "discover" ways to solve these problems in a historical context we hope to facilitate a deeper and better understanding.
The seminar will allow me access to source materials, which will be invaluable in the preparation of this curriculum unit. The materials will be used to develop a curriculum, which is relevant to students of business in the practical application of solving real world problems.
The New Haven Precalculus curriculum covers Analytical Geometry, in general, and Conic Sections in particular, in unit VII. The unit specifically directs students to solve real world problems. As with many - if not most - mathematical applications, the math of conic sections was developed in conjunction with solving real world problems. Specific mathematics strands include:
1 Visualize three-dimensional objects from different perspectives and analyze cross-sections, surface area, and volume. (3.2a1)
2 Explore conic sections and their applications graphically and symbolically (1.1a3)
There will also be considerable attention on the business of mathematics as it relates to the scientific method. In particular, we will observe how data is collected, analyzed, and conjectures are then made.