Although these students represent about 1% of the area's high school population, they are well distributed from the top 10% of the rural/small town population across Berrien and Cass Counties. This series of lectures serves to review basic number concepts, apply these concepts to the mathematics and science they will be studying for four years, and also lay a framework for ISEF/EXPO type projects in mathematics, especially during their freshman year. Fundamental concepts essential to doing well on contests, like 0 being even and 1 not being prime, are reviewed/taught.
Historically, I was their only math teacher for four years of high school math. This had both benefits and pitfalls. One of the major benefits was the ability to tailor our curriculum's timing and content to the science and technology components of our program. Another was the opportunity to introduce such fundamental concepts of slope, area, bases, proof, etc. in such a way as to ease the transition to Calculus. This is still being done by 1) a careful selection and use of a variety of textbooks; 2) different modes of homework usage; 3) selected examples which span a wide variety of subfields of mathematics.
The consolidation of the Berrien County Math and Science Center at Andrews University started in 1992–93, continued in 1997–98, and resulted in a target of 50 students instead of 30 per grade level. Expansion to two sections at each grade level was completed in 2000–01, resulting in multiple mathematics teachers. The schedule dictated grade level sections to occur concurrently. Assuring uniform delivery and coverage was also a motivating factor in standarizing this material. However, in 2001–02, we started a return to one section of 30 students per grade level. This resulted in higher SAT scores (freshmen average over 1050) and thus emphasized the need to keep these students challenged.
Numbers are fundamental to the study of mathematics and science. Their discovery (some insist invention) transformed man into rational beings. Concepts such as ratio, continuity, nth roots, significant figures, etc. introduced early in our Introduction to Statistics unit stretch the ability of many of our students. This unit is thus designed to complement the instruction given our lowest quartile students in Summer Algebra and somewhat decouple the distraction of these number concepts from the study of Statistics. In addition, students accelerating faster than our normal (and already accelerated) program or those joining late (as Freshmen, Sophomores, and even Juniors or Seniors) need this information which is not well summarized elsewhere.
Changes during the 2001–02 school-year revision process included removal of some arithmetic and algebra concepts from the homework which are covered in summer algebra. This served to stream-line the homework so it better fits within our 50 minute (45 on Fridays) daily class period. Changes anticipated last year include work on clarifying the orders of infinity and providing lists of the referenced mathematicians and Latin terms.
I sincerely hope to convey my lifelong passion for numbers as well. I firmly believe mathematics is a "interactive" or participation sport. Although I don't expect to institute cyphering matches (like spelling bee's only doing calculations), lots of other similar activities are planned to involve the students. Someone once said, "I hear and forget, I see and remember, I do and understand." Understanding is essential for a firm foundation.
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