Objectives
At my vocational-technical high school, students expect answers to the question, "Why do I need to learn this?" Using the field of Nanotechnology as a backdrop for the semester, I think my students will be excited and energized (every pun intended) to learn the mathematics related to this emerging field. As I read The Big Ideas of Nanoscale Science and Engineering published by the National Science Teachers Association (NSTA), I found several areas of overlap where science and mathematics support each other. Therefore, this unit will naturally integrate the two subjects to benefit student understanding as the two disciplines reinforce each other.
I am writing this unit for high school math students, primarily in 10 th - 12 th grade. I teach at a comprehensive vocational-technical high school where students spend up to one-half of each day in their chosen career area and the remainder of their day in academic classes. Career areas include auto repair, cosmetology, construction trades, culinary arts, business technology, dental assisting and laboratory, nursing, drafting, landscape design and pre-engineering. My school is one of four high schools in its own vocational school district. Each of the four schools pulls students from any school in the county so that students arrive having used a variety of curricular programs. The vocational schools are "choice" public schools and our students are held to the same academic standards as all public school students in the state of Delaware. Students choose our school for a variety of reasons. Some are focused on what they want to do when they finish high school and use the vo-tech school to get a head start; some have been moderately successful students and are looking for a route to success other than a four-year college.
Our math classes are generally grouped heterogeneously so we do find a wide range of abilities in each class. The district mathematics curriculum is somewhat restrictive. All students take four courses from the Core Plus Math Project (CPMP), an integrated program. We currently stretch the 3-year CPMP curriculum into four semester courses, completing four units (chapters) per semester, but we eliminate some CPMP units completely. The majority of our students complete the four courses in three years because freshmen take two semesters of math. After the required integrated courses, students have the option of taking a traditional Algebra course, followed by Precalculus, or a self-paced, computer-based math course to prepare for acceptance into a vocational Apprentice Program or for the Placement Test at the local community college. Each year of the integrated program contains units in Algebra, Geometry, and Probability/Statistics, and builds on content from previous chapters and years. Despite this thorough preparation in prior coursework, I still see weaknesses when the students reach the upper level courses. Fortunately, the areas of overlap between science and math in Nanotechnology address the most common areas of weakness that I see: Number Sense (estimation, relative size); Exponents (applying properties, negative exponents); and Geometry, (composite area and volume, effects of scaling). This curriculum unit is designed to help students in these areas of weakness, by showing the relevance of these skills to an area that is scientifically important and also significant to society.
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