Overview
For the 2011-2012 school year, I will be working at Mountain View High School with David Romero. The focus of our partnership will be on creating exciting and interesting projects for his Intermediate Algebra and Algebra II students that will allow them to utilize what they are learning in the classroom to solve real world problems. In addition, we hope to expose students to the broader world of mathematics, both its diverse areas of research and its history. Besides making lessons more fun and interesting, we hope this focus will:
- Increase student participation and interest in their math classes.
- Give students a better understanding of how mathematics is used to solve "real world" problems.
- Expose students to possible STEM careers.
I've come away with a great deal of new insight into mathematics education from my time at Mountain View High School. The most important of which has been a better understanding the transition from high school math courses to college math courses. In my own class at the university level, I've had freshman and sophomore students that struggle with the course despite the fact that they did very well in their high school math classes. Being over a decade removed from my own high school math courses, my understanding of why students were having this difficulty and consequently my ability to address it was limited.
This year at Mountain View has taught me a great deal about how mathematics is taught at the high school level, and given me some insight into why this transition from high school to college in mathematics can be so difficult for some. For example, while most of the high school students that I have worked with have memorized the formulas relevant to a given topic, very few of them truly understand the underlying concept, much less where these formulas come from. Because of this they not only see mathematics as an exercise in memorizing arbitrary rules, they have a great deal of difficulty adapting what they've learned to situations not covered in the textbook. This insight will be invaluable for my college level teaching in the future, as it will allow me to organize my classes in such a way that I can ease this transition as much as possible.
Teaching Materials
- Graphing linear data (PDF) - Students were given several sets of data. They were asked to graph the data in whatever way they liked, and use this graph to write a paragraph summarizing the behavior of the data. In addition, students can find their own line of best fit and use this line to make predictions.
- The Monty Hall problem (Keynote) - You are on a game show and are presented with three doors. Behind one of the doors is a pile of money, behind the other two are goats. The host asks you to choose a door. Before opening your chosen your door, the host opens one of the other doors to reveal a goat. The host then give you the choice of sticking with your original door choice or switching to the unopened door. What should you do? This is known as the Monty Hall problem, and the answer is not what most people expect. This is a fun way to introduce experimental versus theoretical probability.
- Quadratic functions (PowerPoint) - A lesson introducing quadratic functions.
- Solving quadratic equations by taking square roots (Keynote) - A lesson showing students how to solve quadratic equations using square roots.
- Chaos theory (Keynote) - A presentation on the Mandelbrot set, which was tied into the section on complex numbers.
- Linear Programming (Powerpoint) - A lesson in which students use their knowledge of linear inequalities and linear systems to solve an airline logistics problem. The students then solved their own real world problems using linear programming.
- Beyond Bread (PDF) - You have been hired by Beyond Bread to determine how many loaves of Focaccia and Ciabatta to bake in order to maximize daily profit.
- NFL Football (PDF) - You have been hired by the head coach of the Oakland Raiders to determine how carries Darren McFadden and Michael Bush should get per game in order to maximize total rushing yards.
- Television Executive (PDF) - You are the CEO of a new television station and you need to determine how many reality shows and how many scripted shows you should have in your weekly show line up in order to maximize profits from advertising.
- Stocks (PDF) - You have been hired by Renaissance Technologies, a hedge fund founded by mathematician James Simon. You have been told to purchase 100 shares of Google and Apple, and want to maximize your total investment while keeping possible losses under control.