## Seeking High Schools to Field Test Linear Algebra Capstone Course from EDC

Friends,

My colleagues and I at EDC are planning to create materials that can be used for a high school capstone course in Linear Algebra and its applications. The materials will contain a core semester curriculum as well as eight standalone modules that develop applications of this core to mathematics, engineering, science, and other fields related to mathematics, providing high schools with up to three semesters of topics. We are looking for high schools that might be interested in field testing the materials.

Our student audience will be made up of

(*) Students who want a 4th year of rigorous mathematics but do not want an AP course

(*) Students who have finished AP and want more mathematics in their senior year

(*) Students who want to take an advanced mathematics elective in addition to the regular sequence that leads to calculus.

I taught such a course for over 20 years to high school students at Woburn, MA high school, a working-class city north of Boston, and I'm convinced that this material is tractable to a wide range of high school students and that it is extremely useful to them after high school, more useful than a second course in calculus. For example, many of my former students said that understanding basic vector and matrix methods gave them a real leg up in their engineering and computer science courses. Another example: Many good students get to "semester 3" of calculus in college and are given a crash course in 2- and 3-dimensional geometry using vectors, and it often goes much too quickly for them. And, of course, a linear algebra course on a high school transcript is very appealing to college admissions.

Our plan is to develop a one-semester core that consists of a term (10 weeks or so) of vectorial methods in geometry: dot product, orthogonality and angle, equations of lines and planes, and intersections of these objects. Matrices will initially be introduced as bookkeeping mechanisms to keep track of the calculations involved in this material (Gaussian elimination and so on). In the second term, matrices will become objects of study in their own right, and we'll look at linear transformations of the plane and space, applications of matrix algebra to discrete mathematics, and determinants as area and volume.

The second semester modules will each take about a half-term and they'll develop applications of the core. Some examples are computer graphics, digital image processing, quadratic forms and conics, linear programming, applications to statistics, and algebraic systems. Other ideas are more than welcome.

We've assembled a team of mathematicians and teachers who have extensive experience both teaching linear algebra and working in high schools. Pearson Learning is interested in publishing the program and TI will work with us to integrate technology into the materials.

If you'd like to be involved, please email me at acuoco@edc.org. We're currently writing proposals to support this work, so, if all goes well, we should be in a position to pilot materials a year from now.

Regards,

Al Cuoco EDC/Focus on Mathematics