Matt has recently began research in mathematics education, focusing on issues of student cognition at the undergraduate level. Before beginning work in math education, Matt studied the Toda lattice, which is a model of a one-dimensional chain of particles. In particular, Matt looked at some of the asymptotic behavior as the spacing of the particles approached zero.
Matt is working at Tucson High Magnet School with Dr. John Willy. He has been involved in pre-calculus/trigonometry classes and an algebra I class. Matt's goals were to bring in a sense of what math research looks like by bringing in guest speakers throughout the year, as well as readings about current activities in mathematics.
In addition to classroom activities, Matt was involved in the creation of a math circle at the high school. This is an informal gathering for students to work through mathematical problems and ideas. Meetings took place Monday mornings before school. Many of the problems are listed here and here. Many of the problems have centered on problems involving combinatorics and graph theory, which allows students with any background to think about and come to solutions to the problems.
While in the classroom, Matt's primary role was being involved in the problems of the week. These involved occasional online readings as well as more traditional problems. The role of the problems was to focus on problem solving skills as opposed to procedural proficiency. Not all the problems had clear solutions, though obtaining the solution was not always the principal goal either. In the write-ups for the problems of the week, students needed to describe their solutions to the problem and the way they thought about it. One successful example of this was a sudoku puzzle. The puzzle was not terribly hard, but the students needed to write about how they thought about the problem and the strategies they used. Describing the ways they thought was much more challenging than solving the problem.
Teaching high school students takes a very different set of skills than teaching college students. High school students have great motivation in solving problems, but don't always know how to go about thinking about a new problem. Approaching a problem in which you have no idea what to do is a difficult task, but developing the skills to solve problems is worthwhile.
High school students are interested in problems which relate to their lives. They also see through problems which have been "manufactured" to seem applicable. Taking a problem and rewording it intentionally turning a principle into a "real life "problem" don't work. The problems need to be things that the student might actually run into. Using logistic functions to model disease spread or using probability to determine where to send teams in search and rescue are real problems that people use mathematics for. It is difficult to make problems both mathematically challenging and relevant, but these problems are worthwhile.
What does a
mathematician do questions for a reading
Mathematical modeling for a reading
Logistic functions with reading
Monty Hall with reading
Slides for supply and demand
Hand-made slide rule