Avi Berman

A L P S: Matrices with nonpositive off-diagonal entries

Abstract The purpose of this paper is to characterize and interrelate various degrees of stability and semipositivity for real square matrices having nonpositive off-diagonal entries. The major classes considered are the sets of diagonally stable, stable, and semipositive matrices, denoted respectively by A , L , and S . The conditions defining these classes are weakened, and the resulting classes are examined. Their relationship to the classes of real matrices P and P 0, whose off-diagonal entries are nonpositive and whose principal minors are respectively all positive and all nonnegative, is also included.

Nonnegative generalized inverses of powers of nonnegative matrices

Abstract We study the nonnegativity of the Moore-Penrose inverse of the powers as well as the product of nonnegative matrices.

What Do High School Teachers Mean by Saying “I Pose My Own Problems”?

The aim of this chapter was to identify mathematics teachers’ conceptions of the notion of “problem posing.” The data were collected from a web-based survey, from about 150 high school mathematics teachers, followed by eight semi-structured interviews. An unexpected finding shows that more than 50% of the teachers see themselves as problem posers for their teaching. This finding is not in line with the literature, which gives the impression that not many mathematics teachers are active problem posers. In addition, we identified four types of teachers’ conceptions for “problem posing.” We found that the teachers tended to explain what problem posing meant to them in ways that would embrace their own practices. Our findings imply that most of the mathematics teachers are result-oriented—as opposed to being process-oriented—when they talk about problem posing. Moreover, many teachers who pose problems doubt the ability of their students to do so and consider problem-posing tasks inappropriate for their classrooms.

Teaching Linear Algebra

Research on students’ conceptual difficulties with linear algebra first made an appearance in the 90’s and early 2000’s (e.g. Carlson, 1997; Dorier & Sierpinska, 2001). Over the past decade, research on linear algebra has concentrated on the nature of these difficulties and students’ thought processes (e.g. Stewart &Thomas, 2009; Wawro, Zandieh, Sweeney, Larson, & Rasmussen, 2011). The aim of the discussion group is to initiate a multinational research project on how to foster conceptual understanding of Linear Algebra concepts. Key questions and issues to be discussed are listed below:

Issues Surrounding Teaching Linear Algebra

Linear Algebra is one of the most important courses in the education of mathematicians, scientists, engineers and economists. DG 3 was organized by The Education Committee of International Linear Algebra Society (ILAS) in order to give mathematicians and mathematics educators the opportunity to discuss several issues on teaching and learning Linear Algebra including motivation, challenging problems, visualization, learning technology, preparation in high school, history of Linear algebra and research topics at different levels. Some of these problems were discussed. Around 50 participants participated in the discussion.