Perspectives on Deepening Teachers’ Mathematics Content Knowledge: The Case of the Oregon Mathematics Leadership Institute

The Oregon Mathematics Leadership Institute (OMLI) project served 180 Oregon teachers, and 90 administrators, across the K-12 grades from ten partner districts. OMLI offered a residential, three-week summer institute. Over the course of three consecutive summers, teachers were immersed in a total of six mathematics content classes– Algebra, Data & Chance, Discrete Mathematics, Geometry, Measurement & Change, and Number & Operations—along with an annual collegial leadership course. Each content class was designed and taught by a team of expert faculty from universities, community colleges, and K-12 districts. Each team chose a few “big ideas” on which to focus the course. For example, the Algebra team focused on algebraic structure and properties of the concept of a group, while the Data & Chance team centered their activities on the exploration of ideas of central tendency and variation using statistics and data analysis software packages. The content in all of the courses was addressed through deep investigation of the mathematics of tasks that had been selected and adapted from resources for K-12 mathematics classrooms. In addition to mathematics content, the courses were designed with specific attention to socio-mathematical norms, issues of status differences among learners, and the selection and implementation of group-worthy tasks for group work. The faculty attended sessions grounded in the work of Elizabeth Cohen on strategies for working with heterogeneous groups of learners (Cohen, 1994; Cohen et al, 1999) which was central to the OMLI design and implementation. Institute faculty modeled these strategies in the Institute classrooms and made their moves as transparent as possible, so that the teachers would be able to grapple with these strategies during the Institute and plan for implementation in their own classrooms. The Data & Chance course also modeled uses of technology in instruction using Tinkerplots. Generalization and justification were emphasized as mathematical ways of learning and knowing, and institute faculty conducted classroom discussions that intentionally modeled pushing for generalization and justification

Building Middle-Level Mathematics Teachers\u27 Capacities as Teachers and Leaders: The Math in the Middle Institute Partnership

This article describes professional development for middle-level mathematics teachers offered through the Math in the Middle Institute Partnership, a National Science Foundation-funded project to build teachers’ capacities to improve mathematics learning for all students. An overview of the project, including descriptions of its goals and curriculum are provided. Detailed descriptions of two mathematics courses and one pedagogy course are offered. The mathematics courses included here are the introductory course to the Math in the Middle Institute, as well as one of the final math courses of the Institute in which participants apply mathematical knowledge and processes to real-world problems. The pedagogy course features curriculum that enables teachers to acquire an understanding of the nature and purpose of action research, and launches teachers into planning and implementing systematic inquiry in their own mathematics classrooms around topics of their choosing. The varied abilities of teachers, as well as growth in teachers’ mathematical and pedagogical capacities, are represented by several samples of student work provided within the article. In addition, mathematical and pedagogical products of student work are also provided through the project’s URL links. Improving teacher quality is identified as a national need in mathematics education and one many universities and schools across the country are working in partnership to try to address. This article describes a professional development project aimed at improving mathematics teaching and learning in the middle grades. An overview of the project, along with a close look at several of its course offerings, are presented highlighting mathematical and pedagogical goals, challenges, and accomplishments

Lectures on Randomized Numerical Linear Algebra

This chapter is based on lectures on Randomized Numerical Linear Algebra from the 2016 Park City Mathematics Institute summer school on The Mathematics of Data.Comment: To appear in the edited volume of lectures from the 2016 PCMI summer schoo

Degeneracy of Landau Level and Quantum Group SL_q(2)

We show that there is a kind of quantum group symmetry $sl_{q}(2)$ in the usual Landau problem and it is this quantum group symmetry that governs the degeneracy of Landau levels. We find that under the periodic boundary condition, the degree of degeneracy of Landau levels is finite, and it just equals the dimension of the irreducible cyclic representation of the quantum group $sl_{q}(2)$.Comment: 10 pages, Preprint ( reprint ) of Nankai Institute of Mathematics. For hard copy, write to Prof. Mo-lin GE, Director of Nankai Institute of Mathematics. Do not send emails to this computer accoun

An Evening Spent with Bill van Zwet

Willem Rutger van Zwet was born in Leiden, the Netherlands, on March 31, 1934. He received his high school education at the Gymnasium Haganum in The Hague and obtained his Masters degree in Mathematics at the University of Leiden in 1959. After serving in the army for almost two years, he obtained his Ph.D. at the University of Amsterdam in 1964, with Jan Hemelrijk as advisor. In 1965, he was appointed Associate Professor of Statistics at the University of Leiden and promoted to Full Professor in 1968. He remained in Leiden until his retirement in 1999, while also serving as Associate Professor at the University of Oregon (1965), William Newman Professor at the University of North Carolina at Chapel Hill (1990--1996), frequent visitor and Miller Professor (1997) at the University of California at Berkeley, director of the Thomas Stieltjes Institute of Mathematics in the Netherlands (1992--1999), and founding director of the European research institute EURANDOM (1997--2000). At Leiden, he was Dean of the School of Mathematics and Natural Sciences (1982--1984). He served as chair of the scientific council and member of the board of the Mathematics Centre at Amsterdam (1983--1996) and the Leiden University Fund (1993--2005).Comment: Published in at http://dx.doi.org/10.1214/08-STS261 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org