Mathematics (MATH)

This course will explore topics important to the mathematical experiences of students in K-5 classrooms including addition, subtraction, multiplication, division, place value, and properties of whole numbers. Relevant connections to the history of mathematics will also be included.

The course is designed to develop an understanding of topics from algebra: variables, patterns, and functions; modeling and interpreting graphs; linear and non-linear functions, connecting these ideas to underlying concepts in primary and middle grades mathematics. Attention will be given to interpreting and assessing students' work and learning. Relevant connections to the history of mathematics will also be included.

This course is designed to help participants develop understanding in: theoretical development of math and students' learning of math within content strands of rational numbers and proportional reasoning; development of pedagogical knowledge of rational numbers and proportional reasoning appropriate for K-8 Mathematics Teacher Specialists; and assessment of K-8 students' mathematical conceptions through interviews. Relevant connections to the history of mathematics will also be included.

The course will develop students' understanding of probabilistic structures, reasoning, data analysis and exploration. These structures will be related to real world problem solving. Attention will also be given to children's thinking, how they learn this basic mathematics, their problem solving strategies, and how they construct their understanding of our number system and arithmetic. Relevant connections to the history of mathematics will also be included.

Explorations of foundations of informal measurement and geometry in one, two, and three dimensions. The van Hiele model for geometric learning is used as a framework for how children understand measurement and geometric relationships. Visualization, spatial reasoning, and geometric modeling are stressed. Transformational geometry, congruence, similarity, and geometric constructions will be discussed and relevant connections to history of mathematics will be included.

A course to update and broaden secondary teachers' capability and point-of-view with respect to topics in analysis. Applications of concepts such as limits, continuity, differentiation and integration. May be taken for graduate credit and for certificate renewal by secondary school teachers.

A course to update and broaden secondary teachers' capability and point-of-view with respect to topics in discrete mathematics. May be taken for graduate credit for certificate renewal by secondary school teachers.

From advanced viewpoint, an investigation of topics in algebra from high school curriculum. Theory of equations, polynomial rings, rational functions and elementary number theory. Course may be taken for graduate credit for certificate renewal by secondary school teachers.

Topics in geometry of concern to secondary teachers in their work and provision for background and enrichment. Various approaches to study of geometry, including vector geometry, transformational geometry and aximoatics. Course may be taken for graduate credit and for certificate renewal by secondary school teachers.

This course provides an introduction to statistics and statistical methods, including descriptive and inferential techniques, as well as regression and analysis of variance, using a modern programming language to perform analyses.

Study of selected topics not otherwise covered in the regular offerings of the department. May be repeated for credit when course content changes.

Topics in the history of mathematics of particular concern to secondary teachers in their work and provision for background and enrichment. Selected topics spanning ancient times to the present. Course may be taken for graduate credit and for certificate renewal by secondary school teachers.

AP probability and statistics topics sampling, experimentation and anticipating patterns. These include Bayes's theorem; binomial, geometric, uniform, normal, t and Chi-square random variables and the mean and variance of linear combinations of random variables. Sampling distributions and central limit theorem, unbiased point estimates of population parameters and the variance of point estimates. Types of generalizations and conclusions that can be drawn including cause and effect. Course may be taken for graduate credit and for certificate renewal by secondary teachers.

AP statistics topics exploring data and statistical inference. Correlation and simple linear regression, interpretation of residual plots, influential points and transformations. Logic of significance testing including hypotheses, errors, p-values and power. Statistical inference methods (confidence intervals, significance tests, and the relationship between one- and two-side tests and confidence intervals) for proportions and means, the slope of a regression line and the Chi-Square tests. Course may be taken for graduate credit and for certificate renewal by secondary teachers.

The design of biological experiments and applications of statistical techniques in ecology, cell biology, physiology, behavior, systematics, genetics, and evolution. Emphasis will be placed on relevant concepts in experimental design and statistical analysis, decision making related to selecting appropriate experimental designs and analysis techniques, and the practical application of design and analysis for graduate research projects.

Continued preparation in anticipation of the comprehensive examination. Course may be repeated.