Mathematical Concepts & Structures II

Fall 2008

This is the second of three sequential mathematics courses (Math 204 is a prerequisite for this course) that enrich the mathematics content knowledge of prospective elementary school teachers. In this course, you will gain a deep understanding of topics from the areas of probability, statistics, and functions. More specifically, you will learn to:

• Apply fundamental ideas in probabilistic scenarios (equally likely outcomes, addition rule, multiplication rule, conditional probability, mutual exclusivity) to solve problems involving chance; apply understanding of permutations and combinations to solve such problems.
• Devise simulations to determine probabilities of “real-life” scenarios; apply law of large numbers to simulation analysis; apply critical thinking skills and understanding of basic experimental design to critique summaries of statistical studies and identify key features of data analyses (variables, types of data, sample, population, statistical summary values, inferential statements);
• Demonstrate understanding of “mean” and “median” and identify those measures of a data set displayed in summary form, graphical form, or raw form; demonstrate flexible understanding of the mean of a data set through problem solving and concrete modeling; determine appropriate graphs to display data; construct those graphs;
• Demonstrate understanding of variability by determining appropriate measure of variability of a data set and correctly comparing variability of data sets given graphical displays or other summary information; demonstrate understanding of center and variation in general and apply these ideas to verbal descriptions of data sets;
• Use correct language to identify and discuss distributions that are uniform, normal, skewed, as well as symmetric or not; understand the relationship between absolute scores and z-scores on a normal distribution and apply knowledge to comparative situations;
• Identify bivariate data, and use correct language to discuss certain patterns of correlation (positive, negative, or none; linear vs. non-linear or none); Perform correlation/regression analysis and interpret findings (r-value, slope, y-intercept);
• Understand implications of linear functions with regard to constant rate of change and recognize linearity from equations, tables, verbal descriptions, and graphs;
• Distinguish linear, quadratic, and exponential functions from tables, graphs, and verbal descriptions; apply appropriate function to determine equation;
• Interpret meaning of the parameters in a linear or exponential function in terms of the context; use regression modeling (linear, quadratic, exponential) to analyze data collected from experimentation and/or real-life scenarios and determine most appropriate function.

A special emphasis will be made on developing problem-solving skills.

If your presentations and participation in discussions are consistently good (feel free to ask me for feedback if you are not sure), I will add a third of a letter grade to your final grade. At worst (if you are not ready or miss the class half the time), I will subtract one full letter grade from your final grade.

Participation in homework teams is an essential part of the course. If you miss a team meeting, it is your responsibility to work out what form should your contribution to the team effort be. Putting your name on a team homework if you have not participated in meetings is a violation of University's academic integrity policy.

You are welcome and encouraged to ask me for help with course material during the office hours or by making an appointment. The rule for team assignments is that as least two of the team's members must be present.

You should expect to spend a considerable amount of time working on this course outside of class. At the same time, try to be efficient. If you are spending a lot of time on homework without making much progress, talk to me.

Tests and quizzes are to be written strictly individually, everyone caught cheating on any test will have the course grade decreased by one letter grade.

Normally, no make-up tests will be given; if for some reason you are not able to take a test, please, let me know as soon as possible.

If you have questions or concerns about the course, be sure to discuss them with me during my office hours or by appointment.