The goal of the course is to develop and use mathematical tools to build models of data that allow one to interpret and understand the situation that generated the data. The definition of model that we subscribe to is "a simplification of a real situation that has value in helping to understand the situation". We begin with an overview of problem solving with an emphasis on understanding the problem and developing ways to collect data to study the problem. The first types of models we use are statistical in nature; we treat one-variable summary statistics as a vast simplification of the data - from a list of potentially thousands of numbers to a much smaller list of perhaps ten numbers. After this, we develop models that emphasize correlation between several variables: single variable regression, multiple regression and regression with categorical data. The last models we develop are nonlinear equations to model relationships in the data and the mathematical tools needed to understand these models, including some aspects of calculus.

Course outline (each item is roughly one week of material):

1. Defining the problem and thinking about how to get data to analyze it
2. Types of data and how to organize it
3. Summary statistics to model what is typical
4. Summary statistics to model the spread of the data
5. Frequency distributions to model one variable data
6. Correlations between variables
7. Linear regression (one explanatory variable)
8. Linear regression (several explanatory variables, both numerical and categorical)
9. Nonlinear models of data and parameters
10. Non-linear regression and transformation of data
11. Marginal analysis and parameter analysis to understand nonlinear models
12. Optimization using calculus
13. More applications of exponential and logarithmic models

Grading policy

This course has forced us to re-examine our assumptions about grading. The nature of the open-ended assignments requires a flexible grading system that rewards students for accomplishment while still helping them push further in their understanding and correcting their misconceptions about the mathematical tools (and the concepts underlying these). After experimentation with several methods ranging from a standard "partial credit" scenario to no grading at all until the end of the semester, we have settled on a system we refer to as C.O.G.S., Categorical Objective Grading System.

At the heart of this system lie our objectives for the course. We expect students to develop in three ways. They should develop an understanding of the mathematical and technological mechanics and terminology needed to analyze data. They should develop in their application and reasoning, relating the mathematical tools to the underlying problem. Finally, students should develop skills in communication and professionalism to prepare for their future roles. In short, they must be able to calculate and work with data, but if they cannot understand what it means, the calculations are useless. And all the understanding and computation in the world is useless if it is not communicated effectively.

Each of our assignments is then evaluated by comparing the student work to a check list of grading criteria that is divided into three rows and two columns. Each row corresponds to one of the three areas described in the preceding paragraph. The columns are labeled "Expected" and "Impressive". After a complete evaluation of a student work sample, the result is three descriptors of the students work, either an E or I (or 0 if there is not sufficient evidence) for each of the three grading areas. At the end of grading period, student work is aggregated across these grading categories first, producing a performance level for each of the three areas; these are then combined to produce a course grade, as shown below:

Here's a copy of the spring 2006 syllabus from one section of the course (MS Word format, 53.5 kB).