Data Analysis and Research Methods

Objectives and Course Outline

The course "Data Analysis and Research Methods" is currently being taught to 9^th graders at three magnet schools for mathematics, science and technology in Macomb County, Michigan. The objective of this foundation course is to become statistically minded: knowing when, where, why, and how to apply various tools; how to interpret the results; and how to verify the appropriateness of the analysis. This objective translates into developing a good understanding of the scientific method and developing the abilities to:

1. Plan data collection, to turn data into information and to make decisions that lead to appropriate action.
2. Apply the methods taught to real life situations.
3. Communicate statistical information in oral and written form.
4. Use computer and graphical techniques.
5. Plan, analyze, and interpret the results of experiments.
6. Recognize if expert analysis is required.

At the core, is the goal of clearly establishing the notion and realization of variability in all facets of life and how to identify, quantify, and measure it. After this, one-factor-at-a-time experimental design is introduced. This leads to an appropriate experience with multivariate experimental design. Multivariate experimental design is widely used in industry today.

Teaching techniques are hands-on, activity-oriented, integrated, and thematic. For example, a unit is done on meteors and craters. Students conduct background research which is followed by an experiment designed by them. The experiment determines the relationship between meteor velocity and crater size. The experiment is later expanded to include studying the effect of other variables such as the size of the meteor and soil type on crater size. Finally, additional areas to investigate are discussed, and connections are made to physics, geology, and ecology.

Although the course is highly innovative, it emphasizes accomplishing many traditional goals and objectives. Emphasizing the theme that "Learning is a Consequence of Thinking", systematic ways to develop higher order thinking, to obtain deep knowledge, and to use creative and critical thinking skills are taught.

The course consists of two basic parts:

1. Descriptive statistics, graphics, and comparing data sets. The series of activities in this first half of the course is designed to stress the need for control, randomization, and replication when collecting data.

1. Summary statistics for central location and spread
2. Dotplots, stemplots, and boxplots
3. Comparing data sets and making decisions in the presence of variability; studying relationships between two data sets (correlation).

1. Experiments

1. What is an experiment? How do you show cause and effect?
2. Experiments with one independent variable are introduced. Designing the experiment is done with control, randomization, and replication in mind. Emphasis is on graphical representation of the design space. Analysis of the adequacy of the proposed model is done and predictions are made.
3. Factorial experiments with 2 independent variables are introduced. Again, control, randomization, and replication are stressed. Acrylic cubes are used for a three dimensional representation of the experiment. Interactions are explained and studied. Interpretation and analysis are heavily graphical. Prediction equation is calculated, and the adequacy of the model is analyzed.
4. Higher order factorial experiments are conducted. The analysis moves from a graphical approach to an algorithmic approach.

The following pages describes the activities that are used to motivate learning the above topics. Each of the activities are aligned with the Michigan Curriculum Framework for Mathematics and Science. Many activities are also aligned with the Michigan Curriculum Framework for English Language Arts and Social Studies. Approximate teaching time for all activities are 90-100 class periods of 55 minutes each.

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