The goal of this project is to explore an innovative model of statistics instruction and assessment that prepares students to learn more effectively from many styles of instruction, including traditional lectures. Many children have difficulty learning to use and understand mathematical representations. One of the reasons for this difficulty is that children often do not understand the work a given representation has been designed to accomplish. For example, they tend to view symbolic formulas as rules that make life harder, not easier. This project will study classroom environments that help middle-school students appreciate the work that statistical representations need to perform, and in this way, it will prepare them to learn about those representations. A central feature of these environments is that students invent their own procedures and representations for solving problems about quantitative situations. For example, if students are learning about variability, very simple situations might include the sets of numbers {2 4 6 8} and {4 5 5 6}. The students are reminded that there is a procedure for determining a single value that captures what is the same about the sets; namely, the average. The students' task is to build a method for determining a single number for each set that can characterize what is different, in this case, the variability. After they create their own methods (often a range formula), they receive new sets that draw their attention to other properties of distributions (e.g., the middle numbers -- {0 2 4 6 8} vs. {0 0 0 0 8}). After several cycles of inventing, assessing, and revising, the students are prepared to learn about and use conventional approaches to variability (e.g., standard deviation). The goal is to help students notice important quantitative properties, and to prepare them to learn how conventional representational solutions elegantly capture those properties.
