Theory of Measurement     Data Displays     Meta-Representational Competence  

Unit 1

Inventing Displays



Unit 1, Inventing Displays, engages students in a simple process: Measure the length of an object, such as the arm-span of a person or the perimeter of a table. Each student independently measures the same attribute. The tool provided for measurement, a 15 cm ruler, ensures that students’ measurements will be different due to chance variation in how they measure. The aim is to help students understand that variability is the result of a repeated process. Here each person’s measurement of the length is a repetition of the process of measuring, which includes moving the ruler. If time allows, students measure the same attribute again with a meter stick or tape measure, and these additional measurements are set aside for future use. Measuring with a meter stick or tape measure provides students with an opportunity to relate a change in process with a change in the resulting variability of the measurements. Students create displays of the ruler data to illustrate "something they noticed" about the collection of data from the entire class. Students then compare the various displays that they make for aspects of the data that are revealed and concealed by each data display. The shapeof the data visible in the display results from designers’ decisions about how to structure the data. Important mathematical means for structuring data include ordering, counting, grouping, and using the measurement scale of the batch of measurements. Milestones of student progress are illustrated by the Data Display (DaD) and Meta-Representational Competency (MRC) constructs.

Performances

DAD1A: Create or interpret data displays without relating to the goals of the inquiry.

DAD2A: Concentrate on specific data points without relating these to any structure in the data.

DAD2B: Construct/ interpret data by considering ordinal properties.

DAD3A: Note similar values or "clumps" in the data set.

DAD4A: Display data in ways that use its continuous scale (when appropriate) to see holes and clumps in the data.

DAD5A: Recognize that a display provides information about the data as a collective.

MRC2B: List and compare observed characteristics of displays without explicit reference to data structure or purpose of data collection.

MRC3A: Compare displays by indicating what each shows about the structure of the data.

MRC4B: Coordinate qualities of multiple displays with what those displays show and hide about the data.