Wednesday, January 03, 2007

Multiple Variable Visual Displays

The third Grand Principle from Edward Tufte is "Use Multiple Variables". As Tufte says, the world that we are trying to understand is multivariate. so our displays should be too. Tufte refers to the Napoleon March poster as a great example of the integration of multiple variables. In his example you have temperature over time, change in the size of the army, direction of movement, and time. It is an extraordinary display of the relationship between variables. Although I disagree with Tufte's assertion that this visual "Shows Causality", it clearly shows important and relevant relationships.

Teachers and administrators should accept the challenge to use multiple variables in their visuals during the exploration of achievement. This principle is espoused by many leaders in education (
Schmoker, Love, Reeves, Stiggins, DuFour, and others) with Victoria Bernhardt being the most recognized champion for multiple measures. Bernhardt advocates for the exploration of the relationship between two or more of four dimensions that are important to school reform (student achievement, school processes, demographics, and perceptions of students, staff and parents). Bernhardt advocates for exploring the intersection of these dimensions to get at the root of a problem.

We are challenged to ask two-dimensional questions like, "what is the relationship between state assessment scores (student achievement) and grades (school processes)?" "Do students with positive attitudes toward school (student perceptions) perform better on the state assessment (student performance)?" Three-dimensional questions might include, "Do grades (school processes) have any relationship to state assessment performance (student achievement) for language learners compared to non-learners (demographics)?" What is key is that as teachers and adminstrators review these data they have access to appropriate visual displays of these data or know how to create usable charts. In addition, teachers and administrators must be compelled to ask the next question and manipulate the data.

Let's just take the first question, "what is the relationship between state assessment scores (student achievement) and grades (school processes)?" This crudely drawn diagram is similar to the relationship we found in our district for high school students. The relationship (shown in a scatter plot) is completely random and cannot be explained by any slope. By adding a third variable/dimension the graphic takes a dramatically different look. We can now see that those students that are not language learners have a positive relationship between grades and state assessment performance. In other words, for non-language learners grades appear to measure something similar to what is being measured on the state assessment.

Although the visual display clearly reveals a pattern (one that is made-up), it does not tell me what causes this. However, it sparks a far deeper and more engaging discussion regarding grading and student performance when placed in three dimensions.

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