Why is an expanded concept of variation necessary in statistical improvement? Is all variation necessarily numerical? How might this approach invalidate concepts and techniques taught in traditional basic statistics courses?

An expanded concept of variation is necessary in statistical improvement because it encourages students to think about data in a comprehensive way. It pushes students to move beyond standard, objective terms like mean, standard deviation, and so on. It compels them to actively think about the real-life problem and context of the data. In a sense, it makes the learning of statistics personal.

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I think you could argue an expanded concept of variation is necessary in statistical improvement because it makes the study of statistics less mechanical. That is to say, students should be able to understand and articulate why a set of data has the distribution that it does. It’s critical to move beyond more objective, empirical evaluations like mean, shape, outliers, and so on. If students only concentrate on the numerical aspect, they are, according to some teachers, not engaging with the data in a comprehensive, intuitive way.

You might want to look into the arguments offered by the professors Katie Makar and Jere Confrey. For them, it's important to provide students with a complete context for any given data. Students who connect variation and the study of statistics with specific situations and dynamic tasks are, according to Makar and Confrey, more likely to have a “robust” learning experience.

More so, by moving the focus away from objective aims, an expanded concept of variation might make the study of statistics more personal and perhaps more meaningful. Makar and Confrey encourage statistics students to deploy their own language to describe what they are seeing in a given data set.

By focusing on the personal, you might claim Makar and Confrey are countering traditional math and statistics teaching techniques. For them, statistics isn’t a fixed, concrete field that students passively absorb. It seems like they want to stress the ways in which students can actively engage with statistics. For Makar and Confrey, it’s almost as if statistics can be taught more like a novel or a poem—the interpretation depends on the reader or, in the field of statistics, the statistician.

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