## Reflection: Developing a Conceptual Understanding Central Tendency - Section 2: Class Notes

Central tendency is a complex concept when it comes to understanding what it describes about data. In 7th grade, students also learn about variability. As educators we must keep in mind the Common Core shifts of depth of knowledge. Before this curriculum existed, “mean” was taught along with median, mode and range. Some of my students this year learned it this way. By grouping mean, median, mode and range this way, it becomes difficult for some students to separate range as a measure of something different. It is no longer expected to solely teach the process by which mean is derived; students must also understand how this measure can be limited so that they are ready to understand the role that measures of variability can play when analyzing data. By changing the way we discuss mean in this grade we can prepare our students for higher levels of statistics, rather than giving them a limited understanding which only ends up confusing them later in life and sometimes discouraging them from seeking careers in this field.

One way to change these notes and encourage rigorous discussions around the limitations of the “mean”  is to give students 2  sets of data with the same averages (or close to), but different variability. The first page of this Common Core lesson includes a great example elated to temperature. Some questions that could push this rigorous conversation include:

“Find the mean temperature for each city” – this question will allow students to practice the process of finding the average

“Are the averages similar? Equivalent? What does this mean?” – this question can push students to gradually consider what mean is measuring. It may require some scaffolds, such as “what does the ___ degrees represent?”, “what does it tell us about the city’s temperature?”, “since they are similar averages, does it mean that both cities have the same kind of climate? Why or why not?”

I would NOT introduce any measures of variability in this lesson, I would still keep that separate and investigate in the next lesson. The push during these notes and discussion should be to get students to recognize that while the two cities have very similar averages, they do not share the same kind of climate. Identifying what is different about those climates (the variability) is a great way to provide extension for the higher kids. This will make them experts the following day when they compare variability of data sets. Additionally, the constant questioning of “what is the mean? What does it represent?” throughout this unit is necessary to push this complex topic.

A More Rigorous Discussion
Developing a Conceptual Understanding: A More Rigorous Discussion

# Central Tendency

Unit 7: Statistics and Probability
Lesson 1 of 11

## Big Idea: students work independently and in pairs to calculate ans use measures of central tendency to describe distributions

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55 minutes