Data and Statistics: A Way of Thinking

One word comes to mind when I think about data and statistics: FEAR.

My own educational experience with data and statistics is not exactly stellar. I don’t remember learning it in high school (apart from mean-median-mode), and in college I took calculus-based statistics before finishing calculus. When I did come across statistics in school, it was taught in a rather anti-revelatory way: as a series of numbers to calculate. When viewed from that perspective, statistics can be scary. The calculations are tedious, and who really knows what they all mean?

So when I entered the classroom as a teacher, I didn’t want my students to have the same experience with statistics that I’d had. The question for me was: How do I teach this material in a way that connects with my students?

What I eventually discovered was that, while algebra and calculus traditionally have a “right” answer, statistics focuses on the interpretation of the result rather than the calculations themselves. In other words, statistics is a way of thinking supported by calculations, not just a series of complicated calculations. To convey this to students, I found they understood it best when they were asked to collect the data and were then given the opportunity to explore it. However, this was still a challenge; being high school students—and relatively young learners—they had very little prior exposure to the concepts beyond calculating the mean, median, and mode.

The Common Core State Standards address these challenges by starting to incorporate this way of thinking into the earlier grades. Although teachers will likely need initial support and professional development in this area, this pedagogical shift has significant potential to increase our students’ understanding of statistics. Take, for example, this sixth-grade standard:

Develop understanding of statistical variability.

  1. Recognize that a measure of center for a numerical data set summarizes all of its values with a single number, while a measure of variation describes how its values vary with a single number.
  2. Recognize a statistical question as one that anticipates variability in the data related to the question and accounts for it in the answers. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question because one anticipates variability in students’ ages.
  3. Understand that a set of data collected to answer a statistical question has a distribution which can be described by its center, spread, and overall shape.

Statistics is an incredibly powerful tool for answering questions—and one that I’m happy to see recognized by the Common Core writers.

What if, after having a discussion about the nature of a statistical question, we asked students to come up with a statistical question, collect data, and represent that data graphically? Students who come up with a non-statistical question would struggle with collecting the data, allowing a teacher to have a conversation about whether the student’s question truly is a statistical one. Once the data is collected and represented, students are invested in their question and data—thereby making it easier to talk about the measures of center and measures of variation discussed in the third part of the standard.

To give an example, I asked 32 8th, 9th, and 10th graders how many text messages they sent yesterday. Below is a graph of the results using TinkerPlots.

Graph of the number of texts each student sent.

To meet the sixth-grade standards I outlined above, we can ask students the following questions about their data:

  • Does the data collected confirm that your question is a statistical question? Explain.
  • Does the data you collected have a center? A range?
  • What shape does the data you collected have?
  • What measures could you use to describe the data you collected? Do these measures summarize the data? Do these measures describe how the data is related to a specific number?

Notice that at this point, we haven’t asked for any calculations. What we have done is get the student thinking about how their data can be represented in a numerical way. From here, we can build on their thinking by asking them to make predictions about what the average number of text messages sent in one day will be, and how variable the data is before asking for calculations. In this way, students are learning to think from a statistical perspective, helping them put the calculations into context.

As students proceed to take on more in-depth evaluations of data—and in turn, more complicated calculations—this foundation becomes more and more important. If I’d been privy to such a foundation as a growing student, perhaps statistics wouldn’t have seemed quite so scary.

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