Ways kids see data  Konold et al. (2015)
By: Kristin HunterThomson
Photo credit: gratuit

How do kids actually “see” the data?

How do they think about the ink — numbers, text, lines, dots — on the page?

How does that influence what claims they make?
If you have ever found yourself wondering about some of these, or other related, questions then I highly recommend reading Clifford Konold, Traci Higgins, Susan Jo Russell, and Khalimahtul Khalil’s 2015 article titled “Data seen through different lenses”.
Being able to ask statistical questions of our data and make inferences to the broader context requires thinking in the aggregate about data. However, that is not often how our students approach or talk about data. Konold and colleagues used teacherwritten case studies (elementary school students), individual student interviews (middle school students), and paired student interviews (high school students) to categorize common ways that students “see” data. The four categories that they described for how students approach data are described here in the loose hierarchy as Konold et al. (2015) present them:

Pointers  Students use the data to point to the larger event that occurred to collect the data value (e.g., we asked each other what our favorite ice cream flavor is).

Case values  Students use the data to learn about the value or characteristic of an individual case (e.g., Amesh says that he likes chocolate best and that is his “dot” on the graph).

Classifiers  Students use the data to determine which attribute values have the highest (or lowest) counts (e.g., four of us like strawberry best).

An aggregate  Students use all of the data to gain an understanding of the broader picture and potentially answer a statistical question (e.g., half of the students like chocolate).
It is important and interesting to note that none of these approaches to “seeing” data are inaccurate and in fact students can hold many of these at the same time within their minds as they work with a given dataset or data visualization. The tricky part comes when we are asking students to answer questions that require one approach, but they are “seeing” the data from a different approach. Or, when we want them to provide an answer from one approach but ask them a question that prompts them to think in another approach.
For example, if we are wanting them to explore the distribution of how long hurricanes last (an aggregate feature of the whole dataset) but ask them to read the graph to find the most frequent (i.e., mode) length of a hurricane (a classifier). Our question does not line up with our desired intention for what the kids get out of the data. Knowing that 5 days is the most frequent length of days of a hurricane, in this dataset, does not help you appreciate that the data are positively (or right) skewed, meaning that while there is a range from 3 to 24 days most hurricanes do not last for very long.
Dot plot that can be used to answer the question “How long do hurricanes last?” Data Source: National Hurricane Center
I encourage you to check out Konold et al.’s (2015) very accessible article, to gain some more perspective of the different ways that students “see” data. It is interesting to think about, and also interesting to use as a framework to better understand what may actually be going on inside their heads.