Interpretations of Boxplots: Helping Middle School Students to Think Outside the Box

Figures & data

Figure 1. A completed boxplot.

Figure 2. Sample boxplot tasks.

Figure 3. This student created both a number line and an organized list.

Figure 4. This student has created an organized list.

Figure 5. In this task, students matched boxplots to their datasets.

Figure 6. Note the use of additive thinking.

Figure 7. This student worked with raw data.

Table 1. Teaching tips.

When fostering students:	We suggest that teachers:
To create boxplots	• Encourage students to see connections to their prior knowledge, particularly between the percent and percentile concepts.
	• Prepare students to fluently determine 25%, 50%, and 75% of a base.
	• Call students' attention to the meaning of the new concepts they encounter.
	• Discuss similarities and differences of different statistical representations that the students know.
To read information from boxplots	• Select mathematical tasks that create opportunities for students to use the five-number summary (that they used to create boxplots).
	• Ask students to explain their reasoning.
To interpret information from boxplots and avoid potential difficulties	• Select mathematical tasks that create opportunities for students to see when their previous knowledge is helpful or hindering.
	• Create multiple representations of the same raw data and ask students to compare them.
	• Create representations that link raw data with its boxplot via hands-on and digital activity.
	• Use technology to create powerfully linked representations of the raw data and its boxplot.
	• Provide hands-on experiences for students.
	• Use one statistical representation to make inferences about another.
	• Use a concrete representation to find meaning in a more abstract representation.

Figure 8. Sticky notes have been placed on a number line for each data point.

Figure 9. A boxplot has been drawn on the board directly above the number line.

Figure 10. Technology allowed students to visualize the data in a boxplot.