## Learning Math: Data Analysis, Statistics, and Probability

# Classroom Case Studies, Grades K-2 Part A: Statistics as a Problem-Solving Process (25 minutes)

A data investigation should begin with a question about a real-world phenomenon that can be answered by collecting data. After the children have gathered and organized their data, they should analyze and interpret the data by relating the data back to the real-world context and the question that motivated the investigation in the first place. Too often, classrooms focus on the techniques of making data displays without engaging children in the process. However, it is important to include children, even very young children, in all aspects of the process for solving statistical problems. The process studied in this course consisted of four components:

Children often talk about numbers out of context and lose the connection between the numbers and the real-world situation. During all steps of the statistical process, it is critical that students not lose sight of the questions they are pursuing and of the real-world contexts from which the data were collected.

When viewing the video segment, keep the following questions in mind: See Note 2 below.

**• **Think about each component of the statistical process as it relates to what’s going on in the classroom: What statistical question are the students trying to answer? How were the data collected? How are the data organized, summarized, and represented? What interpretations are students considering?

**• **How does the teacher keep her students focused on the meaning of the data and the data’s connection to a real-world context?

**• **Thinking back to the big ideas of this course, what are some statistical ideas that these students are beginning to develop?

**Video Segment**

In this video segment, the teacher, Ellen Sabanosh, applies the mathematics she learned in the *Data Analysis, Statistics, and Probability* course to her own teaching situation by asking her students to analyze and interpret the data they collected earlier. (Each child was given two boxes of raisins; the children then counted and recorded the number of raisins in each box.) The children will now compile their data into a class line plot and discuss the distribution of the data.

**Problem A1
**Answer the questions you reflected on as you watched the video:

**a. **What statistical question are the students trying to answer?

**b. **How did the students collect their data?

**c. **How did they organize, summarize, and represent their data?

**d. **What interpretations are the students considering?

**e. **How does the teacher keep her students focused on the meaning of the data and the data’s connection to a real-world context?

**f. **What statistical ideas are these students beginning to develop?

**Problem A2**

As the students examined the data, Ms. Sabanosh asked several times, “What do you notice?” or “What else do you notice?” What are some reasons for asking open-ended questions at these points in the lesson?

**Problem A3**

Ms. Sabanosh gave each student two boxes of raisins for data collection. The students counted the number of raisins in each box separately and recorded both data values on the line plot. What were some advantages and disadvantages, mathematically and pedagogically, of her decision to give each student two boxes of raisins?

**Problem A4**

Ms. Sabanosh asked the students to analyze the data when only about half the data had been compiled onto the class line plot. How might early analysis of partial data, such as in this episode, support students’ evolving statistical ideas?

### Notes

**Note 2**

The purpose of the video segments is not to reflect on the methods or teaching style of the teacher portrayed. Instead, look closely at how the teacher brings out statistical ideas while engaging her students in statistical problem solving. You might want to review the four-step process for solving statistical problems. What are the four steps? What characterizes each step?

### Solutions

**Problem A1
a. T**he question is, “How many raisins are in a box?”

**b.**The students collected the data by counting the number of raisins in each of the boxes of raisins they were given.

**c.**Students organized and represented their data by placing blue dots on a class line plot, and they summarized their data by finding the mode.

**d.**Students interpreted their data by reasoning that smaller numbers meant that they had bigger raisins.

**e.**The teacher asked the students to interpret their results by relating them back to the context.

**Some statistical ideas the students touched on are the nature of data, quantitative variables, variation, range, mode as a summary measure of a data set, sampling, and making and interpreting a line plot.**

f.

f.

**Problem A2
**Asking open-ended questions gives students more opportunities to engage in statistical problem solving and to construct their understanding of statistical ideas.

**Problem A3**

The main advantage is that giving students two boxes of raisins enlarged the sample, making the results slightly more representative of the population than if students had only been given one box. However, the overall sample size is still relatively small. One disadvantage in giving students two boxes of raisins is that the teacher and students had to carefully determine ways to organize their work environment so that each box was counted and recorded separately.

**Problem A4
**The early analysis of partial data encouraged students to begin thinking and making predictions about how the data might evolve.