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Data Session 10, 3-5 Classroom Case Studies
 
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Session 10, Part D:
Examining Children's Reasoning (30 minutes)

As this course comes to a close and you reflect on ways to bring your new understandings of data analysis, statistics, and probability into your teaching, you have both a challenge and an opportunity: to enrich the mathematical conversations you have with your students around data. As you are well aware, some students will readily grasp the statistical ideas being studied, and others will struggle.

The problems below describe scenarios from a classroom case study involving children's developing statistical ideas. Some student comments are given for each scenario. For each student in Problems D1-D3, comment on the following:

 

Understanding: What does the statement reveal about the student's understanding or misunderstanding of statistical ideas? Which statistical ideas are embedded in the student's observations?

 

Next Instructional Moves: If you were the teacher, how would you respond to each student? What questions might you ask so students would ground their comments in the context? What further tasks and situations might you present for each child to investigate? Note 7

Problem D1

Solution  

Ms. Johnson's fourth-grade class was examining height. They measured their heights in inches and then displayed their data on the line plot below.

After plotting their data, here's what the students had to say:

a. 

Damon: "The tallest person is 64 inches, and the shortest person is 52."

b. 

Juanita: "I think 64 is an outlier, because there's a gap at 63."

c. 

Asher: "We don't have a mode, because 55 and 56 are the same."

d. 

Larie: "Most of us are from 54 to 58 inches tall."

e. 

Michael: "The median is 58 because it's the middle of the range."

f. 

Ali: "The range from 50 to 65 is 15."

f. 

Antrell: "I think the median is 57, because it's the middle of our heights."


 

Problem D2

Solution  

Ms. Johnson then told the class that they were going to measure the heights of the first-grade class. She asked the students, "What do you think will be true about the first graders?"

a. 

Ava: "I think they are going to all be shorter than us because they're only in first grade."

b. 

Nichole: "Maybe their data will be more bunched together than ours because it seems like lots of first graders are about the same height."

c. 

Houa: "They're going to be smaller than us so I would say [a typical height is] probably in the 40s."

d. 

Charles: "I think [a typical height is] maybe three feet, so that would be 36 inches."


 

Problem D3

Solution  

The line plot shows the first graders' height measurements:

As the fourth-grade students compared their height data to that of the first graders, they made the following comments:

a. 

Asher: "They are lots shorter than us."

b. 

Charles: "They are taller than I thought because they are more like three and a half feet tall."

c. 

Ali: "Most of [the first graders] are 42 inches tall, but most of us are 55 or 56 inches, so we're 13 or 14 inches taller."

d. 

Nichole: "I think we're 13 inches taller because our median is 56 and their median is 43."

e. 

Tarra: "Wow, I didn't think any first graders would be as tall as us, but that kid is 52 inches tall."

f. 

Juanita: "Their heights are more spread out."

g. 

Larie [responding to Juanita's statement]: "I don't really think their heights are more spread out because most of them are from 41 to 44 inches, and that's only three inches, but most of ours are more from 54 to 60, and that's six inches."


 

For more information about statistics problems for children like the problems in this session:

Russell, Susan Jo; Corwin, Rebecca B.; Rubin, Andee, Rubin; and Akers, Joan (1998). The Shape of the Data. Dale Seymour Publications.

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