 Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum            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 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 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 The line plot shows the first graders' height measurements:    Session 10, Grades 3-5: Index | Notes | Solutions | Video