Penny Basketball: Making Sense of Data

Goals of the Lesson

Goals of the Lesson
Operationalize a definition of mathematics as a sense making process. (What does this data tell me?)
Actively involve the students in the data creation and analysis process.
Provide a meaningful reason for integrating visualization technology into their teaching.
Explore the relative advantages and disadvantages of the iBook lab and the Utah State and Shodor virtual manipulatives.
To have fun and learn within the context of math class.

Tools and Equipments

• Utah State Virtual Manipulative Library: Focus on 1) Comparing Fraction, Parts of a Whole, Comparing Fractions, Percents.
• Shodor Master Tools: Plop It (A tool for visualizing measures of central tendency.)
http://www.shodor.org/master/interactivate/activities/plop/index.html
• iBook Wireless Lab

Lesson Plan

Introducing Technology

Students explored the 4 target virtual manipulatives to develop a baseline understanding of the manipulatives. Additionally, this early exposure was provided to allow them to make connections/define applications of the technology as a tool for allowing kids to make sense out of the data they collected in the penny basketball competition.

Game

Students played a series of penny basketball games. Each child played either two or three games. As they played penny basketball they were collecting data regarding their shooting statistics (field goals, three pointers) and their scoring. The non-standard number of games played is important as it leads children to explore fairness of comparison issues. In determining who is the best they have to explore how to compare two and three game totals

Posing the Problem:

1) Who was the best overall penny basketball player, based on the data collected in a given group?
2) Who was the overall top penny basketball player in the class?
The emphasis was on exploring the problem from the perspective of a teacher and of a student.

Solving the Problem (Group)

Groups decided, among themselves, who was the “top” penny basketball player in their group. This required them to explore their data in terms of accuracy (fractions/percentages) and scoring (overall and average). The ideas of fairness of comparison led to a real need for percentages and averages. Students were encouraged to utilize the technology to explore these concepts in the course of deciding who was the most effective penny basketball player. The group work was envisioned as a time where the pre-service teachers explore the problem and the technology from the multiple perspective of a 5th/6th grader and a teacher.

Whole Class Discussion

Discuss overall class rankings of “who is the best penny basketball player”.
Focus on how the virtual tools enhanced 1) student access to the ranking problem and 2) Understanding of the core ideas (fractions/percents/average/ranking/what is best?/comparison)
Discuss and critique the manipulatives as visualization tools, as “fits” into the lesson and their overall usefulness as a teaching tool.

Evaluation:

Discussion and limited written feedback.