Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
The lesson begins with a review of the differences between mathematical probability and experimental probability. The class discusses and lists the possible sums when rolling two dice and the various ways to get these sums. The students predict which sum will occur most often and then small groups conduct an experiment. Each group member is assigned a specific role: recorder, dice keeper, reporter, or counter (the counter makes sure that the dice are rolled only thirty-six times). Students generate their own recording plan for organizing their data, and they conduct the experiment. Once the groups complete their experiments, they compile their findings on a class bar graph and analyze the graph.
Topics for Discussion
The following areas provide a focus for discussion after you view the video. You may want to customize these areas or focus on your own discussion ideas.
Developing Probability Concepts
- Ms. Kincaid wanted the students to make predictions about their experiment on the basis of mathematical probability. Discuss preconceptions that students exhibited about tossing dice even after discussing the mathematical probability. Discuss the instructional implications of dealing with these preconceptions.
- Were these students too young to discuss mathematical probability? What evidence did you observe that leads you to believe that students did or did not grasp the difference between mathematical probability and experimental probability? At what age should probability be discussed?
- Comment on the students1 responses to Ms. Kincaid1s question, 3Were you surprised by any of your results?2
- The teacher asked the students, 3What can you say about the data we collected as a group?2 and 3What can you say mathematically?2 How did the phrasing of these two questions affect the students1 reasoning?
- Why did Ms. Kincaid require each group of students to roll the dice thirty-six times? What are the advantages and disadvantages of rolling this number of times? Why or why not?
Facilitating Small-Group Work
- Comment on the collaboration among the students as they conducted the experiment. Give evidence that students either worked together as a group or worked as individuals.
- Why do you think Ms. Kincaid assigned roles to each group member? What effect did this practice have on the students? How does assigning roles facilitate collaboration among the group members?
- Why should roles be assigned to students when working in groups? Discuss the pros and cons of assigning roles to group members.
- Describe the types of questions that Ms. Kincaid asked the students in the individual groups. How did this questioning further students1 understanding and learning?
- Why did Ms. Kincaid let each group decide how to record the data rather than giving groups a recording sheet that was already organized? When would it be appropriate to give students an organized recording sheet? Discuss the advantages and disadvantages of allowing students to create their own recording plans.
Hold a probability fair in which students design their own games of chance using dice, spinners, colored cubes, or some other type of material. The students will need to decide whether they want to design a fair game in which the likelihood of winning is the same as that of losing or whether they want to design a game that would allow either the proprieter or player to win most of the time (and why). Have students work in small groups to design a game of chance and then set up the booths for the fair. Using play money or tickets, students can take turns running the booths and playing the games.