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Is Chance Fair? One Student’s Thoughts on Probability

Using a Journal Article as a Professional Development Experience
FOY 2007-2008 Data Analysis & Probability

 

 Title:  Is Chance Fair? One Student’s Thoughts on Probability 
Author:  Cynthia Pratt Nicolson 
Journal:  Teaching Children Mathematics 
Issue:  September 2005, volume 12, issue 2, pp. 83-89 

Rationale/Suggestions for Use 

This article provides teachers with an opportunity to document their students’ prior knowledge related to randomness and chance, theoretical and experimental probability, and independent and conditional events.

It is recommended that this professional development experience take place in a multi-day format with time in between sessions. 

Procedures/Discussion Questions 

Session One
During the initial session, teachers will engage in three probability-related activities.

Activity 1: Coin Toss 

  • Teachers will be asked to predict the possible outcomes of flipping a penny one time. After making a prediction, teachers will carry out the simulation.
  • Teachers will be asked to predict the possible outcomes of flipping a penny ten times.  After making a prediction, teachers will carry out the simulation.
  • Teachers will be asked to predict the possible outcomes of flipping a penny a hundred times.  After making a prediction, teachers will carry out each simulation.

Activity 2: Drawing Cubes 

  • Assume Bag A contains one pink cube and four blue cubes.  Assume Bag B contains two pink cubes and three blue cubes.  Pink cubes represent raspberry candy and blue cubes blueberry candy.
  • Teachers will be asked to pretend that they prefer raspberry candy and to choose which bag would give them the best chance of getting that flavor.
  • When you roll an ordinary die, what are the possible outcomes?

Activity 3: Spinners 

  • For each spinner, use a circle divided into six equal parts. 

Spinner A: 1/6 shaded gray
Spinner B: ½ shaded gray (connecting segments shaded)
Spinner C: ½ shaded (alternating segments are shaded)
Spinner D: 3/6 white, 2/6 spotted, 1/6 striped

  • If you twirl Spinner A six times, will gray or white come up more often?  Is it possible to have all six spins come up gray?
  • If you twirl Spinner B six times, will gray or white come up more often?  Suppose you did 100 twirls, what would you expect?
  • If you twirl Spinner C six times, will gray or white come up more often?
  • If you twirl Spinner D six times, will gray or white come up more often?

After completing the activities, teachers will read and discuss the article.  The article discussion will conclude the initial professional development session.

AssignmentUpon going back to their classrooms, teachers will conduct the three activities with 2-3 students and document their thinking through work samples.

Session Two
Teachers will share and discuss their work samples with the whole group.  Similarities and differences among student work samples will be analyzed and discussed.  Teachers will articulate what they learned about their students’ prior knowledge related to randomness and chance, theoretical and experimental probability, and independent and conditional events.  Further, teachers will discuss how information gained will impact their instructional decision making and practice.

ExtensionsTeachers will extend the lesson to include a real-world investigation. Students will collect a real-world set of data and organize a visual and/or physical representation of the data.  Students will explore and discuss probabilistic relationships of the data.

Connections to other NCTM Publications 

  • Basile, C. G. (1999, September). Collecting data outdoors: Making connections to the real world. Teaching Children Mathematics, 6, 8-12.
  • Cline, L. J. (2001, September). Bubble-mania! Teaching Children Mathematics, 8, 20-23.
  • Gebhard, G. (2006, September). Investigations: A mathematical cornucopia of pumpkins. Teaching Children Mathematics, 13, 68-78.
  • Green, D. A. (2002, November). Last one standing: Creative, cooperative, problem solving. Teaching Children Mathematics, 9, 134-139.
  • Isabelle, A. D. & Bell, K. N. (2007, April). Investigations: Sun catchers. Teaching Children Mathematics, 13, 414-423.
  • Joram, E., Hartman, C., & Trafton, P. R. (2004, March). “As people get older, they get taller”: An integrated unit on measurement, linear relationships, and data analysis, Teaching Children Mathematics, 7, 344-351.
  • Niezgoda, D. A. & Moyer-Packenham, P. S. (2005, February). Hickory dickory dock: Navigating through data analysis. Teaching Children Mathematics, 11, 292-300.

 

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