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Workshop Scenario #2: Participants: Middle school mathematics teachers

In brief: Give the teachers an in-depth experience of integrating various kinds of technologies into math lessons. Teachers will participate as learners in two to four technology-rich lessons and then read and discuss related classroom examples. Suggested length: half to full day.

The planning for this session might involve one or more of the following types of district staff: the district professional development coordinator, the district math director, the technology coordinator, and/or a math teacher. One of the workshop leaders must have content knowledge of mathematics at a middle grades level (preferably higher), and, in particular, knowledge of mathematics used in the examples. This workshop might be led by a team of two people—a technology coach and a mathematics teacher.

Outline of the workshop: Select two to four examples from the Mission: Algebra website that use different kinds of technology; for example: online applet, graphic calculator, dynamic geometry software, and/or spreadsheet. For each example, use an outline similar to the one suggested below. The example that follows is built around the SREB Content Indicator #9, Probability: Determine the number of ways events can occur and the associated probabilities, and the Classroom Example that corresponds to it. For background on the Law of Large Numbers, click here.

1. Establish Common Experience
   As a group, use dice (one die per team) to establish some common experience with probability. Ask: if you role a die 12 times, what will be the outcome? Record the predictions for each group. Let each group do this, and again record the outcomes. Note the variability of outcomes. Introduce the terms theoretical probability and experimental probability and apply to this activity.
2. Demonstrate the Tool
   Give each group a computer and briefly demonstrate for them the Adjustable Spinner. Have them create 6 equal sectors – so the spinner models the behavior of the die. Ask them what experiments they might do. Ask them to write down one experiment, then make a prediction and test it out. Possible experiment: I’ll spin the spinner 1200 times, and the outcome numbers will be within 5 of the theoretical numbers (200 plus/minus 5, i.e., the range 195 to 205).
3. Debrief
   What are participants learning about the probability when you use large numbers of trials? Work towards a statement of the law of large numbers.
4. Design Your Own Experiment
   If time allows, invite each group to create an experiment that uses the Adjustable Spinner to model the problem of their own design. Possible experiment: My friend says that it is impossible to flip a coin 5 times and get all heads. I think it is possible. The group uses the Adjustable Spinner to model a coin toss (2 equal sections), then sets it for one round of 5 spins. They conduct 100 rounds, recording the outcome after each one. (For some participants, this use of the Adjustable Spinner for modeling of their own problem has proven to be a powerful rationale for the use of technology to teach probability concepts.)
5. Group debrief
   Sample questions may include:
    
   
   • What are students learning about probability during this lesson?
   • What features of this lesson help students to learn these concepts?
   • What role did technology play in teaching and learning in this activity? What other concepts could this tool help to develop?
6. Connecting it back to the classroom
   Read Classroom Example #9 – Adjustable Spinner: Experimenting with probability using a digital spinner. In small groups, answer these questions:
    
   
   • What skills and cocepts does Mr. Haddad aim to develop through this activity with his class?
   • Are the skills listed in the “Skills” box the ones he is teaching?
   • In what ways does the lesson support student learning of these skills and concepts?
   • What misconceptions about probability have you experienced with your students? (e.g., students believing that a coin toss always comes out 50-50 for any sample size). Did Mr. Haddad anticipate these same misconceptions? How?
   • How is the lesson here similar or different from what we just did as a group?
   • Finally, what have you learned that you can take back to your classroom to use with your students?

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