Note: Scores not included

2a: Teacher Creates Opportunities for Joint Activity

• Teacher consistently asks students to comment on each other’s ideas and also encourages overall collaboration

• The teacher and all students work together on one board and learn from and with one another

  • T: “I’m asking, ‘how many twos are we gonna get in twelve rolls?’ What do you think we’re gonna fill in for probability?”

  • Teacher fills in the ratio box using student input

  • The use of 1 board encourages collaboration toward the product

• This collaborative activity includes an intangible learning product (the conversation the students and teacher have leads to a shared understanding of the mathematical concept) with a tangible product (the completion of the ratio box by taking turns rolling the dice to determine experimental probability)

2b: Teacher Orients to Others’ Ideas

• Teacher asks students to respond to their peers’ ideas

  • T: “So what are you gonna be doing, Destin?” / Multiple Ss respond. / T: “To find what kind of probability?” … T: “Which one do you think it is, Emily? If he rolls the dice, is it gonna be theoretical or experimental?”

2c: Teacher Positions Self as Learner

• Teacher primes students to use prior knowledge to gain new understandings

  • T: “What does theory mean in science?” … T: “It’s like an idea.” / S: “Their educated guess.” / T: “Right. Educated guess, that’s even better.”

• Teacher guides students in discussing their knowledge and understanding of the topic so they are able to discuss the “why”

• Teacher uses guiding questions and follow-up questions

  • Examples of T’s follow-up questions: “Why do you say that?”; “Where did your numbers come in?”; “What did we use?”

2d: Teacher Integrates Student Contributions

• After acknowledging student contributions, the teacher reincorporates those ideas into the next part of the conversation

  • T: “So we never actually rolled the dice, right? We just thought about it. So what do you think experimental probability’s gonna be?” 

• Teacher integrates students’ contributions to move discussion forward

  • T: “So all this is is our ratio box, but our special ratio, like Destin said, was probability today.”

• Teacher responds to students’ ideas

  • S: “Is it just like a hypothesis?” / T: “Yeah. Which one would be like a hypothesis?” / S: “The theoretical. And then the experimental is we have to find it out if it’s true.” / T: “Beautiful.”

2e: Students Construct Ideas Together and Share Ownership

• All students contribute to conversation and build on one another’s ideas

• Students are consistently on-task for both the tangible (rolling dice) and the intangible (discussion) aspects of the activity

• Students are responsive to teacher questioning and appear comfortable participating in small group discussion with and without teacher prompting

• Students are respectful of and receptive to peers’ viewpoints 

• Students appear engaged and enthusiastic

• Overlapping speech is a natural speech pattern for Hawaiʻi students. It is viewed as a positive aspect of this conversation showing that the students are comfortable and eager to participate in this small group discussion setting