Tim
T1 Tools for the task
Tim typically prepares a range of equipment for tasks, but gets students to reason through about what tools they need. He uses one incident in which a student asks how to measure the circumference to make points about accuracy, and to flag up that there is a problem about measuring circumference. Also, students in his classes are allowed to walk about and collect the equipment they need, similar to practice in many primary schools. Tim opens discussion with another student about the reasons for his use of a calculator, and uses this to get the student to express his conjecture about a relationship.
T2 Orchestrating discussion
Here Tim is tackling the familiar problem of using learner-generated measuring data about circles to conjecture about relationships between radius, diameter, and circumference. Note that he encourages everyone to follow up one conjecture which we know to be wrong. Although the conjecture is generally false, there is one case in which it works. You might just see a tiny smile on Tim's face as the number '3.1' turns up, but in the wrong context! Tim has to orchestrate discussion towards the formula for circumference, and does this using a counter example.
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