“What’s a nicer word instead of the opposite, if you were being mathematical?”

Asking students to do something again, better, can be a powerful way to help them grasp and act upon their teacher’s high expectations. As this video of Dani Quinn (‘10 ambassador) shows, it can also be an effective way to reinforce their understanding and use of key terms in the subject.

Having selected a student at random (using lollipop sticks), Dani receives a correct answer to the problem immediately. She asks for an explanation, checking this was more than a lucky guess and ensuring that all students can follow the steps in reaching the answer. It is clear that Dani has a specific mathematical response in mind. Although the student’s next answer is right, rather than settling for it, she pushes him to use “a nicer”, “more mathematical” word than “the opposite”. Since he struggles to recall the word required she passes the question on to a peer, but once the correct term – “the inverse” – has been identified, Dani returns to the first student and asks him to repeat his answer.
One strength of Dani’s teaching which makes this possible is the culture of error she has created. Dani emphasises that it’s safe to be wrong throughout, both through her smiling probes and reminder of her own error earlier in the lesson: “How would you have worked this out had I not been very silly?” Her challenge manages to combine a gentle, firm request for revision and a clear indication of the change needed. The overall confidence Dani imbues in her students is shown in both the student’s initial answer, “I know that…” and his willingness to keep trying throughout the clip, until he achieves success.
Other strengths we noticed in the clip included:
  • By calling on peers for help while also giving the first student three chances to provide an excellent answer, Dani manages to balance the need to involve all students in the lesson with the desire to allow individuals to refine their ideas to high standards.
  • The pace is fast, but a strong classroom culture ensures that the student involved has the time and space to rethink his answer uninterrupted. (Students’ immediate response to Dani’s request at the beginning of the video, when moving from paired to whole-class discussion is also noticeable).
  • Dani moves to face the student whose name has turned up in her lollipop sticks: by doing so, she both emphasises where the class’s focus should lie and manages to face him while retaining sight of the rest of the room.

This clip  demonstrates a way to obtain a well-explained answer, underline the importance of correct mathematical terminology and send a powerful message about excellence through the simple act of returning to the first speaker and asking him to repeat his answer. For teachers, establishing the quality of answer or action they hope to see while planning a lesson and deciding to invite students to do it again until they reach that standard, may help them show students the successes of which they are capable.

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