Today I observed a teacher using **this tool **built by **Jennifer Silver** to engage her students in mathematical reasoning. It was a powerful reminder to me of the intersection between effective uses of technology to provoke thinking in students, and the pedagogy used to support that student reasoning.

First, the teacher brought up the interactive diagram up on her Smartboard, and then she asked a student to come up to change the slider values. She repeatedly asked students to say what they noticed each time the slider was changed. She took the time to have multiple students clarify what they said, to have their peers restate and respond to each other’s reasoning, and to have students take the time to make mathematical observations. **She engaged students in collaborative mathematical thinking for 30 minutes. **At the end of the class, at least 10 students came up en masse to play with the interactive diagram themselves and continued to ask her questions and make observations. She had to promise them she would email them the link to the diagram so that they could continue to play with it themselves.

The point here is that the technology made the conversation easier. Instead of creating 20 different examples of graphs and seeing what happens as each variable is changed, students were able to visualize the changes, both in the graph representation, and in the formula representation. When asked if they noticed anything after the “Point on the line” slider was changed, one student said they noticed the Intercept-slope form of the equation did not change. Another student responded to him with “that form of the line doesn’t depend on which points you use.”

It was fantastic.