Educating teachers to pose mathematical problems in the digital age: Toward alternative ways of curriculum design

This paper shows how by integrating technology with problem-posing activities prospective teachers of mathematics can learn new ways of creating curriculum materials that address several pedagogical issues associated with the advent of modern digital tools into the classroom. The paper describes and analyses problems posed by the teachers for different populations of students under the umbrella of two interrelated notions: the didactical coherence of a problem and the technology-immune/technology-enabled problem. Digital tools discussed in the paper include an electronic spreadsheet, Wolfram Alpha, and Maple. It is shown that the tools cannot be directly utilized for posing mathematical problems and that such utilization requires one?s appreciation of their hidden educational capabilities and awareness of instructional pitfalls.