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The Kilpatrick rope model reflects NRICH's view of the characteristics of a good mathematician.
Our curriculum tags and mapping documents identify the Conceptual Understanding and Procedural Fluency that each of our problems helps to develop.
If students are going to be good mathematicians, they also require a Productive Disposition. This means that they are positive about the subject and positive about their ability to make progress. When faced with a new task, students demonstrate positive attitudes, by being:
They also need to demonstrate Strategic Competence. In order to make this possible:
Throughout this process, students need to demonstrate Adaptive Reasoning. They are required to communicate their ideas and any general insights by:
To see how we have adapted this model for use with students, see Nurturing Successful Mathematicians.
Alan Wigley's Challenging Model for Teaching Mathematics describes what this might look like in the classroom.