Nurturing Successful Mathematicians: The rope model

The Kilpatrick rope model reflects NRICH's view of the characteristics of a good mathematician.

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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 display a mathematical mindset, by being:

• Curious
• Resourceful
• Collaborative
• Resilient

The final two threads of the rope model focus on key mathematical thinking skills. Students need to demonstrate Strategic Competence. In order to make this possible: 

• students first need to have time to explore, by being given time to be playful and tentative, and to make conjectures
• students then need to have an opportunity to share initial ideas with their partners and the whole class
• students are then in a better position to tackle the problem in an organised, logical and systematic way

Throughout this process, students also need to demonstrate Adaptive Reasoning. They are required to communicate their ideas and any general insights by:

• explaining
• justifying
• proving

To see how we have adapted this model for use with students, see What Makes a Good Mathematician?.