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

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

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?.*

**To offer students the opportunity to develop all five strands of the rope model, you may find the following collections of tasks helpful:**

**For Primary teachers:**

Problems arranged by curriculum topics

Problems arranged by mathematical thinking skills

Problems arranged by mathematical mindsets

**For Secondary teachers:**

Problems arranged by curriculum topics

Problems arranged by mathematical thinking skills

Problems arranged by mathematical mindsets

*Alan Wigley's Challenging Model for Teaching Mathematics describes how these problems could be used in the classroom.*