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# What Makes a Good Mathematician?

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**How do you know if you are good at Maths? **

What would you say if I asked you that question? Take a moment to consider your answer before you read on...

At NRICH, we offer a range of problems for you to work on, which will give you the chance to develop the five key ingredients that we think characterise successful mathematicians.

The five pathways in the image below represent the five ingredients. We hope our descriptions of each pathway are helpful, and offer you ways of talking about your own mathematical capabilities.

**Understanding** - Maths is a network of linked ideas. I can connect new mathematical thinking to what I already know and understand.

**Tools** - I have a toolkit that I can choose tools from to help me solve problems. Practising using these tools helps me become a better mathematician.

**Problem solving** - Problem solving is an important part of Maths. I can use my understanding, skills and reasoning to help me work towards solutions.

**Reasoning** - Maths is logical. I can convince myself that my thinking is correct and I can explain my reasoning to others.

**Attitude/mindset** - Maths makes sense and is worth spending time on. I can enjoy Maths and become better at it by persevering.

This model gives a real sense of the equal importance of the five pathways, and that a recipe depends on all the ingredients working together. As you immerse yourself in NRICH tasks, you will need to make use of the five ingredients, and you could use the sheets on this page to reflect on how you are becoming a better mathematician.

*This model has been adapted from Kilpatrick's rope model. Teachers can read more about it in this article.*

**To help you develop the five key ingredients that characterise successful mathematicians, you may find the following collections of tasks helpful:**

**For Primary students:**

Problems arranged by mathematical topics

Problems arranged by mathematical thinking skills

Problems arranged by mathematical mindsets

**For Secondary students:**

Problems arranged by mathematical topics

Problems arranged by mathematical thinking skills

Problems arranged by mathematical mindsets