There is often a debate about striking the perfect balance between computational fluency (think: basic facts and algorithms) and number sense (think: comparing, ordering, and estimating values). Experience and research indicates that number fluency is as important as number sense, and that each one depends, in part, on the other.  If children have a degree of fluency, they can reduce the chance of cognitive overload when tackling more demanding challenges.

As educators, we have to take care not to create an either or situation.  It is probably more healthy to think of the concept o “flexible numeracy.”  This is an approach where a student is given the opportunity to tackle both approaches and move between the two seamlessly.

As a math teacher, I try to think of my students as number athletes. I want them to be able to slip effortlessly between and around exercises; with operations; bounce from strategy to strategy with ease. Just as athletes stretch every day, with purpose and dedication, students who wish to be flexible with numbers must stretch their numerical skills daily. My role, for five minutes a day, becomes that of a fitness coach, guiding my students enthusiastically in a brief stretching exercise, to keep them nimble with numbers.

The exercises themselves are simple: since the objective is strictly to practice manipulating numbers, there is no need to come up with real-world contexts. (Problem-solving is embedded throughout the rest of the math lesson.) But don’t let the simplicity of the exercise fool you: as they contemplate solutions, students’ minds flow through a range of interrelated number concepts: the relationship between addition and subtraction, the pairs that make ten, ordering numbers on the number line, conservation of number, and plenty more. They are building fluency while exercising number sense; they are accessing number concepts while practicing basic facts. In short, they are becoming numerically flexible.

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The home of mathematics education in New Zealand.

Laying the Foundations of Early Mathematics

This set of resource materials is intended to help practitioners working with children in the Early Years Foundation Stage (EYFS), and teachers working with lower Key Stage 1 children, to plan their mathematics provision and help children to secure some of the key mathematical ideas that they will use throughout the rest of their lives. The materials have a strong focus on Number, particularly counting, and the children’s developing understanding of the patterns that underpin early work within this aspect of mathematics. Download

Teaching Mathematics

Why is Jerome Bruner important to Mathematics education?

In the 1960s American psychologist Jerome Bruner (above) put forward a theory that people learn in three basic stages: by handling real objects, through pictures, and through symbols. Bruner said symbols are "clearly the most mysterious of the three." In the 1980s Singapore developed its model method based on Bruner's theory.

Implications for teaching mathematics

Some of the implications of Bruner's theory for the teaching of mathematics are:
•children's 'readiness' to learn is not linked to age (unlike Piaget's theory);
•development of language is important to concept formation;
•adults are important in structuring and supporting children's developing ideas (compare this with Piaget's theory);
•new concepts (regardless of the age of the learner) should be taught enactively, then ironically and, finally, symbolically as ways of capturing experiences in the memory;
•it is important to include practical activities and discussion as an integral part of mathematics.;
•the use of pictorial recording and the classroom environment are important.

The Times Educational Supplement is an excellent source of research articles and resources.  They also have a dedicated section to support the teaching of Mastery in Mathematics. Read More

There are several organisations that have developed Mathematical Mastery at a whole school level.

Mathematical Mastery organisation have several key principles that underpin all that they do. They have high expectations for every child. They teach fewer topics in greater depth. They emphasise problem-solving and conceptual understanding.  They also promote a 'Growth Mindset'.

Read More

White Rose Maths Hub

Influenced, inspired and informed by the work of leading maths researchers and practitioners across the world, White Rose Maths brings together a team of highly experienced and passionate maths teaching experts to train, guide, help and support all those who want to make change happen in their schools.

Schemes of Learning, Assessments and Mixed-age Learning Plans

White Rose always make a strong effort to keep their content advancing in line with the latest best practice and National Curriculum requirements, White Rose Maths’ latest SOL feature smaller learning steps and additional techniques to help you embed deeper learning.

All of these materials are available for you to download and use FREE.

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Getting to grips... What is mastery? | Prof Ruth Merttens | Teacher training from Hamilton Trust

Professor Ruth Merttens discusses what the new National Curriculum actually means in practice. She explains how to adapt to a curriculum based on skills mast...

Number Sense: A Biological Look at How Our Minds Create Mathematics by Andrea Hayes

How can an infant know that 1 plus 1 equals 2? Why is it that, even after years of school, many of us still aren't sure if 6 times 7 is 42 or 54? How can a...

https://www.youtube.com/watch?v=FG2yyDYrI5M