# Section One: A contribution to teaching

Primary teachers talking about Let’s Think Maths.

“ (Let’s Think) gives you a lot of freedom. There’s not that pressure of thinking that the children have to know a certain thing by a certain date. It’s more a case of the

children learning what they can in the best way.”

We’re talking about long-term benefits, not just covering programmes of study.

The aim of the Primary Cognitive Acceleration in Mathematics Education (Primary CAME) project was to contribute to the teaching and learning of mathematics in Years 5 and 6. The Primary CAME lessons were an outcome of the research from this project. These lessons have been renamed Let’s Think Maths lessons. They stimulate the development of children’s mathematical thinking through carefully selected classroom tasks. Tackling these challenges encourages children to work together as mathematicians, constructing and discussing mathematical ideas.

Each lesson promotes very specific mathematical connections and generalisations but with a focus on reasoning. Pupils grapple with the ‘big ideas’ in mathematics, rather than focusing on the mastery of specific skills. The shared construction of mathematics encourages children to develop a deeper understanding of the mathematical concepts underlying the skills, algorithms and procedures in school mathematics. This includes those specified in the National Curriculum.

Primary Let’s Think lessons are not in themselves a mathematics scheme of work. Children need the regular content-based primary mathematics experiences of good instructional and problem-solving lessons. These lessons should be, at most, a fortnightly supplement to the normal mathematics experiences offered to children. The Let’s Think approach complements and builds upon existing good practice in primary mathematics. It has been shown that these lessons, delivered in conjunction with good mathematical instruction and investigation, can significantly raise the whole thinking capacity of each child, as well as contribute to the meaningful learning of mathematics.

What makes Primary Let’s Think different?

“ *In [these] lessons you end up with lots of questions.* ”

“ *I agree. You can’t stop thinking about them.* ”

Two children talking after a Primary Let’s Think lesson

As mentioned on the previous page, the Primary Let’s Think approach shares many of the features of existing good practice in primary mathematics: children are encouraged to talk, listen, question and debate their mathematical ideas.

Let’s Think Maths is open-ended in the conceptual points which children will reach but very focused in terms of what tasks the children are set. Primary Let’s Think often addresses concepts thought of as beyond the scope of primary mathematics, sowing seeds for later mathematical work. At all times, the emphasis is on depth of mathematical thinking and conjecturing in which children construct mathematical ideas and gain insights at different levels of complexity, all within a mathematical ‘big idea’.

The lessons stimulate children’s mathematical thinking and often leave children with unanswered or partly answered questions. This mathematical ‘unfinished business’ will either be addressed in further Let’s Think Maths lessons or as part of the normal mathematical curriculum, or later in the children’s mathematical career. Let’s Think Maths lessons differ from good instruction and practice lessons in that each one has a clear agenda, involving fundamental concepts in mathematics. The lesson focuses on children ‘struggling on the way’ towards these ideas, rather than on fully understanding and mastering the concepts. The outcomes of a lesson are the thinking processes and the sharing of ideas rather than the specific knowledge gains and skills employed.

Hence, although children are working in an investigative way throughout these lessons, Let’s Think Maths lessons do differ from many good, open-ended investigations or problem-solving lessons. The Let’s Think activities are very focused in terms of the tasks that children tackle, but open-ended in the mathematical understandings that children reach. The lessons provide clear challenge points rather than allowing varied interpretations of the task.

Whole-class teaching

(The) lessons are an opportunity to develop children’s self-esteem with number,

because you value every contribution.

A primary teacher talking about Primary Let’s Think Maths

Let’s Think Maths lessons are centred around whole-class activities. The whole class tackles the same challenges together and in small groups. A key feature is the sharing and discussion of children’s mathematical constructions as a class. Classes involved in the development of the lesson materials have successfully included children of a wide range of abilities through careful grouping and support. Different children reach different levels of thinking. So, rather than differentiation by task, differentiation is by thinking outcome within a task.