TOOLS. TASKS. TALK. Essential Pedagogies for MEANINGFUL MATHS.

I often get asked about the thinking behind the design of our resources and the principles and theories of Learning and Teaching that underpin them. Here's the RATIONALE: TOOLS. TASKS. TALK.

It is hoped that by designing resources which incorporate RICH TASKS, TOOLS and TALK they will come to help children understand mathematics and engage with it in a more  PRODUCTIVE, MEANINGFUL and ENJOYABLE way. This resource will support advancement in children’s mathematical understanding and skills. In his book TRANSFORMING PRIMARY MATHEMATICS (2016) Mike Askew discusses that learning experiences should plan for 'The Tripod. It focuses on these three things:

Our number boxes are packed full of rich, research informed manipulatives. We call these the TOOLS. Manipulates are the mathematical equivalent of phonics and can help children make sense of numbers.

These TOOLS can be artefacts or hands-on practical apparatus but also visual representations, structures, models and images. The central importance of using these TOOLS is to support sense-making, mathematical thinking and reasoning. But it’s not the TOOLS themselves that are important but the ways in which they are used.

 

 

 Previously there has been a misconception that concrete materials were only for learners who find maths hard or difficult. In fact, concrete resources can be used in a variety of ways at every level. All children, regardless of ability, benefit from the use of practical resources in ensuring understanding that goes beyond the learning of procedure.

Ofsted's 2012 report  'Made to Measure' suggests that although manipulatives are used in some Primary Schools they are not used as effectively or widely as they could be. 

Practical resources promote reasoning and discussion, enabling children to articulate and explain a concept. Our FLUENCY TOOLKITS are packed full of rich, research informed manipulatives. Each box has its own set of UNIQUE TOOLS. These support the use of TASKS which help to bring about rich mathematical activity.

 

TASKS

Not all TASKS provide the same opportunities for developing children’s thinking and learning and that even young children need regular experiences with high-quality, rich tasks (Hiebert & Wearne, 1993; Stein et al., 1996).

 

 

 

I would describe a rich task as having a range of characteristics that together offer different opportunities to meet the different needs of learners at different times. What is also apparent to me is that much of what it takes to make a rich task "rich" is the environment in which it is presented, which includes the support and questioning that is used by grown ups and the roles that learners are encouraged to adopt. That is, an environment in which learners are not passive recipients of knowledge, accepting what is given, but independent assertive constructors of their own understanding who challenge and reflect. On its own a rich task is not rich - it is only what is made of it that allows it to fulfil its potential.

In a series of professional development resources designed to support embedding rich tasks into the curriculum, Jennifer Piggott, 2018 reminds us of the following basic ideas that may be useful to draw on when you are planning work with your learners: 

• Rich tasks offer opportunities to find out what learners really do know and reveal the strengths, weaknesses and confidence levels of the learners working on the task. 
• Be prepared to be surprised - your learners are likely to come up with better ideas and questions than you can think of.
• Encourage persistence. This will be difficult if your pupils are not used to taking responsibility for their own learning but it will get easier as they become more familiar with the idea and gain in confidence. One way to do this is to respond to a plea for an answer with a question ... "What should I do next?" ... "What have you tried?"
• Try not to lead learners down an alternative path because they have begun to explore an area of the topic you had not expected - and this may mean saying "I don't know". Learners can learn more from a task they think they 'own'.
• Remember that learners can learn as much, and sometimes more, from their peers as from you.

 

 

 

TALK

Longstanding research of Alexander, Barnes and Mercer has informed much of the thinking on the importance of MATHS TALK . If we genuinely want to enhance the quality of interactions in mathematics with a particular emphasis on extending learners thinking (reasoning) and mathematical talk then we need to carefully consider the kind of high-quality discussion that will develop children’s mathematical understanding. But what will provide the right kind of talk; and how can we help strengthen its power to help children think and learn more effectively than they do?  

 

Where to begin?

CLICK ON THE IMAGE BELOW for some simple and impactful ways to create opportunities for thinking, talking, engaging and enjoying mathematics whilst increasing maths talk and not just talk about maths.

 

 

We strongly believe that our Number Fluency TOOLKITS contain essential pedagogies for building NUMBER SENSE and FLUENCY: TOOLS. TASKS. TALK.

 

Each @fluencywithnumbers TOOLKIT is full of RICH TOOLS and TASKS which promote meaningful TALK. The TOOLKITS can be used at home and in school. They help children to SEE number, FEEL number and HEAR number and encourage the use of fingers, dice patterns and dots. These patterns encourage children to SUBITISE, VISUALISE and build RICH relationships and connections among numbers. The TOOLKITS encourage learners to work with numbers in different ways, to make sense of basic facts and to be able to retrieve them.

 I’d love to hear your thoughts on TOOLS. TASKS. TALK. Which ideas resonate with you? What do you disagree with?  All views are welcome - post in the comments.  

Thank you for all you do to support your children's number journey. Thank you for watching and listening.

Love, Janey x