What are the strong characteristics of effective learning?

The curriculum design principles are a key tool for planning and organizing effective learning in mathematics. The appendix provides reflective questions on the use of the principles to improve practice. Inspection activities and national and international research suggest the following key themes for improving learning in mathematics. By discussing and exploring the nature of these key themes, staff will extend their skills in identifying when and how to make use of them in mathematical activities.

Pace

Pace is not about how quickly tasks and activities can be completed: learning is not a race. Rather, pace can be viewed as one aspect of challenge. Teachers need to plan mathematical tasks and activities which meet learners’ needs well. Key features of well-paced lessons include:

 well-established routines;

 good planning including a clear focus on the purpose of learning activities;

 shared purpose for learning;

 a high proportion of time spent on active learning tasks with minimum interruptions;

 high levels of learner stimulation and engagement in thinking;

 a range of activities that provide the right level of challenge to match everyone’s learning needs in the class; and

 opportunities for learners to demonstrate that they are confident and proficient in achieving the learning outcome(s).

Sharing and demonstrating learning

Characters are used to help P1 children understand what they are learning. Mr What? shares the learning outcomes with children, Miss How? shares the process and Mrs Why? encourages children to transfer skills, understand the purpose of learning and how this can be applied across the curriculum. The characters are used at the end of learning experiences to encourage children to demonstrate new learning.

To achieve an appropriate pace of learning, teachers need to take account of:

 the rate of learning, including the size of learning ‘steps’, taking account of the fact that in mathematics learners progress at different rates and with different levels of facility at different times, in different contexts and when learning different ideas;

 the proportion of time spent on active engagement in thinking, the quality of learning, and time focused on task; and

 the learner’s resilience, patience, ability to concentrate, application (learning new things needs effort), and depth of understanding. The right pace is influenced by a number of factors, including the ethos within the

class. Children need to share with their teachers high and realistic expectations about their engagement in learning and the belief that they can succeed. They need to feel secure in class and valued for the effort they put into their learning. At all stages in their mathematical journey, children need to know what they have done

well and also be clear about what they need to do as next steps for improvement. This interaction between the learner and teacher helps to shape learning and influence pace.

Challenge, enjoyment and positive attitudes

By providing challenge for learners, teachers enable them to gain a sense of achievement as they apply, consolidate and extend their existing skills in a number of ways. On too many occasions, teachers provide extension work for higher-achieving learners which does not lead to new learning. As part of learning, teachers need to promote positive attitudes to mathematics and an understanding of how it equips young people with many of the skills required for life, learning and work.

Effective challenge includes teachers setting tasks and activities which:

 are of increasing levels of complexity or abstraction;

 continually develop, reinforce and extend understanding;

 help learners to make connections to, and build on, their prior mathematical learning;

 require higher-order thinking including analysis, reasoning and deduction;

 depend on learners applying their mathematical and numeracy knowledge and skills to solve problems in familiar and unfamiliar contexts; and

 extend learning within a lesson to meet individual learning needs.

„It‟s really good when young people make connections to work they have done before and someone says, „This is just the same as ….‟. It makes them more likely to have an „I can do this‟ approach to their work‟.

In mathematics as in other areas, the right environment for learning is a key component for successful learning. To foster a challenging learning environment where learners are engaged and enjoying learning, effective teachers:

 work to develop shared, high expectations of effort and success: teachers and learners together promote a culture of ambition;

 ensure that learners feel valued and supported enough to take some risks in learning. Children and young people need to feel confident about asking for support from their teacher and peers when they are unsure and feel that they need help; and

 develop an ethos of self-challenge for learners. Successful teachers involve children and young people actively in their learning, for example by engaging them in thinking and making learning activities enjoyable.

Most children in pre-school are making good progress in early number skills during their play. They show skills and enthusiasm in imaginative activities, including learning out-of-doors where appropriate opportunities are taken to embed mathematics within real life contexts. Their broader mathematical skills are less developed in activities in science and technology. In primary schools, there is increasing use of well-paced interactive learning activities in mathematics, particularly in aspects of numeracy and mental calculation. When implementing the experiences and outcomes, we need to build on this good practice and maintain a

strong focus on mental strategies and skills.

Children begin to develop independence in measuring, using arbitrary units, by working together to make dough. These skills are then transferred to enable children to measure in other contexts, for example, at water play.