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Evaluating current provision


Created on 21 February 2013 by ncetm_administrator
Updated on 10 July 2013 by ncetm_administrator

 

Evaluating current provision

Key questions

  • How do we decide who our high attaining pupils are? What are the particular characteristics of such children?
  • How do we decide which children should be entered for the L6 test?
  • What does excellent provision for high attaining children look like?
  • What types of evidence should I use to evaluate provision?

Things to think about

“Too many able pupils across the 3–16 age range are underachieving”
Mathematics: made to measure (Ofsted 2012)

Assessment data does not give us the full picture when it comes to identifying high attaining children. It is helpful also to think about the characteristics of such children. Typically, they:

  • grasp new material quickly;
  • are prepared to approach problems from different directions and persist in finding solutions;
  • generalise patterns and relationships;
  • use mathematical symbols confidently;
  • develop concise logical arguments.

Mathematical Challenges for Able Pupils in Key Stages 1 and 2 (DfES 2000)

This helps give a clearer picture of the types of mathematical activity that children need to experience on a regular basis in order that they have the chance to develop such characteristics and start to show their potential.

This then leads to greater clarity about how to evaluate current provision for high attaining children in your school and how to improve that provision.

What does research tell us?

What are the characteristics of high attaining children?

QCDA suggested that children who are particularly good at mathematics are ones who are likely to:

  • learn and understand mathematical ideas quickly;
  • work systematically and accurately;
  • be more analytical;
  • think logically and see mathematical relationships;
  • make connections between the concepts they have learned;
  • identify patterns easily;
  • apply their knowledge to new or unfamiliar contexts;
  • communicate their reasoning and justify their methods;
  • ask questions that show clear understanding of, and curiosity about, mathematics;
  • take a creative approach to solving mathematical problems;
  • sustain their concentration throughout longer tasks and persist in seeking solutions;
  • be more adept at posing their own questions and pursuing lines of enquiry.

(QCDA, n.d.)

While Vadim Kruteskii has suggested in The Psychology of Mathematical Abilities that these are children who have:

  • an ability to formalise mathematical material, to isolate form from content, to abstract oneself from concrete numerical relationships and spatial forms, and to operate with formal structure – with structures of relationships and connections;
  • an ability to generalise mathematical material, to detect what is of chief importance, abstracting oneself from the irrelevant and to see what is common in what is externally different;
  • an ability to operate with numerals and other symbols;
  • an ability for ‘sequential, properly segmented logical reasoning,’ which is related to the need for proof, substantiation and deductions;
  • an ability to shorten the reasoning process, to think in curtailed structures;
  • an ability to reverse a mental process (to transfer from a direct to a reverse train of thought);
  • flexibility of thought – an ability to switch from one mental operation to another; freedom from the binding influence of the commonplace and the hackneyed. This characteristic of thinking is important for the creative work of a mathematician;
  • a mathematical memory. It can be assumed that its characteristics also arise from the specific features of the mathematical sciences, that this is a memory for generalisations, formalised structures and logical schemes;
  • an ability for spatial concepts, which is directly related to the presence of a branch of mathematics such as geometry (especially the geometry of space).

(Kruteskii, 1976)

Such lists vary in detail, but have a common focus on mathematical reasoning, not just on arithmetic skills. This has significant implications for how schools assess mathematical ability.

More recently, ACME has argued in its report Raising the Bar: developing able young mathematicians that rich curriculum provision should precede identification of the most able. This suggests that it is through rich mathematical learning that children can not only develop their potential as mathematicians but also display the kinds of characteristics listed above. It argues that:

the development of mathematical talent is a long-term process that is dependent on many variables, including quality teaching and a student’s attitude to the subject. Mastery of core skills and knowledge is necessary for good mathematical progression and should not be undervalued, but developed in conjunction with the range of valued mathematical behaviours in a progressively deep and rigorous way.’
(ACME, 2012, p. 3)

Implications for the use of the Year 6 Level 6 tests

Schools do not always find it easy to decide how to identify pupils who should be entered for the Level 6 tests. Investigation of Key Stage 2 Level 6 Tests (Coldwell et al, 2013) found that some schools entered a large percentage of those expected to get Level 5, while others were more selective, having developed a clearer understanding of the characteristics of high attaining children as being ‘independent, tenacious and motivated, with an innate flair or capability’ (Coldwell et al, 2013, p. 14). Some schools which entered a relatively large percentage of children expected to get Level 5 are reconsidering their approach in view of the fact that nationally only 34% of those entered for the test in 2012 achieved L6. Only a fifth of the sample schools indicated that they had already assessed children as working at L6, and so most were basing their selection on L5 data.

This indicates therefore that decisions about which children should enter the L6 test should combine both a consideration of the personal qualities of the children as learners and a consideration of how secure they are at Level 5. It also indicates the need to develop teacher assessment of children’s attainment at L6.

Working with colleagues

In order to evaluate with colleagues the school’s current provision for high attaining children you are likely to need to consider:

  • developing a shared understanding of the characteristics of high attaining children.
  • agreeing what excellent provision for high attaining children would look like across the school.
  • what the school’s strengths and weaknesses are against such criteria.
  • how the school’s assessment systems can be developed to incorporate L6 attainment.
  • how teachers plan their provision for high attaining children.

Your aim will be to develop clear policy guidelines for teachers as part of your broader mathematics teaching and learning policy, and also then to use these as a basis for formal monitoring and evaluation that can feed into school improvement.

Once you have established clarity about what you and your colleagues consider to be excellent provision you will be well placed to evaluate current practice across the school and establish improvement priorities.

Ideas for staff meetings

To develop a shared understanding about what it means to be high attaining, you could use Mathematics Knowledge Networks - Supporting gifted and talented learners in mathematics as the basis for a staff meeting discussion. It would be useful to engage colleagues in collaborative higher level thinking in mathematics to help reflections on what it means to be high attaining by doing some mathematics together – choose an activity from NRICH to work on together. This will give you a real context to help develop understanding of some of the processes involved in mathematical thinking.

What might excellent practice look like? The following list has suggestions about features of excellent provision. You could use these with colleagues to generate discussion. Put each on a card and ask them to sort them according to, for example, whether they agree/ disagree with the statement and why or whether it is already a feature of the school’s practice and whether it should would be a priority for development.

Features that might indicate excellent provision for high attaining children in mathematics:

  • there is a clear school policy outlining what it means to be high attaining in mathematics and how the needs of high attaining children will be met. This includes clear guidance on the development of mathematical reasoning and problem solving across the school and how this will be assessed. The policy is consistently applied by all staff;
  • progress of high attaining children in mathematics is monitored carefully by class teachers and the subject leader and action is taken if any child shows a dip in their progress;
  • when compared with any available benchmarking data, high attaining children make good or better progress across key stages;
  • attainment in mathematics is monitored consistently for sub-groups (gender, ethnicity, EAL, socio-economic status etc);
  • teachers have opportunities to spend time in each other’s mathematics lessons in order to focus on the learning of high attaining children;
  • lesson observations by the subject leader and senior staff consistently include a focus on the learning needs of all groups of children, and observations show that this is a strength across the school;
  • the views of children about their mathematics lessons are sought on a regular basis and incorporated into development planning;
  • the views of parents about their children’s learning in mathematics are sought on a regular basis and incorporated into development planning;
  • mathematics lessons consistently include opportunities for children to develop mathematical reasoning and to apply their mathematical skills in challenging problem solving contexts;
  • teachers frequently identify challenging opportunities for using mathematics in other curriculum subjects;
  • relevant aspects of mathematical reasoning are incorporated explicitly in lessons through the use of shared learning objectives;
  • purposeful mathematical discussion between teachers and children, and between children themselves, is a consistent feature of mathematics lessons;
  • children’s self and peer assessment consistently includes mathematical reasoning and aspects of problem solving;
  • children consistently enjoy their mathematics lessons;
  • children have a rich understanding of the nature of mathematics. They know that arithmetic is an important aspect but they equally recognise that mathematical reasoning and problem solving are essential features of the subject;
  • the school provides excellent opportunities for enrichment activities outside the regular curriculum, for example through special mathematics days, involvement in mathematics competitions, running a mathematics club.

Monitoring and evaluating current provision

Review the way that your school’s assessment and tracking systems identify high attainment. For example:

  • do you use Level 6 APP resources (or other resources) to help with the assessment of high attaining children in Y5 and Y6?
  • do your school’s tracking systems identify younger children who have the potential to achieve L6 by the end of Y6?

When you are monitoring and evaluating current provision for high attaining children, you may find it helpful to focus on the following:

Planning

To what extent do teachers plan for high attaining children to:

  • do more than other children?
  • do different, more difficult work than other children?
  • do the same, but achieve a higher outcomes?

Teaching

How often are higher attaining children:

  • the focus of an adult supported group?
  • working collaboratively?
  • working individually?
  • supporting other children?

Assessment

  • how do teachers share their expectations with higher attaining children through, for example, their use of curriculum targets and success criteria?
  • to what extent do teachers assess children's mathematical reasoning and problem solving skills alongside assessment of procedural fluency and knowledge about mathematical topics?

Resources to use

Mathematics Knowledge Networks - Supporting gifted and talented learners has further discussion on what it means to be high attaining in mathematics.

Classroom Quality Standards in Gifted and Talented Education has a very useful checklist of provision in mathematics at three levels – entry, developing and exemplary – that you could use with colleagues.

What do my school and I have to offer? on the Schools Working Together microsite includes a useful generic self-evaluation checklist which you could easily adapt for use when evaluating provision for high attaining children.

Self-evaluation on the Excellence in Mathematics Leadership microsite has more general advice on developing self-evaluation as part of your subject leader role.

Improvement Planning on the Excellence in Mathematics Leadership microsite has general advice on moving from self-evaluation to improvement planning that may be especially useful if you are new to your leadership role.

What do your pupils think about mathematics? is a discussion thread in the Primary Forum which explores how children feel about mathematics. Share this with colleagues and use it to encourage discussion about attitudes to the subject in your school, particularly in relation to high attaining children. Discuss ways that you can formalise the way you find out about pupils’ attitudes to their learning and incorporate this into your development planning.

Working with Highly Able Mathematicians is an NRICH article by Bernard Bagnall about working with high attaining children. You could use this to prompt staff meeting discussionh

References

ACME (2012) Raising the bar: developing able young mathematicians

Coldwell, M., Willis, B. & McCaig, C. (2013) Investigation of Key Stage 2 Level 6 Tests. Centre for Education and Inclusion Research & Sheffield Hallam University.

DfEE (2000) Mathematical Challenges for Able Pupils in Key Stages 1 and 2

Kruteskii, V. A. (1976) The Psychology of Mathematical Abilities in School Children. Chicago: University of Chicago Press.

Ofsted (2012) Mathematics: made to measure.

QCDA (n.d.) Identifying gifted pupils: Mathematics.

 
 


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