Explain this
National Curriculum Review • Apr 2011 • ATM Response
This response is distilled from collated views of members of the Association of Teachers of Mathematics (ATM). We have retained the relevant questions together with the respective preamble for each in order to retain the context of the responses.
Section C • General Views on the National Curriculum (Q6a-Q8)
The National Curriculum is one part of the wider school curriculum. Each subject in the National Curriculum has a statutory Programme of Study that is determined by the Government setting out the content to be taught in that subject. Schools are legally required to teach these subjects and the specified content to all pupils at the relevant key stages (a key stage is a group of school years). More information on the current National Curriculum can be found here.
The National Curriculum was originally envisaged as a guide to what children should learn in key subjects, giving parents and teachers confidence that students were acquiring the knowledge necessary at each level of study to make appropriate progress. As it has developed, the National Curriculum has come to include more subjects, prescribe more outcomes and take up more school time than originally intended. It is the Government’s intention that the National Curriculum be slimmed down so that it properly reflects the body of essential knowledge in key subjects and does not absorb the overwhelming majority of teaching time in schools. Individual schools will then have greater freedom to construct their own curricula in subjects outside the National Curriculum, to reflect local circumstances and the needs of their pupils.
The purpose of this section is to find out your general views on the current National Curriculum and what, if anything, you think should be changed.
6a • What do you think are the key strengths of the current National Curriculum?
ATM Response
The key strength is that it provides an entitlement to a common curriculum experience for all learners in each phase of their learning.
6b • What do you think are the key things that should be done to improve the current National Curriculum?
ATM Response
The curriculum should have primacy over its assessment.
The curriculum should not be overlaid with advice and guidance which may become the curriculum in the minds of practitioners.
The curriculum should articulate an entitlement until the age of 18.
Once established the curriculum should be allowed to evolve in the hands of the professionals.
7a • What are the key ways in which the National Curriculum can be slimmed down?
ATM Response
The curriculum should reduce content in the primary phase giving more time for the key concepts to be developed and consolidated in preparation for more secure learning in the secondary phase.
The curriculum should reduce prescribed content in the secondary phase to allow the “big ideas”, coherence and integrity of subjects to be maintained and visible to learners.
7b • Do you think that the proportion or amount of lesson time should be specifiedin any way in the National Curriculum; eg for particular subjects and/or within particular key stages?
ATM Response
No
There should be no specified amount of lesson time for any particular subject.
Core subjects should be part of the curriculum until the age of 18.
Entitlement should be expressed in terms of understanding and not curriculum time.
Section D: English, mathematics, science and physical education (Q9a-Q13)
The remit for the review makes clear that English, mathematics, science and physical education (PE) will remain National Curriculum subjects at all four key stages (i.e. from age 5 to 16). The introduction of the new National Curriculum will be phased, with new Programmes of Study for these four subjects being taught from September 2013. In terms of the detailed content of the Programmes of Study, this initial call for evidence therefore focuses on the four subjects in the first phase of the review. A further call for evidence will be launched in early 2012 in relation to all other subjects that it is decided should be part of the future National Curriculum, and new Programmes of Study for those subjects will be taught from September 2014. This decision will be made in light of responses to this call for evidence (see Section E).
The intention is that in future the National Curriculum should focus on the essential knowledge in key subjects that all children need to acquire in order to progress in their education and take their place as educated members of society.
Against that background, the questions below ask for your views on what is essential to include in the Programmes of Study for the four subjects in phase one. In particular:
- For English, mathematics and science, we would like your views on the essential knowledge that pupils need in order to deepen their understanding at each stage of their education. Your views will help inform the content of new statutory Programmes of Study for each subject.
- For physical education, we would like your views on what should be included in a shorter, less prescriptive Programme of Study.
We are seeking your views on what you regard as the essential knowledge (eg facts, concepts, principles and fundamental operations) that pupils should be taught in each subject considered in this section, and why. Please note that the current National Curriculum uses terms such as "knowledge, skills and understanding" but you are free to use whatever language you see fit in setting out your responses. What is more important is setting out the knowledge itself and why you regard it as essential.
We are particularly interested in any evidence that demonstrates the positive impact of your proposals. This might, for example, be formal research, examination/test results, or evidence of progress for particular groups of students.
If you would prefer to base your comments on either the current or a previous version of the National Curriculum Programmes of Study, please feel free to do so but we would ask you to make clear in your response which version of the Programme of Study you are referring to. If you have produced a draft of one or more Programmes of Study which you would like us to consider, you may wish to submit this to refer to it in your response.
Note that you do not need to respond to all the questions in this section: for example, you may want to focus on particular subjects and/or on particular ages or key stages.
10a • Mathematics: What knowledge do you regard as essential to include in the Programme of Study for mathematics? Please also set out why this is essential and at what age or key stage.
ATM Response
It is essential to specify the skills of mathematical reasoning which include: recognising pattern, articulating, manipulating and representing relationships, hypothesising, generalising, testing, deducing, inferring and proving.
Knowledge of how parts of mathematics inter-relate is as important as knowledge of the constituent parts. Thus, knowledge of the meta-concepts or ‘big ideas’ in mathematics provides learners with the ability to make these connections and more efficiently develop their confidence and competence in mathematics.
Using mathematics to learn and understand more mathematics should be recognised in the curriculum.
10b • Considering your response to the above, should the Programme of Study for mathematics be set out on a year by year basis or as it currently is, for each key stage?
ATM Response
Year by Year: No
Key Stages: Yes
A programme of study set out for a key stage gives time for learners to explore and gain a knowledge of the ‘key stage curriculum landscape’ in a variety of ways. In this sense a Key Stage PoS is more inclusive and allows for periods of ‘study in depth’, and for periods of support when this is needed.
There should be as much flexibility as possible in the PoS so that teachers can help learners see the inter-connections within the subject and appreciate its coherence. Teachers should be responsible for deciding what is taught and when, to best meet the needs of their students.
If the PoS were to include only year on year targets then ATM is concerned this could disenfranchise some pupils from their curriculum entitlement.
Section F: Supporting and Recognising Progress (Q23a-Q26)
Currently, the National Curriculum defines pupils’ attainment through subject specific Attainment Targets which set out 8 level descriptors (Level 1 to Level 8) describing what pupils should be able to do to achieve each level. The expectation is that most pupils achieve:
- Level 2 at the end of Key Stage 1
- Level 4 at the end of Key Stage 2; and
- Level 5/6 at the end of Key Stage 3.
At the end of Key Stage 4 pupils are assessed through GCSE examinations.
Under the 2002 Education Act the specified purpose of statutory assessments for the key stages is to ascertain what pupils have achieved in relation to the attainment targets (eg the knowledge, skills and understanding which pupils of different abilities and maturities are expected to have) for that key stage.
Schools also have a responsibility to provide a broad and balanced curriculum for all pupils, and the National Curriculum statutory inclusion statement sets out three principles for developing an inclusive curriculum:
- Setting suitable learning challenges.
- Responding to pupils’ diverse learning needs.
- Overcoming potential barriers to learning and assessment for individuals and groups of pupils.
In setting out the range of needs of pupils, the current National Curriculum includes the following groups of pupils:
- gifted and talented
- pupils with learning difficulties and disabilities
- pupils from different ethnic groups including travellers, refugees and asylum seekers
- pupils who are learning English as an additional language
- boys and girls with different needs
- children in care
This section is about your views on supporting progress of all pupils. In particular, whether there are credible alternatives to attainment targets that would better support and recognise all pupils’ progress, irrespective of their attainment and background, and how to address the needs of all pupils though the National Curriculum.
23a • Do you think the National Curriculum should continue to specify the requirements for each of the 8 levels of achievement?
ATM Response
No.
We would wish to see an articulation of progression in mathematics. We recognise that the scales within subjects are different and that eight levels of achievement may not be universally valid.
We understand that it is helpful to be able for teachers and learners to see the progression that is being presented. The way levels are currently used in some schools for assessment is limiting and damaging. Learning does not happen in neat steps and situations in real life and at work do not fit into particular levels.
23b • If you have answered no or not sure, what alternative(s) do you propose to replace Attainment Target level descriptors?
ATM Response
Having mathematical themes (the meta-concepts referred to before)with associated progression maps would be useful in helping teachers express mathematics learning as more holistic.
We believe the current system of attainment targets, alongside guidance and advice, has led to the fragmentation of the mathematics curriculum.
24 Within each Programme of Study, how should the curriculum and attainment targets be defined to ensure appropriate education for pupils in a wide range of circumstances as learners?
ATM Response
The PoS should specify the skills, knowledge and concepts in the curriculum. It should make explicit the big ideas which underpin it. It should acknowledge that, through pedagogy, teachers will tailor the curriculum to meet the needs of all learners.
For mathematics the PoS should be expressed as a series of rich starting points for learning.
25a • How do you think the needs of low-attaining pupils should be addressed through the National Curriculum?
ATM Response
The PoS should specify the skills, knowledge and concepts in the curriculum. It should make explicit the big ideas which underpin it. It should acknowledge that, through pedagogy, teachers will tailor the curriculum to meet the needs of all learners.
For mathematics the PoS should be expressed as a series of rich starting points for learning.
25b • How do you think the needs of high-attaining pupils should be addressed through the National Curriculum?
ATM Response
The PoS should specify the skills, knowledge and concepts in the curriculum. It should make explicit the big ideas which underpin it. It should acknowledge that, through pedagogy, teachers will tailor the curriculum to meet the needs of all learners.
For mathematics the PoS should be expressed as a series of rich starting points for learning.
26 • Any other comments you would like to make about the issues covered in this section.
ATM Response
The National Curriculum should not be expressed differently for different groups of learners.
The PoS should specify the skills, knowledge and concepts in the curriculum. It should make explicit the big ideas which underpin it. It should acknowledge that, through pedagogy, teachers will tailor the curriculum to meet the needs of all learners.
For mathematics the PoS should be expressed as a series of rich starting points for learning.
Section G: International Comparisons (Q27a-Q28)
The remit for the review makes clear that we need to learn from the very best that has been achieved in other jurisdictions - countries or regions within countries - and ensure that the construction and content of the new National Curriculum is based upon international best practice.
This section seeks your views on what can be learned from other countries and states to inform the development of the National Curriculum. Your views may be based on particular expertise in international comparisons, or from your own experiences of living or working in particular countries.
We would be particularly keen to learn about international comparisons beyond the commonly assessed areas of literacy, mathematics and science in the PISA, TIMMS and PIRLS studies.
27a • Please give examples of any jurisdictions that could usefully be examined to inform the new National Curriculum.
ATM Response
We should be careful not to cherry pick from other, more successful, jurisdictions without fully understanding the mechanisms that deliver that success.
Useful references for International Comparisons in mathematics include:
Askew, M., Hodgen, J., Hossain, S., Bretscher, N., (2010), Values and Variables: Mathematics in high performing countries, Nuffield Foundation, London.
Andrews, P.,(2011). The cultural location of teachers’ mathematical knowledge: Another hidden variable in mathematics education research?, In T. Rowland & K. Ruthven (Eds.), Mathematical knowledge in teaching (Vol. 50, pp. 99-118). New York: Springer.
Szalontai, T., (2000), Some facts and tendencies in Hungarian mathematics teaching, International Journal of Mathematics Teaching and Learning, CIMT, Plymouth.
27b • Considering your response to question 27a above, what features of their national curricula or wider education systems are most significant in explaining their success?
ATM Response
Research suggests that differences in culture have a more significant impact on achievement in other jurisdictions than the expression of their National Curriculum.
Section H: How Children Learn (Q29)
The remit for the review makes clear that the National Curriculum should express clearly the progression that pupils should make in each subject, and that this progression should be informed by the best available evidence on how children learn. For example, at what age should particular concepts first be introduced, how should these be sequenced in the most appropriate age-related order to develop deep learning and how should this evidence be best reflected in Programmes of Study for particular subjects?
This section is about your views on the best available evidence on how children acquire particular knowledge, and understanding of concepts and principles, to inform the development of the National Curriculum. Your views may be based on particular research, expertise or from your own experiences of teaching.
Our aim in seeking this information is to help inform the sequencing of knowledge at different ages with the National Curriculum Programmes of Study. We would welcome all evidence relevant to this issue, whether broadly based or focused on particular knowledge and concepts within a given subject (eg understanding ratio and proportion within mathematics).
29 • What research evidence on how children learn provides the most useful insights into how particular knowledge should best be sequenced within the National Curriculum Programmes of Study?
If drawing on particular research evidence, please provide a brief summary of the evidence, with a reference or web address to key studies or research summaries.
ATM Response
We believe that the following references are very relevant in developing a deeper insight into mathematical learning.
Gattegno, C., (1970), What We Owe Children, The Subordination of Teaching to Learning, Outerbridge and Diensfrey, New York.
Skemp, R.R,, (1976), Relational Understanding and Instrumental Understanding, Mathematics Teaching, 77, pp 20-26.
Holt, J., (1964), How Children Fail, Penguin, London.
Donaldson, M., (1978), Children’s Minds, Harper Collins, London.
Nunes, T., Bryant, P., Watson, A., (2009), Key understandings in mathematics learning, Nuffield Foundation, London.
Hart, K.M. (ed), (2005), Children’s Understanding of Mathematics:11-16, 11thRevised Edition, Anthony Rowe, London.
Foxman, D., Ruddock, G., McCallum, I, (1990), APU mathematics monitoring 1984-88 (phase 2), a summary of findings, conclusions and implications, Central Office of Information, London.
Hattie, J.C., (2008), Visible Learning: a synthesis of over 800 meta-analyses relating to achievement, Routledge, London.
The transmaths project, www.education.manchester.ac.uk/research/centres/lta/LTAResearch/transmaths/
Section I: Transition (Q30- Q33)
The review will be taking into account the emerging conclusions of the review of the Early Years Foundation Stage (EYFS) by Dame Clare Tickell to ensure a smooth transition from the EYFS to Key Stage 1. The review will also take into account the need for the National Curriculum to be embodied readily into GCSE subject criteria and support the effective operation of public examinations at the end of compulsory schooling. The development of new GCSE criteria themselves is outside the scope of this review.
This section is about your views on how to best take into account the key transition periods in schooling in developing the new National Curriculum.
30 • What are the most important factors to consider in developing the National Curriculum for Key Stage 1 to ensure a smooth transition from the Early Years Foundation Stage?
ATM Response
PoS should be designed that straddle the institutional transition points, for example there could be one PoS for EYFS and KS1.
31 • What are the most important factors to consider in developing the National Curriculum for Key Stage 3 to ensure a smooth transition from Key Stage 2?
ATM Response
PoS should be designed that straddle the institutional transition points, for example there could be one PoS for KS2 and KS3.
32 • What are the most important factors to consider in developing the National Curriculum for Key Stage 4 to ensure the effective operation of GCSE and other public examinations?
ATM Response
The curriculum should have primacy over its assessment.
PoS should be designed that straddle the institutional transition points, for example there could be one PoS for KS4 and KS5.
A 14-18 PoS should inform a review of assessment; there is no logic in having an assessment point at 16 when we are moving to continuous learning until the age of 18.
Section J: Implementation (Q34-Q35)
This section is about what arrangements need to be put in place to support the successful implementation of the new National Curriculum in schools. For example, this may relate to teacher training, inspection, statutory assessment, support and guidance for schools, etc.
As explained in Section C, the Government’s intention is that the implementation of the new National Curriculum should be phased in, with new Programmes of Study for English, mathematics, science and physical education published in autumn 2012 for first teaching in schools from September 2013, and those for other subjects published in autumn 2013 for first teaching in schools from 2014. The remit for the review includes consideration of what further phasing may be necessary (for example whether the new Programmes of Study should be introduced in all key stages/year groups simultaneously, or over a period of time).
34 • What are the particular issues that need to be considered in phasing the introduction of the new National Curriculum in the way proposed, with Programmes of Study in some subjects introduced in 2013 and the rest a year later?
ATM Response
Careful consideration should be given to the burdens already placed on schools.
Sufficiently high quality professional development- best provided by subject associations such as the ATM in collaboration with HEI providers in order to ensure a research based provision.
Encourage membership of subject associations to link teachers into a professional learning community.
Section K: Other Issues (Q36-Q37)
37 Finally, please let us have your views on responding to this Call for Evidence.
ATM Response
We recognise that this first call for evidence is focussed on the overarching structures of a National Curriculum and the ATM looks forward to engaging further with this review.
We think it is disappointing that this call for evidence has been conducted when the majority of teachers are committed to their classroom work and would have found it difficult to make a response.
Video reactions
At the invitation of general Council, Andrew Pollard — member of the National Curriculum Review expert panel — attended ‘conference 2011’ to; both answer member’s questions, and to listen to views on the proposed reforms to the mathematics curriculum. Here two conference delegates share their thoughts on, and contributions to, the discussion.
John White and Sue Pope: reactions to Andrew Pollard’s ATM 2011 Conference session
Other reviews and consultations
All our statements, responses, representations and consultation documents can be read here.
