The majority of the reports were written after the announcement that the national curriculum in England would be reformed and that many include recommendations and advice related to a new curriculum. In terms of the specific mathematics National Curriculum, the main recommendations come from ACME.
At the time of writing, the new curriculum has been published; the extent to which the recommendations were taken into account may be interesting, but here the focus is on the content of the recommendations.
The first set of recommendations relate to the approach taken to developing a new curriculum. In terms of the time allowed for developing the new curriculum, ACME recommends a review cycle that allows enough time to develop resources to support teaching the new curriculum (e.g. textbooks), to provide professional development for teachers and to develop assessments designed to address the new curriculum. They recommend that the review of the National Curriculum takes into account the various processes involved in doing mathematics, such as building on prior knowledge, extending familiar ideas and using a range of notation and methods and that it recognises that students should experience all components of mathematics such as making connections learning facts and using numerical, spatial and algebraic reasoning. They further express concern that the time allowed for the development of the curriculum was not long enough (ACME, 2011a, 2012a, 2013).
Advice and guidance in the NC
A second set of recommendations concern the presentation of the curriculum documents, and in particular the language and tone used. For example, ACME (2012b) recommends careful consideration of the messages implicit within the document, highlighting the fact that the language refers to what should be taught (what teachers should do) rather than what pupils should learn and do. ACME suggests that the impression given is that the approach to teaching is ‘done to’ the pupils (who are seen as passive). The same report recommends the use of precise and accurate mathematical language, saying that
the draft document should also provide clarity for primary teachers and support should be provided for parents and others to understand mathematical language where this is used for necessary accuracy (2012b, p. 13).
Related to this, some reports provide recommendations about the amount of detail provided in the new curriculum documents. Whereas the Vorderman report (for example) suggests that the new curriculum ‘should not predetermine teaching methods in mathematics or the chronology of learning’ (2011, p. 8), other recommendations suggest that more structure would be helpful (ACME, 2012b; Burghes, 2012). There is also a call for a balance in the level of detail provided (ACME, 2011a, 2013). For example:
If the curriculum specifies too many irrelevant details, inexperienced and non-specialist teachers may not be able to decide what is important; if there is not enough detail, teachers may not be able to decide what to teach. (ACME, 2011a, p. 19)
There are further specific recommendations related to supporting teachers, such as reminders to teachers to develop pupils’ reasoning, (ACME, 2012b) and the development of materials to exemplify the expectations and pitch of the curriculum which would help schools interpret the new programmes of study (ACME, 2013). This report also recommends that, at each key stage, a section called ‘working mathematically’ should be included.
ACME provides two recommendations related to the preamble to the National Curriculum. First, it suggests that a statement about the positive attitudes towards mathematics is included (ACME, 2012b) and second that either the aims are re-ordered to emphasise the importance of conceptual understanding for problem solving or to advise that all aims are equally important (ACME, 2013).
There are a number of recommendations related to the use, or application, of mathematics. For example, ACME recommends that greater attention is given to the applications of mathematics (ACME, 2011b), and mentions in particular that students should encounter mathematical modelling at an early stage (ACME, 2011b, 2013), and that they should use real data in the classroom (ACME, 2013). Related to this, it is also recommended that an emphasis should be placed on problem solving activities (ACME, 2013; Burghes, 2012) and that more links should be made to other areas of the curriculum, thus developing the application of mathematics (ACME, 2012b).
Further recommendations emphasise the importance of learning with understanding in addition to developing procedural fluency and memorising facts:
Recalling multiplication and division facts is essential, but understanding relationships between the facts adds the crucial extra level of power and flexibility to the knowledge (ACME, 2012b, p. 11).
As far as ICT is concerned, ACME recommends that the National Curriculum should point to appropriate use of calculators as well as inappropriate use and that other use of ICT should be referred to in the introductory comments to the curriculum or in the programme of study (ACME, 2013)
In terms of mathematical content, some recommendations refer to where specific content is placed, and others recommend the inclusion of content. For example, it is recommended that mathematical concepts are introduced in ‘sizeable chunks’, and that ‘some content’ is moved from Key Stage 2 to Key Stage 3 (ACME, 2013). Other recommendations suggest that specific content is introduced earlier:
… include some topics earlier, that is inequality signs ( < , ≤ , > , ≥ ) introduced in Year 1; multiplication tables up to 10 x 10 by the end of Year 2; Tables and Venn diagrams for use in classifying numbers/objects from Year 2 onwards; probability introduced in Year 2 and developed throughout the following years; algebraic notation and expressions used in Year 1 and throughout the primary phase, with solving equations and inequalities from Year 2 onwards. (Burghes, 2012, p. 18)
In terms of content that should be included, ACME’s recommendation is that the cyclical process of collecting, presenting and analysing data should be included and that in Key Stages 3 and 4, probability and statistics should be grouped together (ACME, 2013).
ACME. (2011a). Mathematical Needs of Learners. London.
ACME. (2011b). Mathematical Needs Mathematics in the workplace and in Higher Education. London.
ACME. (2012a). Raising the bar: developing able young mathematicians (pp. 1–4). London.
ACME. (2012b). ACME’s response to the draft Primary National Curriculum for Mathematics published on 11 June 2012 (pp. 1–15). London.
ACME. (2013). ACME’s response to the consultation on the draft programmes of study for the National Curriculum. London.
Burghes, D. (2012). Primary Problems: A First Curriculum for Mathematics. London.
Vorderman, C., Porkess, R., Budd, C., Dunne, R., & Rahman-hart, P. (2011). A world-class mathematics education for all our young people. London.