The report by Whitehouse and Burdett makes an overarching recommendation, suggesting first that the community needs to ‘move the debate on and start talking about the complexity of mathematics’ (Whitehouse p 3) and second that it is important to be clear about what is meant by mathematics.
Various stakeholders use the terms ‘mathematics’ and ‘numeracy’ with very different meanings. We need to be much more precise in what we mean and in what knowledge, skills, attitudes and abilities we require for learners. (Whitehouse p 3)
The report suggests that ‘the time is right for cross-party agreement on how to tackle the problem of mathematics achievement’ (p 3) and the Royal Society (2011) suggests that experts from learned societies, higher education and ‘key stakeholders’ should develop mathematics curricula.
This section’s focus is the curriculum, together with qualifications and assessment. However, perhaps in-line with Whitehouse and Burden’s suggestions above (to move the debate on), ACME cautions that ‘[l]essons learned in international contexts … indicate that introducing a new curriculum on its own will produce very little change (2013a, p. 3). ACME also suggests, however, that a ‘wider curriculum’ is needed (ACME, 2011a).
A set of recommendations relate to societal values, perhaps more about education generally than about mathematics in particular. These suggest that the curriculum should be accessible to all students (ACME, 2013a; Ofsted, 2012), engaging them both from an early age and at post-compulsory level (ACME, 2013a; Jerrim & Choi, 2013; Whitehouse & Burdett, 2013) and inspiring them (Royal Society, 2011). It should build their confidence (ACME, 2011a), develop their ability to communicate (ACME, 2011a) and meet their needs and the needs of potential employers (ACME, 2011a, 2011b; Select Committee on Science and Technology, 2012; Whitehouse & Burdett, 2013). The curriculum should support students in the transition from school to HE by identifying what skills students will need at undergraduate level (Select Committee on Science and Technology, 2012).
In terms of developing and nurturing ‘the best young mathematicians’ (Jerrim & Choi, 2013, p. 19), a number of reports call for a curriculum that stretches these young people, providing them with incentives and motivation to develop their skills (ACME, 2012a; Jerrim & Choi, 2013; Royal Society, 2011). Reports recommend the provision of enrichment and enhancement activities (ACME, 2012a; Finegold, 2011; NFER, 2013; Science Learning Centre, 2013).
Further recommendations are more closely related to values in mathematics.
Subject-specific values, knowledge and methods of enquiry (including reasoning and application) should be upheld throughout the curriculum, assessment methods and materials, and teaching methods and resources (ACME, 2011b, p. 14)
ACME also suggests that mathematics should ‘be presented as conceptually coherent and cognitive progression of ideas’ (ACME, 2011b); more specifically the same report recommends that the curriculum should be based on key mathematical ideas and the ways in which these are related. Other reports stress the importance of developing understanding (ACME, 2011c, 2013a; Ofsted, 2011a). For example, as the ACME report on Primary Arithmetic (2011c) states,
Development of memorisation, accuracy and fluency is important. However, this must take place in parallel with development of understanding and reasoning (p. 5).
Modelling and problem solving
It is recommended that the curriculum includes more problem-solving and modelling (ACME, 2011b, 2012a; Hodgen & Marks, 2013; Ofsted, 2011a, 2012). As Ofsted argues:
Pupils’ confidence, fluency and versatility are nurtured through a strong emphasis on problem solving as an integral part of learning within each topic. (Ofsted, 2011a, p. 6).
A number of reports suggest that modelling should be a key element of any new provision at school and post-16 (ACME, 2011a; Burghes, 2011; Clark-Wilson, Oldknow, & Sutherland, 2011a; Hodgen, Marks, & Pepper, 2013). ACME, for example, urges for the introduction of the concept of a mathematical model from an early stage, suggesting that the review of the National Curriculum take this into account. (ACME, 2011a).
In particular, a number of reports emphasise the importance of application of mathematics in realistic and complex settings, where solutions to problems might not be simple or straightforward (Hodgen & Marks, 2013; NFER, 2013; Norris, 2012; Science Learning Centre, 2013).
The curriculum should also include more “simple maths in complex settings”, by providing students with problem-solving opportunities involving “messy” contexts that do not have straightforward solutions. (Hodgen & Marks, 2013, p. 1).
Related to this, a number of reports recommend that mathematical content can and should be taught within other subject areas, and that quantitative methods (and numeracy) are built into other subjects at all levels from primary to adult education. (All Party Parliamentary Group on Financial Education, 2011; British Academy, 2012; Harris, 2012; Ofsted, 2011b; Porkess, 2012; Science Learning Centre, 2013; Vorderman, Porkess, Budd, Dunne, & Rahman-hart, 2011). For example, as the Vorderman report states:
Children in primary school should continue to have a daily mathematics lesson, but mathematics must also be actively encouraged in other areas of their daily routine in school. (Vorderman et al., 2011, p. 8).
Recommendations related to specific mathematics mostly concern financial numeracy and statistics, although algebra and mental calculation methods are also mentioned. It is recommended that the curriculum should address financial education at primary and secondary schools (All Party Parliamentary Group on Financial Education, 2011; Vorderman et al., 2011), although the All Party Parliamentary Group also suggests that financial education should be addressed within programmes of personal, social and health education (PSHE).
Personal finance education should be taught cross-curricular in mathematics and PSHE education with the financial numeracy aspect of personal finance education situated in mathematics and subjective aspects taught in PSHE education. It should be packaged in an obvious and clear way to young people. (2011, p. 7)
It is recommended also that statistics (and quantitative methods) is addressed more thoroughly and widely within mathematics (ACME, 2011a, 2013a; British Academy, 2012; Hodgen et al., 2013; Hodgen & Marks, 2013; Porkess, 2012).
National education policy should ensure that all students are equipped with a working knowledge of basic statistics, including the necessary associated mathematical competence, and an appreciation of how it impacts on their daily lives (Porkess, 2012, p. 1).
Both Porkess (2012)and ACME (2013a) draw attention to the cyclical process of collecting, presenting and analysing data, and recommend not only that this appears in primary and secondary national curricula, but also that probability and statistics should be grouped together in the curriculum.
ACME is disappointed that the cyclical process of collecting, presenting and analysing data outlined in numeracy statement does not appear in the curriculum in any key stage. This is a fundamental skill in most walks of life. ACME believes this should be a prominent attribute of the new curriculum. ACME notes that the proposed curriculum splits probability and statistics in Key Stages 3 and 4. ACME recommends that further consideration be given to whether these sections should be grouped together to provide for greater coherence (ACME, 2013a, p. 8)
Porkess (2012) also recommends that hypothesis testing should be addressed in A-level and AS-level courses and ACME (2011a) recommends that post-16 courses that might be developed (those that are not A-level) should go beyond descriptive statistics.
Noyes et al (2011) recommend that more attention is paid to algebra, for students who do well in mathematics and at HE level it is recommended that students should practice mathematics more, using problem sheets and tutorials (Morgan, 2011). At the other end of the school curriculum, Ofsted recommends ‘[u]nderstanding of place value, fluency in mental methods, and good recall of number facts’ for primary school children and the use of ‘[p]ractical, hands-on experiences of using, comparing and calculating with numbers and quantities’ for the youngest age groups (2011a, p. 6).
A number of reports recommend more use of digital technologies within the curriculum. They make the point these technologies are widely used in the workplace and that students need to experience the ways in which they can be used to solve a range of problems (ACME, 2011a; Clark-Wilson, Oldknow, & Sutherland, 2011; Ofsted, 2012). They also suggest that students should use technologies that are specifically designed on mathematical principles:
The curriculum should: fully incorporate the mathematical capabilities, methods and questions that arise from use of all available technologies, especially those used in the workplace and those that are designed on mathematical principles (ACME, 2011b, p. 3).
The suggestion is that the mathematics curriculum should require the use of digital technologies (Clark-Wilson et al., 2011) and that the use of these should be explicitly evaluated within Ofsted inspections (ACME, 2013a)
A large number of recommendations relate to the study of mathematics after the age of 16. Some of these concern A-levels and are discussed below. Here, however, the focus is on students who do not take A-level mathematics (or AS-level).
The earliest of these recommendations came in the Vorderman report (2011):
mathematics, in some form, must be made compulsory to the age of 18. This recommendation is a matter of urgency. (p. 9)
There are some who caution against making mathematics compulsory, however (Harris, 2012) and the further point is made that in countries where mathematics is compulsory, commonly to the age of 18, it is not the only compulsory subject (Harris, 2012; Hodgen et al., 2013).
Whitehouse and Barden (2013), amongst others (e.g. Hodgen et al., 2013) suggest that reform of mathematics should ‘encourage’ more people to study mathematics post-16, and others (Harris, 2012; Hodgen & Marks, 2013) recommend the development of new courses or pathways for those not taking A-level mathematics. These new courses should take into account the needs of employers (ACME, 2011a; Hodgen & Marks, 2013) RSA (e.g. modelling, problem solving, fluency with digital technologies) but also that young people and adults should ‘work towards a qualification that is suitable for their career aims’ (Ofsted, 2011b, p. 9) and that the new courses should meet the needs of all young people (Select Committee on Science and Technology, 2012) and should be attractive to them (ACME, 2012b; Hodgen et al., 2013). It seems clear from the above that, as Whitehouse and Barden suggest:
We all – and especially the mathematics establishment – need to move the debate on and start talking about … the need for multiple routes and end points up to age 16 and beyond. (2013, p. 3)
More specifically, Noyes et al (2011), who evaluated a range of alternative qualifications for mathematics, including a qualification called ‘Use of Mathematics’, recommend that this qualification should be adopted as it will provide new pathways for learners post-16.
In terms of A-level and AS-level mathematics, there were some recommendations that changes should be made to the structure of the subject (Morgan, 2011), with some feeling that AS should be re-designed so that it is more accessible for those young people who achieved a C at GCSE (Harris, 2012). ACME, however, recommends that AS-level mathematics should be seen as the first half of an A-level qualification and that linkages between AS-level and A-level (and between A-level mathematics and A-level further mathematics) should be maintained (ACME, 2013b). ACME further recommends that reforms to A-level should take into account changes the wider mathematics landscape:
Any reform of A level Mathematics and Further Mathematics should have links with those reviewing GCSE Mathematics and those involved with developing the new Core Mathematics qualifications… Any revisions to the content criteria for A level Mathematics need to draw on the needs of other disciplines. (p. 10 and p. 4).
ACME also strongly recommends that reforms to A-levels are not put in place until 2016 (rather than 2015 as proposed by the government) and that whatever changes there are, are minimal.
Review of the national curriculum
The revised national curriculum has now been published. The recommendations related to the revision can be found here.
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