In many countries the notion of mathematical literacy as a twenty-first century competency has emerged either from international studies, such as the OECD’s Programme for International Student Assessment (OECD, 2016), or from national curriculum policy development. In some English-speaking countries, however, it is more common to speak of numeracy rather than mathematical literacy. This chapter traces the emergence and interpretations of numeracy and mathematical literacy as separate but related concepts and examines their role in curriculum reform in four countries: Australia, Ireland, South Africa and Japan. The main question addressed by the chapter is: How have notions of mathematical literacy and numeracy been expressed in curriculum reforms? The analysis aims to shed light on the interpretation and expression of numeracy and its relationship to mathematics.

Conceptualising Numeracy and Mathematical Literacy

Numeracy can be defined in many ways, and sometimes even by using different terms such as mathematical literacy or mathematical competencies. The concept of numeracy evolved from the UK’s Crowther Report (MoE, 1959), in which the word ‘numerate’ was introduced to represent “the mirror image of literacy” (para. 398). In a later UK report, Cockcroft (1982) defined “being numerate” as having two attributes: “The first of these is an ‘at-homeness’ with numbers and an ability to make use of mathematical skills which enables an individual to cope with the practical mathematical demands of his everyday life” (p. 11). The second attribute is the ability to “have some appreciation and understanding of information which is presented in mathematical terms, for instance in graphs, charts or tables” (p. 11).

Attempts to operationalise numeracy within school curriculum documents have been made in many English-speaking countries around the world (e.g. Alberta Education, 2019; Australian Curriculum, Assessment and Reporting Authority, n.d.-b; DfE, 2013). Less common are efforts to theorise numeracy in ways that can be used by teachers for curriculum planning and task design. To this end, Goos et al. (2014) developed a multi-dimensional model of numeracy for the twenty-first century. The model consists of four different domains and gives attention to how one can apply mathematical knowledge in real life contexts by using different representational, physical or digital tools while holding positive dispositions. These four domains are grounded in a critical orientation which involves the ability to make decisions and form opinions based on these four domains.

Compared with numeracy, mathematical literacy is a relatively new term emerging from the OECD’s work on PISA. The PISA definition of mathematical literacy has advanced from a basic skills definition of being able to use the mathematics learned in a school setting and apply it to everyday life, to a much broader definition as:

an individual’s capacity to reason mathematically and to formulate, employ, and interpret mathematics to solve problems in a variety of real-world contexts. It includes concepts, procedures, facts and tools to describe, explain and predict phenomena. It assists individuals to know the role that mathematics plays in the world and to make the well-founded judgments and decisions needed by constructive, engaged and reflective 21st century citizens. (OECD, 2018, p. 7)

Interestingly, the OECD’s Programme for International Assessment of Adult Competencies (PIAAC) uses the term numeracy instead of mathematical literacy, along with a focus on literacy and problem solving in technology-rich environments (Tsatsaroni & Evans, 2014). PIAAC defines numeracy as, “the ability to access, use, interpret and communicate mathematical information and ideas in order to engage in and manage the mathematical demands of a range of situations in adult life” (Tout et al., 2017, p. 9).

At the ICMI 24 Study Conference, Niss (2018) reminded us that the notion of mathematical competence, developed within the Danish “KOM project” (Competencies and the Learning of Mathematics), shaped the PISA mathematics frameworks from 2000 to 2012 and underpinned the notion of mathematical literacy. In a related paper, Niss and Højgaard (2019) defined mathematical competences in terms of “someone’s insightful readiness to act appropriately in response to all kinds of mathematical challenges pertaining to given situations” (p. 4). They revisited the notion of mathematical competences, grouping these into two categories: posing and answering questions in and by means of mathematics; handling the language, constructs and tools of mathematics. As all of the eight competencies in these two categories are specific to mathematics (e.g. mathematical problem-handling competence, mathematical symbolism and formalism competence), it could be argued that the notion of mathematical competence seems to part ways with context-rich definitions of numeracy and mathematical literacy.

Niss and Jablonka (2014) describe mathematical literacy as a concept which is positioned in student and school contexts, whereas numeracy is described as applying mathematics within adult world contexts. On the other hand, Geiger et al. (2015) argued that, while the meaning of numeracy and mathematical literacy varies between countries, being numerate goes beyond using basic arithmetic skills to include the ability to “make sense of non-mathematical contexts through a mathematical lens; exercise critical judgement; and explore and bring to resolution real world problems” (p. 531). Debates surrounding the meanings of numeracy and mathematical literacy need to acknowledge that not only have these terms come into existence at different times, but they are also assumed to operate within somewhat different contexts involving different combinations of school, workplace, and daily life. In his commentary in a journal special issue on numeracy, Askew (2015) claims that much work remains to be done on conceptualising numeracy and mathematical literacy and in realising their role in school curricula.

Conceptualising Curriculum

Remillard and Heck (2014) defined curriculum as, “a plan for the experiences that learners will encounter, as well as the actual experiences they do encounter, that are designed to help them reach specified mathematics objectives” (p. 707; emphasis in original). They presented a visual model of the curriculum policy, design, and enactment system that distinguishes between the official curriculum and the operational curriculum enacted in classrooms. The focus of this chapter is on the official curriculum, as specified by governing authorities, and on curricular aims and objectives as one of its three components proposed by them.

Our comparative analysis is presented via country case studies, each structured around two dimensions: (1) the rationale for including numeracy in the school curriculum; (2) how numeracy is represented in the curriculum through curricular aims and objectives. These countries were chosen for comparison because they highlight contrasting approaches to incorporating numeracy in the school curriculum.

Numeracy as a Cross-Cutting Competency in Australia and Ireland

In both Australia and Ireland, numeracy is identified as one of several general competencies to be developed in all subjects across the school curriculum. This approach has led to curriculum frameworks that attempt to integrate cross-cutting competencies with the disciplinary content of the separate school subjects (Goos & O’Sullivan, 2018).

Rationale for Numeracy in Australia and Ireland

In Australia, the rationale for including numeracy in the curriculum has evolved over 30 years and three national Declarations on the goals of schooling agreed by the State, Territory, and Australian Ministers for Education. In 1989, the Hobart Declaration (Education Council, 2014b) proposed a framework of national collaboration between the States and Commonwealth with ten agreed goals for schooling, including development of skills of numeracy and other mathematical skills. Ten years later, in 1999, the Adelaide Declaration agreed on eight key learning areas for the school curriculum and additionally stated that, “Students should have attained the skills of numeracy and English literacy, such that every student should be numerate, able to read, write, spell and communicate at an appropriate level” (Education Council, 2014a). Whereas the previous declarations were non-binding agreements, in 2008 the Melbourne Declaration foreshadowed action in referring to developing a national curriculum and national assessment program for literacy and numeracy (MCEETYA, 2008), replacing existing state-based curricula and assessments. Having skills in numeracy was seen as essential for creating “successful learners, confident and creative individuals, and active and informed citizens” (p. 8).

In Ireland the rationale for numeracy driving curriculum reform is a more recent phenomenon, in response to the results of the Third International Mathematics and Science Study (TIMSS; Beaton et al., 1996) and Ireland’s substantial decline in PISA mathematical literacy performance in 2009 (Shiel et al., 2016). Performance on these international assessments, together with the national economic crisis of 2010, provided impetus for development of a national literacy and numeracy strategy (DES, 2011). The Irish government has agreed that all young people in Ireland should leave school with the appropriate numeracy and literacy skills to live and participate as informed citizens in society. In the strategy document, numeracy is defined as follows:

Numeracy encompasses the ability to use mathematical understanding and skills to solve problems and meet the demands of day-to-day living in complex social settings. To have this ability, a young person needs to be able to think and communicate quantitatively, to make sense of data, to have a spatial awareness, to understand patterns and sequences, and to recognise situations where mathematical reasoning can be applied to solve problems. (p. 8)

Representation of Numeracy in the Official Curriculum of Australia and Ireland

In Australia, the relationship between mathematics and numeracy has been explored and contested for many years. The National Numeracy Review Report (Council of Australian Governments, 2008), although mixing together research and recommendations regarding both mathematics and numeracy, seemed to set a clear direction for distinguishing between these in its first recommendation:

That all systems and schools recognise that, while mathematics can be taught in the context of mathematics lessons, the development of numeracy requires experience in the use of mathematics beyond the mathematics classroom, and hence requires an across the curriculum commitment. (p. 7; emphasis added)

The Australian Curriculum: Mathematics was developed between 2008 and 2012 and is structured around the three content strands of number and algebra, geometry and measurement, and statistics and probability, and the four proficiency strands of understanding, fluency, problem solving, and reasoning (ACARA, n.d.-a). At the same time, the Australian Curriculum has progressively elaborated the notion of numeracy as a “general capability” alongside literacy, ICT capability, critical and creative thinking, personal and social capability, ethical understanding, and intercultural understanding. General capabilities are meant to be developed in all learning areas, and the curriculum offers advice within each learning area for developing numeracy based on the following general definition:

In the Australian Curriculum, students become numerate as they develop the knowledge and skills to use mathematics confidently across other learning areas at school and in their lives more broadly. Numeracy encompasses the knowledge, skills, behaviours and dispositions that students need to use mathematics in a wide range of situations. It involves students recognising and understanding the role of mathematics in the world and having the dispositions and capacities to use mathematical knowledge and skills purposefully. (ACARA, n.d.-b)

The general capabilities section of the Australian Curriculum contains a set of key ideas in numeracy organised into the following elements: estimating and calculating with whole numbers; recognising and using patterns and relationships; using fractions, decimals, percentages, ratios and rates; using spatial reasoning; interpreting statistical information; using measurement. These elements are further represented in a numeracy learning continuum with statements describing what students can typically do by the end of the various years of schooling. However, it is difficult to see how this set of objectives aligns with the curricular aim of helping students “to use mathematics confidently in other learning areas at school and in their lives more broadly” (emphasis added). The numeracy learning continuum could easily be used to support teachers in implementing the Australian Curriculum: Mathematics without the need to engage with other learning areas, or the world outside school, at all.

In Ireland, as in Australia, there is a lack of clarity in curriculum policy about the distinction between numeracy and mathematics. While the Irish document is referred to as the national strategy to improve literacy and numeracy among children and young people, throughout the document there is frequent reference to mathematics rather than numeracy. Nevertheless, a revised curriculum framework for the lower secondary years (known in Ireland as the junior cycle) has introduced a set of key skills that could be interpreted as cross-cutting competencies: being literate, managing myself, staying well, being curious, managing information and thinking, being numerate, being creative, working with others, and communicating (DES, 2015). Teachers are meant to embed these key skills in the learning outcomes of every subject, but there is not yet any explanation within newly developed subject specifications of how this can be done.

Mathematical Literacy as a Stand-Alone Subject in South Africa

In South Africa, post-apartheid mathematical curriculum reform has been driven by political, ideological and social forces striving towards the goal of mathematics for all and mathematics by all (Volmink, 2018). While the former aspiration refers to equity in curriculum provision, the latter is a statement about quality of mathematical engagement by both learners and teachers. The tension between these twin goals of equity and quality is made visible in recent curriculum reforms that have resulted in a return to differentiated subject offerings at school and the introduction of Mathematical Literacy as a secondary school subject within the field of mathematics.

Rationale for Mathematical Literacy in South Africa

Volmink (2018) argues that curriculum reform has a “contextual ancestry” (p. 101). This means that the expression of mathematical literacy – whether as a general competency or a separate subject in the school curriculum – needs to be understood in the context of choices that have been made during a time of wider political and social reform in South Africa. During the apartheid years, two systems of education co-existed as a means of maintaining severe socio-economic inequalities along racial lines (Graven, 2014). While a People’s Education movement was mobilised in the 1980s to oppose educational inequalities, it was not until after the country’s first democratic elections in 1994 that education policy-making became the vehicle for transforming society.

A new vision for education as a way of redressing the inequalities perpetuated in the apartheid era was realised through major curriculum change. In 1995 a reformed national curriculum framework was introduced, “premised on a learner-centred, outcomes-based approach to education with an explicit political agenda” (Graven, 2014, p. 1040) emphasising common values and citizenship in the new democratic society. This National Curriculum Statement became known as Curriculum 2005 (C2005), with the intention that it should be implemented in all grades by 2005. Although C2005 was overwhelmingly supported, Volmink (2018) explains that it faced challenges in addressing competing priorities, which he described as follows:

The post-apartheid challenge: to provide awareness and the conditions for greater social justice, equity and development. This is the challenge of developing new values and attitudes.

The global competitiveness challenge: to provide a platform for developing knowledge, skills and competences to participate in an economy of the twenty first century.

The challenge of developing critical citizens: citizens in a democracy need to be able to examine the many issues facing society and where necessary to challenge the status quo and to provide reasons for proposed changes. (p. 103)

These challenges highlight the multiple expectations of C2005, in particular the expectation that this curriculum should produce critically numerate citizens who can participate actively in society.

Representation of Mathematical Literacy in the Official Curriculum of South Africa

During the apartheid period and up to 2007, students could choose to take mathematics at Higher Grade (HG), Standard Grade (SG), or not at all. At the beginning of the post-apartheid era in 1994, Volmink (2018) reports that only 20% of black students were taking HG mathematics compared with 70% of white students. Of even more concern was the finding that between 2000 and 2005, as many as 40% of students were taking no mathematics at all (Clark, 2012). Following a Department of Education (2003) investigation into the then-current system of curriculum differentiation, the responsible Ministerial Committee recommended that curriculum reform should provide more equitable access to all subjects: as a consequence, it became a requirement that all learners had to take some form of mathematics. In response to this policy, in 2006 a new subject, Mathematical Literacy, was introduced in the post-compulsory phase of schooling (grades 10–12) as an alternative to mathematics. According to the current Curriculum and Assessment Policy Statement for Mathematical Literacy (DoBE, 2011):

The competencies developed through Mathematical Literacy allow individuals to make sense of, participate in and contribute to the twenty-first century world – a world characterised by numbers, numerically based arguments and data represented and misrepresented in a number of different ways. (p. 8)

Mathematical literacy, as a school subject, has five key elements: it involves the use of elementary mathematical content, authentic real-life contexts, solving familiar and unfamiliar problems, decision making and communication, and the use of integrated content and/or skills in solving problems. The subject is organised into Basic Skills Topics comprising number, calculation, patterns, relationships and representations, and Application Topics including finance, measurement, maps and plans representing the physical world, data handling and probability (DoBE, 2011). It was designed with the intention of providing democratic access to mathematics for all rather than as a watered-down subject for mathematically weak students.

Within South Africa concerns have been expressed about the limited capacity of teachers to engage and teach the Mathematical Literacy curriculum, and concurrent criticisms of the curriculum structure as focusing only on achieving minimum standards rather than empowering learners to access a wide range of future careers (Cranfield, 2012). Nevertheless, evidence from small-scale classroom studies, such as that reported by Graven and Buytenhuys (2011), indicates that the subject does have potential for enabling mathematical metamorphosis of learner identities and increasing their access to quality mathematics education.

Questions of quality were highlighted by Volmink (2018) in his explanation of mathematics by all as a statement meaning that everyone should be “engaged in a quality mathematical experience” (p. 107), a goal consistent with the intent of the Mathematical Literacy syllabus. However, lack of school-based curriculum leadership in mathematical literacy, lack of teacher understanding of how to teach mathematics in real-life contexts, and disparities in access to resources between private schools and poorer public schools threaten to undermine the potential of the Mathematical Literacy subject to meet its transformational aims (Sidiropoulos, 2008).

Infusing Mathematical Literacy into the Mathematics Curriculum in Japan

In Japan, curriculum reform is undertaken on a regular cycle at approximately ten-year intervals. While neither numeracy nor mathematical literacy are identified as cross-cutting competencies (as in Australia and Ireland) or offered as stand-alone subjects (as in South Africa), the concept of mathematical literacy as operationalised by PISA has had a profound influence on the revision of the secondary mathematics curriculum.

Rationale for Mathematical Literacy in Japan

Namikawa (2018) describes the significant influence of TIMSS and PISA results on government education policy and curriculum in Japan. Although Japan is often regarded as a high-performing country in both assessment programs, this is not necessarily how the results are interpreted within the country by the media and the Ministry of Education, Culture, Sports, Science and Technology. Tasaki’s (2017) analysis of the impact of PISA results on educational policy, together with Namikawa’s insights into the nature of Japan’s TIMSS and PISA “shocks”, point to two major concerns. The first is the decline in reading literacy between 2000 and 2003, with a stagnant performance in 2006 that coincided with a decrease in both science literacy and mathematical literacy (where performance was measured in terms of both country ranking and score; see Table 21.1). This apparent decline in academic ability was attributed to so-called “relaxed education” that had led to a reduction of school subject content and increased leisure time for students.

Table 21.1 PISA results in Japan (2000–2015)
Full size table

The second concern pointed to students’ declining interest and motivation for learning in mathematics and science. Both TIMSS and PISA survey students to ascertain their views in these areas. Namikawa (2018) presented previously unpublished data from the 1995 and 1999 TIMSS, summarising the percentage of Japanese students who responded positively to statements about mathematics or science being important in life and their hopes to be involved in these fields in future professions. In both years, Japanese students were well below the international average in their attitudes towards mathematics and science. Similarly, Tasaki (2017) reported that in PISA 2003 and 2012 (triennial PISA cycles in which the focus was on mathematical literacy), the percentage of Japanese students who responded positively to statements about looking forward to mathematics lessons, doing mathematics because they enjoy it, and being interested in the things they learn in mathematics were below the OECD average. Thus, the rationale for addressing mathematical literacy was influenced not only by international rankings and competition, but also by concerns for motivation and interest in learning and a desire to provide children “with the competencies, including academic ability, to be autonomous in this rapidly changing society” (Tasaki, 2017, p. 152).

Representation of Mathematical Literacy in the Official Curriculum in Japan

Namikawa (2018) argues that, “the importance of PISA lies in not only the result of assessment but also the publication of the framework of assessment with the name of ‘literacy’. [… Thus,] a fundamental principle of reform is to foster literacy” (p. 461) in its widest sense. The decline in reading literacy, as assessed by PISA, led to urgent interest in improving reading comprehension – including the ability to understand graphs and other mathematical forms of representation and communication (Tasaki, 2017). Mathematics is thus regarded as a language, and improvement in mathematics is also held to be responsible for improvement in language ability in the form of reading literacy.

A second influence of PISA relates to the way in which the mathematical literacy assessment framework prioritises mathematical activity, that is, not only possessing knowledge but being able to use that knowledge to solve problems. Thus, the new course of study in mathematics for junior high school identifies important mathematical activities, such as using mathematics in daily life and society, that seem to resonate with the notion of mathematical literacy. In addition, a new subject, ‘application of mathematics’, has been developed for senior high school, and the new topic of statistics has been introduced into the existing mathematics I subject taken by almost all senior high school students. All of these developments suggest that aspects of mathematical literacy emphasising real-life contexts, positive dispositions, and using mathematical knowledge for problem solving in complex social settings are being infused into the regular secondary school mathematics curriculum.

Conclusion

The aim of this chapter was to analyse the emergence of understandings about numeracy and mathematical literacy and to compare their relationship to curriculum reform processes in four countries: Australia, Ireland, South Africa and Japan. In relation to the first aim, we discussed various conceptualisations of numeracy and mathematical literacy, some sitting within the school context and others defining this capability as a critical skill needed by all citizens. As Stephens, Kadijevich, Niss, Azrou and Namikawa argue in the Introduction, definitions of mathematical literacy (and numeracy) are themselves fluid and will continue to evolve as a consequence of globalisation and internationalisation of the mathematics curriculum.

To address our second aim, we focused on what Remillard and Heck (2014) refer to as the official curriculum, examining the rationale for including numeracy or mathematical literacy in the school curriculum and how these concepts are represented in the curriculum of four countries. In all four country case studies, we saw that the official curriculum and related documents espoused transformative goals for numeracy or mathematical literacy, for example, referring to critical citizenship enabling full participation in choices that affect people’s lives. However, the representation of these concepts in the curriculum varied. In Australia and Ireland, numeracy was promoted as a cross-cutting competency to be developed in all subjects in the curriculum.

Yet in both countries there was a lack of conceptual clarity concerning the distinction between numeracy and mathematics that threatens to undermine efforts to embed numeracy across the curriculum. In South Africa, a commitment to mathematics for all and mathematics by all frames the offering of a differentiated curriculum, with a stand-alone subject called Mathematical Literacy. Such an approach, while ensuring that all secondary school students will take mathematics in some form, carries a risk of positioning mathematical literacy as a lower-status subject than mathematics. In Japan, concerns over student performance on international assessments have led to aspects of mathematical literacy, as defined in the PISA framework, being infused into the regular mathematics curriculum.

Each of these three forms of curriculum representation has implications for teacher preparation and support, an observation that also raises important questions about who is responsible for developing students’ numeracy or mathematical literacy. Whether the responsibility lies with all teachers or only with those who are teaching mathematics, two requirements seem to be essential. First, the official curriculum should provide teachers with a clear conceptualisation of numeracy and its relationship with mathematics. Second, teacher educators and education systems need to provide practical guidance for teachers to implement curricular goals concerning numeracy. These recommendations highlight the importance of all elements of the broad system of curriculum policy, design, and enactment outlined by Remillard and Heck (2014) and point to the central role of teachers in enacting the officially sanctioned curriculum.