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The National Curriculum Statement (NCS) for Mathematical Literacy (ML) is part of a progressive agenda for increased democracy and social justice. It claims that the new school subject Mathematical Literacy will provide learners with awareness and understanding of the role that mathematics plays in the modern world. However, the analysis developed in this paper indicates that the superficial engagement with complex applications of mathematics implied by the ML NCS is not likely to live up to its claim. In addition, we do not understand enough about the connections between mathematical, technological and reflective knowledge/knowing/competencies to know how to facilitate the awareness and understanding that is part of the vision of the ML NCS.

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... There has been a debate about the introduction, legitimacy, agendas and the implementation of Mathematical Literacy alongside Mathematics since the inception of Mathematical Literacy in 2006 (Venkatakrishnan & Graven, 2006;Graven & Venkat, 2007;Christiansen 2006;Venkat, 2006;Mbonani & Bansilal, 2014;Machaba, 2014). These debates have been centered on teachers' views, interpretation of the curriculum (Gaven & Venkat 2007;Machaba, 2014), teaching of mathematical literacy (Vithal, 2006;Machaba, 2014) and learners 'perceptions on the learning of Mathematical Literacy alongside Mathematics (Geldenhuys, Kgruger & Moss, 2015;Graven & Venkat, 2006;Venkat & Graven 2008). ...

... In the same vein, Christiansen (2006) Graven, 2008). This misinterpretation is despite the strong statement from those involved in the development of the Mathematical Literacy curriculum that Mathematical Literacy is not equivalent to standard grade mathematics (Brombacher, 2006;Laridon, 2004). ...

... One of the influences to the introduction of Mathematical Literacy emanated from a push by government to enable more people to use mathematics to facilitate effective participation and contribution to the twenty-first century world (Brombacher, 2006 Christiansen (2006) argues that it is assumed the role played by mathematics will be known to both teachers and learners. ...

The purpose of this article was to examine tensions associated with
the implementation of Mathematical Literacy alongside Mathematics.
This paper emerges from an analysis of four Mathematics (M)
and Mathematical Literacy (ML) facilitators’ views on implementation of
Mathematics and Mathematical Literacy curricula. Bernstein’s (1996)
constructs of Recognition and Realisation rules were used to interpret
facilitators’ views on Mathematics and Mathematical Literacy. The agendas
foregrounded in the M and ML curricula were used as evaluative criteria to
interpret facilitators’ views and perceptions about M and ML. In the facilitator’s
interview data, key issues emerged in relation to the respondent’s views
about Mathematics and Mathematical Literacy, and the interaction between
these two Learning Areas. Key to the pedagogical practices that emerged in
the interview analysis relate to mathematical rules that were involved in the
teaching practices of Mathematics and Mathematical Literacy. In this paper
the data reveals that from the facilitators’ perspective, ways of working in
Mathematics were seen as specific and only applicable to Mathematics
and not to ML. Similarly, ways of working in Mathematical Literacy were
seen as specific and only applicable to Mathematical Literacy. In this study,
I argue that Mathematics and Mathematical Literacy are inseparable,
though dramatically different, facets of the same thing. Mathematics and
Mathematical Literacy features cannot be separated from each other.

... It also assumes that it is easy to facilitate this awareness and understanding. I challenge these assumptions in another paper (Christiansen, 2006). ...

... Nonetheless, it can be very relevant to develop the competencies to use mathematics as one tool amongst others to deal with these types of information. If the NCS for mathematical literacy was centred around such applications (as well as giving students' knowledge of the role of mathematics in society (Christiansen, 2006)), it would be in agreement with its purposepresuming the teachers would be able to work from such life-related problems to facilitate the development of the general skills of the assessment criteria. ...

... (Adler, Pournara & Graven, 2000, p. 9) The selection of knowledge considered worthwhile in the constitution of the ML curriculum is reflecting a continuation of existing relationships of power and social control 12 , and thus is far from its proclaimed transformation goals. The NCS for ML contains some skills, knowledge and competencies which are very relevant, but generally the mathematics is more than what is required to solve everyday problems, yet -as I argue elsewhere (Christiansen, 2006) -does not engage mathematics in ways which promote getting deeper insights into social or natural phenomena or handling more complex situations/problems such as global warming (12.2.3) or socially responsible trade (12.1.3). These complex phenomena are treated as contexts for the mathematics. ...

As the first country in the world, South Africa is introducing Mathematical Literacy as a school subject. The South African National Curriculum Statement (NCS) for Mathematical Literacy is part of a progressive agenda for transformation towards increased democracy and social justice. I claim, however, that the outcomes – in this outcomes based curriculum – and the assessment criteria are not consistent with this goal. In the paper, I use concepts developed by Paul Dowling to argue in particular two points. Firstly, the NCS assumes simple transfer, which has been challenged by substantial bodies of research. In addition, it refutes learners' agency in determining similarities between activities or practices.

... Recently, there are studies that have been done in South Africa on Mathematical Literacy (see, Webb and Webb, 2004;Julie and Mbekwa, 2005;Vithal & Bishop, 2006;Christiansen, 2006;Mbekwa, 2006;Bowie and Frith, 2006;Frith & Prince, 2006;Brown & Schäfer, 2006;Vithal, 2006;Julie (2006) and Venkatakrishan & Graven, 2006). Mbekwa (2006) views about contexts in Mathematical Literacy. ...

... Mbekwa (2006) views about contexts in Mathematical Literacy. Christiansen (2006Christiansen ( , 2007 presents an important analysis of the issue of Mathematical Literacy as a school subject. Christiansen (2006) interrogates two ways in which the Mathematical Literacy curriculum justifies itself; firstly, it is through claims of utility and secondly through claims that it will provide learners with awareness and understanding of the role that mathematics plays in the modern world (p. ...

... Christiansen (2006Christiansen ( , 2007 presents an important analysis of the issue of Mathematical Literacy as a school subject. Christiansen (2006) interrogates two ways in which the Mathematical Literacy curriculum justifies itself; firstly, it is through claims of utility and secondly through claims that it will provide learners with awareness and understanding of the role that mathematics plays in the modern world (p. 6). ...

... Mathematical literacy is one of the important skills that students must possess (NCTM, 2000;DEMİR, 2020). Mathematical literacy will give students awareness and understanding of the role of mathematics in the modern world (Bolstad, 2021;Baumgartner et al., 2021;Christiansen, 2006;Kuznetsova, 2021). Mathematical literacy has become a major goal in schools in certain countries. ...

... Verbal skills express students' knowledge and experience in an adequate form of language to communicate to others (Vukovic & Lesaux, 2013). Visual ability is someone with a cognitive style will be easier to receive, process, store, and process information contained in an image (Bjorling, 2007;Christiansen, 2006). Visual-verbal abilities also need attention from teachers to support students' mathematical literacy skills. ...

... The mathematics literacy was the ability of the individual in understanding mathematics and applying it in daily life [7,8]. Students could understand and apply the role of mathematics in the context of real [9,10]. ...

... B. Ojose, defines the ability of mathematical literacy is the ability of a person in building and applying mathematical knowledge and skills through the process of solving problems that they faces in everyday life [7]. In other words, students' mathematical literacy skills could be built if (1) students could build mathematical knowledge and skills through the process of solving problems and (2) students could apply the knowledge and mathematical skills that they build to solve problems [7,8]. ...

The teacher’s mathematical ability is one of the factors that influence the achievement of students’ mathematical abilities. In Indonesia, almost all research related to PISA, the subject of research was a student. It is still rare that the subject of research was a teacher. How is the math literacy ability of the teachers? This question will be answered by researchers in this study, especially in the field of space and shape. The subjects were seven Mathematics teachers who taught in junior high schools from seven different schools in Yogyakarta and surrounding areas. In the process of this research, the researcher makes a test adapted from PISA questions. There were 13 questions in the test consisting of three questions in the quantity field, three questions in the uncertainty field, three questions in the field of change and relationship, and four questions in the field of space and shape. In this paper, we will present our result just for the Space and Shape part. The study found that (1) 7 teachers could achieve level 4 for problem 1a, (2) 6 teachers could achieve level 5 for problem 1b, (3) 2 teachers could achieve level 5 for problem 2, (4) 1 teacher could achieve level 5 and 6 for problem 3, and (4) 6 teachers could achieve level 6 for problem 4.

... B. Ojose (2011) said that an individual ability to construct mathematics through their life experience and to apply mathematics in their life is mathematical literacy [7]. If a student had it, then he or she would realize and understand the role of mathematics in his or her life [3,5,8,9]. According to Jan De Lange, there were seven competencies would develop the mathematical literacy skills, namely: (1) the thinking and reasoning mathematically competence, (2) the argument logically competence, (3) the communicating mathematically competence, (4) the problem model competence, (5) the proposing and solving problem competence, (6) the representing idea competence, and (7) the using symbol and formal language competence [3,10]. ...

... The teacher changed this information to 1 IDR = 1 9600 SGD, so in order to obtain the Singapore dollar value obtained by Mei-Ling from this exchange result, the teacher multiplied the exchange rate of 1 rupiah with the amount of rupiah money owned by Mei-Ling. So, from this process, the teacher got the money was got by May-Ling was 9.360.000 9.600 = 975. ...

One of goals of this research was to make descriptions about the mathematical literacy ability of the junior high school teacher for the PISA adaptation test in the quantity area. There were four steps that did by the researchers to get the data, namely: (1) to adapt the PISA test, (2) to validate the test, (3) to ask junior high school teachers to do the adapting PISA test, and (4) to describe the mathematical literacy teachers' ability for quantity area. There were four areas in the PISA test for mathematics i. e. quantity, space and shape, change and relationship, and uncertainty, and six levels. In the test that we adapted form the PISA test, there were 13 questions. Seven teachers from seven junior high schools in Yogyakarta and surrounding areas to become our research subjects. The research type that used by the researchers was a design research developed by Cobb and Koeno. All teachers answer correctly at the quantity area on the level 1 – 4, but only four of seven teachers could solve one quantity problem for level 5.

... Societal issues that could be viewed as controversial are at times included in PISA exams (i.e. the need to reduce diesel fuel use and its impact on the environment; OECD, 2013b). These societal problems, however, are presented in neutral terms, meaning: as problems that face all people, ostensibly in equal ways and with equal outcomes, that demand technical solutions which exact equal prices (Christiansen, 2006). How any issue intersects with power and fairness is not taken up. ...

Current global challenges demand changes to mathematics curricula. In this paper, we draw on intersectional feminist theories to expand current visions of mathematical literacies and real-world problem solving. This expansion is necessary as a response to current crises (e.g., the COVID-19 pandemic and climate change) and how these crises are exacerbating the precarity of girls and women. We begin with the Programme for International Student Assessment's (PISA) framework for mathematical literacy (FML), since it functions as a global guide for curriculum. We first demonstrate what we view as the inadequacy of the FML to solve current crises or to mediate the precarity of girls and women. Then we re-envision the FML by integrating concepts of critical mathematics education with intersectional feminism. We re-envision how to think about mathematical literacies, and in particular, practices of mathematical reasoning and ways of classifying real-world problem contexts. We add practices of feeling, acting, and reimagining to conventional conceptions of mathematical reasoning and explore three thematic categories for real-world problem contexts. 2

... In the 21st century, human needs 21st century skills for survive. Those skills include critical thinking and problem solving, creativity and innovation, communication and collaboration, flexibility and adaptability, initiative and self-direction, social and cross-cultural, productivity and accountability, leadership and responsibility, and information literacy [1,2,3,4]. One of components that needed to build 21st century skills is mathematical literacy [5]. ...

One of goals of this research was to describe the mathematics education department students’ ability in mathematics literacy for change and relationship problem on Programme for International Students Assessment (PISA) test. The procedures of this research were (1) adapt the PISA test, (2) validate the PISA adaptation test, (3) ask seven students from mathematics education department to solve PISA adaptation test, and (4) describe bachelor students’ solution profile. There were (1) three change and relationship problems, (2) four space and shape problems, (3) two uncertainty problems, and (4) four quantity problems. The type of this research is a design research. Subjects of this research were seven bachelor students of mathematics education department. The research results were as follows: (1) level four achieved by one student (14.29%) in problem number 2b.4; (2) level three achieved by (a) six students at problem number 2a, (b) five students at problem number 2b.2; and (c)three students at number 2b.3 and 3; and (3) level two achieved by three students at number 3.

... çocukların erken matematiksel bilginin edinimine yönelik çalıĢmaların çoğunlukta olduğunu ancak disiplinler üstü çalıĢmalarda matematik bilgilerinin uygulanmasına yönelik çalıĢmaların az olduğunu belirtmiĢtir. Bundan dolayı Sawyer, matematiksel okuryazarlığın geliĢtirilmesi için bu alanda daha çok çalıĢmanın yürütülmesinin gerektiğini belirtmiĢtir.Christiansen (2006), matematik okuryazarlığının bir ders olarak okutulduğuGüney Afrika"da, matematik okuryazarlığı için Ulusal Müfredat Bildiriminin sosyal adalet ve demokrasi için bir kılavuz görevi gördüğünü belirtmiĢtir. Bu doğrultuda araĢtırmasında; ulusal müfredat, matematiğin modern dünyadaki rolünü yansıtabilmesi, bu rolü öğrencilerin fark etmesi, b ...

The aim of the research has two purposes. First of all, planning and implementation of teaching activities aimed at improving mathematics literacy of pre-service elementary school teachers. In addition, it is the evaluation of the reflective views of the pre-service elementary school teachers about the development of mathematics activity towards mathematics literacy. The research model was determined as an embedded design among mixed method research designs. The study was carried out with 73 pre-service teachers studying in the third grade of a public university elementary school teachers program. “Mathematical Literacy Achievement Test”, “Mathematical Literacy Awareness Test”, “Reflective Opinion Determination Form”, “Planned Teaching Activities for Developing Mathematical Literacy” were used as data collection tools in the research.
In the first stage of the practice process, “Mathematical Literacy Achievement Preliminary Test” and “Mathematical Literacy Awareness Preliminary Test” were applied in order to determine the mathematics literacy achievements and awareness of pre-service elementary school teachers. Then, pre-service elementary school teachers were applied teaching activities to improve mathematics literacy for eight weeks. Beginning from the fourth week of the practice process, pre-service elementary school teachers designed mathematics literacy activities every week. At the same time, reflective thinking opinions of pre-service teachers about mathematics literacy activities were taken every week after the activity. After the completion of the practice process, mathematics literacy achievement test and mathematics literacy awareness test were applied as a post test to pre-service teachers.
The mean and standard deviation values of the pre-test and post-test results were calculated to determine the effect of teaching on the achievement and awareness of mathematics literacy of pre-service elementary school teachers. In addition, dependent groups’ t test was used to determine whether the pre and post test scores of the achievement test of each group were significant. The descriptive analysis method was used in the analysis of the reflective views of the pre-service teachers about their experiences in designing a mathematics activity.
According to the findings of the research, it was determined that the instructional activities designed to improve mathematics literacy improved the mathematics literacy levels and awareness of pre-service elementary school teachers. It was determined that cooperative learning, problem solving towards mathematics literacy and the activity of pre-service elementary school teachers to form mathematics literacy, which form the basis of the designed teaching activity, had a positive effect on the mathematics literacy achievements and awareness of the pre-service teachers. The reflective views of the pre-service elementary school teachers regarding the development of mathematics activity towards mathematics literacy were discussed under three themes: Pre-active reflections, active process and post-active reflections (self-evaluation) according to the reflective thinking model of Artz and Armor Thomas (1999). The pre-service teachers stated that they determined the purpose of the activity based on the gains in the primary school mathematics curriculum in the context of mathematics literacy before the activity. During the active process, it was determined that pre-service teachers designed activities with a contemporary and student-centered approach. In terms of post-active reflections, pre-service teachers stated that they had difficulties in the first weeks of the design process. They explained this situation with lack of experience. However, as they gained experience in the process, they stated that they became competent in preparing materials, designing activities, creating activity plans and teaching mathematics. Another remarkable result of the pre-service teachers' opinions is that they have difficulty in finding problems related to mathematics literacy. They emphasized that mathematics literacy problems are not included in the textbooks and activity books, but only in national reports published by the Ministry of National Education.

... When referring to mathematical literacy 1 a clear distinction is required between the international and national perspectives. Internationally mathematical literacy refers to the competence of individuals (Christiansen, 2006, p. 6), which ranges from a competence demonstrated in word problems to a critical or democratic competence and whose purpose may be mathematics as a tool in gaining insights into oppression, inequalities, and exploitation; … to become aware of the effects of applying mathematical models in society … and a third component has to do with mathematics as a 'gate-keeper', i.e., access to further education (p. 6). In South Africa, according to the Department of Education ( DoE, 2005) mathematical literacy on national level refers to a fundamental subject where learners are provided with learning opportunities to consolidate and extend their basic mathematical skills. ...

South Africa is the first country in the world to offer Mathematical Literacy as a school subject. This subject was introduced in 2006 as an alternative to Mathematics in the Further Education and Training band. The purpose of this subject is to provide learners with an awareness and understanding of the role that mathematics plays in the modern world, but also with opportunities to engage in real-life problems in different contexts. A problem is the beliefs some people in and outside the classroom have regarding this subject such as teachers believing ML is the dumping ground for mathematics underperformers (Mbekwa, 2007). Another problem is the belief of some principals that any non-mathematics teacher can teach ML. In practice there is Mathematics teachers who teach ML in the same way that they teach Mathematics; non-Mathematics teachers who in many cases lack the necessary mathematical content knowledge and skills to teach ML competently; and Mathematics teachers who adapted their practices to teach ML using different approaches than those required for teaching Mathematics. Limited in-depth research has been done on the ML teachers, what they believe and what knowledge is required to teach this subject effectively and proficiently.
The purpose of this study is to investigate the way in which ML is taught in a limited number of classrooms with the view to exploring the relationship between ML teachers’ knowledge and beliefs and their instructional practices. According to Artzt, Armour-Thomas and Curcio (2008) the instructional practice of the teacher plays out in the classroom where teachers’ goals, knowledge and beliefs serve as the driving force behind their instructional efforts to guide and mentor learners in their search for knowledge. To accomplish this aim, an in-depth case study was conducted to explore the nature of teachers’ knowledge and beliefs about ML as manifested in their instructional practices. A qualitative research approach was used in which observations and interviews served as data collection techniques enabling me to interpret the reality as I became part of the lives of the teachers.
My study revealed that there is a dynamic but complex relationship between ML teachers’ knowledge and beliefs and their instructional practices. The teachers’ knowledge, but not their stated beliefs were reflected in their instructional practices. Conversely, in one case, the teacher’s instructional practice also had a positive influence on her knowledge and beliefs. It was further revealed that mathematics teacher training and teaching experience played a significant role in the productivity of the teachers’ practices. The findings suggest that although mathematical content knowledge is required to develop PCK, it is teaching experience that plays a crucial role in the development of teachers’ PCK.
Although the study’s results cannot be generalised due to the small sample, I believe that the findings concerning the value of teachers’ knowledge and the contradictions between their stated beliefs and practices could possibly contribute to teacher training. Curriculum decision-makers should realise that the teaching of ML requires specially trained, competent, dedicated teachers who value the subject. This exploratory study concludes with recommendations for further research.

... According to Christiansen (2006, p. 10), 200 000 more learners were given the opportunity in 2006 to interact with mathematics than in previous years when mathematics was not obligatory for all learners. Consequently, Christiansen (2006) alleges that Mathematical Literacy would warrant greater access to mathematics for all learners and could offer a more accessible opportunity for learners to succeed in a mathematical subject. ...

... As with the literature dealing with teaching and learning of Mathematical Literacy at the school level (for example, Christiansen, 2006;Graven & Venkat, 2007), the South African literature on quantitative literacy in higher education is limited (see, for example, Brink, 2001;Archer, Frith & Prince, 2002;Prince & Archer, 2008). The discussion in this article is presented as an attempt to stimulate more research and debate about quantitative literacy in higher education. ...

This paper describes the use of diagrams as self-explanatory tools. It considers the use of diagrams, in general, and more specifically, examines research that is currently being undertaken in the broad field of visualisation. The research participants referred to in this article were Advanced Certificate of Education students and the paper attempts to analyse their responses to questions based on simple area problems in mathematics. The outcome of this research underscores the strategic use of diagrams when dealing with problem solving. While this is an ongoing research project, the paper attempts to capture the current status of research on the use of diagrams.

... see Skovsmose and Yasukawa 2009;Frankenstein 2001;Jablonka 2003). While the South African Mathematical Literacy curriculum has been criticized for falling short of this critical perspective (Christiansen 2006), the curriculum rhetoric does encourage focus on the orientations and limitations of mathematical tools through a shift in vantage to a contextual standpoint. ...

In this paper, we share analysis of an episode of a pre-service teacher’s handling of a map artefact within his practicum teaching of ‘Mathematical Literacy’ in South Africa. Mathematical Literacy, as a post-compulsory phase subject in the South African curriculum, shares many of the aims of numeracy as described in the international literature—including approaches based on the inclusion of real-life contexts and a trajectory geared towards work, life and citizenship. Our attention in this paper is focused specifically on artefacts at the boundary of mathematical and contextual activities. We use analysis of the empirical handling of artefacts cast as ‘boundary objects’ to argue the need for ‘boundary crossing’ between mathematical and contextual activities as a critical feature of numeracy teaching. We pay particular attention to the differing conventions and extents of applicability of rules associated with boundary artefacts when working with mathematical or contextual perspectives. Our findings suggest the need to consider boundary objects more seriously within numeracy teacher education, with specific attention to the ways in which they are configured on both sides of the boundary in order to deal effectively with explanations and interactions in classrooms aiming to promote numeracy.

... She cites examples of assessment standards referring to the quadratic formula and positive exponents and roots as examples of mathematics claiming to refer, yet being obviously "self-referential in its alien-ness to the lived practices" (p.98). (See Christiansen (2006) for other arguments noting a focus on 'mathematical skills and concepts' (p.10) throughout the NCS for Mathematical Literacy.) ...

This paper focuses on an emergent spectrum of pedagogic agendas in the teaching of mathematical literacy- a new subject in the Further Education and Training (FET) band—currently being implemented in schools in grades 10 & 11. It is argued that a range of pedagogic spaces are opened up as a result of the ‘newness’ of the subject. Thus we argue that the absence of precedents of what pedagogy and assessment should be like, have enabled a wide spectrum of interpretation of both the curriculum aims and the related pedagogic agendas for both individual lessons and lesson planning across the band.
In this paper, we focus on 3 aspects—the emergence of the spectrum of agendas from our empirical data linked to Bernstein's theory, a delineation of the agendas themselves and a discussion of the different pedagogical issues arising within each agenda.
We believe that the conceptualization of a spectrum provides a useful tool for teachers and researchers for thinking about, and investigating, the vast range of mathematical literacy agendas present in lessons taught as a result of current curriculum implementation in Grade 10 and Grade 11. The paper draws on the work of Bernstein (1982, 1996) as a framework for analysis.

... Several researchers acknowledge this situation (e.g. Christiansen, 2006;. For instance, Thomas (2010), referring to the Australian situation, states: ...

This article reports the results of a literature review focused on identifying the links between mathematics education and democracy. The review is based on the analysis of a collection of manuscripts produced in different regions of the world. The analysis of these articles focuses on six aspects, namely, (1) definitions of democracy used in these texts, (2) identified links between mathematics education and democracy, (3) suggested strategies to foster a democratic competence in mathematics students (4) tensions and difficulties inherent in mathematical education for democracy, (5) the fundamental role of the teacher in the implementation of democratic education and (6) selected criticisms of mathematical education for democracy. The main contributions of this article are to provide the reader with an overview of the literature related to mathematics education and democracy, and to highlight some of the theoretical and empirical topics that are necessary to further development within this research area.

... The literature within mathematics education that has taken the issue of contextualisation as central has focused on critical and emancipatory approaches (Skovsmose 1994;Vithal 2006). Whilst aspects of this literature are useful in analysing the potential of the ML curriculum, critiques have noted that this curriculum takes a much less radical line (Christiansen 2006). ...

In this paper the mathematical working in a series of ‘litter project’ lessons from a South African Mathematical Literacy class is analysed in terms of Kilpatrick, Swafford and Findell's (2001) five strands of mathematical proficiency. The analysis points to evidence of the life skills-oriented Mathematical Literacy frame opening up opportunities for engagement across aspects of all five strands, but shows that the emphases differ from the intra-mathematical emphases within the strands. I argue that this is due to the lack of centrality in the Mathematical Literacy frame of the ‘mathematical terrain’. The shifting of competence to the bridge between mathematics and everyday situations and problems retains mathematical coherence and connectedness. Both of these aspects are grounded in the mathematical tools and thinking that are needed to make sense of the everyday situation, rather than the more intra-mathematical connections and coherence that appear to be in focus within the strands of mathematical proficiency.

... The introduction of Mathematical Literacy in the Further Education and Training phase in South Africa has been accompanied by a swell of recent research papers (e.g. Bowie & Frith, 2006;Brown & Schafer, 2006;Christiansen, 2006;Venkatakrishnan & Graven, 2006) discussing issues -theoretical and empirical -in relation to the subject's emphasis on the use of relevant contexts. All these papers were thus classified in the relevance cluster, although some work intersected with the teacher education cluster too (Brown & Schafer, 2006). ...

In this paper, a review of journal articles containing South African research in mathematics and science education in the 2000 – 2006 period is undertaken, and used to identify significant clusters of research interest on the one hand and areas of under-representation of research on the other. In mathematics education, significant clusters were found relating to: questions of relevance, language issues, mathematics teaching and learning, and mathematics teacher education. In science education, specific clusters of research focused on: tertiary science teaching and learning, school level science teaching and learning, and relevance issues focused on the nature of science and indigenous knowledge systems. Our classification of articles highlighted the paucity of research at the primary level, in rural contexts, and dealing with issues related to language use in multilingual classrooms. Our overview of articles also provided examples of research that linked the issues arising within specific clusters, and considered the consequences of these linked issues for teaching and learning. We conclude by noting examples of research findings within our review that have impacted on policy and practice, and point also to areas where further research appears necessary.

Assessments, in particular high stakes assessments, impact the nature of teaching and learning. Given this, the goal of citizenship if seen as important needs to feature within high stakes school exit assessments rather than only as part of curriculum and assessment policy rhetoric. South Africa’s Mathematical Literacy (ML) curriculum foregrounds critical democratic citizenship. We analyse the ML Grade 12 exit assessments from their start in 2008 to 2020 to understand the emphasis placed on critical citizenship and how this emphasis has shifted over time. The literature base links critical citizenship orientations with reasoning and reflecting questions, so we focused on examination questions in this category. Our findings show shifts away from critical citizenship related agendas towards foregrounding a life preparation orientation for the self-managing person. Linked with this shift, we note a move away from general societal contexts towards more personal/individual contexts and moves from almost entirely national contexts to inclusion of global contexts. We noted movement from more open-phrased questions towards closed ‘check figure calculated is valid’-type questions. Assessment memoranda suggest assessors view these questions as reasoning items, eroding the critical citizenship agenda. While increasing numbers of students are taking ML rather than Mathematics, average performance stands at around 40%. This points to limited and diminishing access to mathematical reasoning and reflecting for critical democratic citizenship. The paper highlights ways in which analysis of examinations over time can provide a window into the presence or absence of the citizenship agenda in mathematics education.

Wenger's community of practice theory is used to illustrate how, through careful curriculum design, teacher identity can be developed by participation in a re-skilling programme. In the context of learning, a community of practice involves the complex intersection of various components of learning, namely, meaning (learning as experience), practice (learning as doing), identity and community (learning as belonging). The Advanced Certificate in Education in Mathematical Literacy programme was designed to expose participants to knowledge and understanding of the ML curriculum (meaning), development of an integrated approach to teaching and learning, classroom didactics, lesson plans (practice), and group work activities where active participation and dialogue in lectures were encouraged (community). The programme design aimed to promote a change in the teachers' way of being (identity). Through semi-structured interviews with teachers their journey as individuals was revealed. The findings indicate how by focusing on both content and on the teacher's becoming a professional can assist educational specialists in their quest for improved teacher development.

In this case study, Mathematical Literacy teachers were interviewed and observed in the classroom in order to provide insight into the way this subject, relatively new in South African schools, is handled. The focus of this research was the instructional practice of these teachers specifically in terms of their mathematical knowledge regarding the subject and its learners. The idea that this subject is inferior to other subjects in general, but to mathematics in particular, was alluded to by some participants, alongside of the notion that it was infra dig to teach it. The study revealed that a working knowledge of mathematics as well as teaching-and-learning skills are necessary for this subject to achieve what it was meant to do when it was introduced into South African high schools in 2006.

This paper provides a documentary analysis of the nature and role of contextualization in the FET (Grades 10-12) subjects Mathematics, Mathematical Literacy and Physical Sciences. The analysis is framed by Bernstein’s notion of classification and an adaptation of Graven’s orientations to Mathematics. Key arguments within our analysis are that within the Science curriculum there is substantive emphasis on scientific literacy and citizenship. On the other hand the Mathematics curriculum focuses largely on the development of abstract mathematics necessary for further studies and assumes the development of mathematical literacy on the part of the learner rather than including this as a goal or outcome. Unlike scientific literacy which is included in the subject Physical Sciences, Mathematical Literacy
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is offered as a separate subject, compulsory for those not taking Mathematics. This leads to a situation where Mathematical Literacy learners may have no exposure to scientific literacy in the FET band and Science learners may have little exposure to Mathematical Literacy in the FET band. Given that in the FET Mathematics/Mathematical literacy learning area, Mathematics is structured as the subject dealing with disciplinary development, and therefore, a more academic track, we argue that differential status is accorded to contextualisation within the Mathematics/Mathematical Literacy curricula. This contrasts with the Physical Sciences curriculum in which contextualisation is drawn within the bounds of the subject and integrated with the need for disciplinary development.

In this article we argue that in South Africa the current format of legitimised participation and practice in the examination papers for Mathematical Literacy restricts successful apprenticeship in the discipline of scientific mathematics and limits empowered preparation for real-world functioning. The currency of the subject, then, is brought into question. We further argue that the positioning of the subject as a compulsory alternative to Mathematics and the differential distribution of these two subjects to differing groups of learners facilitates the (re)production and sustainment of educational disadvantage. We draw on Dowling's theoretical constructs of differing domains of mathematical practice and positions and focus analysis on a collection of nationally set exemplar Grade 12 examination papers to identify legitimised forms of participation in the subject. We conclude by arguing for a reconceptualised structure of knowledge and participation in Mathematical Literacy and make preliminary recommendations in this regard.

At tertiary institutions in South Africa and internationally, academic literacy
practitioners and disciplinary specialists have traditionally functioned as separate
communities of practice. However, research indicates that academic literacy is most
successfully acquired when it is integrated into and taught within the contexts of
specific academic disciplines. This article explores the transgression of the boundaries
between academic literacy teaching and study disciplines, in general, and the
subsequent broadening of the social structures within which academic disciplines
function at tertiary institutions. The relationship between academic literacy
practitioners and disciplinary specialists at Stellenbosch University is correspondingly
investigated as a complex system, focusing on the variable and non-linear interaction
among the co-evolving components of the system and its environment, the emergent
structure of the resultant transdisciplinary community of practice, and the ‘fitness’
of this community – its ability to cope with the challenges and opportunities brought
on by constant change. The article will demonstrate the contribution that a complex
systems approach could make to the collaboration between academic literacy
practitioners and disciplinary specialists at tertiary institutions, in general, and at
Stellenbosch University, in particular, and subsequently, to an understanding of the
collective focus on student success in these two communities of practice.

This paper reports on the findings of the study that assessed the capacity of the School Governing Body (SGB) and School Management team - SMT ( school principal, deputy principal and HODs) to support the teaching and learning of mathematics and science subjects at one school in Mpumalanga Province in South Africa. In this paper, only findings of the mathematical literacy component are reported and findings on the other subjects are reported in other papers. A case study was conducted in one FET school and used a mixed- methods research design whereby qualitative and quantitative data was collected. The learners were from Grades 10 to 12. The data was collected in the year 2012 from the SGB, SMT, school learners, teachers, and general assistants at the school. The findings showed that though the students were enthusiastic to learn mathematical literacy subject, the SGB and School Management comprised of a weak team to support the students in pertinent areas needed to master the subject. It was concluded that lack of communication between the school administration, SGB, teachers, students and parents on issues pertaining to the execution of school policies, activities and security, could have contributed to lack of students’ engagement and assistance to master the subject.
DOI: 10.5901/mjss.2014.v5n1p579

Wenger's community of practice theory is used to illustrate how, through careful curriculum design, teacher identity can be developed by participation in a re-skilling programme. In the context of learning, a community of practice involves the complex intersection of various components of learning, namely, meaning (learning as experience), practice (learning as doing), identity and community (learning as belonging). The Advanced Certificate in Education in Mathematical Literacy programme was designed to expose participants to knowledge and understanding of the ML curriculum (meaning), development of an integrated approach to teaching and learning, classroom didactics, lesson plans (practice), and group work activities where active participation and dialogue in lectures were encouraged (community). The programme design aimed to promote a change in the teachers' way of being (identity). Through semi-structured interviews with teachers their journey as individuals was revealed. The findings indicate how by focusing on both content and on the teacher's becoming a professional can assist educational specialists in their quest for improved teacher development.

This paper is a discussion paper, the main aim of which is to raise what I consider to be central questions and issues for further consideration.
The paper takes as its starting point that in order to further democratic competencies, there is a need to promote critical evaluation of models and their use in society.
I will argue that if someone should have a basis for engaging in reflecting critically on models, their validity, and their use, then s/he must be somewhat familiar with elements of the preceding modelling process. My hypothesis is that there is a correspondence between with which of the sub-processes a person engages and which types of reflections she can unfold. I attempt to illustrate this by a particular way of graphing the modelling process.

Mathematical literacy is more than the ability to calculate. It is the ability to reason quantitatively, the ability to use numbers to clarify issues and to support or refute opinions. Yet the proliferation of arithmetic courses at the college level is evidence that people are not learning even basic computation skills in school. Too many adults cannot use numbers effectively in their daily lives. This article will briefly examine the causes of this situation and will outline a basic arithmetic course that not only teaches adults math effectively, but raises their political consciousness and empowers them to analyze and question the status quo, and to fight back.

In this paper, I discuss some links between mathematics education and democracy, what these links could imply to what and how we teach, and the issues that arise from trying to further these links. I first suggest three links between mathematics education and democracy formulated on the basis of experiences in Denmark, in particular: learning to relate to authorities' use of mathematics, learning to act in a democracy, and developing a democratic classroom culture. The first two are discussed in relation to narratives from real life, with a focus on the tensions which they reveal. From the discussion following the first narrative, it is clear that what is a competency in one context may not be so in another. This is supported by the second narrative which also questions what is most relevant to students in South Africa and thereby gives rise to the formulation of a fourth connection between democracy and mathematics education, related to issues of access.The third narrative informs a discussion of what it means to be critical. It also continues to address the potential tension between wanting to promote students' critical skills and a democratic classroom culture versus wanting to support students in learning what others have developed and what is required in order to succeed in the schooling system. Finally, democracy is linked to the idea of 'mündigkeit', or 'personal authority'. This is not only an issue in relation to the students, but also in relation to teachers. On this basis, I briefly touch on teachers' possibilities for making choices concerning what and how to teach. This comprises a fifth connection between democracy and mathematics education. MATHEMATICAL COMPETENCIES FOR DEMOCRATIC PARTICIPATION

Latin America is committed to build more democratic social relationships as a part of its current democratization process.
Mathematics education is a relevant set of social practices that could contribute to the consolidation of democratic social
relationships in the school. This dimension of social interaction in mathematics education as a source of democratization
is explored conceptually and is given a practical meaning through the discussion of an inservice teacher education program,
which illustrates a deliberative democratic ideology of mathematics education.
Lateinamerika ist dabei, im Rahmen des gegenwärtigen Demokratisierungsprozesses demokratischere soziale Verhältnisse aufzubauen.
Mathematische Erziehung ist ein relevanter Teil der sozialen Praktiken, die zur Festigung demokratischer sozialer Verhältnisse
in der Schule beitragen können. Diese Dimension sozialer Interaktion im Mathematikunterricht als mögliche Quelle für Demokratisierung
wird untersucht. Ein praktisches Beispiel zur Veranschaulichung der “deliberative” demokratischen Ideologie mathematischer
Erziehung wird durch die Diskussion eines entsprechenden Lehrerfortbildungsprogramms gegeben.
ZDM-ClassificationA40-B50-C60

This chapter investigates different perspectives on mathematical literacy that vary with the values and rationales of the stakeholders who promote it. The central argument is that it is not possible to promote a conception of mathematical literacy without at the same time — implicitly or explicitly — promoting a particular social practice. It is argued that mathematical literacy focussing on citizenship also refers to the possibility of critically evaluating aspects of the surrounding culture a culture that is more or less colonised by practices that involve mathematics. Thus the ability to understand and to evaluate these practices should form a component of mathematical literacy.

This paper aims at giving a concise survey of the present state-of-the-art of mathematical modelling in mathematics education and instruction. It will consist of four parts. In part 1, some basic concepts relevant to the topic will be clarified and, in particular, mathematical modelling will be defined in a broad, comprehensive sense. Part 2 will review arguments for the inclusion of modelling in mathematics teaching at schools and universities, and identify certain schools of thought within mathematics education. Part 3 will describe the role of modelling in present mathematics curricula and in everyday teaching practice. Some obstacles for mathematical modelling in the classroom will be analysed, as well as the opportunities and risks of computer usage. In part 4, selected materials and resources for teaching mathematical modelling, developed in the last few years in America, Australia and Europe, will be presented. The examples will demonstrate many promising directions of development.

In a course on population modelling, students constructed meaning which ignored the references to an out-of-school reality. Their meaning-making took place mainly based on their experiences in the mathematics classroom. As a result, the students saw their task as being to decide how to approach the tasks formulated by the teacher, and then construct a suitable ‘virtual reality’ - a theoretical universe where the students' knowledge of mathematical methods becomes the ultimate formatting force. I show how this, at least in part, is a result of the social organisation of the classroom activities.

This study focuses on the attitudes of a sample of Grade 9 mathematics teachers to the national mathematics Common Task Assessment (CTA) 2002 and to the official mathematics curriculum policy. The notion of pedagogic identity provided the theoretical lens to frame the study. These teachers' personal pedagogic identities are compared with official pedagogic identities constructed by curriculum policy and by the CTA. Data analysis revealed significant tension between personal and official pedagogic identities. Teachers' strong discipline-centred retrospective identities based on pure, mathematical knowledge and skills for epistemological access to the discipline, were at odds with official expectations of them as prospective identities. Teachers identify with an absolutist philosophy, purist ideology, old humanism and popular but negative images of mathematics. Furthermore, faced with the lack of official support for meaningful implementation of the new forms of knowledge and contradictory official regulation, teachers justified their teaching of formal, pure mathematical knowledge and skills on the basis of the demands of the high-stakes matric examination. These teachers experienced much cognitive dissonance and frustration and rejected, resisted or superficially complied with official expectations of them. The implications of the incongruence between official and personal pedagogic identities and contradictions within the official recontextualising field for democratic access to mathematics are raised.

As the first country in the world, South Africa is introducing Mathematical Literacy as a school subject. The South African National Curriculum Statement (NCS) for Mathematical Literacy is part of a progressive agenda for transformation towards increased democracy and social justice. I claim, however, that the outcomes – in this outcomes based curriculum – and the assessment criteria are not consistent with this goal. In the paper, I use concepts developed by Paul Dowling to argue in particular two points. Firstly, the NCS assumes simple transfer, which has been challenged by substantial bodies of research. In addition, it refutes learners' agency in determining similarities between activities or practices.

This book is of interest to mathematics educators, researchers in mathematics education, gender, social justice, equity and democracy in education; and practitioners/teachers interested in the use of project work in mathematics teaching and learning. The book brings together diverse developments exploring social, cultural and political dimensions in mathematics education. It builds theoretical ideas from a substantial description of practice, in the attempt to improve both theory and practice in mathematics education. In doing so it interrogates and develops theoretical research tools for mathematics education and simultaneously provides ideas for practice in mathematics classrooms.

New technology poses challenges to mathematics educators. How should the mathematics curriculum change to best make use of this new technology? Often computers are used badly, as a sort of electronic flash card, which does not make good use of the capabilities of either the computer or the learner. However, computers can be used to help students develop mathematical habits of mind and construct mathematical ides.
The mathematics curriculum must be restructured to include activities that allow students to experiment and build models to help explain mathematical ideas and concepts. Technology can be used most effectively to help students gather data, and test, modify, and reject or accept conjectures as they think about these mathematical concepts and experience mathematical research.

The central concern of the philosophy of mathematics is to give an account of the nature of mathematics. Views of the nature of mathematics are particularly important in the teaching of mathematics, where they can strongly influence the mathematics curriculum as taught to pupils. However, the distinction must be drawn between stated beliefs as to the nature of mathematics and views as inferred from actual classroom practice. In mathematics education there is increasing emphasis on the process (as opposed to the product) view of mathematics. This orientation is snared by a new wave in the philosophy of mathematics, represented in the works of Imre Lakatos, which rejects the traditional product orientation of the philosophy of mathematics for deep philosophical reasons. Thus there is a growing school of thought in the philosophy of mathematics which is able to account for the nature of mathematics in a way which is fruitful for the philosophers, educationists, teachers and students of mathematics alike.

A distinction is made between three different types of knowledge related to a process of mathematical modelling: A. (a) mathematical knowledge itself;B. (b) technological knowledge, which in this context is knowledge about how to build and how to use a mathematical model;C. (c) reflective knowledge, to be interpreted as a more general conceptual framework, or metaknowledge, for discussing the nature of models and the criteria used in their constructions, applications and evaluations.Some types of problem relating to the modelling process—important to analyse in an attempt to develop reflective knowledge—are summarized. The first problem, accompanying a mathematization, is the phenomenon of disguising the complexity of the construction of the conceptual system, which constitutes the very foundation of the model. The second problem has to do with the confusion of the different possible guiding interests connected to a modelling. The third problem is caused by the nature of mathematical language, which makes it tempting always to interpret a model as a descriptive model, and by doing so invent an object to be pictured by the mathematical model. Finally, it is emphasized that a reflective investigation consists of much more.

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Bourdieu, Pierre. (1983/2004). The forms of
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RoutledgeFalmer Reader in Sociology of
Education. London and New York:
RoutledgeFalmer. Original edition, Richardson,
J., Handbook of Theory and Research for the
Sociology of Education (1986), Westport, CT:
Greenwood, (pp. 241-258). Originally
published as 'Okonomisches Kapital, kulturelles
Kapital, soziales Kapital,' in Soziale
Ungleichheithen (Soziale Welt, Sonderheft 2),
edited by Reinhard Kreckel. Goettingen: Otto
Schartz & Co., 1983 (pp. 183-98). Translated
by Richard Nice.

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Mathematics Education. Vol. 4, Mathematics
Education Library. Dordrecht, the Netherlands:
Kluwer Academic Publishers.