## No full-text available

To read the full-text of this research,

you can request a copy directly from the author.

This paper investigates pre-service secondary teachers’ perceptions of learning and teaching mathematics through extended explorations that are contextualized in issues of social importance. The study is situated within a research program concerned with mathematical knowledge used in, and useful for, teaching, and how such knowledge may be fostered in teacher education programs.

To read the full-text of this research,

you can request a copy directly from the author.

... Understanding the current conceptions of the PSTs and building a possible strategy for growth can help better prepare teachers to work with the growing population of students holding complex, diverse, and often marginalized identities in their future classes. We agree with Mamolo (2018) that helping prepare teachers to incorporate authentic real-world contexts is an important yet understudied problem that needs further attention. It is therefore helpful to provide examples for PSTs of what this looks like, and to provide spaces for reflection on which contexts they deem appropriate and why, and how to incorporate them into their teaching. ...

... Despite the extensive literature related to diversity and multiculturalism, there are few studies that examine the beliefs of PSTs within the context of teaching mathematics for social justice, specifically, beliefs about the use of controversial issues in the mathematics class. Some notable exceptions are Simic-Muller et al. (2015) and Mamolo (2018). Mamolo examined the perceptions of learning and teaching mathematics using social justice contexts of 29 secondary mathematics PSTs in Canada. ...

... We used these problems because they are a genre that is familiar to students (Gerofsky, 2001), but they are not necessarily as rich as we would like them to be. They do not, as presented, allow for "understanding, unpacking, and critiquing social issues and their implications" (Mamolo, 2018). It is worth noting that these problems were followed up by an assignment where the PSTs created their own mathematical problems where many of them investigated realistic contexts, though related to the ones typically used like cooking and baking, travel, and spending. ...

This study examines the beliefs of 33 preservice teachers (PSTs) from the U.S. have about using different types of real-world contexts in the mathematics classroom. Qualitative data about the participants' reactions to specially designed word problems that varied in contexts from 'neutral' to controversial were collected. A thematic analysis of the responses indicated that they could be arranged into three typologies on a continuum based on their openness towards the use of controversial issues in the mathematics classroom. Drawing on the analysis of PSTs' responses and the literature, a fourth typology was inferred. The typologies can be useful to teacher educators and education programs as they seek to prepare PSTs to work with increasingly diverse students in their future mathematics classes. The study also highlights the potential of using word problems as a tool to understand PSTs' beliefs.

... In the three countries involved in the study, we find several aspects of the connection between mathematics and society in the curricula: in South-Africa students need to be critically aware of such connections (Department of Basic Education, 2011); in Norway students need to make their own choices and take a stand on important issues in their lives and in society (Ministry of Education, 2020); and in Albania, students should be able to critically use and interpret mathematics in a variety of contexts (Ministry of Education and Sports, 2014). Research is required for ways to support teachers in implementing social issues in mathematics teaching (Mamolo, 2018). Mathematical modelling researchers highlight its relevance for realizing the relationships between mathematics and the world we live in. ...

... If we want PTs to engage in teaching mathematics while focusing on the role of mathematics in society, they need to both get experience with such examples and to think that it is worthy to spend time on. As Mamolo (2018) demonstrated in her study, when the PTs engaged as learners with social justice tasks in mathematics, they became aware of the relevance of those kinds of tasks for exposing their students to social issues and connecting mathematics to real-life. In particular, the need for PTs to experience mathematical modelling in order to implement it in their own teaching is argued for in many research articles (see for example Biembengut & Hein, 2010;Borromeo Ferri & Blum, 2010;Maass & Engeln, 2018;Niss, Blum et al., 2007). ...

... While we cannot claim that this is a direct consequence of the PTs engaging with the BMI task, neither that the PTs will change their values, it is certain that the task created the conditions for the PTs to think about and discuss some of the issues connected to mathematics in society and its connection to the classroom mathematics. We find support in Mamolo's (2018) study with PTs who gained awareness about the relevance of using social justice tasks in mathematics to develop students' critical thinking about the world after some sessions where they themselves worked with social justice tasks as learners. Seah et al. (2016) in discussing a mathematical curriculum based on values, pointed to determining how different mathematical classroom activities can activate different mathematical values as a means to develop values together with the mathematical concepts. ...

This article explores the values that come to the fore when preservice mathematics teachers (PTs) engage in critical discussions about the role of mathematical models in society. The specific model that was discussed was the Body Mass Index (BMI). From the analysis of the PTs’ discussions of the BMI from a mathematical and societal point of view several mathematical and mathematics educational values were identified such as openness, rationalism, progress, reasoning, evaluating, and problematizing the instrumental understanding of mathematics. In addition, critical thinking about mathematics in society as emphasized in curricula in the three
countries involved in the study, was identified with four categories of complementary pairs. Knowing the mathematical and mathematics educational values underpinning PTs’ discussions and their connection to critical thinking is important for successfully engaging with the role of mathematics in society.

... That is, how mathematics is understood and experienced by teachers can influence their understanding of, and expectations for, students and student learning (Mamolo & Pali, 2014). To enact a pedagogical approach that contextualizes mathematics within issues of social justice, a teacher requires an understanding of mathematics that includes structures, values, and practices that extend beyond familiar school experiences (Mamolo, 2018). In this research, we focus on the shifts of attention observed in learners using the micro-controller, micro:bit © which can be programmed to collect, model and interpret climate-related data using a block-based coding environment. ...

... Such as with Sonya, a young teacher who felt that societal issues were important to address with students, but that it would be "unfair" to take time away from the traditional curriculum (Mamolo & Pinto, 2015, p.89). Similarly, prospective teachers reported feeling torn between competing ideas about the irrelevance of textbook-based mathematics and a perceived injustice of deviating from such an approach (Mamolo, 2018). An analysis of these tensions led to an articulation of pedagogical goals for preparing teachers to teach mathematics for social justice (Mamolo, 2018, p.39): ...

... In teacher education, engaging with mathematical problems that address societal inequities can broaden teachers' awareness of, and experiences with, mathematics curriculum and its relevance to authentic world issues (Mamolo, 2018). Navigating these complexities can draw prospective teachers' attention toward ways in which mathematical knowledge can enhance understanding of social justice issues, as well as toward ways in which understanding of social justice can enhance mathematical inferences and decision-making (ibid). ...

This research is part of a broader research program that explores teacher educators’ mathematical knowledge. We examine the experiences, perceptions, and needs of prospective teachers as they navigate a complex set of new and interweaving ideas for how to teach mathematics with socially relevant and responsible connections. In doing so, we draw on Mason’s (1998) perspectives about the structure of attention and awareness for mathematics teaching, to investigate the pathways of attention of middle school prospective teachers in a technology-intensive undergraduate coding course. The research findings show that teachers face challenges when they try to navigate the interdisciplinary space of mathematics, technology and societal issues (climate change) and that curiosity acts as a potential stimulus for determining how each pathway is developed and sustained.

... Laurens et al. (2017) claimed that the ease of learning can be experienced if learning content and context are related to students' daily activities. As a starting point for learning, Mamolo (2018) also proposed that the use of realistic contexts would help students to get involved in meaningful mathematical activities, including exploring, modeling, visualizing data, abstracting, and concluding. ...

Public schools are not always believed to be able to support the development of an individual's potential comprehensively. Homeschooling, an educational program where students learn from home, is currently an alternative education. This study aims to reveal why parents choose to homeschool their children and describe how a homeschooler parent as a single tutor develops her child’s numeracy literacy skills in living book homeschooling. This research is a holistic single-case study with two subjects: a homeschooler (J) and his mother (UPL) as the tutor. Data were collected through in-depth interviews and document analysis of J’s learning activities. Thematic analysis with Atlas.ti software was employed. Findings reveal that the parents’ main reasons for homeschooling are dissatisfaction with public school instruction and flexibility to comprehensively develop homeschoolers’ skills. In addition, the integration of RME (Realistic Mathematics Education) in the living book homeschooling model is a very powerful support to students’ literacy numeracy development. Practically, there are three main strategies implemented; the use of real contexts and concrete teaching aids, as well as an emphasis on conceptual understanding and high-order thinking skills.

... The whole questions above argue the need for mathematics to be understood concerning culture, social, and politics is inventible (Carraher et al., 1993;D'Ambrosio, 2001;Mamolo, 2018;Walshaw, 2014). As a result, mathematics will be different as well depend on what kind of perspective do, we have. ...

Penelitian ini bertujuan untuk mengidentifikasi matematika informal siswa dan cara guru dalam menyelesaikan masalah matematika informal tersebut. Penelitian ini melibatkan 5 orang guru dan 1 orang siswa yang bekerja pada perusahaan pencuci sepeda motor. Sebagai gambaran, matematika seorang pekerja (siswa) doorsmeer (pekerjaannya mencuci motor), yang dianggap sebagai jenis matematika di luar sekolah (matematika informal) bisa menyelesaikan masalah matematika siswa yang terkait dengan kegiatan keseharian siswa yang bekerja pada tempat doorsmeer. Akan tetapi, matematika formal yang digunakan oleh guru dan yang diajarkan di sekolah, tidak bisa menyelesaikan masalah yang sesuai dengan realita yang dihadapi siswa doorsmeer, walaupun algoritmanya sudah benar. Sebagai kesimpulan, guru matematika mengira bahwa matematika yang dipelajari di sekolah sudah cocok untuk siswa yang bekerja di doorsmeer dengan kata lain, matematika yang diberikan di sekolah bisa aplikasikan di tempat siswa bekerja. Akan tetapi, cara matematika yang diaplikasikan oleh siswa doorsmeer tidak sama dengan matematika yang diajarkan oleh guru di sekolah yang berpikir bahwa matematika sekolah cocok di tempat siswa bekerja.

... The contextual teaching and learning (CTL) model might be a better alternative for improving students' abilities (Hoogland, de Koning, Bakker, Pepin, & Gravemeijer, 2018;Rustam & Handayani, 2017;Rustam & Adili, 2016). Mathematical abilities, including representation, develop through learning from the context (Clarke & Roche, 2018;Mamolo, 2018). Jaenudin (2008) stated that in the contextual approach, the students are given chances to construct the learned mathematical concept through an inquiry process. ...

This study aimed to determine the effect of the implementation of the Contextual Teaching and Learning (CTL) model with the outdoor approach towards students’ ability in mathematical representation. It was quasi-experimental research consisting of two experimental classes and one control group. It used a pretest-posttest control group design. The population of this study was the students of SUPM Tegal. Sampling was conducted using cluster random consisting of three classes. The first experimental group was carried out by implementing the learning model of CTL with the outdoor approach. The second experimental group was carried out by implementing a learning model of CTL, while the control group was conducted by implementing a conventional learning model. The research instrument was a 7-point mathematical representation test in the form of an essay. The results of the research were 1) the learning model of CTL with an outdoor approach affected the improvement and achievement of the students’ ability in mathematical representation and was higher than CTL and a conventional learning; 2) the improvement of the students’ ability of representation in the groups of CTL with outdoor approach, CTL, and conventional learning respectively was in high, medium, and low category.

... For example, since the mathematics curriculum is usually ordered around carefully sequenced concepts and procedures, school mathematics likely does not correspond with how a thematic investigation inherently involves a nonlinear web of ideas and disciplinary perspectives. Some studies note reluctance from teachers because of a perception that social problems do not have clear-cut solutions or that students will not be interested (Mamolo 2018;Simic-Muller and Fernandes 2020). Furthermore, CoM around social justice can inadvertently reinforce deficit notions about students and families (Larnell et al. 2016) via teachers' "blind spots to race, racism, and racialization," (27), a caution we return to when discussing our findings. ...

We frame teachers’ contextualization of mathematics (CoM) as a classroom-based identity resource. We explore CoM in secondary classrooms in the segregated school landscape of the US, focusing specifically on schools that serve primarily low-income Black and Latinx students. We review literature that discusses commonly-cited affordances for CoM according to formative, affective, functional literacy, and critical literacy rationales and problematize those rationales relative to prior research. We analyze 58 lessons from 12 classrooms at 11 schools to reveal patterns in CoM relative to those commonly-cited affordances. The formative, affective and functional literacy rationales were frequently evident. Teachers draw largely on generic human experiences and marketplace contexts, positioning students as consumers or employees. There were few instances of CoM naming racism or inequality, and our analysis further reveals blind-spots in these efforts. Our discussion considers the implications of these patterns.

... The concept of critical mathematical competencies is not clearly defined in the research literature. Alrø and Johnsen-Høines (2016), Kennedy (2018), and Mamolo (2018), and Sikunder (2015) refer to aspects such as understanding the world, empowering, critical citizens, society, mathematical literacy, and CME. A related concept is critical democratic competence. ...

This study took place at Western Norway University of Applied Sciences. The research question is: How can teachers facilitate students’ critical mathematical competencies in a climate change context? To enable students to act as critical citizens and empower them for a lived democracy is a crucial task for education. From a critical mathematics perspective, students can become aware of mathematics’ role in shaping society. They can be capable of critiquing the use of mathematics and applying mathematical competencies to empower themselves both personally and for the greater good of society.
The question contains four research focuses that are addressed in four individual papers. Research focus no. 1 identifies and critically reflects on concepts and perspectives emphasised as important in the literature of two fields – critical mathematics education and post-normal science – and is addressed in a literature overview (paper I). Research focuses 2, 3, and 4 involve a research partnership (papers II, III, and IV) with three teachers and their four classes in lower-secondary school. For about a year, 42 classroom lessons were designed by the teachers to develop students’ critical mathematical competencies in a climate change context. Research focus no. 2 involves how teachers’ values can influence their teaching by investigating their facilitation and reflections of value-aspect with respect to climate change and school mathematics. Research focus no. 3 identifies the potential for facilitating students’ awareness and understanding of the formatting power of mathematics. Lastly, research focus no. 4 identifies how students’ critical mathematical competencies can appear in their argumentation. This study has, therefore, a perspective on students’ critical mathematical competencies and how teachers facilitate them.
The findings from the four papers are structured and discussed in six themes. In the first theme, lived democracy and critical citizens, I discuss how the teachers connect climate change, students’ critical mathematical competencies, and democracy. They emphasise critical competencies as a crucial skill for students and treat the students as critical citizens by engaging them in discussion and debates. In the second theme, the mathematical formatting of climate change, I identified, amongst others, how the teachers express it as vital that students identify, understand and reflect on how mathematics can influence how we perceive climate change issues. I also discussed how teachers deliberate or un-deliberate that choices of graphs, numbers or topics can influence students or others.
In the third theme, critique and critical reflections, I identify how the teachers facilitate students’ critical reflections regarding mathematics-based argumentation in complex scientific issues. In addition, I explore how they prepare them to deal with uncertainties, consider implications of graphs, and include their critical agency in taking justified standpoints. In the fourth theme, mathematical literacy and kinds of knowing, I discuss students’ intertwined mathematical, technological, and reflective knowing. Examples of how students sometimes struggle to move beyond the mathematical borders of a task are contrasted with how they use their everyday knowledge and relate the task to the real-world. The students’ mathematical literacy is discussed in relation to local and global climate change concerns and 21st-century skills.
In the fifth theme, controversies and values, I identify how the teachers emphasise the controversies in climate change issues to deliberately create debate and reflections, instead of avoiding the controversies. In the sixth theme, student-centred and dialogic learning, I discuss six aspects characterising the learning environment in the research partnership, for instance, student-centred approaches, types of understanding, and the content and qualities of dialogues.
These six themes are relevant when teachers facilitate students’ critical mathematics competencies in a climate change context. They are neither exhaustive nor exclusive but can provide a foundation for teachers and researchers who consider including complex real-life problems in the mathematics classroom and aim at developing students as critical citizens in a lived democracy.

... On the other hand, another paper suggests using complexities of social justice contexts to encourage mathematical understanding in educational programs [29]. Finally, there is a need to increase the number of research works analyzing how teachers support active participation of students in mathematics classes [30]. ...

In this paper, a teaching experience carried out within the framework of the subject of mathematics is presented. This subject is taught at several levels in secondary schools. In addition to some specific content related with mathematics (percentages, fractions, graphics, and bank interest), the methodology is designed in order to enhance the development of transversal skills (e.g., oral exposition, poster design and presentation, the analysis of social inequalities, etc.). Survey results based on the responses from over 110 students across four consecutive years, as well as the teacher’s self-assessment, indicate that the proposed methodology enhanced the students’ motivation and was helpful for developing mathematical content in a more pleasant way than in a conventional class based on a master class and problem-solving class.

Teachers who commit themselves to change embark upon a difficult and sometimes lonely journey of self-doubt. In this chapter, we meet Nora, a Canadian educated middle school teacher who was hired as part of a school-wide initiative to introduce curricular change in an elite South American international school. Nora’s attempts to introduce socially relevant project-based teaching to her mathematics class were met with resistance, even amongst a backdrop of reform. We explore and analyse the tensions that emerged for Nora as she navigated the competing perspectives and expectations of her supervisors, colleagues, students and parents. This chapter contributes new insight into the experiences, supports, and shifts needed to help teachers persist through the uncertain journey of curricular change.KeywordsTeacher tensionsTeaching mathematics for social justiceSocial justice context problemsCollegial tensionsStudent tensions

This article articulates how mathematics (e.g., what they are, how they can be used, who they are by and for, who is able to do and understand them) are a social construct, just like racial or gender identities are social constructs. The authors describe how Political Conocimiento in Teaching Mathematics-a relational knowing that involves the entanglement of mathematics, pedagogies, students, and politics-can be used as a lens to reveal narratives about mathematics re(told) through stories (e.g., "Mathematics is culture-free, objective, and universal"). Drawing on their work with teachers, the authors offer an example scenario/activity and a teacher discussion that unpacks where mathematical stories are being told, from a dominant perspective, as well as how focusing on healthier narratives can help teachers work toward liberatory futures. Implications for teaching, teacher education, and future research are described.

سعت الدراسة إلى التعرف على درجة مراعاة مقررات الرياضيات في المرحلة المتوسطة لمهارات الرياضيات المجتمعية المتعلقة بـكل من: (إعداد الفرد للحياة، إعداد المجتمع للحياة، الربط بين الرياضيات والمواد الأخرى) من وجهة نظر المعلمين والمشرفين، والتعرف على ما إذا كان هناك فروق ذات دلالة إحصائية بين متوسطات استجابات أفراد عينة الدراسة حيال درجة مراعاة مقررات الرياضيات في المرحلة المتوسطة لمهارات الرياضيات المجتمعية تعزى لمتغيرات (المسمى الوظيفي، المؤهل، سنوات الخبرة). اتبعت الدراسة المنهج الوصفي المسحي، وتمثلت أداة الدراسة في استبانة مؤلفة من (31) عبارة موزعة ثلاثة محاور. طبقت الدراسة على عينة مكونة من (350) من معلمي الرياضيات بالمدارس الحكومية للمرحلة المتوسطة بإدارة تعليم جدة، و(24) مشرفًا تربويًا للرياضيات. وتم استخدام المتوسطات الحسابية والانحرافات المعيارية واختبار مان ويتني (Mann-Whitney Test))، واختبار كروسكال واليس (Kruskal-Wallis) في أساليب التحليل الاحصائي للدراسة. وقد أظهرت نتائج الدراسة ما يلي: أن درجة مراعاة مقررات الرياضيات في المرحلة المتوسطة لمهارات الرياضيات المجتمعية المتعلقة بإعداد الفرد للحياة من وجهة نظر المعلمين والمشرفين جاءت بدرجة متوسطة، أن درجة مراعاة مقررات الرياضيات في المرحلة المتوسطة لمهارات الرياضيات المجتمعية المتعلقة بإعداد المجتمع للحياة من وجهة نظر المعلمين والمشرفين جاءت بدرجة منخفضة. أوصت الدراسة بعدد من التوصيات، منها زيادة اهتمام القائمين على تطوير مناهج الرياضيات بتصميم أنشطة وتدريبات تستهدف تعزيز قدرة الطلاب على فهم القضايا الاجتماعية، وتفعيل دور مشرفي الرياضيات في توجيه المعلمين إلى تصميم أنشطة لاصفية تدعم مهارات التواصل مع الآخرين داخل البيئة المدرسية لإيجاد حلول للمشكلات الحياتية.

The purpose of the research is to reveal the problems of studying mathematics by students of the humanities and specialties, using the example of students of the Faculty of Philology and the Institute of Foreign Philology and Regional Studies of the Ammosov North-Eastern Federal University and describe the experience of teaching mathematics, contributing to the formation of general cultural competencies focused on the use of mathematical methods in professional activities. A sociological study was carried out in the form of a written survey of students and conversations with teachers of the Faculty of Philology and the Institute of Foreign Philology and Regional Studies, covering 114 students and 4 teachers. Based on the results of the study, the authors summed up the possibility of spreading this experience, using the proposed educational and methodological complex in other humanitarian areas and specialties.

This story is a playful retelling of ideas related to infinity. Presented as a historical fiction, the story reflects the thinking of research participants who addressed the ping pong ball conundrum, and where indicated, the individuals who contributed to modern formal understandings of infinity. This story offers a way of engaging with questions, controversies, ideas, and beliefs related to infinity. The characters in the story are confronted with a situation that challenges the notion of an ‘objective’ truth. Through their musings, April and her friends stumble upon the contextually-dependent nature of mathematical truth and open the door to further conversation.

In this article, we explore notions of risk as perceived or experienced by individuals involved in mathematical education. We present this exploration in the form of vignettes, each illustrating a form of risk: a parent's reaction to classroom "propaganda"; a teacher trying to do justice by her students; a teacher confronted by his administration; and a college professor who believes university policy to be unjust. Each vignette sheds light on areas in which teacher education may offer additional support in fostering the mathematical knowledge, pedagogical sensitivity, and social awareness required to foster, what are in our view, much needed risks in the mathematical (and otherwise) education of pupils. Following the vignettes, we offer a discussion of factors that contributed to the risks perceived or experienced by teachers: neoliberal discourses, and the powerful cultural scripts that leave teachers feeling that they must hold all control, authority, and knowledge.

Mathematics in teaching In this paper I try to think about mathematical knowledge in teaching as a way of being and acting, avoiding categorisation and acquisition metaphors of knowledge. I think of MKiT as participation in mathematical practices in the classroom, and also during preparation for teaching. Thus development and deepening of knowledge take place through doing mathematics and being mathematical in social contexts in which mathematical habits of mind are embedded, recognised and valued. I shall explain how some of the tasks of teaching can be seen as particular contextual applications of mathematical modes of enquiry. However, I am not arguing that an enquiry stance about teaching is enough on its own; it is mathematical enquiry that I am interested in, and that includes learning the traditional mathematical repertoire. Professional development opportunities that offer only collaborative enquiry as a panacea can be as irrelevant as those that offer only mathematical procedures. A colleague in Alberta has reported that collaborative PD in her school has led to acceptance of a 'lowest common denominator' of practice; a PD session in South Africa offered 16 different rules to factorise quadratics according to relationships between the coefficients. These are extreme but not unusual cases. We can see immediately the nonsense of presenting 'sixteen rules'; they do not relate to the essential activity of seeing quadratics as multiples of binomials, or of seeing the process as revealing roots; nor do they encourage adaptation of general methods in specific cases. Any process of identifying types can go too far and losing overarching insight. This is why I am, in this paper, arguing that a typographical approach to MKiT (knowledge of curriculum, knowledge of students, knowledge of textbooks, etc.) can mask the essential activity within which those nouns connect and inform each other. Experience of doing mathematics, on one's own and with others, in an environment that encourages listening, questioning and pedagogic reflection (which may be the teacher's own classroom), develops and deepens mathematical knowledge both in and for teaching. One problem with identifying types of knowledge is that we end up with definitions which can be unhelpful for teacher educators – being too unwieldy to fit into institutional constraints– and unhelpful for novices who then get a fragmented sense of what is relevant without yet having the practical perspective to make sense of it.

Researchers and theorists in education have offered persuasive arguments and evidence documenting the need for, and benefits of, education for social justice. Despite these efforts the intersection of social justice with interdisciplinary curricular designs remains underexplored. This article argues that social justice education is enriched through interdisciplinary curricula, in that it holds the potential for students to develop deeper conceptions of social justice and experience deeper learning outcomes related to content knowledge across subject matter areas. Central to this argument is the notion that situating disciplinary relationships explicitly within social justice perspectives encourages an emphasis on broader and richer sociopolitical consciousness among learners. We draw on historical and contemporary narratives to position social justice in mathematics and social studies education. As researchers in these two fields, we envision greater possibilities for the advancement of knowledge, and we envision learning from inequalities and resisting oppression by nurturing deeper, more explicit connections between mathematics and social studies. We conclude this article with three overviews of learning segments as potential representations of interdisciplinary mathematics-social studies for social justice work in secondary school contexts.

This chapter examines two recommendations for classroom practices from curriculum and instruction Standards (National Council of Teachers of Mathematics [NCTM], 1989; 2000) and research in mathematics education. One recommendation, informed in part by research uncovering the mathematical practices in everyday activities (Carraher, Carraher, & Schliemann, 1985; D'Ambrosio, 1985, 1991; Lave, 1988; Saxe, 1991), is to close the gap between learning mathematics in and out of school by engaging students in real-world mathematics rather than mathematics in isolation from its applications. The second recommendation is to make mathematics classrooms reflect the practices of mathematicians (Cobb, Wood, & Yackel, 1993; Lampert, 1986, 1990; Schoenfeld, 1992). These two proposals have different implications for changing classroom practices: one emphasizes the need for classroom activities to parallel everyday mathematical practice; the other emphasizes classroom activities that parallel those of academic mathematical practices. This chapter explores the tensions between these two proposals by juxtaposing everyday and academic mathematical practices.

This article examines pre-service secondary school teachers’ responses to a learning situation that presented a student's struggle with determining the area of an irregular hexagon. Responses were analyzed in terms of participants’ evoked concept images as related to their knowledge at the mathematical horizon, with attention paid toward the influence of one on the other. Specifically, our analysis attends to common features in participants’ understanding of the mathematical task, and explores the interplay between participants’ personal solving strategies and approaches and their identified preferences when advising a student. We conclude with implications for mathematics teacher education research and pedagogy.

Over the past decade, the mathematics education research community has incorporated more sociocultural perspectives into its ways of understanding and examining teaching and learning. However, researchers who have a long history of addressing anti-racism and social justice issues in mathematics have moved beyond this sociocultural view to espouse sociopolitical concepts and theories, highlighting identity and power at play. This article highlights some promising conceptual tools from critical theory and post-structuralism and makes an argument for why taking the sociopolitical turn is important for both researchers and practitioners.

We propose that what teachers can say or write about their views of mathematics and about a range of pedagogic strategies and didactic tactics that they use is of minor importance compared to what comes to mind moment by moment when they are planning or leading a lesson. Beginning with a quote from a teacher that provoked a focus on the role and nature of in-the-moment choices made in the midst of teaching, we offer some comments provoked in us. Following a concise history of attempts to articulate 'mathematics needed for teaching', three further brief accounts of incidents led us to propose that what really matters, in the words of Heidegger and others, is one's 'mathematical being', because it orients awareness and is the source and basis for choices, whether consciously or unconsciously made. The development of mathematical being is described using the discourse of awareness in the sense of Gattegno, making use of the discipline of noticing to educate awareness. These are then used to extend the analysis of prepositional suffixes for the gerund knowing begun by Ryle in order to focus on the development of 'connective tissue' between mathematical awareness and in-the-moment pedagogical choices of actions.

Awareness is a complex concept comprising both conscious and unconscious powers and sensitivities which enable people to act freshly and creatively in the moment. In the case of mathematics teachers, and teachers of those becoming mathematics teachers, it is possible to lead students mechanically through a sequence of ritualised tasks by means of trained and habitualised reactions. But the result is that even though student attention is indeed directed, their behaviour trained, and their awareness educated to some extent, the students have not been taught in the fullest sense of that word. I argue that to be a real teacher involves the refinement and development of a complex of awarenesses on three levels, and that this is manifested in alterations to the structure of attention.
The problematic nature of what students are attending to when a teacher is teaching them, led to the conjecture that each technical term in mathematics and in mathematics education signals a shift in the structure of attention of people using that term, and that a corresponding shift is required for students to appreciate that term. Investigations of attention led to the development of Gattegno's very general but rather subtle notion of awareness into a three-layer structure which applies both to mathematics and to teaching, and so demonstrates why becoming a teacher is such a complex matter.

In this article, the author reports on a study that explored, in part, the developing identities of seven New York City public high school mathematics teachers as teachers of mathematics and agents of change. Meeting regularly as a community of practice, the teachers and author/researcher discussed issues of teaching ma-thematics for social justice; explored activities and lessons around social justice; and created a unit of study that attempted to meet high school level mathematics standards, while addressing a social justice issue affecting the lives of urban stu-dents. The author reports on the mathematics teachers' growing awareness of and concerns about infusing issues of social justice into their teaching as well as the teachers' evolving conceptions of what it might mean to teach mathematics in an urban school, of the nature of mathematics itself, and of what their roles as edu-cators might include.

In this article we introduce a usage-goal framework within which task design can be guided and analyzed. We tell a tale of
one task, the Pentomino Problem, and its evolution through predictive analysis, trial, reflective analysis, and adjustment.
In describing several iterations of the task implementation, we focus on mathematical affordances embedded in the design and
also briefly touch upon pedagogical affordances.

The current push to marry off mathematics with social justice compels one to ask such critical questions as “What is social justice?” and “How does (or can) mathematics look and act when viewed in/through the lenses of social justice?” Taking
a critically reflective approach, this article draws the reader into a discussion of what is amiss in the currently promoted
picture-perfect marriage of mathematics and social justice, presenting perspectives on both the content and context of mathematics teaching and learning. In this article, the author’s account of her experience in teaching a mathematics curriculum
course for prospective middle years' teachers highlights a call to re-imagine the relationship between mathematics and social
justice as more than a perfunctory integration of a “statistics and figures” approach. The author’s reflections acknowledge
the complexity and potentiality of the relationship while challenging current status quo practices and paradigms in mathematics
education.

This article describes teachers' collective work aimed at learning to teach mathematics for social justice. Teacher interviews, discussions, lessons, and written reflections were analyzed using grounded theory methodology, and teachers' conversations were examined concerning the relationship between mathematical goals and social justice goals. Analysis revealed that early tensions arose around balancing these goals, that teachers focused more attention on the social justice component, and that the instantiation of these goals in practice proved difficult.

The education community knows that improvements can and must be made for the mathematics education of underrepresented groups. Native American schools, in particular, have struggled due to colonialism, racism, and the mistaken notion of members of the dominant society that Native people wish to be assimilated. In fact, sovereignty is a huge issue for Native people across the country; it is an especially sore point in our state, where a 1981 land claims settlement act clouded rather than clarified Native sovereignty. Mathematics education has learned a tremendous amount through the pioneering academic work done in ethnomathematics. We also know that so many others are doing the good work daily, impacting children's lives, but never receive recognition beyond the walls of their classrooms. We are learning about the positive difference of a Culturally Appropriate Curriculum and finally, we are learning how to respect Native America. This is a preliminary paper that intends to open a discussion on the challenge of passive resistance to education in a Native American school in the eastern United States.

This book brings together research and professional knowledge to enhance the teaching of lower attaining students in secondary mathematics. Attainment in mathematics is an important social issue, since underachievement can make a difference to future life choices, particularly amongst certain groups of students. This book shows how well-meant teaching strategies and approaches can in practice exacerbate underachievement in maths by making inappropriate demands on learners. As well as criticizing some of the teaching and grouping practices that are considered normal in many schools, the book also offers an alternative view of attainment and capability, based on real classroom incidents in which "low attaining students' show themselves to be able to think about mathematics in quite sophisticated ways. The author argues that teaching could be based on learners' proficiency, rather than on correcting deficits in knowledge and behaviour. She describes how a group of teachers who believed that their students could do better with higher expectations developed a range of principles and strategies to support their work, the students showed significant progress and the teachers felt they were doing a better job. This book contains the following nine chapters: (1) Social justice and school mathematics; (2) Abilities and understanding; (3) Teachers' judgements; (4) The impact of differences in practice and belief; (5) The fallacy of "getting to know" learners; (6) Thinking mathematically in low attaining groups; (7) Approaches to reconstruction: test cramming versus developing proficiency; (8) Improved attainment; and (9) Construction, reconstruction and renewal.

To illustrate aspects of critical mathematics education a project involving 14–15 years old students is described. Mathematics education can be organized so as to develop different types of knowing: mathematical knowing, which can be associated with skills developed in traditional teaching; technological knowing, which can be associated with a competence in mathematical model building; and reflective knowing, which can be seen as a competence in evaluating applications of mathematics. The thesis discussed says that if mathemacy should be developed as a competence of importance in a critical education, it must integrate mathematical, technological as well as reflective knowing. Via the description of the project, a possible educational meaning is given to this thesis. Especially, it is discussed what it could mean to involve students in reflections about mathematics as a tool for technological design.

Student teachers have difficulty planning lessons that fully integrate social justice with mathematics/science content. This study was a content analysis of 26 poster presentations of mathematics or science lessons incorporating social justice issues made by student teachers (20F, 6M) at a mid-sized college in central New York State. The presented lessons applied four pedagogical approaches to integration (data collection followed by graphing analysis; discussion of text/video; modeling; library/internet investigation) and addressed three major social justice themes (diversity, system disparities in human communities, and in stewardship of earth). Deeper content knowledge, faculty lesson modeling/reflection and practice delivering lessons are recommended.

With an eye on the mathematical horizon: Knowing mathematics for teaching to learners’ mathematical futures

- Ball

Ball, D. L., & Bass, H. (2009). With an eye on the mathematical horizon: Knowing mathematics for teaching to learners' mathematical futures. Paper Presented at the
43rd Jahrestagung der Gelleschaft fur Didaktic der Mathematik. Retrieved May 15, 2011 from www.mathematik.uni-dortmund.de/ieem/BzMU/BzMU2009/
BzMU2009-Inhalt-fuer-Homepage.htm.

Mathematics for critical numeracy: A case study of social justice mathematics course for preservice elementary teachers

- S Bateiha

Bateiha, S. (2010). Mathematics for critical numeracy: A case study of social justice mathematics course for preservice elementary teachers. Unpublished doctoral
dissertationUSA: University of Oklahoma.

Pennsylvania school set maths homework on sex abuse of girl

BBC (2017). Pennsylvania school set maths homework on sex abuse of girl. January 13. BBC News Retrieved from: http://www.bbc.co.uk/news/amp/38613255.

Rethinking mathematics: Teaching social justice by the numbers

- I Esmonde
- J Quindel

Esmonde, I., & Quindel, J. (2006). Globalization, labour, and the environment. In E. Gutstein, & B. Peterson (Eds.). Rethinking mathematics: Teaching social justice by the
numbers (pp. 62-63). Milwaukee: Rethinking Schools Ltd.

A handbook on rich learning tasks: Realizing a vision of tomorrow's mathematics classroom. Queen's University, Faculty of Education

- G Flewelling
- W Higginson

Flewelling, G., & Higginson, W. (2001). A handbook on rich learning tasks: Realizing a vision of tomorrow's mathematics classroom. Queen's University, Faculty of
Education, Centre for Mathematics, Science and Technology Education.

Rethinking mathematics: Teaching social justice by the numbers

- M Frankenstein

Frankenstein, M. (2006). Reading the world with math. In E. Gutstein, & B. Peterson (Eds.). Rethinking mathematics: Teaching social justice by the numbers (pp. 19-30).
Milwaukee: Rethinking Schools Ltd.

Reading and writing the world with mathematics: Toward a pedagogy of social justice

- R Gutierrez

Gutierrez, R. (2013). The socio-political turn in mathematics education. Journal for Research in Mathematics, 44, 37-68 Special Equity Issue.
Gutstein, E. (2006). Reading and writing the world with mathematics: Toward a pedagogy of social justice. New York, NY: Routledge.

Making mathematics meaningful in multicultural contexts

- Ladson-Billings

Ladson-Billings, G. (1995). Making mathematics meaningful in multicultural contexts. In W. G. Secada, E. Fennema, & L. B. Adajian (Eds.). New directions for equity in
A. Mamolo
Journal of Mathematical Behavior 51 (2018) 28-40

- A Mamolo
- L Pinto

Mamolo, A., & Pinto, L. (2015). Risks worth taking? Social risks and the mathematics teacher. The Mathematics Enthusiast, 12(1-3), 85-94.

Choosing maths/doing gender: A look at why there are more boys than girls in advanced mathematics classes in England

- Mendick

Mendick, H. (2003). Choosing maths/doing gender: A look at why there are more boys than girls in advanced mathematics classes in England. In L. Burton (Ed.). Which
way social justice in mathematics education? (pp. 169-188). London, UK: Praeger Publishers.

International perspectives on social justice in mathematics education

- T L Shockey
- R Gustafson

Shockey, T. L., & Gustafson, R. (2007). Some thoughts on passive resistance to learning. In B. Sriraman (Ed.). International perspectives on social justice in mathematics
education (pp. 127-138). Charlotte, NC: Information Age Publishing, Inc.

Food in Nunavut still costs up to 3 times national average

- E Skura

Skura, E. (2016). Food in Nunavut still costs up to 3 times national average. Retrieved fromCBC Newshttp://www.cbc.ca/news/canada/north/nunavut-food-price-survey-2016-1.3650637.

Maththatmatters: A teacher resource linking math and social justice

- D Stocker

Stocker, D. (2006). Maththatmatters: A teacher resource linking math and social justice. CCPA education task.

Globalization, labour, and the environment

- Esmonde

Reading the world with math

- Frankenstein

Connections: Mathematical, interdisciplinary, personal, and electronic

- Hughes-Hallett