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Abstract

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.

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... 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. ...
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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. ...
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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]. ...
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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.
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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.
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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.
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With an eye on the mathematical horizon: Knowing mathematics for teaching to learners' mathematical futures
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