Explicit language objectives are included in the Swedish national curriculum for mathematics. The curriculum states that students should be given opportunities to develop the ability to formulate problems, use and analyse mathematical concepts and relationships between concepts, show and follow mathematical reasoning, and use mathematical expressions in discussions. Teachers’ competence forms a crucial link to bring an intended curriculum to a curriculum in action. This article investigates a professional development program, ‘Language in Mathematics’, within a national program for mathematics teachers in Sweden that aims at implementing the national curriculum into practice. Two specific aspects are examined: the selection of theoretical notions on language and mathematics and the choice of activities to relate selected theory to practice. From this examination, research on teacher learning in connection to professional development is proposed, which can contribute to a better understanding of teachers’ interpretation of integrated approaches to language and mathematics across national contexts.
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The aim of this paper is to present materials designed for adult numeracy training. In the successive Erasmus+ projects, "The Common European Numeracy Framework" (2018-2021) and "Numeracy in Practice" (2022-2024), professional development modules have been designed for teachers specialising in adult numeracy education. The primary objective of these modules is to enhance teacher awareness of the competencies required for teaching numeracy and to address the changing demands of numeracy in adults’ personal and professional lives.
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The artcle describes the outcomes of a pilot study on professional development of teachers. The project was initiated by the school management. Nine teachers volunteered to work on their professional development in a programme consisting of: meetings discussing on relevant teacher topics meetings discussing video fragments of own performances meetings exploring ways to coach each other and how to use videotapes for feedback peer-coaching-sessions in small groups. Within these groups three teachers took turns in different roles: trainee, coach and observer. Aims of the study are: to develop a coaching programme, to describe extensively the process and the outcomes in order to identify the main factors influencing the learning processes of teachers in peer coaching settings with video feedback.
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Mathematics teacher educators in primary teacher education need expert knowledge and skills in teaching in primary school, in subject matter and research. Most starting mathematics teacher educators possess only part of this knowledge and skills. A professional development trajectory for this group is developed and tested, where a design based research is used to evaluate the design. This paper describes the professional development trajectory and design. We conclude that the professional development design should focus on mathematical knowledge for teaching, should refer to both teacher education and primary education, should offer opportunities for cooperative learning, and need to use practice based research as a developmental tool.
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In this chapter, we discuss the education of secondary school mathematics teachers in the Netherlands. There are different routes for qualifying as a secondary school mathematics teacher. These routes target different student teacher populations, ranging from those who have just graduated from high school to those who have already pursued a career outside education or working teachers who want to qualify for teaching in higher grades. After discussing the complex structure this leads to, we focus on the aspects that these different routes have in common. We point out typical characteristics of Dutch school mathematics and discuss the aims and challenges in teacher education that result from this. We give examples of different approaches used in Dutch teacher education, which we link to a particular model for designing vocational and professional learning environments.We end the chapter with a reflection on the current situation.
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It has been argued that teachers need practical principled knowledge and that design research can help develop such knowledge. What has been underestimated, however, is how to make such know-how and know-why useful for teachers. To illustrate how principled knowledge can be “practicalized”, we draw on a design study in which we developed a professional development program for primary school teachers (N = 5) who learned to design language-oriented mathematics lessons. The principled knowledge we used in the program stemmed from the literature on genre pedagogy, scaffolding, and hypothetical learning trajectories. We show how shifting to a simple template focusing on “domain text” rather than genre, and “reasoning steps” rather than genre features made the principled knowledge more practical for the teachers.
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Nowadays, digital tools for mathematics education are sophisticated and widely available. These tools offer important opportunities, but also come with constraints. Some tools are hard to tailor by teachers, educational designers and researchers; their functionality has to be taken for granted. Other tools offer many possible educational applications, which require didactical choices. In both cases, one may experience a tension between a teacher’s didactical goals and the tool’s affordances. From the perspective of Realistic Mathematics Education (RME), this challenge concerns both guided reinvention and didactical phenomenology. In this chapter, this dialectic relationship will be addressed through the description of two particular cases of using digital tools in Dutch mathematics education: the introduction of the graphing calculator (GC), and the evolution of the online Digital Mathematics Environment (DME). From these two case descriptions, my conclusion is that students need to develop new techniques for using digital tools; techniques that interact with conceptual understanding. For teachers, it is important to be able to tailor the digital tool to their didactical intentions. From the perspective of RME, I conclude that its match with using digital technology is not self-evident. Guided reinvention may be challenged by the rigid character of the tools, and the phenomena that form the point of departure of the learning of mathematics may change in a technology-rich classroom.
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This paper is a summary paper of the Thematic Working Group (TWG) on Adult Mathematics Education (AME). As the only thematic working group that focuses on adults’ lived experiences of mathematics, the research makes an important contribution to the field of Mathematics Education. The main themes in this group identify that adult numerical behaviour goes beyond the mathematics skills, knowledge, and procedures taught in formal education It is multifaceted, requiring the use of higher order skills of analysis and judgement, applied within a broad array of life’s contexts, experienced through a range of emotions. The research in this group points to the need to raise the profile of research that shows the benefits to adults of learning mathematics but also the long term economic disbenefits in the neglect of teaching and teacher training for this group.
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Worldwide, pupils with migrant backgrounds do not participate in school STEM subjects as successfully as their peers. Migrant pupils’ subject-specific language proficiency lags behind, which hinders participation and learning. Primary teachers experience difficulty in teaching STEM as well as promoting required language development. This study investigates how a professional development program (PDP) focusing on inclusive STEM teaching can promote teacher learning of language-promoting strategies (promoting interaction, scaffolding language and using multilingual resources). Participants were five case study teachers in multilingual schools in the Netherlands (N = 2), Sweden (N = 1) and Norway (N = 2), who taught in primary classrooms with migrant pupils. The PDP focused on three STEM units (sound, maintenance, plant growth) and language-promoting strategies. To trace teachers’ learning, three interviews were conducted with each of the five teachers (one after each unit). The teachers also filled in digital logs (one after each unit). The interviews showed positive changes in teachers’ awareness, beliefs and attitudes towards language-supporting strategies. However, changes in practice and intentions for practice were reported to a lesser extent. This study shows that a PDP can be an effective starting point for teacher learning regarding inclusive STEM teaching. It also illuminates possible enablers (e.g., fostering language awareness) or hinderers (e.g., teachers’ limited STEM knowledge) to be considered in future PDP design.
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A primary teacher needs mathematical problem solving ability. That is why Dutch student teachers have to show this ability in a nationwide mathematics test that contains many non-routine problems. Most student teachers prepare for this test by working on their own solving test-like problems. To what extent does these individual problem solving activities really contribute to their mathematical problem solving ability? Developing mathematical problem solving ability requires reflective mathematical behaviour. Student teachers need to mathematize and generalize problems and problem approaches, and evaluate heuristics and problem solving processes. This demands self-confidence, motivation, cognition and metacognition. To what extent do student teachers show reflective behaviour during mathematical self-study and how can we explain their study behaviour? In this study 97 student teachers from seven different teacher education institutes worked on ten non-routine problems. They were motivated because the test-like problems gave them an impression of the test and enabled them to investigate whether they were already prepared well enough. This study also shows that student teachers preparing for the test were not focused on developing their mathematical problem solving ability. They did not know that this was the goal to strive for and how to aim for it. They lacked self-confidence and knowledge to mathematize problems and problem approaches, and to evaluate the problem solving process. These results indicate that student teachers do hardly develop their mathematical problem solving ability in self-study situations. This leaves a question for future research: What do student teachers need to improve their mathematical self-study behaviour? EAPRIL Proceedings, November 29 – December 1, 2017, Hämeenlinna, Finland
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