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The article provides an overview of research focusing on pre- and in-service teacher education, conducted in the Czech Republic by teams of researchers of which the authors were members. It employs the methodology of a qualitative meta-analysis of studies aimed at distinguishing key areas of research and their main results. Twenty-one studies were analyzed, 11 of which targeted pre-service teachers and 10 in-service teachers. The article briefly describes the historical and cultural context that informs mathematics education in the Czech Republic. It also elaborates on key theoretical concepts shared by the studies analyzed, including teachers' pedagogical content knowledge, competence and pedagogical reflection. The meta-analysis uncovered a common core of the studies in their focus on the process of professionalization for mathematics teachers in its three dimensions: professional vision, professional knowledge, and professional action. Six core research strands are identified within the group of studies: lesson study as a means of developing teachers' pedagogical content knowledge; joint reflection; professional vision and its development; culture of problem solving and teacher development; problem posing to support subject-didactic competence and teachers' competencies for content and language integrated learning and culturally responsive teaching. The article outlines the methodology and main results of the studies in each research strand and discusses their implications. Finally based on the meta-analysis, a discussion of the core concepts of teacher reflection, problem solving and problem posing is developed. [ABSTRACT FROM AUTHOR]

A characterization of recent Nordic research in didactics of mathematics is presented based on the 32 research reports from the Nordic and Baltic countries in the proceedings from NORMA17 (The eighth Nordic conference on didactics of mathematics). Recent Nordic research in didactics of mathematics is observed from several aspects such as choice of problem, theory, method, result, and target for the message. The analyses of the papers on different levels and from a manifold of perspectives build up an image of what Nordic research in DM (didactics of mathematics) contains and represents currently. The closeness and cooperation between researchers in the Nordic countries is characteristic as well as the breadth and variation in the choice of questions, theories, and methods. Research activity seems to flourish most in Norway. Small-scale studies as well as larger projects are visible. A variety of messages about mathematics teaching and learning for all age groups are directed to students, mathematics teachers, teacher educators, and policymakers. Quantitative and qualitative empirical studies dominate. Conceptual or theoretical investigations are rare. Studies of outcomes of interventions, including teaching approaches and experiments are most common, followed by studies of learning and cognition, including problem-solving. There is a need for surveys and overviews as so many new results are exposed. [ABSTRACT FROM AUTHOR]

In this article we analyze the current state of the didactics of mathematics in the U.S. as it relates to research on equity. The sociopolitical turn in U.S. mathematics education resulted in a push for critical mathematics pedagogies (CMPs) in which predominantly marginalized populations of students explore social injustices through mathematics. We argue that mathematics education for equity must access broader populations of students and develop students' ethical reasoning skills to build an ethical and equitable future. To address didactical limitations in U.S. mathematics education, we introduce the Ethical Reasoning in Mathematics Framework (ERiM) as a tool to analyze high school students' ethical reasoning in real-world mathematics tasks. Using data from the initial phase of a Design Research project with students of privilege, we show how the ERiM Framework can be used to design lessons that elicit students' critical math consciousness (CMC). We end the article with design implications and recommendations for future research on the didactics of equitable mathematics. [ABSTRACT FROM AUTHOR]

There is, in France, a long-term tradition of research in the didactics of mathematics. In this paper, we revisit this tradition using, as a specific lens, the research carried out on the educational use of digital tools and resources for teaching and learning mathematics. We first briefly introduce this tradition and the three main theories at the base of it: the theory of didactical situations, the theory of conceptual fields, and the anthropological theory of the didactic. Then, considering three different technological lenses, i.e., dynamic geometry environments, computer algebra systems, and digital resources, we show how these theories and the long-term connection established in this tradition with the fields of cognitive ergonomics and computer sciences have influenced technological research and its outcomes. We also show that, conversely, didactic technological research has led to original and influential theoretical constructions, such as the instrumental approach and the documentational approach to didactics, and that it has contributed in a substantial way to the opening of this didactic tradition to other didactic cultures and other communities, beyond the didactic one. [ABSTRACT FROM AUTHOR]

Despite the construct of challenge being recognized as an essential element of mathematics instruction, concerns have been raised about whether such approaches benefit students with diverse academic needs. In this article, we focus on the beliefs and instructional practices of teachers teaching students in the first three years of school (5 to 8 years of age). These teachers participated in professional learning focused on challenging mathematical tasks differentiated through their open-ended design and the use of enabling and extending prompts. The instructional practices are explained using the Theory of Didactical Situations. Questionnaire data from pre-intervention (n = 148) and post-intervention (n = 100) groups of teachers indicated that teachers in the post-intervention group held more negative beliefs than those in the pre-intervention group about the capability of instructional approaches involving a priori grouping of students by performance levels. Interviews with ten teachers from the post-intervention group revealed and characterized the ways teachers employed open-ended tasks with enabling and extending prompts to engage all learners. Findings reveal that teachers knowing their students as individual learners accompanied by knowledge of a range of teaching practices to differentiate instruction are central to engaging all learners. [ABSTRACT FROM AUTHOR]

The main aim of the present study is to analyze the differences that may exist when students address the resolution of verbal problems in their mother tongue and in the language of instruction when these are different. We understand that knowing the type of verbal problems and their semantic structure can be helpful for students' contextual and mathematical understanding and will allow teachers to improve instruction during the first years of elementary education in bilingual schools specialized in the area of second language acquisition as well as in CLIL (Content and Language Integrated Learning). This study shows how children, as they are acquiring a greater command of the second language, show similar effectiveness to those students who work on mathematics in their mother tongue. This transversal study was conducted on 169 bilinguals studying in international schools. The sample was made up of 80 1st grade students (39 girls, mean age of 7.1 years and 41 boys, mean age of 7.3 years); and 89 2nd grade students (38 girls, mean age 8.2 years, and 51 boys, mean age 8.2 years). The exploratory analyses let us show how 1st grade students demonstrate lower effectiveness in solving problems when they do it in a second language, compared to 2nd grade students whose effectiveness is higher in carrying them out. It is also relevant that in first graders, the largest number of errors are found in the simplest tasks as students' effectiveness is less when they are taught in a second language, since it takes them longer to create effective resolution models. This fact will allow us to reconsider appropriate strategies and interventions when teaching mathematics in bilingual contexts. [ABSTRACT FROM AUTHOR]