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Research in mathematics education can be understood as a system of activities addressing the basic and applied problems related to teaching and learning of mathematics. Such a system includes the activities of foundation, planning, implementation, evaluation of mathematics instruction, and teacher professional development, which are supported by different theories. This diversity of theories raises interest in their comparison, coordination, and possible integration. The paper aims to present a case of application of the Cultural Historical Activity Theory (CHAT), in its 3rd and 4th generation versions, to analyze the emergence of the Onto-semiotic Approach to mathematical knowledge and instruction as a theoretical framework that addresses the study of the five partial activities mentioned above. This use of the CHAT can be useful in studies on theory articulation by focusing not only on the subjects, the object, and the instruments but also on the community context, the ecological-normative environment in which these activities take place, and the dilemmas or contradictions between theories.

Educating students to apply probability literacy and reasoning in out-of-school contexts requires the previous preparation of teachers, which should include the assessment of their mathematical and didactic knowledge. Consequently, we investigated three research questions concerning the probabilistic reasoning and literacy of 66 prospective secondary school teachers when solving probability questions related to a report taken from the media news, their ability to identify the fundamental stochastic ideas needed to solve the task, and their capacity to predict their students’ potential difficulties. The participants needed to compute the probability of a complementary event, several conditional probabilities, and perform critical reading of the information in the report. Despite the participants’ good mathematical knowledge, a high percentage showed reasoning biases, such as the fallacy of the transposed conditional, confusion between conditioning and causation, and few identified the information missing to solve a question. There was a poor capacity to determine the stochastic ideas needed to solve the questions, beyond probability, sample space, conditional probability, and sampling. The participants quoted a few potential errors of their students, mainly conceptual mistakes with scarce recognition of interpretation errors. These results reveal the need to reinforce teachers’ probabilistic literacy, reasoning, and related didactic knowledge.

In tracing recent research trends and directions in mathematical problem-solving, it is argued that advances in mathematics practices occur and take place around two intertwined activities, mathematics problem formulation and ways to approach and solve those problems. In this context, a problematizing principle emerges as central activity to organize mathematics curriculum proposals and ways to structure problem-solving learning environments. Subjects’ use of concrete, abstract, symbolic, or digital tools not only influences the ways to pose and pursue mathematical problems; but also shapes the type of representation, exploration, and reasoning they engage to work and solve problems. Problem-solving foundations that privilege learners’ development of habits of mathematical practices that involve an inquiry method to formulate conjectures, to look for different ways to represent and approach problems, and to support and communicate results shed light on directions of current research trends and the relevance of rethinking curriculum proposals and extending problem-solving environments in terms of teachers/students’ consistent use of digital tools and online developments.

Information technology enhances the nature of mathematics as an empirical discipline, leading to an approach called “experimental mathematics” (EM). It fosters the use of technology-based interactive resources (IRs) in mathematics education, giving mathematics an experimental dimension and reflecting a tension between the empirical-inductive nature of IRs and formal mathematics (FM). Our qualitative research focused on professional development (PD) for IR-based teaching of EM intertwined with FM based on a threefold theoretical framework that combines the mathematical knowledge required by EM, the pedagogical functionality of IRs, and instrumental orchestration. The research analyzed 14 high school teachers’ documents generated in the course of a PD program, revealing the evolution of their orientation. We argue that teachers’ evolving orientation toward IR-based EM inclusion in school mathematics is the result of meticulous dynamic PD design implementing three key aspects framed by the threefold theoretical framework: teachers playing various roles during the PD, teacher-researcher collaboration, and theoretical support. The beginning of the evolution of the teachers’ orientation toward IR-based EM inclusion in school mathematics was made possible by a design grounded in the above theoretical framework and observed through its lens.

Situated in the education reform launched by the Egyptian Ministry of Education (MOE), which called for a socially-foreign shift away from memorization-based mathematics instruction, this paper explores the role of school-based teacher professional networks in implementing reform. Adopting the Goodson Change Model as a theoretical framework, we map out the power play between external agency (national society), internal agency (teacher professional networks) and the personal agency of individual teachers. Using an embedded case study model and a dataset consisting of the recordings of two full-day focus group discussions with teacher professional networks at two national schools, we contrast the two cases from the perspective of teacher group tensions and power dynamics in relation to the reform implementation. In one case, the teacher professional network (internal agency) was dominantly embracing the change, thus empowering the local teacher (personal agency) and enforcing its dogma on its stationed national society (external agency). In the other case, the teacher as a personal agent was solely attempting to break through both layers of internal and external agency. Our findings cast light on the role of teacher professional networks in curricular reform contexts, particularly within a collective cultural setup such as Egypt. Implications for the role of teacher professional networks in the diffusion of reform initiatives are discussed in light of the findings.

Research shows the salient place of mathematical teaching talk, including the mathematical-linguistic practices of naming and explaining, in the enactment of students’ mathematical talk and learning with understanding in the classroom. Our study was developed to examine the noticing of two groups of secondary-school mathematics teachers in one-day workshops with tasks about these practices. The two workshops were mathematically content-specific, with teaching and learning accounts and prompts aimed at guiding focused attention to naming and explaining in the teaching of linear equations and probability. Thematic text analyses led to identify three foci of the two groups’ noticing: (i) missing practices of mathematical naming in own teaching talk; (ii) relative impact of mathematical explaining in teaching talk; and (iii) tensions around mathematical naming and explaining in teaching talk. Our results show that the social construction of teacher noticing is a feature of noticing development that can be documented in the context of one-day workshops. Whereas time for individual thinking and responses to the tasks created a context of support for noticing development, participation in the group discussions allowed the teachers to notice nuances of mathematical naming and explaining in teaching talk unaddressed in the task prompts. The group discussions thus amplified and opened up the opportunities to develop some focused noticing on the content of the workshops, specifically in connection with the teachers’ own teaching practice.

Adaptive learning support provided by kindergarten teachers before and after (macro-adaptive learning support) as well as during mathematical learning activities (micro-adaptive learning support) is a cross-cutting concept of teaching quality. Effective adaptive learning support enhances children’s learning. However, providing it is challenging and teachers need professional development (PD) to improve the quality of their support. This study investigates the mediating role of teaching quality between PD programs for kindergarten teachers and the development of children’s mathematical competency. 122 kindergarten teachers and their 825 pupils participated in the study. The teachers were randomly assigned to three groups. Two groups attended PD sessions designed to foster either macro- or micro-adaptive learning support. The third was the materials-only control group. The data was analyzed using a self-developed rating instrument focusing on generic and domain-specific elements of teaching quality related to macro- and micro-adaptive learning support. The multilevel latent change model analysis revealed that the PD programs had positive and significant effects on the teaching quality of kindergarten teachers. A significant positive relationship was also found between micro-adaptive learning support and changes in children’s mathematical competency. However, an indirect effect of teaching quality could not be detected, and the PD programs did not have a total effect on children’s mathematical competency. The study reinforces the importance of PD that specifically targets macro- and micro-adaptive learning support for kindergarten teachers. The mediation between PD and mathematical competency development requires further investigation.

We study the experts’ practices developed with the support of digital technologies (DT), when they take aware in-the-moment decisions during classroom discussions to promote the development of effective formative assessment (FA) processes. In this investigation, we complement a macro-analysis of paradigmatic examples of classroom activities, focused on the functionalities of DT and on the implemented FA strategies, with a micro-analysis, developed with reference to a theoretical construct useful for interpreting and analysing expert teachers’ roles during classroom discussions (the Model of Aware and Effective Attitudes and Behaviours, M_AEAB). More specifically, we explore how the expert uses DT to empower these roles with the aim of promoting FA processes. This study has two implications: (1) at the theoretical level, the study will introduce a model aimed at characterising the ways in which the expert can promote FA during classroom discussions when they are mediated by the use of DT; (2) at the pragmatic level, the use of this model to analyse paradigmatic examples from teaching experiments will introduce potential guidelines for teacher professional development aimed at promoting teachers’ autonomous use of DT to carry out effective FA practices.

Calculus continues to be an important topic of discussion among mathematics education researchers given how it often acts as a gatekeeper for students in STEM. In their extensive 2017 review of calculus literature, Larsen and colleagues identified two main areas of applied research that had largely been neglected: research related (1) to efforts to improve calculus teaching and learning and (2) to equity and social justice. In this review we investigate how scholars have answered this call by reviewing recent literature related to these two themes. First we identified some promising intervention studies that investigated changes at the course level (e.g., calculus courses intended for engineering students) and at the level of specific calculus topics (e.g. using digital tools to help students understand the Fundamental Theorem). Second, we identified several studies on diversity, equity, and inclusion. We found that some studies in this collection still approached this research through traditional methods (e.g., so called achievement gaps) but we also identified promising new directions for research in which scholars utilize critical theories and provide counter-narratives that highlight the strengths of calculus students from historically marginalized groups. We conclude our review by discussing future directions we hope to see in the field that we argue will strengthen current work.

This survey describes the structure of the field of research on curriculum resources in mathematics education in the period from 2018 till 2023. Based on the procedures of a systematic review relevant literature was identified using Web of Science as a database. The included literature was analyzed and categorized according to the type of curriculum resource and the area of study. Seven areas of studies were identified: studies on the role of curriculum resources, content analysis, user studies, studies on the effects of curriculum resources, studies on curriculum resource design, curriculum resources as data, and reviews. The areas were further subdivided into different subcategories based on the research questions of the included papers. The findings show that research on mathematics textbooks is still predominant in the field. The most popular areas of research are content analysis, user studies, studies on design, and studies on effects. Emerging areas are research on students’ use of curriculum resources and the employment of user data from digital curriculum resources as data basis in mathematics education research.