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Mathematics education is like many scientific disciplines witnessing an increase in scientific output. Examining and reviewing every paper in an area in detail are time-consuming, making comprehensive reviews a challenging task. Unsupervised machine learning algorithms like topic models have become increasingly popular in recent years. Their ability to summarize large amounts of unstructured text into coherent themes or topics allows researchers in any field to keep an overview of state of the art by creating automated literature reviews. In this article, we apply topic modeling in the context of mathematics education and showcase the use of this data science approach for creating literature reviews by training a model of all papers (n = 336) that have been presented in Thematic Working Groups related to technology in the first eleven Congresses of the European Society for Research in Mathematics Education (CERME). We guide the reader through the stepwise process of training a model and give recommendations for best practices and decisions that are decisive for the success of such an approach to a literature review. We find that research in this period revolved around 25 distinct topics that can be grouped into four clusters: digital tools, teachers and their resources, technology experimentation, and a diverse cluster with a strong focus on student activity. Finally, a temporal analysis of these topics reveals a correlation between technology trends and research focus, allowing for reflection on future research in the field. [ABSTRACT FROM AUTHOR]

Professional development (PD) courses are the main context for mathematics teachers' lifelong learning. Leaders with expertise are needed to facilitate these courses; thus, there is a growing interest in understanding the nature of this profession, its core practices, and the challenges it entails. This paper focuses on a specific group of facilitators: experienced mathematics teachers who have just begun facilitating PD courses in addition to their classroom teaching. To better understand these novice facilitators' practices, a commognitive approach was implemented to examine how they draw on their mathematics teaching experience when leading PD courses. In commognitive terms, these practitioners draw on multiple professional discourses, but mostly on the discourses of teaching and facilitation. The analysis of the challenges and affordances associated with participating in these two professional discourses showed that novice facilitators bring into play their teaching practices in four distinct ways: enacting a familiar practice, negating a familiar practice, questioning the relevance of a familiar practice, and generating a new practice based on their teaching experience. We claim that novice facilitators' well-established identity as teachers is both a challenge and an asset in grounding successful facilitation practices. Overall, facilitators modify their teaching experience through the adoption, adaptation, and retraction of their teaching practices. Implications for the preparation and support of facilitators, within processes of upscaling PD programs, are discussed. [ABSTRACT FROM AUTHOR]

In a recent paper (Weber & Mejia-Ramos, Educational Studies in Mathematics, 76, 329-344, ), we reported findings from two small-scale interview studies on the reasons why and the ways in which mathematicians read proofs. Based on these findings, we designed an Internet-based survey that we distributed to practicing mathematicians working in top mathematics departments in the USA. Surveyed mathematicians ( N = 118) agreed to a great extent with the interviewed mathematicians in the exploratory studies. First, the mathematicians reported that they commonly read published proofs to gain different types of insight, not to check the correctness of the proofs. Second, they stated that when reading these proofs, they commonly: (a) appeal to the reputation of the author and the journal, (b) study how certain steps in the proof apply to specific examples, and (c) focus on the overarching ideas and methods in the proofs. In this paper, we also report findings from another section of the survey that focused on how participants reviewed proofs submitted for publication. The comparison of participant responses to questions in these two sections of the survey suggests that reading a published proof of a colleague and refereeing a proof for publication are substantially different activities for mathematicians. [ABSTRACT FROM AUTHOR]

In this paper, we draw on the contemporary perspective of inclusive materialism offered by de Freitas and Sinclair to contribute to current discussions on the role of the body in the learning of mathematics. Using the notions of distributed agency and assemblage, we illustrate the way in which three students engage with a patterning task. We discuss this as an example to show how the mathematics activity involves, besides the students' bodies, other materialities that populate the classroom, and how all the human and non-human bodies form a moving assemblage that constantly reconfigures and reorients learning. The inclusive materialism helps us talk about learning as a dynamic assemblage rather than in terms of individual achievements and directs attention to the material learning environment. [ABSTRACT FROM AUTHOR]

This paper responds to the burgeoning literature on mathematics teacher noticing, arguing that its cognitive orientation misses the cultural and ideological dimensions of what and how teachers notice. The author highlights Goodwin's concept of professional vision as a way of bringing analyses of culture and power into studies of teacher noticing. The case of a high school algebra teacher who learned to notice the mathematical strengths of students from marginalized groups is used to illustrate how this might be done. The teacher's noticing involved not only cognitive processes like attending to, interpreting, and deciding how to respond to students' thinking, but also managing dominant ideologies that position students-especially students from non-dominant communities-as mathematically deficient rather than as sense-makers whose ideas should form the basis for further learning. The paper advances the field's capacity for understanding the challenges that teachers face as they attempt to notice in ways that are ambitious as well as equitable. [ABSTRACT FROM AUTHOR]

Research on learner errors in mathematics education is beginning to focus on how teachers can learn to identify and engage with the reasoning behind these errors. Research on professional learning communities is beginning to show that they present powerful opportunities for on-going teacher collaboration and learning. In this paper, I bring the two areas of research together. Drawing on data from one professional learning community in the Data Informed Practice Improvement Project, I show how teachers in this community came to understand key concepts about learner errors and shifted their ways of talking about learner errors. I identify three important shifts that the teachers made in their learning about learner errors: from identifying to interpreting errors; from interpreting to engaging errors; and from focusing on learner errors to focusing on their own knowledge. I argue that these three shifts suggest a deepening of teachers' thinking in relation to learner errors. [ABSTRACT FROM AUTHOR]

This paper proposes a framework for identifying the mathematical knowledge teachers activate when using curriculum resources. We use the term knowledge of curriculum embedded mathematics (KCEM) to refer to the mathematics knowledge activated by teachers when reading and interpreting mathematical tasks, instructional designs, and representations in mathematics curriculum materials. The KCEM framework is situated within existing research on content-specific teacher knowledge. Through analysis of elementary mathematics teacher's guides from the USA, we identified elements of curriculum resources teachers interact with when using them to plan instruction. These findings were complemented by interviews of teachers using curriculum guides to plan lessons, uncovering how they interacted with different elements of their guides. From this analysis, we propose four overlapping dimensions of KCEM: foundational mathematical ideas, representations and connections among these ideas, problem complexity, and mathematical learning pathways. Using an excerpt from one elementary curriculum guide and one of the teacher interviews on using this guide to plan a lesson, we illustrate how these dimensions might be activated as teachers read and use their guides. [ABSTRACT FROM AUTHOR]

This paper describes a study in which we investigated relationships between defining mathematical concepts - increasing and decreasing infinite sequences - explaining their meanings and classifying consistently with formal definitions. We explored the effect of defining, explaining or studying a definition on subsequent classification, and the effect of classifying on subsequent explaining and defining. We report that (1) student-generated definitions and explanations were highly variable in content and quality; (2) explicitly considering the meaning of the concept facilitated subsequent classification, and giving a personal definition or explanation had a greater effect than studying a given definition; (3) classifying before defining or explaining resulted in significantly poorer definitions and explanations. We discuss the implications of these results for the teaching of abstract pure mathematics, relating our discussion to existing work on the concept image/concept definition distinction and on working with examples. [ABSTRACT FROM AUTHOR]

This paper concerns proof presentation at the university level. We report on a study in which we observed ten mathematicians constructing or revising proofs for pedagogical purposes. We highlight the factors that they claimed to consider when completing these tasks. We found that intended audience and medium (lecture or textbook) influenced proof presentation. We also found that, although mathematicians generally valued pedagogical proofs featuring diagrams and emphasizing main ideas, these mathematicians did not always incorporate these aspects in the proofs they constructed or revised. [ABSTRACT FROM AUTHOR]

Mathematics educators have long emphasised the importance of attitudes, beliefs, and feelings towards mathematics, as crucial in motivating (or not) its learning and use, and as influenced in turn by its social images. This paper is about images of mathematics. Our search for advertisements containing such images in UK daily newspapers, during 2006-2008, found that 4.7 % of editions included a 'mathematical' advert, compared with 1.7 % in pilot work for 1994-2003. The incidence varied across type of newspaper, being correlated with class and gender profiles of the readership. Three quarters of advertisements were classified as containing only very simple mathematics. 'Semiotic discursive' analysis of selected advertisements suggests that they draw on mathematics not to inform, but to connote qualities like precision, certainty, and authority. We discuss the discourse on mathematics in advertising as 'quasi-pedagogic' discourse, and argue that its oversimplified forms, being empty of mathematical content, become powerful means for regulating and 'pedagogising' today's global consumers. [ABSTRACT FROM AUTHOR]

This paper explored (1) the developmental trend of student level of reasoning across grade level in pattern generalization; (2) the mediatory role of task variables in the developmental trend of student level of reasoning within and across tasks; and (3) developmental trend of student level of reasoning associated with strategy use across grade level. A test designed to measure student level of reasoning was given to a sample of 1232 students from grades 4 to 11 from 5 schools in Lebanon. The Structure of the Learned Outcomes or Responses (SOLO) was used as a theoretical model. Results show that student level of reasoning exhibited an increasing trend across clusters of grade levels and that there were several SOLO levels in each cluster of grade levels. Type of task (immediate, near, far) and function type (linear, non-linear) seem to mediate the development of level of reasoning across grade level but the complexity of the task (simple, more complex) did not. Students used several strategies in each cluster of grade levels and the developmental trends of student level of reasoning associated with strategy use were not uniform and varied across clusters of grade levels, thus supporting a neo-Piagetian interpretation of the results. [ABSTRACT FROM AUTHOR]

This study examines the classroom practice and craft knowledge underpinning one teacher's integration of the use of GeoGebra software into mathematics teaching. The chosen teacher worked in an English secondary school and was professionally well regarded as an accomplished user of digital technology in mathematics teaching. Designed in accordance with the Structuring Features of Classroom Practice framework (Ruthven, 2009), the study triangulates evidence from lesson observations and post-lesson interviews to analyse how this teacher's classroom practice and professional knowledge support the integration of technology. This analysis shows how the teacher managed a number of aspects of classroom teaching related to using GeoGebra such as including technology-mediated tasks aligned with his pedagogical goals, preparing his students to use the technology efficiently, adapting formats for classroom activity and extending his curriculum scripts for the topics studied. [ABSTRACT FROM AUTHOR]

Mathematics-specific learning difficulties and disabilities (MLD) have received increasing attention in scholarly research. In this study, we place MLD research in its wider context of risk societies by discussing the manufacturing of MLD as a risk. This framing of MLD builds on a certain idea of hope in how research could provide the means to better understand and support learners with MLD. We conduct a Foucault-informed analysis to understand how scholarly knowledge about MLD has been produced through discourses of risk and hope. Our material consists of 30 influential journal articles published in the three fields of MLD research: cognitive sciences, special education and mathematics education. Our study indicates that MLD has been predominantly conceptualised through a technico-scientific risk discourse that frames MLD as harmful for learners and societies alike; such risk discourse relies on a discourse of hope in scientific methods. We also analyse a social risk discourse that identifies risks in social exclusion and marginalisation of students with MLD, finding hope in inclusive learning environments. Based on our analysis, we propose that the mere conceptualisation of MLD has thoroughly revolved around discourses of current liminalities (risk) and enunciations of better futures (hope). However, what has been unexplored is the politics of such risk and hope discourses themselves. We propose a socio-politically oriented discourse of risk/hope as a way to reframe scientific knowledge production about MLD. This discourse identifies risks not in MLD itself but in how research manufactures MLD as a threat to both economic growth and student identities. Instead of asking research communities to mitigate the risk of MLD, we call for them to embrace it. [ABSTRACT FROM AUTHOR]

Our research aimed to investigate the potential learning benefits to young children of implementing digital interactive multimodal technologies that provide both visual and haptic experiences in elementary mathematics classrooms. We studied the ways in which fourth-grade students collaboratively create collective strategies for solving mathematical problems utilizing dynamic geometry software with multi-touch interfaces, a combination we call a multi-touch Dynamic Geometry Environment. We examine in-depth two case studies each illustrating how mathematical strategies, collaboration, and socially mediated metacognition emerge in the small groups of children while working on an activity using the Geometer's Sketchpad® on the iPad to make sense of an intuitive idea of covariation. We found that children's interactions with their peers, the interviewer, and the mDGE favored the emergence of varied collaborative behaviors and socially mediated metacognitive processes that fostered the co-construction and development of mathematical strategies over a short period of time. [ABSTRACT FROM AUTHOR]

This study focuses on adults who are neither preschool teachers nor professional caregivers and investigates their beliefs regarding the importance of engaging young children with numerical activities. It also examines the types of numerical activities adults report having observed children engaging with, as well as the types of activities they propose as a way for promoting counting, enumerating, recognizing number symbols, and number composition and decomposition. Findings showed that participants believed to a great extent that engaging young children with numerical activities is important. Most reported that they had observed children engaging with at least some numerical activity. In general, participants relayed more activities and more detailed activities when suggesting activities for each competency, than they did when reporting observed activities. Findings also suggested a need to enhance adults' knowledge regarding the necessity to promote verbal counting, separate from object counting, as well as to increase adults' awareness of number composition and decomposition. For mathematics educators wishing to plan workshops for adults, this study offers a method for investigating adults' knowledge of early numerical activities, as well as a starting point with which to plan appropriate workshops. [ABSTRACT FROM AUTHOR]

We investigate how students make sense of irrational exponents. The data comprise 32 interviews with university students, which revolved around a task designed to examine students' sensemaking processes involved in predicting and subsequently interpreting the shape of the graph of f x = x 2 . The task design and data analysis relied on the concept of sensemaking trajectories, blending the notions of sensemaking and (hypothetical/actual) learning trajectories. The findings present four typical sensemaking trajectories the participants went through while coping with the notion of an irrational exponent, alongside associated reasoning themes that seemed to have guided these trajectories. In addition to irrational exponents, the analysis revealed the participants' reasoning and sensemaking of related mathematical ideas, such as rational exponents, approximations of irrational numbers by rational numbers, even/odd functions and numbers, and the meaning of exponentiation in general. The findings provide a step towards a better understanding of students' conceptual development of irrational exponents, which could in turn be used for the refinement of tasks aimed at promoting students' comprehension of the topic. [ABSTRACT FROM AUTHOR]

Exploring language provides us with one approach to better understanding the practices and beliefs of a community. With advances in technology—specifically, computational text processing and machine learning tools—we can now examine written language on a large scale. In this study, we investigate the language of mathematics teaching and learning in the USA over a decade (2009–2018) by analyzing text from articles published in Mathematics Teaching in the Middle School. Our analyses explore the terminology used by middle school teachers and teacher educators to discuss their practice, revealing terms that are used widely, terms that have largely been absent from such writing, and terms that have shifted in usage over the past decade. This research provides insight into the zeitgeist of mathematics teaching and learning during a particular period of time, while also suggesting a fruitful approach to examining language as a means of uncovering the beliefs and practices of a community. [ABSTRACT FROM AUTHOR]

The use of authentic real-world problems that reflect the applied nature of mathematics is not prevalent in formal secondary school settings. In this study, we explore the interface between workplace mathematics, particularly tech-related real-world (TRW) problems, and school mathematics, through the explication of mathematical modeling. The research questions are (1) in which tech domains can real-world problems be identified that can be addressed using mathematical modeling for the secondary school level? (2) Which methods do engineers use to simplify tech-related problems for non-experts in their field? (3) In which areas in the secondary mathematics curriculum can TRW problems be mapped? We present a three-phase model which yielded the creation of a pool of 169 TRW problems. The first two phases of the model included extracting authentic problems from the work of tech engineers and simplifying them to be meaningful or perceivable to students. These were explored by conducting task-oriented interviews with senior tech engineers and scientists from leading companies and universities. The third phase was accomplished by interviewing mathematics education experts, and included verifying the compatibility of the problems with the formal, secondary-level mathematics curriculum. The study has methodological, theoretical, and practical contributions. These include methodology that enables identifying TRW problems that are compliant with the secondary mathematics curriculum; adding to the literature about mathematical modeling by demonstrating the interface between workplace mathematics and school mathematics; and creating a large pool of TRW problems that can be used in secondary school math lessons. [ABSTRACT FROM AUTHOR]

An introduction to the article is presented in which author discusses various reports within the issue on topics including research-based interventions in mathematics classrooms, innovative approaches to teaching mathematics, and the relationship of mathematics education and contemporary theory.

This study examines adult students enrolled in pipe trades preapprenticeship training to identify distinguishing features of the mathematical activity within their program and sources of their mathematics-related difficulties. Two closely related sociocultural perspectives, specifically cultural historical activity theory and the theory of knowledge objectification, frame this investigation. Like workplace mathematics practices reported elsewhere, mathematics within this preapprenticeship program was inextricably tied to the efficient production of objects of workplace activity, in this case, the design and fabrication of a limited number of well-defined objects of pipe trades production. This form of mathematical activity was also mediated intensely by semiotic tools and norms of practice specific to the pipe trades. The contribution of this study is the finding that the great majority of the mathematics difficulties encountered by students can be attributed to their novice levels of awareness of the objects of pipe trades production and related ways of working rather than the mathematics understandings that they brought to this endeavor. Implications are identified for the teaching of mathematics in skilled trades training generally, developing students' mathematical subjectivities within trades training, and the mathematics preparation of secondary school students who will be entering skilled trades. Questions are also raised for further research. [ABSTRACT FROM AUTHOR]

The purpose of this cross-national study is to understand teachers' views about the meaning of instructional coherence and the ways to achieve instructional coherence. With respect to the meaning of instructional coherence, whereas the majority of U.S. teachers paid attention to connections between teaching activities, lessons, or topics, the majority of Chinese teachers emphasized the interconnected nature of mathematical knowledge beyond the teaching flow. U.S. teachers expressed their views about ways to achieve instructional coherence through managing a complete lesson structure. In contrast, Chinese teachers emphasized pre-design of teaching sequences, transitional language and questioning based on the study of textbooks and students beforehand. Moreover, they emphasized addressing student thinking and dealing with emerging events in order to achieve 'real' coherence. The findings of the study contribute to our understanding about the meaning of instructional coherence and ways to achieve instructional coherence in different cultural contexts. [ABSTRACT FROM AUTHOR]

This study is part of a wider research program, which seeks to investigate the existence (or not) of relationships between sociomathematical and mathematical norms at different academic levels. Here, we consider the norms that arise in the interaction between primary student teachers when they solve a mathematical task related to the mathematical definition. We hypothesize that in the colloquial mathematical discourse between these students coexist two types of discourse as follows: sociomathematical and mathematical, each one with its specific norms. This coexistence can originate commognitive conflicts. We have been able to identify different commognitive conflicts that arose from the simultaneous existence of sociomathematical norms and mathematical norms linked to defining, approaching their generation. [ABSTRACT FROM AUTHOR]

We investigate the different school mathematical discourses that are made available for students who all share an unfavourable social and economical position and experiences of low achievement in primary school, and who have been streamed into three different ability groups at the very beginning of secondary school. Our investigation is built on the premise that schools distribute different forms of knowledge to different social groups and thus provide different opportunities to develop consciousness. We look at teacher-student interactions as expressions of social structure at the micro-level and as constituents of social structure on the macrolevel. Employing analytic tools from social semiotics, we carried out a register analysis of the school mathematical discourse in each stream. We found systematic differences and linked them to the work of Dowling () on the construction of ability and its implications for social hierarchies. As a result, the upper of the three streams was freed from a discourse of low expectations, while such a discourse was reinforced for the lower stream. Finally, we will discuss our findings in relation to the contemporary debate about the role of mathematics education in social stratification. [ABSTRACT FROM AUTHOR]

The mathematical situations of play and exploration introduced here have been developed as an empirical research instrument for the longitudinal study 'erStMaL' (early Steps in Mathematics Learning). They are designed as situations that allow children and a guiding adult to construct situation-related knowledge in common dialogue processes and in mutual conditions. In addition, the situations focus on the activity of the persons involved, as well as the meaning of artefacts as objects of different cultural worlds. Besides relevant theoretical aspects for the development of the mathematical situations of play and exploration, exemplary analyses are introduced to clarify the conceptual aims. [ABSTRACT FROM AUTHOR]

This study tested the hypothesis that intuitions about the effect of operations, e.g., 'addition makes bigger' and 'division makes smaller', are still present in educated adults, even after years of instruction. To establish the intuitive character, we applied a reaction time methodology, grounded in dual process theories of reasoning. Educated adult participants were asked to judge the correctness of statements about the effect of operations. Their accuracy and reaction times were measured. For items where the correct answer was not in line with the assumed intuitions, more mistakes were observed; moreover, we found longer reaction times for correct responses, indicating that these intuitions interfere in participants' reasoning on these tasks, even when they provide a correct response. [ABSTRACT FROM AUTHOR]