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Example-generation tasks have been suggested as an effective way to both promote students’ learning of mathematics and assess students’ understanding of concepts. E-assessment offers the potential to use example-generation tasks with large groups of students, but there has been little research on this approach so far. Across two studies, we investigate students’ responses to a particular sequence of example-generation tasks, posed either on paper or through e-assessment. We identify a striking difference in students’ example-generation strategies and success, for e-assessment and paper-based versions of the same tasks. This suggests the use of example-generation tasks in e-assessment may not be straightforward, and we conclude by discussing the implications for teaching and research. [ABSTRACT FROM AUTHOR]

In this paper, we offer a comparative review of research on understanding and promoting students' mathematical thinking. The sources for the review are papers that were published in Educational Studies in Mathematics (ESM) during two windows of time: 1994–1998 and 2014–2018. Selection of these two time periods enables us to comment on the "state of the art" in research as well as identify changes over the past 25 years. The review is guided by an analysis of conceptualizations of "mathematical thinking" proposed in the research literature, selected curriculum documents, and international assessment programs such as the OECD's Programme for International Student Assessment (PISA). The review not only documents salient features of research studies, such as the country of origin of the authors, educational level of the participants, research aims, theoretical perspectives, and methodological approaches, but also identifies the contribution to knowledge made by this body of work as well as future research directions and opportunities. [ABSTRACT FROM AUTHOR]

In this concluding commentary, I embed the articles of the special issue "Transition from school into university mathematics: experiences across educational contexts" into the current landscape of research on secondary–tertiary transition, and discuss the advancement they made related to the synthesis published in 2008 by Gueudet. My aim is to elaborate a new synthesis across the topics of affect and the use of sociocultural perspectives that have framed the work of all contributions. For that, I focus on four major themes. First, I consider the complex relationship between affect and socio-cultural dimensions in the papers, which raises the need for theory networking in further research clarifying mutual roles of the two dimensions. Second, international diversity is only partially expressed in the collection of papers, thus should be a major topic of research in future that would provide a more comprehensive view on the transition from school to university mathematics. I thirdly discuss how the collection of papers deepens our understanding of the complexity and diversity related to the students' experience with the secondary–tertiary transition and its potential impact for teaching. Finally, I propose and justify the need for systematic design and evaluation of interventions targeting a change in students' affect related to the transition. In sum, the wide range of the significant findings in this special issue and their mutual relations add new perspectives to the research on secondary–tertiary transition and evidence a new spectrum of research directions. [ABSTRACT FROM AUTHOR]

School mathematics examination papers are typically dominated by short, structured items that fail to assess sustained reasoning or problem solving. A contributory factor to this situation is the need for student work to be marked reliably by a large number of markers of varied experience and competence. We report a study that tested an alternative approach to assessment, called comparative judgement, which may represent a superior method for assessing open-ended questions that encourage a range of unpredictable responses. An innovative problem solving examination paper was specially designed by examiners, evaluated by mathematics teachers, and administered to 750 secondary school students of varied mathematical achievement. The students' work was then assessed by mathematics education experts using comparative judgement as well as a specially designed, resource-intensive marking procedure. We report two main findings from the research. First, the examination paper writers, when freed from the traditional constraint of producing a mark scheme, designed questions that were less structured and more problem-based than is typical in current school mathematics examination papers. Second, the comparative judgement approach to assessing the student work proved successful by our measures of inter-rater reliability and validity. These findings open new avenues for how school mathematics, and indeed other areas of the curriculum, might be assessed in the future. [ABSTRACT FROM AUTHOR]

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]

Mathematicians frequently attend their peers' lectures to learn new mathematical content. The goal of this paper is to investigate what mathematicians learned from the lectures. Our research took place at a 2-week workshop on inner model theory, a topic of set theory, which was largely comprised of a series of lectures. We asked the six workshop organizers and seven conference attendees what could be learned from the lectures in the workshop, and from mathematics lectures in general. A key finding was that participants felt the motivation and road maps that were provided by the lecturers could facilitate the attendees' future individual studying of the material. We conclude by discussing how our findings inform the development of theory on how individuals can learn from lectures and suggest interesting directions for future research. [ABSTRACT FROM AUTHOR]

In this conceptual paper, the author argues that equity research in mathematics education is a genre that operates according to certain implicit ideological and rhetorical rules and assumptions—or discursive formations—that form how one can think about equity and inequity. One such rule that forms the basis of this paper is the axiom of racialized deviance, a logical tool developed by whiteness to establish its dominance and to justify physical, psychic, and epistemic violence against blackness. The author takes up whiteness and blackness related to global systems of racialization beyond the reference to white and Black people that is more typical in the United States. The author proposes three ways that the deviance axiom shows up in equity research in mathematics education: ethnomathematics, repair orientations, and success counternarratives. This issue of racialized deviance unveils equity research in mathematics education as a project whose logical foundations undermine its stated aims. The logic of global white supremacy under which school mathematics operates creates a situation where it is impossible for equity in mathematics education to exist outside because the genre requires that anyone who elects to participate accepts the axiom of racialized deviance on some level. [ABSTRACT FROM AUTHOR]

Research in mathematics education is a discursive process: It entails the analysis and production of texts, whether in the analysis of what learners say, the use of transcripts, or the publication of research reports. Much research in mathematics education is concerned with various aspects of mathematical thinking, including mathematical knowing, understanding and learning. In this paper, using ideas from discursive psychology, I examine the discursive construction of mathematical thinking in the research process. I focus, in particular, on the role of researchers' descriptions. Specifically, I examine discursive features of two well-known research papers on mathematical thinking. These features include the use of contrast structures, categorisation and the construction of facts. Based on this analysis, I argue that researchers' descriptions of learners' or researchers' behaviour and interaction make possible subsequent accounts of mathematical thinking.

The article announces a call for papers for a special issue of the journal "Educational Studies in Mathematics" that will focus on research-based interventions in mathematics classrooms that are aimed at improving students' abilities to create mathematical proofs.

The article focuses on the International Commission for Mathematical Instruction (ICMI) Study 21, which examines the relationship between language diversity and mathematics education. Topics discussed include the influence of historical multilingualism, migration, colonization, globalization, or other factors on mathematics classrooms, as well as learning through second or additional languages, minority or oppressed languages, and dominant languages.

Changes in school mathematics curricula, pedagogy and assessment, and as a consequence the pressure for changes in initial teacher preparation, are consequences both of government policy initiatives and pressure from unofficial agents such as the research community, teachers and others, though with great variation across the world. In the case of England, it has resulted in strong regulation, including inspection, of initial teacher education too. In this article, I draw on sociological theory to help in mapping the relations between official and unofficial agents and in interpreting the effects on mathematics teacher educators, in particular. The article draws in the main on the changing position in England over the last decade or so, and a case study analysis is carried out of a key official document to illustrate the application of theoretical tools provided by sociologists and others for examining the relations between agents and agencies and on their consequences.

Grasping mathematical objects as related to processes is often considered critical for mathematics understanding. Yet, the ontology of mathematical objects remains under debate. In this paper, we theoretically oppose internalist approaches that claim mental entities as the endpoints of process–object transitions and externalist approaches that stress mathematical artifacts—such as physical manipulatives and formulas—as constituting mathematical objects. We search for a view on process–object duality that overcomes the dualism of mind and body. One such approach is commognition that describes mathematical objects as discursive entities. This paper expands the nature of mathematical objects beyond discourse and highlights the role of learners' interaction with the environment by adopting ecological onto-epistemology. We develop a functional dynamic systems perspective on process–object duality in mathematics learning emphasizing embodied actions and the re-invention of artifacts' affordances. As a main result, we reconsider process–object duality as a reification of repetitive actions into a cultural artifact that consists of two steps: (1) forming a new sensory-motor coordination that brings new perception to the fore and (2) crystallizing a new artifact in a mathematical environment that captures this new perception. An empirical example from research on embodied action-based design for trigonometry illustrates our theoretical ideas. [ABSTRACT FROM AUTHOR]

Teachers' questioning plays an essential role in shaping collective argumentative discourse. This paper demonstrated that rationality dimensions in teacher questions can be assessed by adapting Habermas' three components of rationality. By coordinating Habermas' construct with Toulmin's model for argumentation, this paper investigated how two secondary mathematics teachers used rational questioning to support student participation in collective argumentation. This paper identified various ways in which two participating teachers used rational questioning to support student participation in argumentation via contributions of argument components. The results establish a theoretical connection between the use of rational questions and students' contributions of components of arguments. The results indicated that not all rational questions were associated with a component of argument, and rational questions may additionally support argumentation in general for the development of a culture of rationality. The study has implications in terms of theory and professional development of teachers. [ABSTRACT FROM AUTHOR]

Investigating the transition between educational levels is one of the main themes for the future of mathematics education. In particular, the transition from secondary school to STEM degrees is problematic for the widespread students' difficulties and significant for the implications that it has on students' futures. Knowing and understanding the past is key to imagine the future of a research field. For this reason, this paper reports a systematic review of the literature on the secondary-tertiary transition in Mathematics Education from 2008 to 2021. We constructed two corpuses: one from the proceedings of three international conferences in mathematics education (PME, ICME, and INDRUM) and the other from peer reviewed research papers and book chapters returned by the databases ERIC and Google Scholar. A clear evolution in perspectives since 2008 emerges from the analysis of the two corpuses: the research focus changed from a purely cognitive to a more holistic one, including socio-cultural and — to a lesser extent — affective issues. To this end, a variety of research methods were used, and specific theoretical models were developed in the considered papers. The analysis also highlights a worrisome trend of underrepresentation: very little research comes from large geographical areas such as South America or Africa. We argue that this gap in representation is problematic as research on secondary tertiary transition concerns also consideration of socio-cultural and contextual factors. [ABSTRACT FROM AUTHOR]

Assessment is a crucial factor in the implementation of curriculum reform. Little is known, however, on how curriculum changes can be reflected adequately in assessment, particularly if the reform concerns process skills. This issue was investigated for the case of assessing mathematical thinking in a mathematics curriculum reform for 15–18-year-old students in the Netherlands. From 2011 until 2017, these reform curricula were field tested in pilot schools, while other schools used the regular curricula. The research question is how this reform was reflected in national examination papers and in student performance on corresponding assignments. To address this question, we developed a theory-based model for mathematical thinking, analyzed pilot and regular examination papers, and carried out a quantitative and qualitative analysis of students' work on assignments that invite mathematical thinking. The results were that the pilot examination papers did address mathematical thinking to a greater degree than the regular papers, but that there was a decrease over time. Pilot school students outperformed their peers in regular schools on assignments that invite mathematical thinking by 4–5% on average and showed more diversity in problem-solving strategies. To explain the decreasing presence of mathematical thinking in examination papers, we conjecture that conservative forces within the assessment construction process may push back change. [ABSTRACT FROM AUTHOR]