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The current study compared the effects of technological environments with that of the paper-and-pencil environment on reasoning about the concept of derivatives in the context of maximum and minimum problems. The data consisted of clinical interviews conducted with three pre-service secondary mathematics teachers and a newly registered graduate student all of whom had quite a lot of mathematics courses in their repertoire. The study revealed that participants mostly depended on and were limited to analytical reasoning within paper-and-pencil environments, whereas they were able to refer to practical and creative reasoning with the help of the facilities technology environments provided. On the other hand, although participants made progress and used different reasoning types within technology environments, there were cases where they could not move beyond analytical reasoning even within the presence of technological tools. The reason for such a limitation seemed to be because of the way they treated technology as an analytical tool and they depended on 'learning from technology' instead of 'learning with technology' [Hanna, G., 1989, Proofs that prove and proofs that explain. In: G. Vernaud, J. Rogalski and M. Artigue (Eds), Proceedings of the International Group for the Psychology of Mathematics Education (Paris: ERIC), pp. 45-51]. [ABSTRACT FROM AUTHOR]

This note demonstrates multiple representations (numerical and graphical) of spreadsheet-based quadratic sequences together with prospective teachers' pencil-paper transformations of these numerical sequences into a corresponding symbolization as algebraic expressions. With the majority of prospective teachers, the experience of school mathematics is one of disaffection. They are in a teacher education programme that offers them certification to teach up to grade nine in the public schools. Their work illustrates processes, such as recognizing and extending patterns, by specializing and generalizing particular functional relationships. Insights gained from various methods used by them, together with the instructional affordances, i.e. the instructional benefits of spreadsheets, represent a curricular continuity between quadratic, numerical sequences and related algebraic expressions and suggest a possible change to the order in which the two are introduced. [ABSTRACT FROM AUTHOR]

In this article, I will discuss a collective research project that I designed for my History of Mathematics course. My students, who are by and large pre-service teachers, explored online, digital versions of 18th-century British almanacs that contained question-and-answer sections for mathematics. In a multi-stage research process, they explored the primary sources, investigated selected mathematical problems from the almanacs, conducted prosopographies of the contributors to the almanacs, and finally surveyed secondary sources. They then presented their results in pairs to their classmates. Through these presentations, as well as the prosopographies and notes they shared on our online classroom management system, the working pairs of students wrote research papers that placed their findings within the context of the research of the whole class. This collective research project allowed my students to begin focused and purposeful research within the first week of classes. Moreover, this project encouraged them to become highly engaged with their primary sources and enabled them to work as a team. This collective research project framework could be applied to a variety of groups of primary sources from the history of mathematics (such as textbooks and journals), now widely available online, to a variety of mathematics courses. [ABSTRACT FROM PUBLISHER]

The purpose of this study was to examine how pre-service mathematics teachers (PMTs) integrated a dynamic geometry environment (DGE) into their reasoning process while solving geometric locus problems. Task-based interviews based on the locus problems were conducted with eight PMTs working in pairs. The PMTs could use a computer with access to GeoGebra in addition to plain papers, pencils, graph paper, a ruler, and a compass in the interview environment. They were free to use any of them. The PMTs' reasoning was analyzed by focusing on their use of DGE as they were producing mathematical arguments during problem-solving. Toulmin's argumentation model and Hollebrands' strategies for using DGE were combined to analyze the data. The results revealed that the PMTs used DGE reactively to make claims and proactively to test or justify their claims. Their proactive use of DGE differed depending on whether they included their warrants for this use or not. [ABSTRACT FROM AUTHOR]

In recent decades, the aims and objectives of education – and therefore public discourse on the appropriate skills and attributes of mathematics teachers – have been rapidly shifting due to forces from outside the teaching profession. The forces driving change in mathematics are as diverse as the emergence of "Industry 4.0" and "STEM," new directions in transnational education policy making, and the COVID-19 pandemic. This paper contributes to a growing literature seeking to empower teachers to respond to the complexity of such multifaceted change expansively rather than defensively. It does so through the refinement and application of practical theories of educational change and approaches to building actionable practice knowledge. Specifically, this paper will argue for the use of the epistemic object as a practical focus for changes to practice chosen by the profession. This argument will be made within the framework of practice architectures offered by Kemmis and others. The paper first considers the impact of some recent disruptions on teaching and then provides a "worked example" of using mathematical proficiencies as an epistemic object able to practically support teachers to develop actionable knowledge grounded in the specifics of their own professional context. [ABSTRACT FROM AUTHOR]

In this paper, the authors discuss their experiences with ungrading at a small public university in the U.S. and a large public university in Germany. The courses described are Calculus 1 and a content course for pre-service secondary teachers of mathematics. The professors teach differently: one with lecture, the other with inquiry-based learning, and choose to use elements of ungrading in different ways. In one case, the professor lets students self-evaluate their homework, while in the other the professor uses a mix of specifications grading and ungrading for the final grade. We outline and compare our assessment approaches and discuss student performance and feedback. We also present some patterns relating to gender: in both cases, we observed that women students chose lower self-evaluations than men students. We end this paper with a general reflection on our teaching experience and our plans to use ungrading in the future. [ABSTRACT FROM AUTHOR]

The issue of social justice has been regularly addressed in many published papers in mathematics education research, particularly after 2000, when the discipline took a more explicit socio-political turn. However, there does not appear to be a consensus as to what the term designates and includes. This paper is a systematic review of the empirical studies published from 2000 until the middle of 2019 that explicitly address social justice from the perspective of practising mathematics teachers and/or teaching. More specifically, we examine (a) how social justice is conceptualised in the identified studies, (b) what specific issues are investigated and methodological approaches employed to do so, and (c) the main key points that arise from their empirical findings. Implications and suggestions of how the field can move forward are discussed at the end. [ABSTRACT FROM AUTHOR]

The research question studied in this paper is how teachers' task designing can be enhanced in professional development. We show that this can be done by scaffolding. Scaffolding is used in problem solving and we apply it by considering designing a task as a problem. In the paper, we describe a professional development of four teachers led by a mathematics educator. The professional development consisted of 10 meetings. The teachers were first exposed to a well-designed task in geometry as learners and then were asked to design new geometry tasks for their students. The mathematics educator helped them by supplying scaffolds such as modelling, reflection, articulation and worked examples. The data consisted of video-recordings of the workshops and a semi-structured interview with each of the teachers at the end of the project. The data analysis shows how the use of particular scaffolds was helpful while preserving the teachers' autonomy as task designers. [ABSTRACT FROM AUTHOR]

The paper addresses the potential relationships between shared authority in mathematics classrooms and students' mathematical reasoning. Even though tensions and challenges related to shared authority are explicated in the literature, there are few examples of how these issues play out in mathematics teaching. We investigate the case of a mathematics teacher attempting to share authority as well as applying several moves recognized as supporting meaningful student learning. Data has been collected in a fourth-grade Norwegian classroom and is analyzed by means of open coding, inspired by literature. We identify the moves used by the teacher, and we rank these moves along two dimensions: (1) their potential to support mathematical reasoning and (2) their potential for sharing authority. From this, we uncover how a teacher's work of orchestrating mathematical discussions involves moves in all four quadrants, and we discuss how the interplay of moves affects the authority structures and the collaborative reasoning in the classroom. [ABSTRACT FROM AUTHOR]

Using a theoretical framework of policy assemblage, we analyse current primary mathematics teacher professional development in England, in the context of a transnational policy of mastery in mathematics influenced by East Asian practices. As well as the increased discourse of marketisation, and school and teacher autonomy, there has also been a paradoxical process of greater state influence over the content and form of professional learning. This paper maps the mathematics mastery market to show how marketisation and competition form a mirage that masks state-market assemblage. An analysis of these assemblages illuminates the state's role in fostering a market whilst also operating as an actor in this market, in this case in mastery professional development. Within the mastery market, tensions arise between the phenomena of replication and isomorphism and differentiation of 'offers' that develop affinity groups and networks. Thus, we extend previous descriptions of the hierarchy, markets, and networks, and the roles of state funded actors within teacher professional development by identifying the importance of multiplicity of logics, assemblage as a process of labour, and the dynamic nature of relationships and activity. Resources to support teacher professional learning are mobilised in competitive processes with apparent choice hiding state direction. [ABSTRACT FROM AUTHOR]

This paper examines the extent to which teacher factors of the dynamic model of educational effectiveness can explain variation in student achievement in mathematics. It also searches for the extent to which any of these factors matters more for academically resilient students than for all the other low-socioeconomic-status students. Participants were all teachers (N = 66) of 14 schools in socioeconomically disadvantaged areas who teach mathematics to students of Grades 4–6 (N = 904). Teacher factors were measured through a student questionnaire, whereas mathematics achievement at the beginning and the end of the school year was measured through written tests. Student background characteristics were measured through a student questionnaire. Information on parents' occupational status was also collected. Multilevel modelling analysis revealed that all teacher factors explain variation in mathematics achievement. Differential effects for all factors but modelling and assessment were identified. Implications of findings are discussed. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses articles in the issue on topics including relationship between research and scholarship; mathematics educators; and challenges of mathematics teaching at university level.

Teacher quality in primary schools in South Africa is a serious concern, and how best to prepare teachers in initial teacher education—with regard to mathematics—remains an open and vexing question. There is a confluence of challenges facing the mathematics education community in South Africa: poor conceptual understanding of mathematics amongst teachers; poor attainment in Primary Teacher Education mathematics tests at both first and fourth year levels; and few initial teacher education programmes having evidence of improving knowledge for teaching mathematics. In addition, few lecturers in initial teacher education make explicit the theoretical tenets informing their course design for mathematics. In response to the latter challenge, this paper makes explicit the design choices made in the Emergent Number Sense first year mathematics module in Bachelor of Education degrees, used across six universities in South Africa. It then theorises the choice to commence the B.Ed mathematics programmes with two pathways into number knowledge: (1) a counting pathway, making use of discrete objects or events which can be quantified by counting in ones; and (2) a measurement pathway, making use of continuous extents which can be quantified by introducing a unit of measurement. Each has a distinct metaphor, strategy for the reification of the 10 and supporting representation. This offers the lecturers using the course in their own design trials, and initial teacher educators beyond the Maths4Primary Teachers collective, a conceptual framework for this design choice, which can now be critiqued and further improved. [ABSTRACT FROM AUTHOR]

Lesson study, a popular method of professional development in which instructors collaborate to critique and improve a lesson, can be used for curriculum development. This paper describes an implementation of lesson study that went through two iterations across different, related, contexts: an undergraduate mathematics content course for secondary preservice teachers and a professional development session with practicing middle and secondary teachers. We describe the ways in which the lesson study process helped us develop curriculum for advanced undergraduate courses for future teachers and provide our insights into the benefits and challenges of this approach. [ABSTRACT FROM AUTHOR]

This study critically examines the mathematics knowledge of pre-service post-primary mathematics teachers (N = 85) on commencing their Professional Master of Education (Level 9) initial teacher education (ITE) programme across four institutions in Ireland. Given the nature of a consecutive approach to mathematics teacher education, pre-service teachers enter their ITE programme from a variety of undergraduate degree backgrounds and it is largely accepted that their mathematical content knowledge does not change during their teacher qualification programme. This study utilises a paper-and-pencil test to assess participants' cognitive and conceptual proficiency with curriculum-aligned mathematical content. Between group comparisons in relation to participants' undergraduate studies and cognitive and conceptual proficiency are also examined. The data suggest that pre-service teachers demonstrate a strong proficiency with Junior Cycle curriculum-aligned content and poor proficiency with Senior Cycle content, irrespective of the curriculum strand. In addition, significant mean differences exist between participants who had undertaken undergraduate degree studies in physics and mathematics in comparison to other degree programmes. Such investigations are essential given the increased focused on developing highly qualified teachers and policy revisions on ITE programmes. This research alerts us to issues within ITE programmes that may be addressed prior to mathematics teachers' induction into the profession. [ABSTRACT FROM AUTHOR]

We provide an introduction to the special issue on Teaching Inquiry, through its motivation and themes. We focus here on Part I: Illuminating Inquiry. [ABSTRACT FROM PUBLISHER]

This article shares a paper presented as the keynote for the Terry L. Wood Memorial Conference that was held virtually on May 20, 2022. This paper starts with a reference to the project, The Coordination of a Psychological and Sociological Perspective, that was funded by the Spencer Foundation. The results of the research in this project are published in the book, The Emergence of Mathematical Meaning, edited by Cobb and Bauersfeld (1995). [ABSTRACT FROM AUTHOR]

Classroom management is an emotionally demanding task for mathematics teachers, especially if students exhibit frequent discipline problems. Intense classroom conflicts can result in persistent latent emotional dispositions, such as fear or anger, that teachers are not directly aware of but that have a strong influence on their classroom management. However, little is known about the relationship between mathematics teachers' latent emotions and their classroom management strategies. This paper reports on findings from an exploratory, video-based single case study in an urban secondary school in Germany. One mathematics double lesson (95 minutes in total) was videotaped to conduct a depth-hermeneutical analysis of identified classroom management strategies and the corresponding latent teacher emotions. The results suggest that mathematics teachers use classroom management strategies not only to establish orderly lessons but also to regulate intense latent emotions that arise during classroom teaching. [ABSTRACT FROM AUTHOR]

This paper set out to contribute to mathematics education research by elaborating on a methodology developed during a study, trying to understand, view and follow shifts in prospective teachers' discursive patterns. The methodology aims to illustrate and describe how prospective teachers adapt to the context of teaching through a flexible process. This flexible process is then described in the result as a narrative. It is argued that the methodology can be used in relation to different theoretical directions, such as research about beliefs, knowledge, or identity. Another contribution is that the methodology presented gives insights into bridging the gap between different analytical levels, micro and macro. With a theoretical foundation in 'Cultural Worlds' [Holland, D., Skinner, D., Lachicotte, W., & Cain, C. (1998). Identity and agency in cultural worlds. Harvard University Press.] the Social Semiotic approach of Systemic Functional Linguistics, SFL [Halliday, M., & Hasan, R. (1989). Language, context, and text: Aspects of language in a social-semiotic perspective (2nd ed.). Oxford University Press] is used as a methodological tool. SFL offers a toolkit that allows the analysis of meaning at the clause level to uncover how and why a speaker produces a particular wording rather than any other in a specific social practice. The paper aims to illustrate and describe how to go beyond findings in the micro-analysis and then present the result as a narrative case. [ABSTRACT FROM AUTHOR]

This paper captures and reports on mathematics pre-service teacher (PST) voices. Mathematics PSTs, in a tertiary mathematics secondary curriculum teaching subject assessment, were asked to perform a small-scale literature review on an issue they identified as important in mathematics teaching. The assessment, written as an article, required literature-based recommendations, a reflection on how this would impact the PST's future teaching and guidance for all mathematics teachers. The article was aimed for publication by the Mathematics Association of Victoria—a state-based mathematics professional association in Australia. PSTs were advised that articles would potentially be published, and their voice would reach practicing mathematics teachers. The published articles, which capture pre-career mathematics teacher voices were analysed for insight into what four PSTs said of their future teaching to a mathematics teacher audience. The professional teacher standards were recognised to influence comments given the strong emphasis of standards within initial teacher education courses. Findings speak to what mathematics PSTs expect of their future teaching role prior to being in-service. The paper contributes a snapshot of early established professional voices in a discipline where there is currently a shortage and highlights the messages that emerged. [ABSTRACT FROM AUTHOR]

This paper argues that the practice of teaching and learning is being re-defined as technology enables a re-imagining of what can be taught, and how it could be taught. In Namibia, demands on mathematics teachers to incorporate technology use into their teaching practice are often mismatched with the curriculum. This theoretical paper proposes meaningful mathematics teaching via technology, instead of a mere response to societal adoption of digital tools. The concept of meaningful teaching is viewed through a Vygotskian lens. Kilpatrick et al.'s five Strands of Mathematical Proficiency inform the interpretation of goals for teaching mathematics with technology. We discuss the gaps in current models for professional development for teaching with technology when we take the Namibian cultural historical context into consideration. Activity Theory is used to conceptualise a two-triangle embedded activity system of teachers and professional developers, and to reflect on nodal interactions. We conclude by proposing some principles for the design of professional development programmes that aim to support mathematics teachers in using technology in their teaching. The principles may be useful for professional development in other developing countries with uneven access to both technology and reformed mathematics curricula. [ABSTRACT FROM AUTHOR]

This paper contributes to research in responsive teaching in a context of collaborative discussion using video stimulated recall (VSR) techniques. The aim was to gain deeper understanding of the kinds of teachers' reflective awareness that prompts changes (or lack of change) in responsive primary mathematics teaching. Using a case study methodology, I analysed the VSR interviews of two teachers who demonstrated different patterns of changes in responsive teaching. The findings revealed two distinct and complementary forms of evidence of states of awareness and reflections that support change in responsive teaching practices: (a) teachers acknowledging limitations of their practice; and (b) teachers expanding repertoires of tasks and example spaces. These two forms of evidence provide insights into ways of supporting primary mathematics teaching in the context of VSR techniques. The implication of these findings is that for effective use of VSR interviews, attention should be geared towards getting a teacher to acknowledge the limitations of her practice, and through reflection-oriented questions to encourage the teacher to expand task and example space to respond to the limitations noted within the teacher's practice. [ABSTRACT FROM AUTHOR]

The field of mathematics education has seen an increase in research focused on the concept of identity, with many researchers focusing on the role of teacher pedagogies in shaping learners' identities and their participation in and engagement with mathematics. In this paper, the actual and narrated practices of two teachers, which incorporate teachers' pedagogical approaches and social relationships with learners, are analysed in relation to how they provided opportunities for the construction of learner identities. The paper draws on data that were collected over two years in the form of videotaped lessons, field notes and audiotaped semi-structured interviews with teachers and learners. Data were analysed using qualitative data analysis techniques. The analysis suggests a relationship between the teachers' actual and narrated practices, with the teachers' practices influencing the kinds of identities constructed by learners in their classrooms, in terms of learners' enjoyment of learning mathematics and their willingness to participate in and become fully fledged members of their classroom community. [ABSTRACT FROM AUTHOR]

Research shows that teachers influence students' attitudes towards; performance in; and perceptions of a subject. Hence, the need to improve the teaching and learning of many curricular subjects has been well documented for many years. This paper focusses on efforts made to develop competence among out-of-field teachers of mathematics and evaluates the impact of one component of a continuous professional development (CPD) programme on teachers' self-efficacy and self-reported teaching styles. As part of this CPD programme, teachers engaged in a series of subject-specific pedagogy workshops and while classroom observations were not feasible they did complete pre- and post-workshop questionnaires to determine the impact that these workshops had on their mathematics teaching efficacy and their reported approach to teaching, both of which researchers consider to be key to effective teaching. Analysis of the quantitative data showed that the workshops led to statistically significant improvements in mathematics teaching efficacy among participants, while analysis of the qualitative data highlighted a shift from procedural or teacher-led approaches to more student-centred approaches that focussed on developing understanding. As such the programme was deemed to have a positive effect on the effectiveness of these teachers. [ABSTRACT FROM AUTHOR]

This paper focuses on the development of a model of research and professional development which aims to bring about transformations in classroom practice in situations that have previously proved resistant to change. We explore reasons why conventional models have failed to address one such situation, the continuing predominance of teacher-centred pedagogies in mathematics classrooms. We draw on findings from the Visible Mathematics Pedagogy research project to highlight how a critical model of participatory action research can be refined to enhance its potential to bring about changes in classroom practice. We report on research tools and processes that were developed, distinct from those commonly used in research, including the organisation of research team meetings around participatory principles, the active involvement of teachers in designing and employing data collection tools, and in generating protocols associated with video-stimulated reflection. We demonstrate how these research tools and processes enhanced collaboration and teacher agency, the trustworthiness of the research findings and teachers' critical reflection on existing practice. We argue that our refined model of participatory action research can inform and support teachers and researchers wishing to transform classroom practice, especially in situations analogous to many mathematics classrooms, in which conventional models have had limited impact. [ABSTRACT FROM AUTHOR]

Mathematics teacher candidates enter teacher education with knowledge that could support or limit their learning. It is therefore important to gain insights of this knowledge to inform teacher education. This paper offers such insights for prospective mathematics teachers' initial knowledge of problem solving (PS) for teaching at the beginning of their teacher education programme. It reports on a study that investigated three categories of problem-solving knowledge for teaching: problem characterization, the PS process, and PS disposition. Participants were 109 prospective primary teachers at a university in Spain. Data sources were questionnaires designed for the study to explore the initial knowledge held by the participants for three categories of problem-solving knowledge. Findings indicated that the participants' knowledge was stronger regarding the PS process and disposition than for problem characterization but had limitations that needed to be addressed in their teacher preparation programme. [ABSTRACT FROM AUTHOR]

This paper argues that there is a gap in the research on teaching and learning mathematics, and thus a need for research into effective teaching practices. From a selective review of literature, reasons are examined as to why less emphasis appears to have been placed on generating knowledge about teaching and effective mathematical teaching practices than on mathematics teachers and their knowledge. Possible reasons for this lack of attention to teaching include assumptions that, as researchers, we already know what effective teaching is or that if teachers embrace certain principles about teaching or learning, then effective teaching will necessarily ensue. Arguing that both of these positions neglect to address important aspects of developing knowledge about effective teaching, the paper raises a number of questions that research might address in moving the balance more towards examining the actual practices that might characterise effective teaching. [ABSTRACT FROM AUTHOR]

This study aims to analyse teachers' understanding of realistic mathematics education (RME) through a blended workshop on designing an RME-based learning trajectory. Data was collected via online pre-test and post-test, involving mathematics teachers of junior high schools in Banda Aceh, Indonesia. The tests were accompanied by interviews, chats on WhatsApp groups, and video recording. A descriptive analysis of the various sources of data indicated that the teachers made varying shifts in understanding the principles of RME. The teachers slightly altered their understanding of the intertwinement and level principles. However, their comprehension of the reality principle remained the same; they considered real problems as daily life problems only, even though some teachers had already written the meaning of real problems as problems that students can imagine. They also have already possessed a satisfactory understanding of the activity principle before the workshop. Moreover, nearly half of the teachers showed a good understanding of RME-based learning trajectories. The findings reported that teachers benefited from the blended workshop and obtained knowledge of the RME-based learning trajectory after participation. Finally, the implications for further research were discussed in this paper. [ABSTRACT FROM AUTHOR]

This paper explores the specialized knowledge mobilized by a mathematics teacher in the selection and use of examples for teaching sequences. Taking an experimental case study approach, we analyse the examples deployed in a series of third-year secondary level lessons on sequences and identify the different knowledge subdomains activated according to the mathematics teachers' specialized knowledge analytical model. We will analyse active and passive examples, pointing out the mathematical entity that is being exemplified and the aspect of this entity which is being emphasized by the example. The results identify the different subdomains and categories which are drawn on in the selection and use of examples, along with the various interconnections across knowledge subdomains which interact in the process. [ABSTRACT FROM AUTHOR]

In this paper, we examine the relationships between teachers' subject matter preparation and experience in teaching and their performance on an instrument measuring mathematical knowledge for teaching Algebra 1. We administered the same instrument to two different samples of teachers−high school practicing teachers and community college faculty − who teach the same algebra content in different levels of institutions, and we compared the performance of the two different samples and the relationships between the measured knowledge and their educational and teaching background across the samples. The comparison suggested that the community college faculty possess a higher level of mathematical knowledge for teaching Algebra 1 than high school teachers. The subsequent analyses using the Multiple Indicator Multiple Causes (MIMIC) models based on our hypothesis on the factors contributing to the differences in the knowledge between the two teacher samples suggest that experience teaching advanced algebra courses has positive effects on the mathematical knowledge for teaching Algebra 1 in both groups. Highlighting the positive effect of algebra-based teaching experience on test performance, we discuss the implications of the impact of subject specific experience in teaching on teachers' mathematical content knowledge for teaching. [ABSTRACT FROM AUTHOR]

Mathematics pre-service teachers (PSTs) need opportunities to learn best practices in teaching mathematics, e.g., productive struggle. Productive struggle happens when students work through challenging problems that are not straightforward. This paper describes mathematics PSTs' engagement with productive struggle in a mathematics methods course. PSTs critiqued high cognitive demand tasks, planned and implemented them, and reflected on their experience focusing on productive struggle. Findings have implications for mathematics teacher preparation. [ABSTRACT FROM AUTHOR]

This article aims to delve into the meaning of school mathematical concepts by their semantic analysis. Concretely, this paper aimed primarily to describe and characterize the meaning of derivative of a function at a point expressed by mathematics pre-service teachers. In order to achieve this goal, we use a semantic framework, in which the meaning is composed of: (a) conceptual structure, (b) representation systems, and (c) sense and usage. This qualitative, descriptive study analysed the replies of 37 pre-service teachers to questions involving the definition, requirements, and structural concept of derivatives. It also explores the sense and usage attributed by participants to this mathematical concept. At least five profiles of meanings for derivatives could be constructed from the results. The most prominent findings included the prevalence of the geometric interpretation of the concept and participants' failure to mention elements and requisites essential to the definition of derivatives. [ABSTRACT FROM AUTHOR]

Although we know that asking questions is an essential aspect of online tutoring, there is limited research on this topic. The aim of this paper was to identify commonly used direct question types and explore the effects of using these question types on conversation intensity, approach to tutoring, perceived satisfaction and perceived learning. The research setting was individual online synchronous tutoring in mathematics. The empirical data was based on 13,317 logged conversations and a questionnaire. The tutors used a mix of open, more student-centred questions, and closed, more teacher-centred questions. In contrast to previous research, this study provides a more positive account indicating that it is indeed possible to train tutors to focus on asking questions, rather than delivering content. Frequent use of many of the question types contributed to increased conversation intensity. However, there were few question types that were associated with statistically significant effects on perceived satisfaction or learning. There are no silver bullet question types that by themselves led to positive effects on perceived satisfaction and learning. The question types could be used by teachers and teacher students when reflecting on what types of questions they are asking, and what kind of questions they could be asking. [ABSTRACT FROM AUTHOR]

In this article, we explore Terry Wood's participation in the Purdue Problem-Centered Mathematics Curriculum Project, along with the rich and enduring personal and professional friendships that she built with the classroom teachers who were so important to the project. We highlight connections between these working relationships and the research publications that resulted from the project. The contributions of classroom teachers, Graceann Merkel and Janell Uerkwitz are evident in several of the papers published by Terry and the other researchers, including Erna Yackel, Paul Cobb and others. The testimonies and personal stories that each of these teachers shared during and following the May 2021 Terry Wood Memorial Event provide an enhanced picture of her contributions to their teaching practice and professional lives. As such, we gain insights into the reciprocal relationships and learning that occurs between education researchers and their partner classroom teachers. [ABSTRACT FROM AUTHOR]

This paper describes a course designed to introduce students to mathematical thinking and a variety of lower level mathematics topics using baseball while satisfying the goals of quantitative reasoning. We give suggestions for sources, topics, techniques, and examples so any mathematics teacher can design such a course to fit their needs. The course assumes no previous college level mathematics and includes statistics, linear functions, modeling, and simulation. [ABSTRACT FROM AUTHOR]

Providing students with the necessary skills to apply mathematical knowledge in real-life situations through mathematical modelling is a common goal of contemporary mathematics curricula. As such, it is important that prospective mathematics teachers develop the ability to design learning environments that serve this purpose in their future teaching. This paper presents an activity presented as part of a course that, among other outcomes, aimed to establish awareness in mathematics teacher candidates of the potential use of computers in mathematical modelling. The activity included an experimental investigation of Buffon's needle problem. The steps used to solve the problem using a GeoGebra environment are described in this article. [ABSTRACT FROM AUTHOR]

This paper reports on a study that explored the subject and pedagogical content knowledge displayed by high school mathematics teachers in the Khomas education region in Namibia. The study was based on a quantitative approach using a survey design. A stratified random sampling method was used to select the participants in all the four school circuits in the region. The study population consisted of 79 Grade 12 mathematics teachers from public schools. A sample of 40 mathematics teachers took part in the study, completed a questionnaire and wrote a test. A Microsoft Excel spreadsheet was used to sort the data and produce graphs and tables. A paired t-test was also used to determine if a significant difference existed between the participants' subject content knowledge (mathematical knowledge in our context, (MCK) and pedagogical content knowledge (PCK). The findings revealed that the participants had some deficiencies on MCK topics such as quadratic equations, angles properties and numbers. They also portrayed weak PCK on fractions, simultaneous and linear equations. This shows that a significant difference exists between the teachers' MCK and PCK with tcalculated = 11.092 greater than the tcritical (between 2.712 and 2.704) at a significance level, α = 0.01 but also that the participants' MCK and PCK were moderately and positively correlated (r = 0.681, p < 0.01). This study recommends that mathematics teachers in the Khomas region be provided frequently with in-service training to strengthen their shortcomings regarding MCK and PCK (knowledge of mathematics tasks, knowledge of learners' misconceptions and difficulties, and knowledge of mathematics instructions). We also recommend further studies to determine how high school mathematics teachers' knowledge can impact learners' academic performance in other education regions in Namibia. [ABSTRACT FROM AUTHOR]

Improving mathematical skills is a priority in England, and a series of policy levers and government change projects have focused on improving mathematical outcomes in further education (FE) in recent years. Yet little is known about the mathematics teacher workforce that supports these students on vocational and technical programmes. This paper addresses this knowledge gap by examining important features of the mathematics teacher workforce in colleges and the implications for recruitment, initial training and ongoing professional development. We report findings from a national survey targeted at all mathematics teachers in around one-sixth (N = 31) of England's general FE colleges. Teachers have transitioned into FE from three main areas: another career, curriculum area, or educational context. We discuss the varied assets and training needs of these three subgroups and argue that the mathematics teacher cohort in FE should be seen as distinct from that in either primary or secondary education. We highlight the bimodal distribution of mathematics qualifications amongst this workforce; those having level 2 mathematics qualifications being more likely to be teaching functional skills mathematics courses than GCSEs. The rapid expansion of the mathematics teacher workforce that followed the changes to the condition of funding in 2014 has come disproportionately from teachers who were previously working in schools. This, together with a trend of funnelling increasing numbers of FE students into academic mathematics rather than functional skills courses, raises important questions about the nature of mathematical education for learners on vocational and technical programmes, and the teachers thereof. [ABSTRACT FROM AUTHOR]

This paper describes a research project implemented in a course of Real Analysis II. The aim of this project is to analyse students' comprehension of the limiting behaviour of a function from R2 to R at a point focusing on the formal definitions. Alternative definitions and other statements are discussed, some of which meet both sufficient and necessary conditions, while others meet only sufficient conditions; some involve neighbourhoods and others 'paths'. Emphasis is placed on the criteria according to which students choose one of the given definitions, equivalence or not of these and their overall influence on the concept images formed by the students for the limit concept. In particular, the paper discusses how students come to a conclusion about the existence of the limit of a function in R2 through the consideration of contour curves. We also present and analyse data from a written test as well as from the conducted interviews. [ABSTRACT FROM AUTHOR]

In this response paper to Hoyles' contribution "Transforming the mathematical practices of learners and teachers through digital technology" focuses on three points. First, more knowledge is needed on why teaching and learning practices should transform, into what will they transform, and by what or by whom will they be transformed. Second, a suggestion is made for a more specific taxonomy on the didactical functionality of digital tools in mathematics education. Third, a plea is made for a future research agenda that addresses the ways in which activities with digital tools mediate the learning of mathematics in a fruitful way. This includes the interpretation and grading of online student work through intelligent mathematical software, and the notion of embodiment, as to do justice to the bodily experiences in which mathematical experiences are rooted. [ABSTRACT FROM AUTHOR]

This paper makes an important and original contribution to the updating of methodological approaches to research syntheses. We analysed all 813 Proceedings of the British Society for Research into Learning Mathematics from 2003 to 2018, first using a quantitative corpus-survey and qualitative thematic coding and, again, independently, using topic modelling. We found strong convergence between findings from the different methods. We compare our findings to those from an earlier Proceedings review (1995–2002) and to a recent review of the corpus of publications in the Journal for Research in Mathematics Education and Educational Studies in Mathematics, as well as to a review by the European Society for Research into Learning Mathematics and several other reviews. We found considerable similarity between the issues discussed, and similar trends over time. We conclude that the efficiency of topic modelling makes it a powerful option to include among a range of methodological approaches to research review. [ABSTRACT FROM AUTHOR]

The present paper aims at investigating the relationship between students' attitudes toward online homework use and mathematics anxiety among secondary school students. In this study, a model has been proposed by integrating the technology acceptance model (TAM) with mathematics anxiety theory. Three hundred and forty-five secondary school students participated in the instrument of the study that included 20-item based on a 5-point Likert scale. The subsequent analysis using Partial Least Squares Structural Equation Modeling (PLS-SEM) supported the negative relationship between attitude toward an online homework (OHW) tool and mathematics anxiety. The results revealed that perceived usefulness and perceived ease of use are predictors of attitude toward the use of OHW. This study maximized the capability of acceptance of the OHW tool in mathematics learning. The findings provided by the study will encourage mathematics educators to implement mathematics OHW tools in the learning process. [ABSTRACT FROM AUTHOR]

The paper evaluates math performance at four high-need middle schools during a four-year intervention, which was designed to help math teachers diagnose students' areas of need and to design lesson plans responsive to those needs. Before the intervention began, the researchers pre-selected four comparison schools by matching based on achievement and also on demographics. A difference-in-difference analysis finds a significant increase of about 0.11 standard deviation in test scores per year for students in the program schools. Supplementary event study and synthetic control analyses to detect year-by-year effects lack precision but are weakly suggestive of a smaller impact in year 1 than later years. A cost analysis considers the affordability of extending similar programs. [ABSTRACT FROM AUTHOR]