Search

Work in teacher noticing has captured to what extent teachers notice students' thinking on paper and pencil tasks and technology tasks, yet no one study has considered how the same group of teachers notices across task types. This study used Jacobs et al.'s (Journal for Research in Mathematics Education, 2010, 41(2), pp: 169–202.) professional noticing of students' thinking framework to guide the design and analysis of prospective secondary mathematics teachers' (PSMTs) noticing of high school students' thinking on two geometry tasks: a paper and pencil task and a technology task. High school students' written work and a video clip were shared as the artifacts from which to notice for each task. PSMTs responded to a set of noticing prompts to capture how they were attending, interpreting, and deciding to respond to students' thinking for each task. Their written responses to these questions were then open coded for each noticing component and codes from each task were compared to reveal any differences in the content of PSMTs' noticing across task types. Results revealed differences between tasks for each component skill of noticing. Implications of these findings for mathematics teacher educators and future research are discussed. [ABSTRACT FROM AUTHOR]

This article focuses on initial teacher education, in the development of teaching study tasks, especially related to the end-of-course work. The research question is: Which reasons support the mathematics undergraduates' choices for the theme and development of the end-of-course work? In connection with the problem, this research analyzes the reasons that justify undergraduates' choices in the production of that work. The text is based on historical-cultural theory, with emphasis on the psychological and didactic principles of activity theory, on the development of students' reasons and meanings when faced with the social meanings of initial education. The methodology is developed through a formative pedagogical intervention carried out with two mathematics undergraduate students. The data production has an empirical reference in the transcripts of interviews and moments of collective advice for the development of academic work materialized in article format. The analysis is carried out from the perspective of historical-dialectical materialism, which demonstrates results through the reasons that lead students to create meanings of their experiences in the development of initial training, especially during the training processes throughout graduation. In addition to these cases, the persuasion of peers was also observed, demonstrating relationships on the theoretical-methodological/ideological orientations in their perceptions about the pedagogical activity in the interventions carried out. [ABSTRACT FROM AUTHOR]

The article is based on the lecture ‘Mathematics teacher training from the perspective of STEM – a particular case’ given by its author at the ATCM 2023 conference and is an extension of a related paper that was published in the conference proceedings. It further develops the idea that the task of teacher training schools is to create a suitable environment for the provision of education, impulses for the development of the necessary knowledge and skills, as well as to support these. It provides a detailed description of specific creative activities for future teachers, which develop their awareness of the applicability of mathematics in solving real problems and knowledge of its overlap with technology. It is based on historical problems and their context, as presented in the conference paper. Emphasis is placed on the use of computers, especially dynamic geometry software GeoGebra, to model the geometric nature of given problems and for their effective solution. [ABSTRACT FROM AUTHOR]

This research addresses the issue of how to support students' representational fluency—the ability to create, move within, translate across, and derive meaning from external representations of mathematical ideas. The context of solving linear equations in a combined computer algebra system (CAS) and paper‐and‐pencil classroom environment is targeted as a rich and pressing context to study this issue. We report results of a collaborative teaching experiment in which we designed for and tested a functions approach to solving equations with ninth‐grade algebra students, and link to results of semi‐structured interviews with students before and after the experiment. Results of analyzing the five‐week experiment include instructional supports for students' representational fluency in solving linear equations: (a) sequencing the use of graphs, tables, and CAS feedback prior to formal symbolic transpositions, (b) connecting solutions to equations across representations, and (c) encouraging understanding of equations as equivalence relations that are sometimes, always, or never true. While some students' change in sophistication of representational fluency helps substantiate the productive nature of these supports, other students' persistent struggles raise questions of how to address the diverse needs of learners in complex learning environments involving multiple tool‐based representations. [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]

In this paper we report on a review of papers written by teachers aimed at knowing more about teachers’ perceptions of the current situation of classroom assessment in primary mathematics education in China. The review is based on 266 papers included in the China National Knowledge Infrastructure database. We found that the teacher-authors reflected various aspects of their classroom assessment practice, including the purpose of assessment, the content of it, the person who is the assessor, the assessment methods that are used, and the feedback that is provided. Most attention was paid to feedback; it seems many teacher-authors considered classroom assessment to be equivalent to feedback. In general, the conceived classroom assessment practice as described in the papers echoed well nearly all aspects that are advocated in the Chinese mathematics curriculum standards. The only aspect that was scarcely discussed in the papers was the use of assessment results to adapt and improve instruction. [ABSTRACT FROM AUTHOR]

Teacher beliefs and practices related to them could provide varying opportunities for students to develop their agency related to learning math. The aim of the current paper is to explore how different math teacher beliefs (concerning the nature of mathematics, constructivist beliefs, and self-efficacy) relate to different dimensions of student agency in primary education. A two-level multilevel model was analyzed to find out to what extent selected teacher beliefs are associated with student math competence and agency dimensions. The study was conducted in Estonia and data from 3rd and 4th grade students (N = 1557) and their teachers (N = 121) was included in the analysis. The results showed that teacher self-efficacy beliefs, constructivist beliefs, and static views on the nature of mathematics were related to students' agency dimensions. Possible explanations and directions for further studies are discussed. [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 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]

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]

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]

This study was an investigation of the use of manipulative materials in the mathematics classroom. The researcher guided students to create paper triangles, which were then used as a manipulative to calculate the sum of the interior angles of a triangle. On pre- and post-measures of quantitative data, although the data indicated a positive correlation on attitudes toward math, there was no statistical difference on an 11-item assessment composed of public-released questions taken from the National Assessment of Educational Progress (NAEP) exam. Mixed methods data collection and analysis found that students enjoyed the lesson and wanted more opportunities to engage with manipulative materials. Implications include the need for mathematics teachers to deploy novel approaches as instructional strategies. [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 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]

In the 1610s and 1620s, a new computational technology took hold in England: printed mathematical tables for compound interest and discounting ("present value") problems. Historians of finance and accounting have long recognized these paper tools as predecessors of essential modern techniques like "discounted cash flow." Yet the history of these tables remains hazy. What did early seventeenth-century users do with them? Who used them? Why did they appear when they did? This article turns to one obscure but influential text—Ambrose Acroyd's Tables of Leasses and Interest (1628)—as a guide to these questions. Two key facts emerge. First, despite the prominence of similar calculations in financial applications today, these early tables were not confined to England's nascent financial sector. Rather, their foremost use related to agricultural property, specifically in assessing certain payments ("fines") landlords charged tenants for farm leases. Second, among the leading "early adopters" were institutions of the Church of England. Amidst the inflation of the early modern "price revolution," bishops, cathedrals, and colleges confronted a complex of economic, political, and social pressures. Mathematical tables like Acroyd's emerged out of long-running conflicts between church landlords and tenants over how to determine just and reasonable fines on church lands. Discounting tables were thus not tools of instrumental rationality evincing a new capitalist mentality, but tools of social accommodation and products of the era's "economy of obligation." This early modern tale offers a vivid example of how and why one community turned to a mathematical algorithm to resolve conflicts about fairness. [ABSTRACT FROM AUTHOR]

This paper is theoretically driven by doctoral research data. The corresponding doctoral research involved fifteen participants who live in Brazil: immigrants and parents of immigrant students from Haiti and Venezuela and mathematics teachers in schools with immigrant students in São Paulo (Brazil). The research aims to consider socially and racially structured exclusions, to discuss perspectives and approaches, and to challenge mathematics education with immigrant students towards inclusive actions. Thinking about what inclusion and inclusive mathematics education with immigrant students could mean goes toward glimpsing the roots of what can obstruct such a process, which means taking the path towards unwrapping the processes of exclusion and violence against the immigrant population. Immigrants’ and teachers’ voices will be heard in this article to support discussions about the issues around inclusive mathematics education. I present situations that illustrate that microexclusions may accompany the inclusive context in subtle practices. Microexclusions tend to isolate people in a given environment, even if that environment is considered inclusive. This paper aims to discuss a crucial situation: the barriers to including immigrant students have to do with various levels of oppressive social structures. I identify four types of microexclusion related to immigrants having to do with exoticization, misleading identification, second-class citizen treatment, assimilation, and misprise. [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]

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]

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]

The article provide a range of conceptual approaches to the development of fraction-based understanding including paper folding, the use of number lines and using multiple fraction representations to build a foundation of success in mathematics. Topics include earliest experiences students have when learning fractions are hands-on activities involving paper folding and the coloring of 2D shapes; and useful to work with the length model first and then transition students to the number line.

Mathematics Anxiety (MA) is an increasing challenge for mathematics educators and is a barrier to mathematical learning. Through reflection on the implementation of a lesson sequence designed to elicit regular use of explicit metacognitive questions (EMQ’s), this paper explores the impact of the incorporation of self-regulated learning (SRL) strategies on MA within a Year 7 classroom in Australia. Findings have shown that when students become ‘stuck,’ the use of the explicit metacognitive questions can help overcome a range of challenges including the reduction of MA. The use of EMQ’s within this paper explores an example of the kind of lesson design that lends itself to the explicit metacognitive questioning strategy. [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]

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]

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]

National assessments can be used to explore the strictness of teachers in grading students by comparing student grades to their scores on standardised tests. Several factors influence teacher-given grades, including student gender, school type, geographical regions, and socioeconomic status. In this paper, we used data from the Italian institute INVALSI, responsible for the organisation of national mathematics assessments, to investigate how these factors influence teachers' grading standards. We considered a sample of 36,589 Grade 13 Italian students from 2,062 classes at 990 high schools. The relationships between the variables were analysed using hierarchical linear modelling. The findings reveal that teacher-given grades are related to student-level variables (e.g. gender, socioeconomic status, and score on the INVALSI test) and school-level variables (e.g. school type and location). When the difference between teacher-assigned grades and scores on the INVALSI test was considered, only student gender, school type, and location accounted for the gap in student achievements. Therefore, student socioeconomic status has a lower influence on their performance on the INVALSI test, suggesting that using standardised assessments might improve equity in assessment. [ABSTRACT FROM AUTHOR]

This reflective paper explores Tara's doctoral research journey of realization and adaptation in auto/ethnography as a transformative research methodology. While reflecting on Tara’s journey, the auto/ethnographic paper emphasizes cultural perspectives, interpreting one's own experiences, thoughts, actions, and behaviors relating to society and culture. Likewise, auto/ethnography investigates and associates an individual's confrontation within specific educational, societal, and cultural contexts. With this ethos, the paper demonstrates how Tara, a mathematics teacher and doctoral student, encountered and observed auto/ethnography and discovered it as a path to transformation as a paradigm shift in transformative educational research by connecting lives and research (Dahal et al., 2022) considering the basis of ethics in auto/ethnography (Dahal & Luitel, 2022). Next, in this scenario of residing in cultural and societal context dealing with Tara’s emotions and settings of an education system, we have explored the journey of realization and adaption on how auto/ethnography blends analytic, evocative, and performative realms. Overall, we also realized that auto/ethnography guided us to delve through the past, present, and possible future experiences and unlatch Tara’s eyes to visualize a new era of research for upcoming generations in teaching and learning mathematics that reaches out to society and the nation whilst shifting to transformative educational research. [ABSTRACT FROM AUTHOR]

The paper is an exposure to the latest practices of questioning in teaching and learning math (TLM) on the basis of psychological-semiotic approach. Emphasis is placed on the degree of semantic support of the expected answer when formulating educational questions. The paper explored: whether teachers are able to distinguish between types of questions and to use them in sync with didactic purpose; what types of questions teachers consider to be the most effective; what factors influence this process. To achieve these goals, survey-based research was conducted among 173 high school mathematics teachers across Ukraine. The research proved that, in their majority, teachers are able to correctly distinguish among the types of the questions offered. According to the teachers, questions with full semantic support for the answer are less useful in TLM. The study showed teachers' lack of ability to identify the goals of the questions. There has been revealed a gap between the teachers attitude to the expedience of using questions with several possible answers and the practice of their implementation in TLM. The study yielded 35 variables characterizing the current status of the problem. They were optimized to 13 factors. It was stated that questioning should comply with the content of educational material, and the questions formulated with the use of topical vocabulary known to the students are viewed as most cost-effective. The research revealed the significant impact of the number of questions that teachers or students ask. The factor of primary importance appears to be that of time. [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]

This paper introduces a system that supports student-centered online one-to-one tutoring and evaluates the practical value of the system by running an experiment with 64 experienced mathematics teachers and 810 students in Grade 7. The experiment lasted for 50 days. A comprehensive evaluation was performed using students' academic performance before and after usage of the system and the system log files. By classifying the students into active and inactive usage groups, it was determined that active students significantly outperformed inactive students on posttests, but with a small effect size. The results also suggested that high prior knowledge students tended to benefit more from using the system than low prior knowledge students. An explanation for this result was that students with a high level of prior knowledge were more likely to have good-quality interactions with their teachers. Therefore, although some advantages of this type of student-centered online one-to-one tutoring are observed, in this system, both the students and the teachers need to be further facilitated to produce more effective tutoring interactions. [ABSTRACT FROM AUTHOR]

Intending to explore the terminologies, practices, and attitudes that permeate neurodivergent students’ inclusion and are shown in the mathematics teacher’s vocabulary, this paper presents a study that answers the following research question: Which assumptions can we identify in mathematics teachers’ vocabulary regarding autism? The data produced in the study consisted of registers by eight mathematics teachers from two public schools in the city of São Paulo answering an online questionnaire. The analysis assumes the principles of neurodiversity as a theoretical framework. It identifies three assumptions in the vocabulary of the participating teachers: (1) the recognition of needs arising from neurodivergence as a criterion for validating teaching practice, with the search for adjustment, adaptation, and pedagogical support that complements the school inclusion process; (2) the introduction of terminologies derived from the neurodiversity movement; and (3) medical explanation aligned with definitions and related descriptors in healthcare manuals. We conclude that neurodiversity is a movement with the potential to bring about such changes in the educational scenario. Still, as mathematics educators, we are incited to think how close we are to the sociological and critical ground in which this movement originates. [ABSTRACT FROM AUTHOR]

What do ethical relations look like in the context of the many injustices that pervade mathematics education? In this paper, I argue, first, that violence is the relation that characterizes much of contemporary mathematics education and, second, that understanding ethical relations requires considering mathematics as an equal actor in creating possible relations rather than simply treating it as a context for human relations. I examine how literature in care theory, emancipatory pedagogies, and mathematics education have framed ethical relationality and suggest that the feminist new materialist conceptualization of response-ability offers several contributions for rethinking agency, justice, and praxis for mathematics teachers concerned with addressing mathematical violence. [ABSTRACT FROM AUTHOR]

Lower and upper secondary school mathematics offers a few tools for solving mathematical problems (e. g., equational strategy or other algorithmic ones). At the beginning of the university study our students (pre-service mathematics teachers) know how to use them, but they have no experience with solving strategies such as systematic experimentation or drawing a picture. This paper presents our lesson plan to improve their solving competencies and its results. The special attention is given to the process of mathematics problem-solving and its fourth phase 'looking back' that we understand in a broader sense, not only as a test of correctness. The results of this case study aim to show and understand how students learn and use various solving strategies in problem-solving and how they pose other word problems with the same solution as the solution of the given word problems. The analysis finds that even though students understand the importance of non-standard strategies (e.g., trial and error or estimationverification-correction), they still understand the school equational strategy as the most advantageous. For problem-posing to contribute to the improvement of problem-solving competences, it must be more often involved in the problem-solving process. [ABSTRACT FROM AUTHOR]

In application-oriented mathematics, particularly in the context of nonlinear system analysis, phase plane analysis through SageMath offers a visual display of the qualitative behaviour of solutions to differential equations without inundating students with cumbersome calculations of the plane-phase. A variety of examples is usually given to illustrate phase-plane behaviour. We approach these problems by considering a problem containing a single real parameter that exemplifies the various situations clearly and simply. We developed two computer programs in SageMath: one program calculates aspects of the Jacobian matrix and displays the phase plane portraits, the other determines the centre manifold. Computations and images generated with computer codes are useful in understanding dynamic models in biology, physics and engineering that involve planar non-linear autonomous differential equations. This paper covers analytical and computational skills that are helpful for students and teachers. [ABSTRACT FROM AUTHOR]

In Sweden, as in many other countries, programming has been added to the curriculum in recent years. This paper explores how and under what conditions programming is transformed into teaching in technology education. Teachers in grade 7–9 were interviewed about what and how they teach about programming in the context of technology education, and what influenced the choices they made. Data was analysed using content analysis. The results suggest that teachers mainly see programming as a medium to explore and understand technological systems and construction work. The results further implies that teachers are uncertain of what programming means in terms of practices and concepts, and how programming knowledge can be assessed. The process of transformation presents teachers with several challenges, related to their own knowledge of programming, quality of teaching materials, and knowing pupils' prior knowledge about programming. In addition, the results indicate that technology teachers work in isolation. In consequence, the intended interdisciplinary collaboration between technology and mathematics teachers on programming is largely absent. [ABSTRACT FROM AUTHOR]

Out-of-field teaching refers to the practice of assigning teachers to teach subjects that do not match their training or education. This paper reports on a study evaluating the impact of a national professional development programme for out-of-field teachers of post-primary school mathematics in Ireland – the Professional Diploma in Mathematics for Teaching. Evidence of impact was collected from three surveys. Two surveys evaluated changes in the prevalence of out-of-field teaching before and six years after the introduction of the programme. The third survey investigated programme graduates' beliefs about mathematics, mathematics teaching and mathematics learning, and reported changes in teaching practices. Outcomes of the programme included a reduction in out-of-field teaching of mathematics and increased opportunities for graduates to teach higher level mathematics in the senior post-primary years. These teachers also endorsed child-centred beliefs and reported teaching practices consistent with the problem-solving orientation of the new mathematics curriculum. The findings go some way towards testing a theory of teacher change in order to enhance our understanding of how professional development works to upskill out-of-field teachers. [ABSTRACT FROM AUTHOR]

In this paper, we describe how pre-service teachers portray stereotypical mathematics teachers. Using longitudinal data – from 2007 to 2020 – of pre-service teachers' drawings ( N = 767), we report on four clusters of stereotypical mathematics teachers. In all clusters, we find significant gender differences. Stereotypical teachers in two clusters share some physical, often unfavourable, appearances, and the stereotypical teachers in these clusters are primarily men. The remaining clusters show how pre-service teachers associate gender with mathematical content: Women teach simple arithmetic; men teach advanced algebra. [ABSTRACT FROM AUTHOR]

This paper reports on the development of the Teaching Mathematics for Social Justice beliefs (TMfSJ-B) scale and its psychometric properties. Preservice elementary education teachers enrolled in teacher education programmes at seven universities completed multiple surveys designed to understand the evolution of attitudes and beliefs about teaching mathematics. To our knowledge, the TMfSJ-B scale is the only survey specifically designed to measure pre- and in-service teachers' beliefs about teaching mathematics for social justice. Confirmatory factor analyses (n = 655) provided here indicate that the TMfSJ-B scale is a valid and reliable assessment of beliefs about social justice in mathematics teacher education, with three factors: (1) value of mathematics for all students; (2) integration of social justice into mathematics instruction; and (3) mathematics and its relation to inclusiveness. The purpose of this study was to validate measures produced by the TMfSJ-beliefs scale and discuss its potential use in teacher education programmes and research. [ABSTRACT FROM AUTHOR]

Teachers' and students' values influenced the teaching and learning process in the mathematics classroom. Few studies were conducted to compare teachers' and students' value in mathematics learning. This paper explores Malaysian mathematics teachers' and students' values in mathematics learning. Fifty-three mathematics teachers and 354 secondary school students participated in the online survey. This study reports ten semantic differential items and an open-ended question related to mathematics learning. An independent t-test was conducted on the semantic differential items. Thematic coding analysis was performed to code the open-ended questions based on the framework of three intersecting values: mathematical values (the discipline), mathematics educational values (the pedagogy), and general educational values (the ethical and moral principles). The findings showed significant mean differences in mathematics educational values between teachers and students. No significant difference was found in mathematical values between teachers and students. Moreover, the qualitative data confirmed the similarities in mathematical values and differences in mathematics educational values between teachers and students. The current study also discusses possible reasons for the differences in teachers' and students' values. The findings imply that teachers' and students' values are crucial in enhancing teaching and learning in the mathematics classroom. [ABSTRACT FROM AUTHOR]

International literature is increasingly disclosing the relevance of cultural aspects within the processes of teaching and learning mathematics. Knowledge is inextricably linked to the activities in which the subjects engage, and must be considered in relation to the socio-cultural context wherein the activity takes place. Literature reveals the relationship between the background culture (e.g. language, nationality, etc.) of prospective elementary teachers and their beliefs about mathematics and its teaching. In this paper, we define culture with reference to the wider discussion from cross-cultural psychology literature about cultural values, and we investigate if and how differences in individuals' cultural values are related to prospective teachers' beliefs about being successful in mathematics and in its teaching. We adopt a questionnaire from the studies by Schwartz to measure participants' values. We assign each prospective teacher of our sample to a cluster of beliefs and we analyse how the beliefs of prospective teachers are related to their values. Results show that cultural values and beliefs about mathematics are related, while this is not the case for beliefs about the teaching of this subject. [ABSTRACT FROM AUTHOR]

Although research in mathematics education has yielded a great number of results on mathematics teachers' beliefs in recent decades, it is still an open question as to whether these teachers' beliefs are stable or not. However, since mathematics teachers' beliefs are perceived to be the default of their classroom practices, it is important to gain insight into these beliefs and into their development. In this paper, we contribute to this field of research by providing an approach designed to analyse a change in teachers' belief systems. We study a sample of 20 prospective teachers during their first practical experience. We analyse the structure of teachers' belief systems with interviews and a questionnaire set twice within one year. To analyse development of these teachers' belief systems, we assigned the young teachers of the first and second survey to clusters that were developed in a former study and re-analysed for our purposes here. Our results show considerable changes in mathematics teachers' central beliefs during their first practical experience. However, a general pattern of belief changes is not found. [ABSTRACT FROM AUTHOR]

Respect and listening are two issues that are complicated to research. This paper presents how respectful listening may constitute one aspect of a teacher's role in child-centered learning. The analysis focus on a teacher's reflections about events that took place after she and a colleague carried out a mathematics teaching unit on culturally diverse children's understanding of 'pattern'. The teacher observed situations that she found interesting and relevant for the children's learning. She communicated with the researcher about this for some months. A closer look at the teacher's reflections caused the research focus to change from what the teacher observed, to how she carried out the observations. So, the research focus is the teacher's application of respectful listening skills when these observations were made. Our analysis reveals the outcomes of two situations. Situation 1 is about communication between the teacher and a child's mother, while situation 2 is about communication between the teacher and a child. [ABSTRACT FROM AUTHOR]

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]