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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]

Following the increasing impacts on the value of Western play-based pedagogy, early childhood (EC) teachers in China face developmental challenges related to understanding and implementing play-based mathematical education. The purpose of this paper is to explore Chinese EC teachers' perspectives on play-based mathematics teaching. In this qualitative study, semi-structured interviews and lesson plans are collected from six EC teachers in a Chinese kindergarten. Hedegaard's model is applied to frame analysis for capturing EC teachers' views and practices from a holistic perspective. The findings show that all six EC teachers valued play as a pedagogical tool for teaching mathematics, while their pedagogical decisions in applying play to children's mathematics are determined by the various demands from society, parents and children. The multiple demands from different perspectives result in challenges for teachers in designing collective play. This study revealed that only when play activity caters to the possibility of satisfying those demands can teachers pedagogically implement play for children's mathematical learning. The insights emerging from this study might address the pragmatic challenges that teachers face by enhancing teachers' professional development to support the advance of culturally sensitive play-based mathematics teaching in China. [ABSTRACT FROM AUTHOR]

The International Journal of Mathematical Education in Science and Technology has published a special issue on the INDRUM2022 conference, which focused on research in university mathematics education. The conference featured numerous papers and posters on topics such as the transition to university mathematics, teaching and learning of mathematical concepts, teacher education, and student practices and assessment. The special issue includes 16 papers that provide in-depth analyses of these topics, using theoretical frameworks such as the Anthropological Theory of the Didactic and the Action, Production and Communication approach. The papers offer insights into the challenges and opportunities in university mathematics education and propose instructional strategies to enhance learning outcomes. The editorial encourages readers to explore the papers and join the INDRUM network. Additionally, the text titled "Commognition" is a chapter in the Encyclopedia of Mathematics Education, providing an overview of the concept of commognition, which refers to the cognitive processes involved in mathematical communication and collaboration. The chapter explores various aspects of commognition, including its theoretical foundations, its role in problem-solving and learning, and its implications for mathematics education. The text is part of a larger collection of proceedings from the fourth conference of the International Network for Didactic Research in University Mathematics. [Extracted from the article]

This article discusses the growing attention and research activity surrounding early grade mathematics (EGM) in South Africa and Malawi. The introduction of curriculum reforms and policy-linked interventions, such as the Teaching Mathematics for Understanding model and the Primary Teacher Education initiative, have led to increased research in this field. The article highlights the importance of foundational understandings of mathematics in addressing low performance in the subject. It also examines different approaches to EGM research, including large-scale interventions and projects that engage with the mathematics education literature base. The article concludes by emphasizing the need for ongoing attention to both larger-scale and smaller-scale intervention studies in order to improve mathematical outcomes. [Extracted from the article]

This paper presents a research framework for investigating the role of language use in mathematics learning. The paper draws on the wider M2EID study, which explores whether differences in languages (English and Irish) and their use by bilingual mathematical students have a differential impact on their mathematics meta-level developments. A primary consideration of the M2EID study was to design a rigorous research framework to support such complex, real-world educational research. In particular, the study explored how to integrate the varied theoretical constructs underpinning this type of research and how to design the most appropriate data capture and analysis procedures. It is focused on adapting a discursive approach to examining bilingual students' mathematical thinking. The resultant LCM2 research framework outlines four phases for designing research within the combined fields of linguistics and mathematics. Exemplars from the M2EID study are provided. [ABSTRACT FROM AUTHOR]

The connections between critical pedagogy, living theory and participatory action research (PAR) are discussed to explore their combined strength for empowering students, positively impacting on their attitudes towards their mathematics learning and creating social change in their primary-secondary mathematics transitions. This transition is recognised as creating social inequalities which existing transition research has failed to resolve. The interpretation of critical pedagogy, living theory and PAR are described before a summary of their application in a small scale, two-year study in a British curriculum school in Muscat, Oman. Critical pedagogy combined with living theory and PAR provides the theoretical and methodological framework to empower the students epistemologically. This paper gives an example of how PAR with students was conducted within the framework of critical pedagogy theory and living theory methodology. This account provides a valuable reference for participatory action researchers. The paper concludes that the combination of critical pedagogy, living theory and PAR can empower students to create social change. [ABSTRACT FROM AUTHOR]

Improving the mathematical skills of undergraduate Engineering and Information Technology (EIT) students has been an enduring challenge for educators. Lecturers continually implement new strategies that try to overcome the challenges encountered in teaching university students with varying levels of success being encountered. This paper provides insight into how educators have handled the challenges students face in their mathematics learning journey. In addition, the paper highlights some of the methods used to improve the performance of these students as problem solvers, as well as the development and implementation of creative techniques that may have made the situation more successful and less challenging. The literature was searched through using a structured literature review approach based on the primary databases: Scopus; the Education Research Complete (ERC); and the Education Resources Information Centre (ERIC). This study followed the three main steps of a systematic literature review: retrieval, selection, and analysis of the literature. Analysis of the literature showed that there is still a need to further develop and deliver innovative pedagogical strategies for teaching mathematics to EIT students. It is recommended that an interdisciplinary approach, inclusive of technology, will lead to increased understanding, improve performance and, ultimately, enhance student satisfaction. [ABSTRACT FROM AUTHOR]

The following paper continues the previous part, and examines the influence of crystallography on Fröbel's conception of mathematics. In this part we focus on yet unpublished material. These unpublished notes of Fröbel underline the visual transfer of drawing and images of crystals, mainly developed by Haüy, which were widespread at the turn of the eighteenth to the nineteenth century, into the Fröbelian activities. Hence, the paper shows that a transfer of knowledge occurred from crystallography to mathematical education as well as the interweaving of philosophical and scientific reflections in Fröbel's thought as early as the late 1810s. [ABSTRACT FROM AUTHOR]

Measures of association, which typically require pairwise data, are widespread in many aspects of educational research. However, due to the need to reduce their content to equal numbers of units of analysis, they are rarely found in the analysis of textbooks. In this paper, we present two methods for overcoming this limitation, one through the use of disjoint sections and the other through the use of overlapping moving averages. Both methods preserve the temporal structure of data and enable researchers to calculate a measure of association which, in this case, is the complementary Euclidean average distance, as an indicator of the books' similarity. We illustrate these approaches by means of a comparative analysis of three commonly-used English and Swedish mathematics textbooks. Analyses were focused on individual tasks, which had all been coded according to the presence or absence of particular characteristics. Both methods produce nearly identical results and are robust with respect to both densely and sparsely occurring characteristics. For both methods, widening the aggregation window results in a slightly increased level of quantified similarity, which is the result of the 'smoothing effect'. We discuss the relation between the window width and the choice of research question. [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]

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]

Studies have shown that failure experiences play a role in pre-service teachers' development. Given that autobiographical experiences are a foundation of learning and that failure is a wide-spread experience, particularly in mathematics, we need further insight into what kind of experience failure actually is. This paper draws on 59 pre-service teachers' written experiences of failure in order to map them out and provide insight into what counts as failure from the perspective of the future teachers of mathematics, that is, pre-service mathematics and pre-service elementary school teachers. The findings, alongside the earlier research on negative experiences, form a basis for conceptualising failure in mathematics as an autobiographical experience and distinguishing it from a negative experience. A theoretical insight into the nature of failure is gained; the failure experiences seem to be less relational than anticipated. The paper also discusses the relevance of failure experiences for teacher education. [ABSTRACT FROM AUTHOR]

Even prior to COVID-19, there had been an increase in the use of technology in undergraduate mathematics education to support the development of mathematical understanding and skill, and to enhance the student learning environment. Technology-enhanced resources can be used to provide formative assessment which can help students identify gaps in their knowledge and point towards appropriate action. In this paper, we report on the evaluations of a number of technology-enhanced resources that used formative assessment techniques and were provided for students attending non-specialist first-year undergraduate mathematics modules in Ireland. Analysis of the evaluations and consultation with literature identified 12 decisive factors that encourage students' successful engagement with the resources, covering aspects such as the educational context, affordances and types of technology, technological communication and formative assessment. These factors constitute important knowledge for practitioners as they can use them in the planning, design, and development of technology-enhanced resources for use in their modules. The measures observed during the evaluations indicated both positive and negative engagement providing a link between observations and resultant student engagement, which was found lacking in previous studies on student engagement. [ABSTRACT FROM AUTHOR]

In this paper we studied the personal mathematical work of 14 students in initial teacher training, in their first year of studies at a public university in Chile, based on two tasks on complex numbers. These tasks were set in a Computer Aided Assessment System (CAA) based on Moodle and Wiris and it was proposed to solve them using different Computer Algebra Systems (CAS), such as GeoGebra, Symbolab, Photomath and Wolfram Alpha among others. Difficulties and potentialities were observed in the mathematical work of the students. In the difficulties, it was observed that the students had problems interpreting the information from the CAS and the CAA feedback because their previous mathematical knowledge was not solid enough to do so. In the potentialities, it was observed that different characteristics of the task, together with the articulation of two or more artifacts allowed students to give meaning to the mathematical objects involved. [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]

In summer 2013, Manhattan College introduced an online summer "bridge to calculus" course for incoming first-year students in science, engineering, and mathematics education who marginally did not receive a calculus recommendation based on a mathematics placement test. In this paper, we describe the development of the bridge course and demonstrate statistically that this course continues to prepare its students for Calculus at a level comparable to those who took a full semester of Precalculus, yet at a significantly lower cost in terms of both time and money. [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]

The article offers information on the increasing interest in affect-related research in mathematics education, particularly within the MAVI community. The topics include the growing recognition of the role of affect in teaching and learning, the collaborative spirit of MAVI in promoting research on mathematical beliefs and education, and the contributions from different communities in a special issue of the International Journal of Mathematical Education in Science and Technology (IJMEST).

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]

Teacher practice is rife with tensions. Tensions around what and how best to teach, how to manage situations with students, and how to manage situations with colleagues, administrators, and parents. These tensions are often seen as pairs of opposing internal and external forces: this assessment is better, but it takes a lot of time. These forces are inescapable, and teachers have to learn to either manage them or resolve them. In this paper we look closely at tensions through the lens of opposing forces and, more interestingly, how teachers either learn to live with them or work to resolve them. And, in particular, we look at how this work differs if the tension exists between internal forces, external forces, or a tension between an internal and external force. Drawing on case studies of seven different participants we dive deep into the murky world of the lived experiences of teachers to understand better the way that tensions contribute to their beliefs, decisions, and actions. [ABSTRACT FROM AUTHOR]

This paper targets patterns of expressed emotional directions towards mathematics. By using TIMSS data and recoding two of the instruments, we compared responses from the same student cohort in Grade 4 (11 years old) and Grade 8 (15 years old) in Sweden. Two hypotheses were tested: negative emotions including negative motivations increase with age, and there will be gender differences. By using statistical analyses, including Cramer's V, the two hypotheses were confirmed. The results also illuminated patterns within the responses, such that boys and girls in Grade 4 differ in expressed intrinsic motivation but not extrinsic motivation. There are also indications that girls might be more likely to form negative emotional directions between grades 4 and 8 than boys, and some implications of this is discussed. [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]

As it is a common practice in Dual Language Education (DLE) classrooms throughout the United States, language separation tends to be a planning policy that is usually enforced by curriculum designers, school administrators, and bilingual teachers. However, research has shown that DLE teachers and students have the potential of teaching and learning bilingually in their own terms. Using theoretical perspectives from Anthropolitical Linguistics coupled with Ruíz's seminal work on language as problem, resource, and right; and other socio-cultural frameworks, this paper presents an ethnographic case of a seventh-grade DLE mathematics classroom, and examines how the members of this mathematics community use their bilingual abilities in a flexible way; which in turn, influence the development of mathematics biliteracies. Drawing from a larger ethnographic project, this study shows how the members of a bilingual mathematics community of practice break language norms, which prevail in DLE classrooms, to promote mathematics biliteracies. Findings suggest that using a 'translanguaging' approach in DLE classrooms is an effective way for teaching and learning mathematics with a biliteracy approach. Some implications for schools, teachers, and teacher educators are discussed. [ABSTRACT FROM AUTHOR]

Mathematical memes are an Internet phenomenon with an epistemic potential noteworthy for the teaching and learning of mathematics. The aim of this paper is to conceptualize this phenomenon on an empirical base, elucidating its educational potential. To pursue this goal, a two-year ethnographic research study has been conducted in a selection of social media communities that exchange mathematical memes. In the paper, a twofold theoretical lens is used to investigate the phenomenon from a memetic perspective focused on the general characteristics of Internet memes, and from a cultural perspective considering the Web 2.0 environment. Analysis tools derived from the memetic and cultural theoretical background are applied to an instrumental case study, to reconstruct how mathematical memes activate the interaction among members of an online community. The investigation elicits key characteristics of the phenomenon, provides grounds to conceptualize mathematical memes as hybrid representations of mathematical statements, and sheds light on the traits of the epistemic culture they establish in the community. [ABSTRACT FROM AUTHOR]

The study described in this paper investigated a unique collaboration among a special education and two general educators that sought to prepare students for success in the general education mathematics curriculum and that consisted of coordinated, reform-based instructional design across classroom and pull-out services provided by the special educator including preteaching. During preteaching, the special educator delivered instruction on key mathematics and collaboration skills that special education students would need a few days before they would receive instruction on the same content in their general education classrooms. Their collaboration produced high levels of teacher satisfaction, substantive teacher change, and increases in student engagement, self-efficacy, and achievement. [ABSTRACT FROM AUTHOR]

Numerous studies affirm the importance of students' attitudes for mathematical education. This study uses mathematical autobiographical essays to examine the mathematical experiences and attitudes of undergraduate students enrolled in mathematics classes at a Midwestern University in the United States. The essays of 41 students (20 men, 21 women) out of 170 enrolled in College Algebra, Precalculus, and Calculus were analyzed using the categories of (1) confidence in mathematics ability, (2) value of mathematics, and (3) liking of mathematics. This paper provides context and theoretical depth to student reports of their attitudes in these categories. Statements at the intersections of both confidence and liking, and value and liking provide additional insights. First, students who perceive mathematics as valuable are more likely to like it. Second, the vast majority of students talk about confidence and liking together, and with a positive correlation. Further, these students tend to talk about liking or not liking mathematics because of their perceived ability in mathematics. Our study suggests the importance of proactive teaching strategies to improve students' perceptions of the value, liking of, and their confidence in, mathematics, and also suggests self-efficacy as a potential theoretical basis for this work. [ABSTRACT FROM AUTHOR]

Owing to its recognition as a 21st-century skill, computational thinking (CT) is currently being introduced into school curricula around the world. However, in-service teachers are largely unprepared for this implementation, which, in turn, makes teacher educators (TEds) important stakeholders in preparing prospective teachers to integrate CT into their classroom practices. In this regard, TEds are charged with a twofold responsibility: they must develop not only their own CT skills and digital competence but also a way of teaching these to the next generation of teachers who will facilitate future pupils' learning. In this paper, we report on 17 TEds' experience regarding the challenges and opportunities of integrating CT into Norway's primary teacher education mathematics and science courses two years after CT's introduction into Norwegian primary schools. A data-driven thematic analysis of semi-structured interviews was conducted. Our analysis suggests that it is challenging to integrate CT into existing courses. Such challenges, as well as opportunities, seem to apply at four levels: the systemic, teacher educator, student teacher, and subject levels. The results provide valuable insights for key stakeholders into the challenges and opportunities of integrating CT into teacher education, thus contributing to the body of research on professional digital competence. [ABSTRACT FROM AUTHOR]

In this paper, we briefly introduce three theoretical frameworks for mathematical identity and why they matter to practitioners teaching undergraduate mathematics courses. These frameworks are narrative identities, communities of practice, and figured worlds. After briefly describing each theory, we provide examples of how each framework can be used to interpret or inform classroom discourses by applying the framework to a selected transcript from a student-centered mathematics project called the Catwalk problem. We summarize how an awareness of students' forming mathematical identities can be used positively in the undergraduate classroom to help educators support students to form productive mathematical identities. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate how small-group and whole-class discussions during whole-class teaching contribute to students' learning. The study includes 33 video-recorded small-group discussions in four mathematics lessons on enlarging and reducing two-dimensional geometric figures in Grade 8. The results show that different objects of learning were enacted in the different small-groups' discussions, and that in the majority of the small-group discussions the students did not have the possibility to learn what was intended, since critical aspects were not explored. The combination of group and whole-class discussions contributed to that critical aspects of the specific subject matter came to the fore and thereby were possible to discern. The results indicate that small-group discussions without subsequent whole-class discussions may have less effect on student learning. [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 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]

In the disciplines of dance and mathematics, binary identities commonly split individuals into either (non)dance and/or (non)math people. However, these shorthand assessments become dangerous because they constrain disciplinary knowledge, and limiting one's identity and capabilities remains antithetical to broad education goals. Capitalizing on dance as a situated, embodied form of knowledge, as well as an engaging, interactive, and social endeavor, we facilitate instruction that uses a dance-based approach to teach geometric transformations in a teacher education program. In this paper, we discuss findings from a case study intervention in a graduate-level geometry education course where we engaged participants in this transformations dance activity. We ask: What disciplinary practices did participants use in a dance-based intervention on geometric transformations? And, how did they use them? We found that the parallel disciplinary practices that the participants engaged in, in dance and mathematics, sheds light on a need in education to resist binary identities and to encourage inquiry-based practices. We aim to inspire future professional development and collaborative teaching opportunities for dance teachers in math and math teachers in dance, along with research that investigates intersections of learning, practice, and identity, particularly in dance + math. [ABSTRACT FROM AUTHOR]

Due to the fixed school start in Norway in August of the calendar year of students' sixth birthday, the age span in one class is up to twelve months. This can impact academic performance both in the early years and later. In this paper, we investigate the relationship between birth month and mathematics performance by paying attention to the content and cognitive domains addressed in the Trends in International Mathematics and Science Study (TIMSS) 2015. In Norway, the TIMSS 2015 included four cohorts, enabling a comparison between grades. We find significant correlations between birth month and mathematics performance overall as well as in all content and cognitive domains for grades 4, 5 and 8. Furthermore, the gap in mathematics results between the youngest and the oldest in a cohort is less in grade 9 than in grade 4. We suggest that these findings have implications for mathematics teachers' practice. [ABSTRACT FROM AUTHOR]

Previous studies have emphasised that play can promote children's learning of mathematics. However, little research has been directed towards understanding how collective imaginary play motivates children's mathematical learning. Informed by the cultural-historical conception of play and motives, this paper examines how Conceptual PlayWorld (CPW) creates conditions for Chinese children's meaningful mathematical learning using the concept of repeating patterns as an example. Video observations of teachers interacting with children (4–5 years) during the CPW implementation (8.54 h), as well as children's interviews (5.75 h), were gathered and analysed. Following the focus child Zeng's motives and intentions but all children's experiences in the CPW, the findings show CPW appears to create mathematical conditions that promote thinking, imagining and play. Zeng's motives for mathematical learning are stimulated by his play motives which are amplified through his active participation and problem-solving in a CPW, and this creates conditions for his personally meaningful learning of mathematics in the Chinese kindergarten context. [ABSTRACT FROM AUTHOR]

Since the standards-based education movement began in the early 1990s, mathematics education reformers have developed and evaluated many interventions to support students in mastering more rigorous content. We conducted a systematic review and meta-analysis of U.S. PreK-12 mathematics intervention effects from 1991 to 2017 to study sources of heterogeneity. From more than 9,000 published and unpublished study reports, we found 191 randomized control trials that met our inclusion criteria, with 1,109 effect size estimates representing more than a quarter of a million students. The average effect size on student mathematics achievement was 0.31, with wide heterogeneity of most effects ranging from −0.60 to 1.23. Two modeling approaches—meta-regression and machine learning—provided converging evidence that outcome measure type (researcher-created vs. standardized) and technology delivery (vs. teacher or interventionist delivery) were predictors of effect size. Intervention type, intervention length, grade level, and publication year were also identified as potentially explanatory factors. [ABSTRACT FROM AUTHOR]

Spatial reasoning, recognised as playing a critical role across STEM disciplines, is gaining prominence in mathematics education, not only as fundamental to mathematics, but also as embodied mathematical activity. In this paper, we discuss spatial reasoning and its embodiment in mathematics. We then present a systematic review of the topics as researched and related to deaf and general education from 2010 to 2019. Publication trends during the ten years reveal similarities and differences across both fields. Based on the findings, we share insights, prospects, and provocations for promoting spatial reasoning in mathematics with an emphasis on research and pedagogy for deaf education. [ABSTRACT FROM AUTHOR]

In this paper, we aim to untangle positioning theory (Davies & Harré, 1990) and its implications for the field of mathematics education research, considering both existing use and potential use. Specific theoretical assumptions of positions or positionings in the context of learning mathematics are outlined. In this paper, a classroom-based instrumental case study illuminates examples of how students are positioned within their mathematical experiences as a means to understand some of the factors that affect how students come to exist within mathematical spaces and how classroom-based positionings impact students' opportunities to engage in learning. Our goal is to present positioning theory as a potential tool for how our teaching practices impact students' experiences in mathematical spaces. We present a moment-by-moment analysis, from an ethnographic perspective of the case, to clearly demonstrate how positioning theory may be utilized for both research and practice within mathematics education research. Implications for methodology and positioning theory through an ethnographic perspective are shared. [ABSTRACT FROM AUTHOR]

Mathematics education faculty working in mathematics departments are commonly involved in teaching undergraduate mathematics courses, teaching and supervising postgraduate students of mathematics education, and developing mathematics teachers (pre-service and/or in-service). This paper proposes a new elective course that can be taken by either undergraduate mathematics majors or by graduate teaching assistants pursuing degrees in mathematics and teaching undergraduates themselves. Twenty-eight topics are suggested, and the rationale for each is briefly described. Offering such a course provides different opportunities for students; for example, familiarizing them with effective ways to teach and learn mathematics, which has the potential to improve their effectiveness as tutors within the department. A similar course has been successfully taught to undergraduate students majoring in mathematics at an Iranian university for nearly two decades. [ABSTRACT FROM AUTHOR]

Links between mathematical attainment and economic performance, coupled with England's poor showing in international comparisons of skills, have focussed attention on post-16 mathematics education, for example, in the UK Government's 2017 Industrial Strategy. Whilst high-stakes academic qualifications at 16 (GCSE) and 18 (A-level) have stood the test of time, the 'forgotten third' of students in England's Further Education colleges have fared less well. Over the last 30 years a series of mathematics qualifications for vocational students have been established and then discarded. This paper utilises a theory of change approach to understand this repeating pattern for three successive curricula: core, key and functional mathematics. Waves of rise and decline include critical moments of reinforcement, or synergy with wider reforms, but trajectories are also affected by shifting policy visions for Further Education and entrenched knowledge hierarchies that value academic mathematics qualifications over vocational ones. Whether 'alternative' mathematics curricula for FE students can achieve longevity and widespread recognition remains to be seen. The implications from this analysis of historical trajectories are that changes to established attitudes and educational values are needed to halt this repeated cycle of short-lived alternatives to GCSE Mathematics. [ABSTRACT FROM AUTHOR]

In Australian universities, mathematics is often an essential core subject for disciplines such as engineering, information technology and science. These first-year mathematics subjects may have large enrolments of which a significant number fail the subject and repeat. While interventions to retain students are common, those who have failed before and are repeating the subject are often overlooked. In this paper, we undertook a statistical analysis based on demographic and performance data of six cohorts of students undertaking a first-year university-level mathematics subject. We found that pass rates for students on their second attempt were significantly lower than pass rates for students enrolled on their first attempt, and that age, degree enrolled in and pathway into university were predictors for who was more likely to repeat. Students in their second attempt were less likely to complete all assessment items and were more than twice as likely not to attend the final exam. We argue for an increased focus on and efforts targeting repeating students; that demographic data are used to predict students likely to repeat before they have failed a subject, and that this group of students, as well as those repeating, are supported to increase their chances to pass. [ABSTRACT FROM AUTHOR]

Mastery-grading techniques such as mastery-based grading, specifications grading, and standards-based grading are assessment techniques professors are implementing in order to support a growth mindset of learning, decrease test anxiety, and help students develop a deeper understanding of course objectives. In this paper, we provide an analysis of research conducted in a variety of courses which used mastery-based testing (MBT). Some of the questions we explore include whether the students' attitudes about mathematics and learning changed throughout the course in addition to whether MBT impacted test anxiety and growth mindset. [ABSTRACT FROM AUTHOR]

The curriculum resources used for teaching secondary mathematics vary considerably from school to school. Some schools base their teaching largely on a single published scheme, while others design their own schemes of learning, curating their resources from a range of (often free) online sources. Both approaches seem problematic from the perspective of experiencing the mathematics curriculum as a coherent story, and neither seems likely to take best advantage of the accumulated body of knowledge in the education research literature about effective didactics for mathematics. In this position paper, as we embark on the collaborative, research-informed design of a complete, fully-resourced, free-to-access mathematics curriculum for students aged 11–14, we use the conceptual framework of mathematics curriculum as a story to draw out five key curriculum design principles. A mathematics curriculum should harness and develop the skills and expertise of teachers; balance the teaching of fluency, reasoning and problem solving; give explicit attention to important errors and misconceptions; compare and contrast alternative methods; and engineer coherence through strategic use of consistent representations and contexts. We use these five principles to set out our vision for the next step in research-informed mathematics curriculum design. [ABSTRACT FROM AUTHOR]

In this article, we consider how to make data more meaningful to students through the choice of data and the activities we use them in drawing upon students lived experiences more in the teaching of statistics and data science courses. In translating scholarship around culturally relevant pedagogy from the fields of education and mathematics education we develop the idea of culturally relevant data. We see this development as a key ingredient to implementing culturally relevant pedagogy in teaching data-intensive courses leveraging the centrality of context through data in both statistics and data science to engage students particularly from historically marginalized groups in STEM. We provide suggestions as to ways of finding or creating culturally relevant data and using them in implementing culturally relevant pedagogy to support the learning and flourishing of students in statistics and data science courses. We also present findings from pilot work we have done in implementing these data in statistics courses. Finally, we discuss lingering questions and possible next steps for research in this area. for this article are available online. [ABSTRACT FROM AUTHOR]

This article presents a networking of two theories, the Extended Theory of Mathematical Connections (ETC) and the Onto-semiotic Approach (OSA). In particular, concordances and complementarities are identified in the respective conceptions of mathematical connections, as a result of applying these theoretical frameworks to a student's response protocol when solving a task on the derivative. First the mathematical connections were identified from the perspective of the ETC and, second, an onto-semiotic analysis was carried out where the mathematical practices, the primary mathematical objects activated in them and the semiotic functions established between these objects were analysed. The main conclusion is that both theories complement each other to make a more detailed analysis of the mathematical connections. In particular, the more detailed analysis carried out with the OSA tools, visualizes a mathematical connection like the tip of an iceberg of a conglomerate of practices, processes, primary objects activated in these practices and semiotic functions that relate them, which enables a thorough analysis that details the structure and function of the connection. [ABSTRACT FROM AUTHOR]

We give an unconventional, mythopoetic response to the question of Why teach mathematics to all learners in school? In our work with pre-service teachers, we attempt to teach how to value the vulnerability of the multispecies world in a relational, anti-colonial way through passionate immersion, and to use mathematics education towards the ends of promoting its and our own (human) flourishing through taking on relationships of curatorial care. Our contribution includes the novel theoretical assemblage and elaboration of the metaphors of plot and curating as "medicine" [Doolittle, E. (2007). Mathematics as medicine – plenary lecture. In P. Liljedahl (Ed.), Proceedings of the 2006 CMESG Annual Meeting (17–25), Burnaby, BC, Canada.] for addressing challenging ethical questions for mathematics education [Karrow, D., Khan, S., & Fleener, Y. (2017). Mathematics education's ethical relation with and response to climate change. Philosophy of Mathematics Education Journal, 32 (Special Issues on Mathematics Education and the Living World: Responses to Ecological Crisis). ISBN: 1465-2978.] of its ongoing relationship with the precarity produced by unexamined plantation commitments. [ABSTRACT FROM AUTHOR]

Studies have shown that learning mathematics through programming can be complex and that the programming itself might even hamper students' learning. However, few studies have focused on the role of the teacher and the teacher-student interaction that aims to support students' learning when using programming. The present study examines a didactic design in which a teacher uses well-prepared questions and suggestions that focus on students' reasoning to solve mathematical problems using Scratch, a block-based programming environment. Forty students, 10–11 years old, solved a geometry problem using Scratch supported by their teacher. The students' screen activities and teacher-student interactions were recorded. The results indicate that well-prepared general and task-specific questions targeting students' creative reasoning can help to overcome some of the complexities of learning mathematics while programming. The study furthermore shows that when students have sufficient programming skills, Scratch could even have the potential to support their reasoning and at the same time guide the teacher to give timely feedback. [ABSTRACT FROM AUTHOR]

Despite the documented influence of motivation on mathematics learning for most students, we understand far less about this relation for students identified with learning disabilities. Based on Rogoff's three planes of analysis (i.e., personal, community, and interpersonal), we gathered survey, interview, and video data to understand the motivations of sixth graders in a special education mathematics classroom as well as classroom conditions that supported motivation during a unit on fractions. By the end of that unit, students reported improved ability beliefs and attributed the changes to increased conceptual understanding of fractions, exposure to strategies for sense making, and the additional time and assistance provided to them. Through video analysis, we also found that having students verbalize their thinking about the mathematics can provide opportunities to identify remediation needs and thus support productive participation and positive ability beliefs. These findings highlight the motivational value of effective mathematics instruction for students with learning disabilities. [ABSTRACT FROM AUTHOR]

Pupils' ability to represent mathematical concepts in multiple ways is a central aspect of mathematical competence and communication. Thus, classroom instructions should be able to support learners in using multiple representations (MRs) to increase the quality and quantity of connections to a network of ideas. Given the importance of bansho (board writing and organisation) in Japanese mathematics classrooms, this study aimed to investigate how MRs are presented as bansho in a mathematics classroom. Guided by a coding scheme of MRs on bansho content, the analysis revealed the ways the MRs are facilitating (or hindering) pupils' understanding. In considering the effect of the sequence and translation of MRs identified in this study, it is important to focus on these aspects of lesson design in the future. The relevant findings are also crucial to illustrate to the educators and researchers how to explore the processes involved in the use of MRs and the critical factor that contribute to the success/failure of such processes through a detailed examination of the bansho. [ABSTRACT FROM AUTHOR]

This study investigates teachers' beliefs about the inquiry-based learning approach in mathematics. In particular, as the first research problem, it addresses teachers' beliefs about the appropriateness of inquiry activities for all students, after three years of attendance in a professional development programme, focused on inquiry. As a second research problem, it studies the evolution of teachers' beliefs and practices, during their fourth year of attendance of the programme. The results show that, at the beginning of the fourth year, the teachers, despite thinking that inquiry activities in mathematics have several valuable aspects, held the belief that they are not appropriate for all the students, but only for the high-achieving ones. The two case studies, analysed to address the second problem, refer to two teachers with different outcomes of their developmental paths. During the fourth year, in which the teachers have been invited to experiment with inquiry activities in their whole classes, one of them accepted the challenge and, as a consequence, had the opportunity to change both her practices and her beliefs. The second teacher, instead, continued to propose inquiry activities only to her high-achieving students and, consequently, showed no signs of change, either in her practices, nor in her beliefs. [ABSTRACT FROM AUTHOR]