Search

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 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]

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]

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]

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 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]

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]

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]

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

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

In this paper we address the questions: What is synesthesia? What support(s) can teachers provide for students who have synesthesia? Nicole, a future mathematics teacher who possesses this synesthesia "superpower", describes how it has impacted her learning. We collected data for this case study through an audio-recorded and transcribed interview, as well as from subsequent email correspondence between the three authors. We asked Nicole three kinds of questions: questions she is frequently asked, questions she would like to be asked, and questions teachers (like Shelly and Beth) might ask. Results indicate that synesthesia may have helped Nicole learn English as a second language as well as memorize certain mathematical formulas and procedures. Questions arose that, if answered, may influence the learning of not only other synesthetes in the mathematics classroom but also their classmates. [ABSTRACT FROM AUTHOR]

Many research studies have been conducted on students' or pre-service teachers' geometric thinking, but there is a lack of studies investigating in-service teachers' geometric thinking. This paper presents a case study of two high school teachers who attended the dynamic geometry (DG) professional development project for three years. The project focused on the effective use of dynamic geometry software to improve students' geometry learning. The two teachers were interviewed using a task-based interview protocol about the relationship between two triangles. The interviews, including the teachers' work, were videotaped, transcribed, and analyzed based on the three levels of geometric thinking: recognition, analysis, and deduction. We found that the participating teachers manifested their geometric skills and thinking in constructing, exploring, and conjecturing in the DG environment. The study suggests that the DG environment provides an effective platform for examining teachers' geometric skills, and levels of geometric thinking and encourages inductive explorations and deductive skill development. [ABSTRACT FROM AUTHOR]

This paper introduces the model of instrumental meta-orchestration (IMO), as an extension of the model of instrumental orchestration. This IMO model is defined as a systematic and intentional monitoring, by a teacher educator, of artefacts and teachers (or pre-service teachers) for facing a Metasituation, defined as a composition of situations of different natures and difficulty levels. An IMO, in itself, is a composition of instrumental orchestrations (sequenced or interwoven). This paper presents and discusses an instrumental meta-orchestration experienced in a class of undergraduate mathematics teachers. The development of the initial model results in: new concepts, such as ad hoc reaction, didactic meta-configuration, exploitation modes and didactic meta-performance; new features, such as flexibility and interactivity; and new phenomena, such as cascade effects. It also reveals the importance of unexpected events that occur between orchestrations. Moreover, it expanded the forms of destination for evaluating specific online documents, which are named webdocs. Finally, the paper discusses the contribution to mathematics teacher education of such an extended model. [ABSTRACT FROM AUTHOR]

In this paper, we describe an educational experience in the context of the Master's degree that is compulsory in Spain to become a secondary education mathematics teacher. Master's students from two universities in Madrid (Spain) attended lectures that addressed—emphasizing the concourse of a dynamic geometry software package—some historical, didactic and mathematical issues related to linkage mechanisms, such as those arising in the 18th and 19th centuries during the development of the steam engine. Afterwards, participants were asked to provide three different kinds of feedback: (i) working on an assigned group task, (ii) individually answering a questionnaire, and (iii) proposing some classroom activity, imagining it would be addressed to their prospective pupils. All three issues focused on the specific topic of the attended lectures. In the framework of Mason's reflective discourse analysis, the information supplied by the participants has been analyzed. The objective was to explore what they have learned from the experience and what their perception is of the potential interest in linkages as a methodological instrument for their future professional activity as teachers. This analysis is then the basis upon which to reflect on the opportunities (and problems) that this particular bar-joint linkages methodological approach could bring towards providing future mathematics teachers with attractive tools that would contribute to enhancing a STEAM-oriented education. Finally, the students' answers allow us to conclude that the experience was beneficial for these pre-service teachers, both in improving their knowledge on linkages history, mathematics, industrial, technological and artistic applications, and in enhancing the use in the classroom of this very suitable STEAM context. [ABSTRACT FROM AUTHOR]

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

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

Self-efficacy in mathematics is related to engagement, persistence, and academic performance. Prior research focused mostly on examining changes to students' self-efficacy across large time intervals (months or years), and paid less attention to changes at the level of lesson sequences. Knowledge of how self-efficacy changes during a sequence of lessons is important as it can help teachers better support students' self-efficacy in their everyday work. In this paper, we expanded previous studies by investigating changes in students' self-efficacy across a sequence of 3–4 lessons when students were learning a new topic in mathematics (nStudents = 170, nTime-points = 596). Nine classes of Norwegian grade 6 (n = 77) and grade 10 students (n = 93) reported their self-efficacy for easy, medium difficulty, and hard tasks. Using multilevel models for change, we found (a) change of students' self-efficacy across lesson sequences, (b) differences in the starting point and change of students' self-efficacy according to perceived task difficulty and grade, (c) more individual variation of self-efficacy starting point and change in association with harder tasks, and (d) students in classes who were taught a new topic in geometry had stronger self-efficacy at the beginning of the first lesson as compared to those who were taught a new topic in algebra (grade 10), and students in classes who were taught a new topic in fractions had steeper growth across the lesson sequence as compared to those who were taught a new topic in measurement (grade 6). Implications for both research and practice on how new mathematics topics are introduced to students are discussed. [ABSTRACT FROM AUTHOR]

This paper explores how different schools of thought in mathematics education think and speak about preparing mathematics for teaching by introducing and proposing certain metaphors. Among the metaphors under consideration here are the unpacking metaphor, which finds its origin in the Anglo-American school of thought of pedagogical reduction of mathematics; the elementarization metaphor, which has its origin in the German school of thought of didactic reconstruction of mathematics; and the recontextualization metaphor, which originates in the French school of thought of didactic transposition. The metaphorical language used in these schools of thought is based on different theoretical positions, orientations, and images of preparing mathematics for teaching. Although these metaphors are powerful and allow for different ways of thinking and speaking about preparing mathematics for teaching, they suggest that preparing mathematics for teaching is largely a one-sided process in the sense of an adaptation of the knowledge in question. To promote a more holistic understanding, an alternative metaphor is offered: preparing mathematics for teaching as ecological engineering. By using the ecological engineering metaphor, the preparation of mathematics for teaching is presented as a two-sided process that involves both the adaptation of knowledge and the modification of its environment. [ABSTRACT FROM AUTHOR]

While international research has demonstrated that ability grouping is inequitable, Australian research has often overlooked equity concerns, predominantly focusing on studying the benefits of grouping for students perceived to have high ability, especially in mathematics. This paper investigates the effect that mathematics ability grouping has on senior secondary mathematics participation for low and middle grouped students in New South Wales, Australia. We drew on interviews about mathematics participation with 85 students and 22 mathematics teachers from 11 government high schools. Our thematic analysis of these data identified that secondary school grouping practices often serve to entrench student interest and/or performance from primary school. This has consequences for many students, with a differentiated curriculum in Years 9 and 10 precluding low and middle grouped students from participating in high-level mathematics when they reach senior secondary school. These findings raise serious equity questions about the current push in Australia for universities to re-introduce high-level mathematics as a prerequisite to entering certain degrees. We argue that stakeholders need greater awareness of the consequences of ability grouping and that those seeking to lift post-compulsory mathematics participation should be targeting primary and early secondary school. [ABSTRACT FROM AUTHOR]

This paper introduces lessons designed to incorporate applications to teaching high school mathematics in an undergraduate Discrete Mathematics course. Because many prospective high school teachers do not take courses that are specifically designed for teachers, providing materials aimed at teacher preparation that can be easily integrated into courses that serve a general mathematics major is one strategy for addressing mathematics teacher preparation. We developed lessons using four guiding features: choosing appropriate content; making school mathematics connections; incorporating active learning; and providing robust lesson notes. Our interview-based findings document how the lessons were used by instructors and analyze the mathematical ideas and understandings that arose from the use of the lessons at two different sites. [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]

This paper reports on how 10 middle and high school preservice teachers (PSTs) designed a social justice focused lesson using the culturally responsive mathematics teaching (CRMT) tool. Results from our analysis indicate that most of the PSTs were able to select appropriate social justice topics, though not all the PSTs integrated mathematics and social justice throughout their lessons. The results show that most of the PSTs need more experience with mathematization, handling controversial discussions, and developing transformative student action. Our work also led to a modification of the tool (CRMT-M). We discuss the implications of the study for mathematics teacher preparation. [ABSTRACT FROM AUTHOR]

Mathematical problems that contain a common condition and an ordered list of tasks are traditionally called cascade problems. Problems of this type are extremely popular during teaching of mathematics. At the same time, they can be used both in the formation of knowledge, skills and abilities (competencies) of students, and to assess their academic achievements. In the paper we give a thorough theoretical analysis of possible types of cascade problems, describe methodology and provide examples of their applications on different stages of studying mathematics at school, in particular, during the final attestation of graduates. According to our statistical survey of mathematics teachers in Ukraine and Republic of Moldova, we clarify their attitude to problems of cascade type, as well as the advantages and disadvantages of using such problems. It is shown that the use of cascading problems in the school course of mathematics contributes to the adequate formation of important competencies of students in their learning process. [ABSTRACT FROM AUTHOR]

The main challenge to the teachers in the field of mathematics in higher education is the fact that they are often confronted with the generally negative attitude of the students towards mathematics. This is partially due to their inadequate experience in the previous periods of learning mathematics that results in a certain mixture of essential mathematical illiteracy and personal animosity towards the subject. It is the main reason why mostly of the mathematics teachers in higher education are not able to achieve the needed efficacy in teaching mathematics. In this paper part we will envisage part of the problems we had to deal with in our efforts in making mathematics in higher education more approachable and more acceptable to our students. The main goal is to present suggestions for overcoming the existing problems and drawbacks that we are facing as mathematics teachers, mainly in faculties in technical sciences. [ABSTRACT FROM AUTHOR]

This paper deals with gender gap in Mathematics across Africa. Reducing the gender gap in Mathematics in Africa, is the major aim of African Women in Mathematics Association (AWMA) through various activities. Using macrodata from two international surveys and microdata from two African universities (Joseph Ki-Zerbo of Burkina Faso and Monastir in Tunisia), differences in favor to men in the participation of female teachers and teacher-researchers in Mathematics, Physics, Chemistry and Computer Sciences are highlighted. Some practices, considered by AWMA, aiming to reduce the Gender Gap are also evoked. [ABSTRACT FROM AUTHOR]

Wenger's theory of learning proposes the concepts of participation and reification as dimensions of educational design. Based on this proposal, this position paper looks at the design of one Mathematics Professional Development Program (MPDP) through the lenses of these concepts. We argue that the reification concept allows professional designers to keep in mind the resources they should use to organize teachers' learning, while the participation concept allows them to ponder the types of activities that should be implemented in order for the teachers to adequately assimilate the meaning of those resources. The example that serves as the context in which we situate our discussion is the Data Analysis Project, a professional development project on statistics in which 5 in-service secondary school teachers participated. Due to the dialectic relation between participation and reification, we explain how these two processes intertwine to maintain the balance needed to allow teachers' learning to proceed within an MPDP. We argue that this dialectic relation is the key element for MPDP designers to connect the resources produced by research in mathematics education to the practice of mathematics teaching. Such a connection allows an MPDP to act as a bridge between two communities of practice: that of researchers in the field of mathematics education and that of mathematics teachers. Ultimately, the article shows how Wegner's concepts of participation and reification may be used to design an MPDP. [ABSTRACT FROM AUTHOR]

Anyone involved in mathematics education will at some point encounter a classroom situation in which a student's statement provides an opportunity for the teacher to enhance students' mathematical understanding. This paper aims to characterize such classroom situations, known as critical events, as noticed by pre-service mathematics teachers during classroom observations and teaching. Analysis of 80 critical events reported by 20 pre-service mathematics teachers during a field-based teaching preparation program yielded a model that enables teacher-educators and researchers to characterize critical events while reflecting on the wide variations within these events. The model comprises three axes: the participants in the event, the focus of the event, and the dimensions in learning and teaching mathematics (i.e., cognitive, affective and social). The paper discusses the theoretical and empirical construction of the model and demonstrates its potential contribution using examples taken from our research. • Pre-service teachers identified critical events during classroom observations. • A model for characterizing critical events was constructed theoretically and empirically. • The model affords eliciting the multidimensional nature and complexity of critical events. • The model's potential contribution is presented using examples from our research. [ABSTRACT FROM AUTHOR]

In this paper, we examine the impact of a massive open online course (MOOC) in the context of outdoor mathematics on the participating teachers' professional development. We firstly introduce the theoretical background on outdoor mathematics, focusing on math trails with the digital tool MathCityMap and professional development to be accomplished using MOOCs. By taking into account the MOOC "Task Design for Math Trails", with 93 finalists, we analyze the learning progress of 19 selected case studies from different nations and learning levels by taking into account their answers in a pre- and post-questionnaire and their posts on a specific communication message board, with a special focus on the MOOC's topics' task design for outdoor mathematics and the digital tool MathCityMap. The analysis is performed using different quantitative and qualitative approaches. The results show that the teachers studied have benefited from professional development, which is evident in the expansion/evolution of their knowledge from a content, pedagogical, and technological perspective. Finally, we formulate consequences for professional development in STEM education, and conclude the paper with limitations to be drawn and a perspective for further research. [ABSTRACT FROM AUTHOR]

The paper is a reflection on the author's work with students enrolled in undergraduate and graduate elementary mathematics content and methods courses. Two specific pedagogical issues make up the focus of the paper. The first issue deals with demonstrating to future teachers the diversity of mathematical ideas behind a contextual question asked by a second-grade pupil allowing for multiple solution strategies to be used in addressing the question. The second issue deals with the use of Wolfram Alpha in aiding different mathematical features of this demonstration. The paper is congruous with mathematics teaching standards used across six continents and illustrated by reflective comments of the author's students regarding their mathematics teacher education experiences. Teaching ideas shared in the paper may be of interest to instructors who want to explore elementary mathematics in depth with teacher candidates. [ABSTRACT FROM AUTHOR]

Students with learning disabilities are often excluded from conversations about high-quality mathematics instruction as well as conversations about equitable mathematics instruction. As such, they may not be provided many opportunities to engage in mathematics with teachers who implement practices that the field of mathematics education would consider "high-quality" or "equitable". In this paper, we examine how three students with learning differences participate in instruction that demonstrates aspects of high quality and equitable mathematics instruction. Our findings outline practices that appeared to support increased opportunities for students to demonstrate their own reasoning and sense making in mathematics. Contributions of this work include illuminations of specific pedagogical moves that may support students identified as having learning disabilities to engage in more student-centered, conceptually-oriented mathematics. • We examine how three students with learning disabilities participate when math instruction is designed to be student-centered. • Practices that aimed for equity & were conceptually-oriented appeared to improve sense making opportunities for the students. • This work outlines specific pedagogical moves that supported these students in using their own reasoning while "doing math. [ABSTRACT FROM AUTHOR]

The Trends in International Mathematics and Science Study (TIMSS) is an influential mathematics and science assessment administered at fourth and eighth grades in around 60 countries across the world. Under current practices, TIMSS does not support claims about teachers unless the inference is drawn as a student characteristic ("Half of the eighth graders in the country have mathematics teachers with Master's degrees."). With this in mind, this paper proposes and tests through a simulation study two methods that would allow for teacher-centric inferences ("More than half of the eighth-grade mathematics teachers have Master's degrees.") if links between sampled teachers and the unsampled yet eligible classes were known. The first method posits that with such links inverse-probability weights could be calculated, and the second method, the Multiplicity-Adjusted Indirect Sampling (MAIS) approach, posits that teacher estimates could be obtained by adjusting downward the classroom weights based on these links. • Discusses teacher reporting in Trends in International Mathematics and Science Study. • One method creates and implements inverse-probability weights for teachers. • Another method reweights the class weights for each teacher. • A simulation study shows that both methods produce unbiased results. • Both methods would require collecting data on teachers' links to unsampled classes. [ABSTRACT FROM AUTHOR]

• Novice facilitators' changes in practices in two different countries are examined. • Despite the different contexts, changes in practices are found to be similar. • Practices are linked to facilitators' resources, orientations, goals and identity. • Managing mathematics teachers' PD discussions can be learned and developed. • Recommendations for supporting novice facilitators of are presented. Novice facilitators of professional development (PD) programs for mathematics teachers often face challenges in leading productive discussions and achieving the goals of these programs. Although research in this area is gradually accumulating, not much is known about how novice facilitators address these challenges and change their practices accordingly. This paper presents case studies of two novice facilitators of PD programs in two different countries. The analyses look at their work over one year, to illustrate the changes in their practices while managing discussions. The results show that although the facilitators operated in different contexts, their practices and their processes of change resembled, suggesting that these processes are not idiosyncratic. We argue that novice facilitators' changes in practices correspond to changes in their resources, orientations, goals, and identities and that PD program teams can support these changes. [ABSTRACT FROM AUTHOR]

The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher's professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra. [ABSTRACT FROM AUTHOR]