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 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]

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]

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]

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]

Preparing students placing into developmental mathematics for success in undergraduate mathematics and preparing future teachers for the increasing demands of K–12 school settings are both persistent, yet seemingly divergent, problems facing higher education. In this paper, we shed light on a model that attempts to address aspects of each problem and share preliminary evidence of success in a multi-year application of this model. The paper highlights the benefits of implementing the model, particularly to support collaboration between faculty in mathematics and teacher education. [ABSTRACT FROM AUTHOR]

Learning to teach out-of-field is a challenge that many teachers worldwide face at some time in their career. Whether they are motivated to seek formal professional development as additional qualifications in this area, however, depends on many factors. Alignment between the specific professional development needs of out-of-field teachers and the planned learning experiences is essential to maximise sustained learning and applicability to teachers' classrooms. This paper reports on a government-funded program designed to support teachers teaching 'out-of-field' in science and mathematics. The initial design of the program drew on existing literature on effective teacher professional learning. Using the theoretical lens of 'boundary crossing' this paper reports on the perceived discontinuities that teachers 'brought with them' in order to understand where the potential for learning lay, and compared this to teachers' perceptions of their changed practice. Growth in teachers' confidence and relational understandings of content, pedagogy and curriculum was evident. Implications for future programs to support out-of-field teachers are provided. Teaching out of field (TOOF); Professional Learning (PL); Professional Development (PD) [ABSTRACT FROM AUTHOR]

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

England’s Further Education (FE) sector is in permanent flux with policy interpretations and translations taking place at multiple levels within increasingly large and complex multi-site organisations. Devolved responsibility gives managers considerable influence in policy enactment processes which can lead to within-college tensions between vocational and mathematics teachers. This paper examines two within-college policies affecting students’ mathematics learning opportunities: (1) subject choice, and (2) examination entry levels. These policies have produced inequitable opportunities for students on different vocational study programmes. Given the strategic importance of improving mathematics education, this paper explains how multiple actors and structures interact in the enactment of policy in complex FE college settings. Such understandings are needed to inform better policy design and implementation that in turn can improve mathematics education in Further Education colleges in England. [ABSTRACT FROM AUTHOR]

This paper considers the policy ‘roles’ adopted by teachers enacting policy in a department. It draws on a longitudinal study of two secondary mathematics departments endeavouring to make deep change aligned with a demanding curriculum policy. The study validates aspects of an existing typology, demonstrates the existence of a variety of policy ‘critics’ and adds a category of ‘survivor’ teacher, showing the role can have considerable impact on enactment. The paper argues for an extension to a group construct of ‘policy role’, here at a department level, and shows that as teachers struggle to marry the constraints of the range of policies to which they are subject with the time and effort needed to maintain deeply espoused professional values, an adopted group role can serve either to support or constrain individual teacher efforts. [ABSTRACT FROM PUBLISHER]

This paper reports on some aspects of an investigation on the impact of an instructional approach aimed at generating and maintaining students' interest in mathematics for secondary school students in displaced and re-settled communities in South Sudan. Two groups of Grade 11 students, an experimental group (E-group) and a control group (C-group), participated in the study. The E-group (n = 31) was taught using a Humour-supported Instructional Approach (H-SIA) and the C-group (n = 20) was taught using a Regular Instructional Approach. Preliminary indications from the pilot phase of the main study suggest that the method of instruction (H-SIA) generates and maintains at least similar levels of interest as the regular Regular Instructional Approach. The H-SIA also suggests some slight modifications and enhancement to the Interpersonal Competent Communication Model, the recommended existing guiding theory for humour communication in the classroom. It is concluded that H-SIA does indeed generate and maintain interest in mathematics in the classroom. Hence, it is recommended that mathematics teachers should consider infusing humour into their lessons to enhance students' interest in mathematics. [ABSTRACT FROM AUTHOR]

Mathematical reasoning and tools are intrinsic to science, yet the close and dependent relationship science has to mathematics is not reflected in either school education or science education research. This paper asks what the barriers are to a mutually beneficial relationship between the two disciplines. A two-phase qualitative interview study was used to explore the relationship between school science and mathematics education through the perspectives of science and mathematics education policy-makers and of teachers in departments which are unusual in collaborating. In total there were 36 participants. Interview data were analysed using thematic analysis. Findings show that there is an asymmetry in the dependency between school science and mathematics: science is dependent on mathematics but the reverse is not true. We discuss three consequences of this asymmetric dependency: there is greater benefit for science from any collaboration; 'maths blame' can arise from science teacher frustration; and science educators may believe they should have some ownership of the mathematics curriculum. Asymmetry of dependency, and therefore of benefit, will make it very difficult for mathematics and science to work together in a way which is genuinely mutually beneficial. [ABSTRACT FROM AUTHOR]

The study presented in the paper has the following goals. The first is to review and compare teacher competence frameworks developed in Eastern (Chinese) and Western (German) contexts, exemplified for the domain of mathematics. Major similarities of the two contexts could be reconstructed in the conceptualization of teacher competence as a multidimensional construct comprising knowledge, teaching-related skills and beliefs. Distinct differences could be identified as well, with the Chinese frameworks including a wider range of teacher-competence facets and emphasizing more teaching-related competencies than the Western (German) frameworks. The second purpose is to adapt and validate a German framework of the measurement of mathematics teacher competence in a Chinese context. This adaptation and validation uses exemplarily mathematics teacher, in detail follow-up-studies of the international Teacher Education and Development Study: Learning to Teach Mathematics (TEDS-M). With the integration of a qualitative approach (e.g. elemental validity) and a quantitative approach (e.g. construct validity) to validate the framework, the results of both approaches suggest a satisfactory validity for the adaptation. Overall, the results point out that the examined teacher competence framework and its instruments can be used for comparative analyses in Germany and China. [ABSTRACT FROM AUTHOR]

Teaching teachers to participate in mathematical inquiry has the potential to both transform belief systems about mathematics and to transform teachers from consumers of mathematics to producers of mathematics. The focus of this paper is to describe the use of a problem, based on a non-traditional binary operation, to encourage and teach pre-service and in-service teachers inquiry and problem-posing. We present a brief mathematical solution for the problem and we then discuss problem-posing activities and discussions of connections to the Standards of Mathematical Practice from the Common Core State Standards. We discuss several key aspects of the problem that make it well-suited for the purposes of teaching inquiry and problem-posing. [ABSTRACT FROM PUBLISHER]

Mathematics teachers across the Western world are faced with an expectation that they make significant change to their teaching, but repeated attempts have shown little embedded success. This paper draws on a longitudinal study of two apparently well-placed English mathematics departments attempting to make change aligned with both policy and internationally-valued ‘good practice’. It suggests deep teacher change draws on a wide range of both social and affective characteristics, as well as sophisticated professional skills and knowledge. The study supports a construct of ‘(mathematics) teacher capacity for change’ at both individual and group levels within teachers’ ‘personal domains’, synthesising the range of characteristics apparently needed by teachers in times of change. In particular, it argues for the development of dispositions for collaborative learning and of other learning-supportive affects. Such an approach has the potential to place teachers in a better position to respond to demanding aspirations. [ABSTRACT FROM PUBLISHER]