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With the rapid application of blended learning around the world, a large amount of literature has been accumulated. The analysis of the main research topics and development trends based on a large amount of literature is of great significance. To address this issue, this paper collected abstracts from 3772 eligible papers published between 2003 and 2021 from the Web of Science core collection. Through LDA topic modeling, abstract text content was analyzed, then 7 well-defined research topics were obtained. According to the topic development trends analysis results, the emphasis of topic research shifted from the initial courses about health, medicine, nursing, chemistry and mathematics to learning key elements such as learning outcomes, teacher factors, and presences. Among 7 research topics, the popularity of presences increased significantly, while formative assessment was a rare topic requiring careful intervention. The other five topics had no significant increase or decrease trends, but still accounted for a considerable proportion. Through word cloud analysis technology, the keyword characteristics of each stage and research focus changes of research were obtained. This study provides useful insights and implications for blended learning related research.

Simonas Vainbergas, a teacher of Jewish primary schools in prewar Lithuania (1894?), was one of few his colleagues that actively collaborated with Lithuanian pedagogical journals. He published in them 11 papers in didactics of mathematics about teaching mathematics at primary schools. The said papers helped young teachers of primary schools to improve their qualification. There is a great probability that S. Vainbergas was a victim of holocaust.

It is generally accepted that teachers' beliefs impact their instructional choices, but characterizations of that relationship are limited in college settings. Furthermore, examinations of instructor beliefs, instruction, and student beliefs together in one setting are rarely described. Based on interviews with two Abstract Algebra instructors, classroom video from three units of instruction, and survey and interview data from students in the classes, this paper examines instructors' stated beliefs, ways these beliefs manifested in their teaching, and students' beliefs across the course. Both instructors made curricular choices clearly aligned with their stated views of the nature of mathematics, learning, and teaching. Day-to-day instructional choices reflected these stated beliefs as well, but the difficulty of material and tensions with other beliefs like the importance of interactivity manifested. Characterizations of the interactivity of classes and placement of the mathematical authority in class are provided through descriptive and quantitative measures. These characterizations of instruction provide nuanced portrayals of classroom norms and changes in those norms throughout the semester. Furthermore, subtle shifts in student beliefs about teaching and learning are noticeable, suggesting students' beliefs about teaching and learning mathematics can be influenced even by modest changes in instructional practice.

Purpose: Greater understanding about how variables mediate the relationship between leadership and achievement is essential to the success of reform efforts that hold leaders accountable for student learning. The purpose of this paper is to test a model of integrated transformational leadership including three important school mediators. Design/methodology/approach: In total, 5,392 students provided data on student engagement, and 569 teachers provided survey data on principal leadership and the collective teacher efficacy (CTE) and extra effort of their colleagues. Data were analyzed at the school level (n = 51) using mediation analysis with the PROCESS macro to calculate the direct and indirect effects of all of the variables in the serial multiple mediator model. Findings: The model explained a significant amount of variance in both reading (38 percent) and mathematics (35 percent). CTE and student engagement mediated all of the leadership effects, demonstrating the importance of teacher and student relations in school improvement. The combined effect sizes are significantly greater than the effects of earlier TL models. Originality/value: This study contributes to "leadership for learning" research by demonstrating that refining transformational leadership behaviors to include instructional management can enhance a leader's impact on achievement. As one of the few studies to examine student engagement as a mediator along with teacher mediators, the current study highlights the importance of teacher-student relations in school improvement. While collective efficacy mediated all of the effects of leadership on achievement, student emotional engagement also contributed to mathematics achievement. The study's findings advance research into mutual influence processes, indicating that reciprocity may extend throughout the leader-teacher-student loop.

In this survey paper, we describe the state of the field of research on teaching mathematics with technology with an emphasis on the secondary school phase. We synthesize themes, questions, results and perspectives emphasized in the articles that appear in this issue alongside the relevant foundations of these ideas within the key journal articles, handbooks and conference papers. Our aim is to give an overview of the field that provides opportunities for readers to gain deeper insights into theoretical, methodological, practical and societal challenges that concern teaching mathematics with technology in its broadest sense. Although this collection of articles was developed prior to the global coronavirus pandemic, we have taken the opportunity to survey the contributing authors to provide some country perspectives on the impact the pandemic has had on mathematics teaching with technology in the period January–July 2020. We conclude the survey paper by identifying some areas for future research in this increasingly relevant topic. [ABSTRACT FROM AUTHOR]

The exploration of children's drawings as mathematical representations is a current focus in early years mathematics education research. This paper presents a qualitative analysis of 72 kindergarten to Grade 3 (5 to 8 years old) children's drawings produced during problem-solving tasks centred on multiplicative strategies. Existing frameworks for the developmental sequence of mathematical drawings and the progression of children's strategies for multiplicative situations were an interpretive lens through which to analyse the drawings. Children used pictographic and iconic drawing types to represent the "story" in the problem and the multiplicative strategies employed to solve the tasks. Exploration of the children's drawings suggested that as children's drawings become more structural, schematic in nature, it may be easier for children to show their understanding of the structural elements of multiplicative relationships. Results revealed that structural elements of multiplicative relationships were more easily seen in iconic representations; however, both pictographic and iconic drawings were useful to observe counting, additive, and multiplicative strategies when mathematical elements of the problem were visible. Additional representations attached to the drawings (e.g. numerical) were needed to confirm children's strategies when their drawings lacked structure. These findings have implications for how young children's drawings are interpreted by classroom teachers. The interpretation of these drawings suggested that some children may not yet realise how their drawings in mathematics need to shift from illustrations of the problem's story context to representing mathematical ideas and processes — which requires intentional teaching of the purpose of drawings for mathematical contexts. [ABSTRACT FROM AUTHOR]

Evaluating the impact of a scholarly article is of great significance and has attracted great attentions. Although citation-based evaluation approaches have been widely used, these approaches face limitations e.g. in identifying anomalous citations patterns. This negligence would inevitably cause unfairness and inaccuracy to the article impact evaluation. In this study, in order to discover the anomalous citations and ensure the fairness and accuracy of research outcome evaluation, we investigate the citation relationships between articles using the following factors: collaboration times, the time span of collaboration, citing times and the time span of citing to weaken the relationship of Conflict of Interest (COI) in the citation network. Meanwhile, we study a special kind of COI, namely suspected COI relationship. Based on the COI relationship, we further bring forward the COIRank algorithm, an innovative scheme for accurately assessing the impact of an article. Our method distinguishes the citation strength, and utilizes PageRank and HITS algorithms to rank scholarly articles comprehensively. The experiments are conducted on the American Physical Society (APS) dataset. We find that about 80.88% articles contain contributed citations by co-authors in 26,366 articles and 75.55% articles among these articles are cited by the authors belonging to the same affiliation, indicating COI and suspected COI should not be ignored for evaluating impact of scientific papers objectively. Moreover, our experimental results demonstrate COIRank algorithm significantly outperforms the state-of-art solutions. The validity of our approach is verified by using the probability of Recommendation Intensity. [ABSTRACT FROM AUTHOR]

In recent years, there has been an increasing amount of literature on online teaching and learning. Teaching mathematics in the fourth industrial revolution offers entry-level mathematics teachers formidable challenges. Despite using various teaching aids in explaining the learning area, entry-level mathematics teachers, those with zero to three years of teaching experience, have experienced challenges in blended teaching during the COVID-19 pandemic. Such challenges could support the preconceived notion identified by others that the field of learning (mathematics) is difficult. This paper hinged on constructivist epistemology and investigated the challenges that entry-level mathematics teachers face in conducting blended teaching in the Sedibeng West District of Gauteng Province in the Republic of South Africa. Eight entrylevel mathematics teachers were purposely sampled from four selected schools that participated in the article. This article adopted a case study design and responses were analysed thematically. The focus group interviews were used as tools to collect data in this study. The study revealed a variety of perceptions that entry-level mathematics teachers shared about the impact of blended teaching in mathematics learning. These included, but were not limited to, the use of teaching programs or software, the effects of load shedding and blended teaching challenges related to learners' performance and behaviour. The results of this study could provide program developers, subject advisors, school principals with other members of the management team, and mathematics teachers to support the entry-level mathematics teacher's confidence, sense of future and communication skills, as well as foster multigenerational connections in blended teaching. [ABSTRACT FROM AUTHOR]

UDC 51(091) The present collection of papers (in two parts) is dedicated to the memory of our advisor Yuri Petrovich Solovyov--an outstanding mathematician and person, whom we always remember with [...]

It is the intention of this special issue to provide an opportunity for mathematics education researchers from all around the world to offer their complementary accounts and to engage in reflective scholarly exchange regarding research into the complexity of classroom practice. Other major international projects informed by the LPS, and led by Clarke, cohered around a desire to understand, model and ultimately optimise the practices of the mathematics classroom. For most of his career Clarke's research activity centred on capturing the complexity of classroom practice through a programme of international video-based classroom research in more than 20 countries. The work of David Clarke The work of David Clarke profoundly influenced the field of mathematics education. [Extracted from the article]

This paper draws from a broad study that explored mathematics teachers’ engagement with textbooks within the Lesson Study context. In the current paper, we report on teachers’ use of mathematics textbook activities to inform their instructional decisions during collaborative lesson planning of numeric and geometric patterns. The study took place within the Lesson Study (LS) context – a teacher development practice that emphasises, inter alia, collaborative lesson planning. Data was collected by observing teachers during collaborative lesson planning and through interviews. Data analysis was informed by the Mathematics Knowledge for Teaching (MKT) framework and Modes of teacher engagement with the textbook. Findings suggest that teachers’ instructional decisions are mainly stimulated by the textbooks, teachers use textbook activities with fidelity, and they seldom adapt the activities drawn from the textbooks. However, where adaptation occurs teachers do it superficially. We contend that the capacity to conduct in-depth interrogation of the text is a derivative of mathematics subject matter knowledge (SMK) as well as pedagogical content knowledge (PCK). Therefore, the widespread adoption of text without interrogation could be indicative of the lack of requisite content knowledge and pedagogical skills. [ABSTRACT FROM AUTHOR]

Mathematical modelling competencies have become a prominent construct in research on the teaching and learning of mathematical modelling and its applications in recent decades; however, current research is diverse, proposing different theoretical frameworks and a variety of research designs for the measurement and fostering of modelling competencies. The study described in this paper was a systematic literature review of the literature on modelling competencies published over the past two decades. Based on a full-text analysis of 75 peer-reviewed studies indexed in renowned databases and published in English, the study revealed the dominance of an analytical, bottom-up approach for conceptualizing modelling competencies and distinguishing a variety of sub-competencies. Furthermore, the analysis showed the great richness of methods for measuring modelling competencies, although a focus on (non-standardized) tests prevailed. Concerning design and offering for fostering modelling competencies, the majority of the papers reported training strategies for modelling courses. Overall, the current literature review pointed out the necessity for further theoretical work on conceptualizing mathematical modelling competencies while highlighting the richness of developed empirical approaches and their implementation at various educational levels. [ABSTRACT FROM AUTHOR]

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

Student motivation has emerged as a major issue in mathematics education in recent years. Utilizing the capabilities of contemporary technology and the accessibility of a STEM environment is crucial for the creation and application of educational materials. Integration of the created resources will increase the interest of students to pursue in-depth studies of science and math. In this paper are presented the results of the conducted study on the effectiveness of using problem-based learning (PBL) modules to learn mathematics. The study was carried out in Israel with the participation of teachers and ninth graders. As part of our research, we created a novel program and conducted an experimental study, evaluated its impacts on the designated target groups, and analyzed how the program affected student subgroups. Pre- and post-program questionnaires measured ability feeling, relevance perception, and motivation. The results of the analysis of the students indicate a considerable rise in the motivating factors associated with self-esteem and the utility of mathematics training. [ABSTRACT FROM AUTHOR]

In the research reported in this paper, using a modified version of the interconnected model of teacher professional growth (IMTPG) proposed by Clarke and Hollingsworth (Teaching Teacher Educ 18:947–967, 2002), we aimed to understand the learning dynamics in a lesson study of a group of five teachers of grades 5–6, during their work around mathematical tasks and in the elaboration and analysis of a diagnostic test of students' knowledge. We draw on examples from a lesson study that took place in a school in Lisbon, involving five teachers that constituted the whole mathematics group of the school. The main feature of our adaptation is the consideration of a Group Domain instead of the Personal Domain of the original model. In the original model, the Domain of Practice had a broad definition but usually it was restricted to classroom experimentation. In the research reported in this paper, the lesson study sessions were taken as part of the Domain of Practice. For data collection, there was audio and video recording of the lesson study sessions and of the research lesson and the writing of a research journal. Data analysis was done using the modified IMTPG. The results suggest that this model is helpful in understanding the processes that make lesson study a valuable professional development setting, contributing to responding to the question of 'how lesson study works' (Lewis et al., Theory and practices of lesson study in mathematics: an international perspective, Springer, New York, 2019). In addition, the use of this model showed that the lesson study promoted the teachers' development regarding knowledge of didactics, especially knowledge of students and their learning processes and of teaching practice. [ABSTRACT FROM AUTHOR]

Introduction: The authors examined a tablet computer application (iPad app) for its effectiveness in helping students studying pre-algebra to solve mathematical word problems. Methods: Forty-three visually impaired students (that is, those who are blind or have low vision) completed eight alternating mathematics units presented using their traditional literacy medium or an iPad app. Twenty percent of the mathematics problems included graphics such as maps, line graphs, and bar graphs. During each session, teachers of visually impaired students rated the amount of support they provided for students and the student motivation. Results: Students answered more mathematics problems correctly when using the iPad app and, overall, teachers reported that their students were more motivated with the app than with their traditional literacy medium. Students often used the hints provided in the app when they did not solve a problem correctly the first time. Discussion: Visually impaired students and their teachers found the app and graphics to be easy to use and motivating. The built-in Scratch pad was used by almost all students who were print users. Implications for practitioners: The study results contribute to the growing body of knowledge about the potential value of tablet-type devices for use by visually impaired students. [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]

Informal Australian discussion suggests that calculators are still widely regarded as devices for calculation, consistent with their naming, and are rarely recognised as potentially helpful to support students learning mathematics. In this paper, Barry Kissane explores some of the ways in which modern calculators might support students learning about irrational numbers, of key significance to the study of the real number system, characterising lower secondary school mathematics. [ABSTRACT FROM AUTHOR]

Engaging students in processes of mathematizing and active knowledge organization (instead of telling and rehearsing ready-made mathematics) is a key demand for high quality mathematics instruction. Although many mathematically rich context problems have been designed and published in textbooks, their impact on regular mathematics classrooms remains limited, as teachers face challenges in shaping and enacting the important phase of knowledge organization. The 15-year project KOSIMA presented in this paper was aimed at supporting teachers in really enhancing these processes by means of a textbook for Grades 5–10. The paper provides an overview of different studies conducted during the project in order to show how the project developed a research base for the support of teachers. The paper also shows that different research approaches need to be combined to establish an appropriate research base: In iterative design research cycles of topic-specific didactical design research, learning environments were designed and investigated with the aim of understanding the obstacles encountered in implementing the desired processes. In this paper, we focus on an example of one particular obstacle, namely, teachers' need of support in engaging students in processes of active knowledge organization. This obstacle was overcome by developing new types of tasks for active knowledge organization. The theoretical outcome of the design research resulted in two hypotheses for improving relevant features of the design of these tasks, which were tested in two controlled trials. Finally, a longitudinal field study of 312 students gave first indications that the classes that worked with the textbook had significantly higher learning gains than classes using other textbooks. In sum, we can show that textbooks can support changes in classroom practices when the obstacles that occur for both teachers and students are carefully investigated and treated. [ABSTRACT FROM AUTHOR]

Creativity, attitudes, and conceptions of teachers regarding creativity in teaching mathematics have been examined in this study. The instrument used is a questionnaire consisting of three groups of questions. The first group of questions includes questions to gather general information about the teachers, while the second and third groups of questions include questions to gather data about teachers' attitudes and conceptions of creativity in teaching mathematics. The questionnaire was completed by 115 class and Maths teachers. After data analysis, the findings indicate that the majority of teachers have knowledge about creativity and believe that teachers are responsible for developing students' creativity. From the proven hypotheses of this paper, we can conclude that if the teachers know creativity, then they will teach the students to be creative, which they will further develop creativity, as a requirement of the 21st century. [ABSTRACT FROM AUTHOR]

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

Copyright of Canadian Journal of Science, Mathematics & Technology Education is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Deep learning is an important concept introduced into modern learning science. It is different from the surface learning of mechanically and passively acquiring knowledge and storing individual information but emphasizes learners' active and critical learning. It wants them to understand the full meaning of what they have learned. By establishing a link between existing knowledge and new knowledge, it transfers existing knowledge to a new environment, makes decisions, and solves problems. Deep learning plays an important role in students' learning. Deep learning ability is the key factor affecting the quality of learning and the development of students' academic ability. The quality of in-depth teaching is difficult to guarantee, which requires a complete, comprehensive, and evaluation system to evaluate it. This paper introduces the analytic hierarchy process to weight the indexes in mathematics deep learning and puts forward some suggestions on creating an environment for deep learning. The experimental results show that teachers' teaching accounts for the highest proportion of primary indicators, reaching 67%. Multimedia resources account for the highest proportion of secondary indicators, reaching 73.01%. This paper then puts forward some suggestions for indicators with large weights. [ABSTRACT FROM AUTHOR]

This is a methodological critique of research by the Best Practice in Grouping Students (BPGS) project claiming teacher bias in allocating students to first‐year secondary school mathematics teaching sets (British Educational Research Journal, 45(4), 873–879). The research assumes that bias could be shown by non‐random relationships between 'misallocations' to sets and memberships of gender, ethnic and/or socio‐economic subgroups. This paper questions the authors' prescriptions for correct set placements and demonstrates two ways in which non‐random relationships between subgroup memberships and (alleged) misplacements could be generated despite all students with similar scores within a school being given the same chance of a set position deemed correct by the researchers. It suggests that the BPGS project results are largely artefacts of their evaluation approach. No claim is made herein that teacher bias plays no part in set allocation, merely that, if it does, the approach by Connolly et al. could not evidence it. A lesson from the critique is that, before drawing inferences from data aggregated from diverse clusters, it is wise for researchers to investigate the way the data are generated at source and patterned by aggregation. [ABSTRACT FROM AUTHOR]

This paper determined the effectiveness of Science Teachers Academy for the Regions (STAR) trainings on the teaching practice of participants in Region 6 - Western Visayas. The research participants of this study were STAR trainees who attended the STAR Trainings from 2014-2017. The researchers employed an explanatory sequential mixed methods design. Quantitative data were collected through an online survey with regards to the effectiveness of their teaching practice. The extent and quality of adaptation of STAR training content and skills in their practice through focus group discussions consisting of 8 participants each in Science and Mathematics were determined. The methods of data collection were online survey, Focus Group Discussion (FGD), classroom observation, and interview guide questions for In-depth interview. The findings of the study showed that Science and Mathematics teachers showed a great change in their teaching experiences after undergoing Project STAR training. Moreover, the participants insights about the STAR trainings were the different inquiry-based activities that they applied in their classroom, application of the 7Es in the lesson plan, improvement of the learning pedagogy, concepts and skills were easily learn through interdisciplinary contextualization of teachers in preparing a lesson plan was effective in ensuring the appropriate strategies in the lesson. Furthermore, students developed and enhanced their science process skills from the participant's learnings in the STAR trainings. The quality of the adaptation of STAR trainings revealed that trainees had a great transformation from the traditional method of teaching to the inquiry-based method of teaching. The STAR trainings were unique in such a way that participants did not feel that they are bored, it is interactive and less stressful, it is specific and lots of hands-on activities, and it focus more in the content on how to apply it in the classroom. The STAR trainings made a great impact to the STAR trainees in their professional growth by giving them an opportunity to become speakers in their respective institutions and by living the expectations of other people and enabling them to study more. [ABSTRACT FROM AUTHOR]

Over the past decade, teaching mathematics ambitiously has received increased attention. In this paper, we argue that to materialize this vision in contemporary classes we need to understand how practicing teachers experiment with certain aspects of this teaching and what challenges they encounter. Toward this end, we focus on an aspect of teaching ambitiously—designing and using enablers and extenders—and examine how four elementary schoolteachers experimented with it in their practice while also participating in a video-club setting. Drawing on a corpus of data including lesson plans, videotaped lessons, pre- and post-lesson interviews, end-of-program interviews, and videotaped video-club sessions, and looking across the four cases, we sketch how these teachers worked with enablers and extenders and the challenges they faced. Our analysis helped identify certain components entailed in working with enablers and extenders during the phases of lesson planning and enactment; it also yielded a classification of observed and reported challenges encountered as teachers engage with this work. This mapping of work associated with designing and using enablers and extenders, along with the classification of challenges generated, can inform professional learning development attempts aiming to support teachers enact ambitious teaching by identifying and naming separate components of practice that merit consideration and by providing insights into the types of scaffolds needed to support teachers in teaching ambitiously. [ABSTRACT FROM AUTHOR]

In the Hungarian "Guided Discovery" approach to teaching mathematics, teachers' planning work plays a crucial role. Teachers following the approach develop teaching trajectories based on "series of problems". This work includes the choice, creation, transformation, organization and networking of problems with regard to various teaching objectives. However, most of this planning work remains implicit; the structure and rationale of the teaching trajectories are often inaccessible for an external observer (including, for example, student teachers). An ongoing project based on teacher–researcher collaboration aims to reveal the hidden characteristics and principles of teachers' work with series of problems through the creation of innovative resources for teachers. In this paper, we present the design of this collaborative work, a process we designate "reverse engineering", and analyse the development process of resources, focusing particularly on the emergence of new vocabulary and representation tools serving as mediators in the communication between teachers and researchers. [ABSTRACT FROM AUTHOR]

In this paper, we report an enquiry into elementary preservice teachers' learning, as they engage in doing mathematics for themselves. As a group of researchers working in elementary Initial Teacher Education in English universities, we co-planned and taught sessions on growing pattern generalisation. Following the sessions, interviews of fifteen preservice teachers at two universities focused on their expressed awareness of their approach to the mathematical activity. Preservice teachers' prospective planning and post-teaching evaluations of similar activities in their classrooms were also examined. We draw on aspects of enactivism and the notion of reflective "spection" in the context of teacher learning, tracing threads between preservice teachers' retro-spection of learning and pro-spection of teaching. Our analysis indicates that increasing sensitivity to their own embodied processes of generalisation offers opportunities for novice teachers to respond deliberately, rather than to react impulsively, to different pedagogical possibilities. The paper contributes a new dimension to the discussion about the focus of novice elementary school teachers' retrospective reflection by examining how deliberate retrospective analysis of doing mathematics, and not only of teaching actions, can develop awarenesses that underlie the growth of expertise in mathematics teaching. We argue that engaging preservice teachers in mathematics to support deliberate retrospective analysis of their mathematics learning and prospective consideration of the implications for teaching can enable more critical pedagogical choices. [ABSTRACT FROM AUTHOR]

Another significant research area relevant to teacher awareness and its development is teacher reflection on teaching. In this process the role of the researcher/mathematics teacher educator involves development of awareness in mathematics, teaching, teacher education and research. [Extracted from the article]

Attempts to better conceptualize and measure teacher knowledge, and through that examine its association to instructional quality have been intensified over the past decades. Despite the progress made, a review of pertinent literature points to four challenges related to studying this association: proximity (i.e., the extent to which the measures of teacher knowledge and instructional quality are proximal to the actual work of teaching); alignment (i.e., the degree to which these measures are aligned to each other); comparability (i.e., the extent to which the instructional interactions and milieu are comparable across the lessons investigated and the degree to which the conceptualization, operationalization, and measurement of teacher knowledge are comparable across studies); and occurrence (i.e., the degree to which instructional settings provide the possibility for certain events to occur to study how teacher knowledge plays out in instruction). Teaching simulations that allow for the investigation of teacher action-related competence—a construct occupying the intermediate space in between static aspects of teacher knowledge and instructional quality—can partly address these challenges. In this paper, I present such a teaching simulation and explain how it can support the capture of teacher action-related competence, by manipulating instructional complexity and providing a productive platform for performing the work of teaching in controlled environments. I partly illustrate the potential of this approach for disentangling and unpacking the focal association, by presenting results from an exploratory study examining the association between preservice teachers' paper-and-pencil mathematical knowledge for teaching (MKT) and their action-related competence yielded by studying their performance in the simulation. [ABSTRACT FROM AUTHOR]

Teacher expectations not only relate positively to student achievement, but also to student beliefs such as their self-concept. Nevertheless, most studies focus on the relations with student achievement, followed by studies on beliefs. Beliefs are a significant determinant of academic success and can include student self-concept or emotions, such as anxiety. The extent to which anxiety can be influenced by teacher expectations has been investigated in very few studies. This paper examined how teacher expectations related to changes in student achievement, self-concept, and anxiety in mathematics within a school year. The data were from a longitudinal study "Outcomes of teacher education", funded by the Swiss National Science Foundation and based on 28 teachers and 509 primary school students. Teacher expectations were operationalized using the residual approach. Student mathematics achievement was assessed via a standardized mathematics test and their self-concept as well as their mathematics anxiety via a questionnaire. The multi-level structure was considered in the analyses, because the interclass-correlation of student mathematics achievement exceeded the critical value of 10%. The results showed that teacher expectations were positively related to student achievement as well as self-concept and negatively related to anxiety towards mathematics. The change in the explained variance was small (self-concept and anxiety) to large (achievement). The results extend findings on the expectation effect in the classroom, as they focus not only on student achievement but also on student beliefs and are discussed regarding their significance for academic success. [ABSTRACT FROM AUTHOR]

This paper focuses on the importance of identifying students' Prior Knowledge (PK) for the teaching and learning of mathematics. Specifically, we present a framework that exemplifies the core elements teachers need to consider in relation to the purpose, design and implementation of learning experiences that enable PK to be activated and assessed. The paper concludes by offering practical insights for the design and implementation of a PK learning experience using this framework, with a geometry-based example. [ABSTRACT FROM AUTHOR]

In this paper we report on an activity developed in the context of the Erasmus+ PUNTE Project, using the Poly-Universe material, which led to the learning of logic and mathematics among the 10th grade students of a school in the central region of Portugal. Three teachers, two of mathematics and one of philosophy, and 21 students of secondary education participated in the study. The data obtained, following the observation and application of questionnaires and pre- and post-tests, reveal the usefulness of Poly-Universe for the acquisition of notions about logical operations, for analysing arguments and their validity and solving mathematical problems, motivating the students for carrying out the activity. [ABSTRACT FROM AUTHOR]

It is wildly held belief that one way to interest students in mathematics is to use real-world examples. Mathematics teachers are aware of the lack of interest in mathematics by many students and seek ways to improve their motivation. It seems reasonable to suggest that demonstrating to students the ubiquitous nature of mathematics may help overcome this lack of interest. This paper examines the literature pertaining to the use of real-world examples and suggests, that, unless carefully chosen, their use may not be successful in improving students' motivation. [ABSTRACT FROM AUTHOR]

Copyright of Educação Matemática Pesquisa is the property of Pontificia Universidade Catolica de Sao Paulo, Programa de Estudos Pos-Grad. em Educacao Matematica and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Zeitschrift für interpretative Schul- und Unterrichtsforschung is the property of Verlag Barbara Budrich GmbH and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

Different conceptualizations exist about the components of the knowledge teachers need to teach mathematics with professional consciousness, and a researcher needs to describe and assess that knowledge. The fact, however, is that different conceptualizations respond to different needs, and thus, the variety is even a chance to develop the field further, the field of mathematics-related knowledge for teachers and for teaching. This paper sketches basic ideas of selected theoretical approaches, their goals, their fields of application, and their methods. First, three quite influential projects are introduced: The “Michigan Project” (US), “COACTIV” (Germany), and “TEDS-M” (international). Then three conceptualizations with particular approaches are presented: “Mathematics-for-Teaching” (Canada), Rowland’s “Knowledge Quartet” (UK), and Lindmeier’s “Structure Model” (Germany). The paper closes with some remarks concerning horizons: The first remark points to the restriction of all models of evaluating teachers’ professional knowledge, namely, the everlasting gap between the knowledge per se and the need for acting in the classroom. The second remark reads the recently discussed idea of theory-building as a somewhat neglected aspect of professional knowledge. Thirdly, I discuss briefly how far the seminal CK/PCK distinction could really be an appropriate way into perceiving teachers’ professional knowledge. Finally, I close with a few words on the need not to forget the policy issues of our work. The basic overall idea of the paper is to create—within the limited space—a sufficiently broad spectrum of the issue itself, and what was done in recent years to find a basis for research into teachers’ knowledge as a salient issue for the effective teaching of mathematics. [ABSTRACT FROM AUTHOR]

This paper addresses the importance of understanding the personality traits of teachers and their impact on the educational process. It mentions the existence of stable personality traits and variable personality states that vary over time. It also refers to the five-factor personality model (FFM), which includes the domains of Extraversion, Affability, Conscientiousness, Neuroticism, and Openness to Experience. The study is carried out in the context of Higher Education Institutions (HEIs) in Ecuador, where professors perform functions related to teaching, research, extension, and academic management. It is noted that emotional contagion between teachers and students can be relevant in this environment. The paper presents a qualitative analysis based on a Neutrosophic Cognitive Map (NCM) of nine personality traits: Empathy, Openness to Experience, Introversion, Emotional Stability, Kindness and Respect, Flexibility, Excessive Authoritarianism, Neuroticism and Egocentrism. The causal relationships between these traits are highlighted, emphasizing the importance of empathy as a central factor. It discusses how traits such as empathy, kindness, patience, and emotional stability contribute to a positive and productive learning environment. Furthermore, it is noted that the modification of negative traits, such as excessive authoritarianism and egocentrism, can improve the professional development of teachers and benefit students in the long term. Finally, this study is compared with previous research, and it highlights that the results may vary. For example, a study that did not find significant relationships between personality traits and teaching performance is mentioned, while this study suggests that excessive authoritarianism and egocentrism can affect communication with students and the quality of training.

Background: Eye movement modelling examples (EMME) are demonstrations in which learners' not only see a model's (e.g., a teacher's) task performance on a computer screen (as in regular video examples) but also the model's eye movements (represented as moving coloured dots overlaid on the screen). Thereby EMME help guide learners' attention towards the relevant information and can model cognitive strategies which are otherwise unobservable for learners. Objectives: This study investigated whether EMME can help to learn deductive reasoning strategies and how the presence/absence of a teacher's verbal explanation affects learning from EMME. Methods: Secondary education students (N = 137) were randomly assigned to study video examples under one of four conditions in a 2 (EMME: yes/no) x 2 (verbal explanations: yes/no) between‐subjects design. Results and Conclusions: Results revealed only a beneficial effect of the presence of verbal explanations on performance on the practice problems, but no pretest‐to‐posttest learning gains. Implications: Seeing the teacher's eye movements does not appear to enhance learning of deductive reasoning. The presence/absence of the teacher's verbal explanation does not seem to affect learning deductive reasoning. Lay Description: What is currently known about the subject matter?: Eye movement modelling examples (EMME) are demonstrations in which learners not only see a teacher's task execution on a computer screen (as in video examples) but also the teacher's eye movements.The eye movements in EMME were visualized as moving coloured dots overlaid on the screen recording.EMME help direct attention to relevant information and enhance learning; it is not yet known if this also applies to reasoning problems.It is unknown if and how presence/absence of a teacher's verbal explanation affects learning from EMME. What our paper adds to this?: Secondary education students watched EMME or regular video examples with/without a teacher's verbal explanation.The examples demonstrated how to solve deductive reasoning problems (adapted version of the Mastermind game).Performance and learning gains were examined and revealed no differences between conditions. The implications of study findings for practitioners: Seeing the teacher's eye movements does not appear to enhance learning of deductive reasoning.The presence/absence of the teacher's verbal explanation does not seem to affect learning deductive reasoning. [ABSTRACT FROM AUTHOR]

Variance and invariance are two powerful mathematical ideas to support geometrical and spatial thinking, yet there is limited research about teachers' knowledge of variance and invariance. In this paper, we examined how high school teachers deal with the task of looking for invariant properties in a dynamic geometry environment (DGE) setting. Specifically, we investigated if they even attend to invariant properties; what invariant properties they discern and discuss; and how DGE can support such discernment. Our analysis found that teachers tend to discern and discuss invariant properties mainly when they were probed to consider invariance. We also found four categories of invariant properties that seem to be important for a robust and rich understanding of geometric objects in the context of invariance and DGE. The use of DGE allowed teachers to see and interact with invariant properties, thus suggesting that accessing geometry dynamically may have structural affordances especially when exploring invariance. Teachers were able to enact different DGE movements to discern and discuss invariant properties, as well as to reason with and about them. We also saw that teachers' backgrounds and past experiences can play an important role in their descriptions of invariant properties. Possible future research directions and implications to teacher education are discussed. [ABSTRACT FROM AUTHOR]

This paper reports on nine elementary, middle, and high school in-service teachers who participated in a series of workshops aimed at exploring the wonder, joy, and beauty of mathematics through the creation and application of digitally fabricated tools (i.e., laser-cut and 3D printed). Using the Technological Pedagogical and Content Knowledge (TPACK) framework to investigate technological, pedagogical, contextual, and content knowledge, researchers applied qualitative methods to uncover the affordances and constraints of teaching and learning math concepts with digitally fabricated tools and examined how the workshops supported broadening participation in mathematics by focusing on the connections between mathematical inquiry, nature, and the arts. Affordances include opportunities for hands-on learning, visual support at the secondary level, and real-world connections that go beyond the state standards. Barriers include purchasing a laser-cutter, ventilation and noise issues, time constraints, misalignment with school and district priorities, and a lack of administrative support. All participants indicated that they were interested in additional workshops focused on designing their own digitally fabricated mathematics tools that better align with their grade level(s) and standards. [ABSTRACT FROM AUTHOR]