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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]

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 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]

This cross-sectional study looks into how students' perceived teacher support is linked to achievement emotions in mathematics via academic control and value. The data was gathered from 602 secondary students (13-16-year-olds) in 16 mathematics classrooms from three public schools in Jiangsu province, China. Participants were asked to respond to the paper-pencil questionnaire assessing students' perceived teacher support, cognitive appraisals, and achievement emotions in mathematics. Findings showed that cognitive appraisals played complete mediation roles in teacher support and achievement emotions. Intrinsic value and mathematics self-concept were shown to serve a positive role in teacher support and achievement emotions, whereas extrinsic value was found to play a negative one. Besides, teacher support showed the greatest indirect effect on achievement emotions through mathematics self-concept. Lastly, findings indicated the great relevance of teacher support to students' anger, boredom, enjoyment and relaxation in mathematics classrooms. [ABSTRACT FROM AUTHOR]

Grouping by attainment is a relatively new and contested practice in Norway, where strong historical discourses of heterogeneous education are under pressure from international test comparisons, particularly in mathematics. At the same time, research indicates that Norwegian teachers have a high degree of autonomy in education policy enactment. Analysing thirteen Norwegian mathematics teachers' reflections on grouping practices, we seek to understand their decision-making processes within this context. Our findings indicate that teachers report a high degree of autonomy in grouping practices which is exercised through considerable diversity in practice and defended when necessary. Using an ecological model of teacher agency reveals how teachers explore and explain their highly situated practice and its tensions and contradictions. We find that teachers who are removed from the central locus of autonomy have less to draw on in making and justifying their pedagogic choices, while those who are more central are able to continually reassess in this highly sensitive arena. We note the implications for practice and research on attainment grouping, particularly the need for teacher autonomy and support for professionally-based local decision-making. [ABSTRACT FROM AUTHOR]

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]

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]

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]

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]

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]

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]

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]

Mathematics teaching efficacy is an important construct as confidence in one's ability to teach influences teaching practices. This paper explores pre-service primary teachers' mathematics teaching efficacy on entry to initial teacher education and the extent that pre-tertiary mathematics experiences and resultant beliefs affected their mathematics teaching efficacy. A mixedmethods approach combined the Mathematics Teaching Efficacy Beliefs Instrument (N=420) and qualitative interviews (N=30). The findings suggest medium personal mathematics teaching efficacy among participants with limited conceptions of what mathematics teaching involves. While uncertain regarding their immediate teaching ability, participants reported confidence regarding their potential. Mathematics teaching outcome expectancy was high; however, an undercurrent of conviction exists that external factors, most notably learners' natural mathematical ability, are critical to student learning. [ABSTRACT FROM AUTHOR]

Parents' and teachers' beliefs and evaluations of young people are important. Using a feminist institutionalist perspective, and drawing on rich data from one in seven nine-year-old children in Ireland, this paper examines mothers' (who make up the overwhelming majority of primary care-givers) and teachers' perceptions of boys' and girls' mathematics performance. The evidence shows that girls' mathematics performance is underestimated by both relative to boys'. Mother's gender bias was evident among high performing children, at all levels of children's academic self-concept, and among mothers with at least third level education. While the judgements reflect children's actual performance and engagement, a notable gender gap remains. It is suggested that the results reflect gender stereotypes: overestimating boys' and underestimating girls' mathematics achievements. The article indicates the importance of the informal dimension of institutions and the part played by women in the effective devaluation of girls by endorsing gendered stereotypes. Women teachers are less likely to rate children highly in mathematics, taking account of performance: arguably reflecting their own lack of confidence in mathematics assessment. The findings raise concerns for girls' futures since mathematics is seen as an indicator of intelligence. Given the move towards teacher-assessed grading during COVID-19, understanding, and challenging, gender-stereotyping is pressing. [ABSTRACT FROM AUTHOR]

Teaching mathematical modeling is a demanding task. Thus, fostering teachers' competencies in this regard is an essential component of teacher education. Recent conceptualizations of teachers' competencies include situation-specific skills based on the concept of noticing, which is of particular interest for the spontaneous reactions needed when teaching mathematical modeling. The study described in this paper aims to analyze the development of a video-based instrument for measuring teachers' noticing competencies within a mathematical modeling context and obtain evidence for the validity of the instrument. Three kinds of validity are examined in three different studies: content validity, elemental validity and construct validity. Indicators for content validity could be found through different expert ratings and implementation with the target group, where participants were able to perceive all relevant aspects. The qualitative analysis of participants' reasoning, which is consistent with the coded level, indicates elemental validity. Moreover, the results of the confirmatory factor analysis suggest construct validity with one overall factor of noticing competence within a mathematical modeling context. Taken together, these studies imply a satisfactory validity of the video-based instrument. [ABSTRACT FROM AUTHOR]

Although mathematical modeling plays an important role in many curricula worldwide, significant discrepancies persist in the importance of mathematical modeling in ordinary mathematics classrooms and teacher education. This paper compares pre-service mathematics teachers' professional mathematical modeling competencies in three different regions—Germany, Mainland China, and Hong Kong—where educational and cultural traditions differ, including the role of mathematical modeling. In total, 232 pre-service mathematics teachers from the three regions completed a modeling task covering mathematics content knowledge (MCK) of modeling and mathematical pedagogical content knowledge (MPCK) of modeling. The results show that pre-service teachers from Germany demonstrated the strongest MCK and MPCK of mathematical modeling; by contrast, pre-service mathematics teachers from Mainland China and Hong Kong demonstrated relatively weaker MCK and MPCK of mathematical modeling. MCK and MPCK of mathematical modeling were also found to be unevenly developed at different competence levels for the three regions. These differences may be attributed to the history of mathematical modeling in mathematics curricula, teacher education, and teaching culture in these three regions. [ABSTRACT FROM AUTHOR]

For the past forty years, United States school districts have increasingly hired mathematics specialists to support the teaching and learning of mathematics. Despite the prevalence of this professional development structure, this is a relatively new research topic for the mathematics education field. In this paper, we report findings from an exploration of literature between 1981 and 2018 to examine the role of mathematics specialists (MSs). In particular, we examine: (a) MS positioning across research; (b) historical trends of school‐based MS research; and (c) orientations of school‐based MSs within research. Using the McGatha and Rigelman framework as an analytic lens, we found that beyond the positions identified in their framework (coach, intervention specialist, teacher), there were four additional MS positionings within the research (learner, other p‐12 stakeholder, university stakeholder, unknown). Ultimately, we forward an expansion to the McGatha and Rigelman framework to include these new categories, as well as contextual descriptions and working definitions to support future research in more accurately and robustly capturing the ways in which MSs are investigated and reported on in research. [ABSTRACT FROM AUTHOR]

This paper reports an action research study I conducted into the mathematical productive disposition of 29 tenth grade learners in the Philippines by analyzing their metaphorical conceptualizations of mathematics in a series of lessons following principles of Realistic Mathematics Education. Analysis of participants' pre-intervention metaphors of mathematics revealed four conceptualizations that capture learners' perceptions of mathematics reflective of their productive disposition: mathematics as a process, mathematics as a puzzle, mathematics as a problem, and mathematics as a difficulty. Insightful changes in the learners' metaphors of mathematics support the argument that making mathematics matter to students can be achieved if teachers make considerable and devoted attempts at making what matters to students mathematical. Several challenges in the implementation of realistic mathematics lessons on Permutation included developing and enabling students' awareness of their social and cultural environment and encouraging critical thinking. Reflecting on my experience, I argue that constant exposure to lessons that present mathematics as contextually and socially relevant can potentially improve students' mathematical productive disposition together with other strands of their mathematical proficiency. [ABSTRACT FROM AUTHOR]

In this paper, we approach modelling mathematics dispositions from a different methodological perspective in order to shed more light into the complex interplay between teaching practices and students' learning outcomes. We draw on survey data from around 5000 students from Year 7–11 (age 11–16) from 40 Secondary schools in England. Our methodological approach includes Rasch modelling to produce measures of attitudinal outcomes as well as students' perceptions of pedagogic practices. We then employ fuzzy-set Qualitative Comparative Analysis (fs/QCA) to explore the relationships between students' characteristics and the perceived type of teaching they receive in mathematics. We use two measures of 'transmissionist teaching' which aim to quantify the degree to which teaching practices are perceived as 'teacher-centred'. One measure gives the students' perceptions and the other gives the teacher's perspective. We find that different configurations of student and teacher perceptions of transmissionist teaching are associated with high and low mathematical dispositions for different year groups and for boys and girls. We discuss the methodological merits of this approach along with the substantive educational implications of these findings. [ABSTRACT FROM AUTHOR]

Background: Building on the Realistic Accuracy Model, this paper explores whether it is easier for teachers to assess the achievement of some students than others. Accordingly, we suggest that certain individual characteristics of students, such as extraversion, academic self‐efficacy, and conscientiousness, may guide teachers' evaluations of student achievement, resulting in more appropriate judgements and a stronger alignment of assigned grades with students' actual achievement level (as measured using standardized tests). Aims: We examine whether extraversion, academic self‐efficacy, and conscientiousness moderate the relations between teacher‐assigned grades and students' standardized test scores in mathematics. Sample: This study uses a representative sample of N = 5,919 seventh‐grade students in Germany (48.8% girls; mean age: M = 12.5, SD = 0.62) who participated in a national, large‐scale assessment focusing on students' academic development. Methods: We specified structural equation models to examine the inter‐relations of teacher‐assigned grades with students' standardized test scores in mathematics, Big Five personality traits, and academic self‐efficacy, while controlling for students' socioeconomic status, gender, and age. Results: The correlation between teacher‐assigned grades and standardized test scores in mathematics was r =.40. Teacher‐assigned grades more closely related to standardized test scores when students reported higher levels of conscientiousness (β =.05, p =.002). Students' extraversion and academic self‐efficacy did not moderate the relationship between teacher‐assigned grades and standardized test scores. Conclusions: Our findings indicate that students' conscientiousness is a personality trait that seems to be important when it comes to how closely mathematics teachers align their grades to standardized test scores. [ABSTRACT FROM AUTHOR]

This study addresses teachers' activity when working with digital technologies (DT) in their classrooms. We build upon a model that considers teaching as managing open dynamic situations. Within the model, teachers' activity is viewed as diagnosing students' mathematical activity, managing uncertainties due to the characteristics of the situation and decision-making about didactic interventions. The study extends our earlier work and focuses on teachers' interventions in DT-based lessons, as they manage disturbances caused by unexpected difficulties. Our first observation is that there is a substantial change in how teachers diagnose these difficulties compared to paper-and-pencil environments. Notably, they need to make more inferences about the pedagogical support that is provided. Second, we show that in such conditions, rather than facing the single dynamicity of the class as a whole, the teacher has to deal with multiple, open dynamic situations (small groups named mini-classes), which are themselves intertwined in the dynamics of students' interactions with technology. Moreover, even if teachers are able to make reliable inferences concerning an individual student's current difficulties, they must also be able to make inferences about the scope of such difficulties within the class as a whole. We present four case studies that illustrate the diverse approaches that teachers take when managing such open dynamic situations and use them to illustrate the concepts and analytical tools that are introduced. [ABSTRACT FROM AUTHOR]

With the technological improvements of innovative portable recording gadgets, augmented researchers' interest in exploring students' visual attention in their natural and normal occurring classrooms. The purpose of this study was to gauge students' visual attention in their Mathematics and English classrooms. This article reports on a study conducted in three schools in Santiago, Chile, where a sample of 113 randomly selected students wore a mini‐video camera mounted on eyeglass in their Mathematics and English lessons. Using Google images, we automatically and objectively examined 723,600 frames from the recordings where the classroom teacher appeared in the students' visual field. The results show that students' visual attention varies depending on four factors: (a) gender of the student, (b) age of the students, whether students are low/high attainers and (d) whether students are in English or Mathematics lessons. Surprisingly, students significantly paid more visual attention in their Mathematics than in English lessons. High attainers were more visually engaged than their low attainers counterparts. Students appeared to be visually engaged differently at different stages in their education. Furthermore, girls were more visually engaged than boys. The results of this study can have enormous practical implications for teachers and teacher education, in order to be better visually engaged with students during teaching. Lay Description: What is already known about this topic: The advantage of computers and technologies as tools in analysing teaching and learning.Measuring students' visual attention to teachers in different subject disciplines.Using first person's perspective (students' perspectives) in analysing classroom interaction. What this paper adds: Measuring students' visual attention to teachers in Mathematics and English classrooms using 723,600 frames.Students are more visually engaged to teachers in Mathematics versus English classrooms.Higher grade point average students are more visually engaged to teachers than their lower GPA counterparts.Female students significantly pay more visual attention to their teachers than their male peers.Students' visual attention to teachers is dependent on the year of study. Implications for practice and/or policy: Identifying students with lack of visual attention to the teacher objectively and automatically.Practical implications for teacher education courses, and also continuing Professional Development courses for in‐service teachers. [ABSTRACT FROM AUTHOR]

This paper reports changes of the quality of instruction and students' attitudes towards mathematics at one high school during 3 years while teachers participated in a teacher community. The setting for this research was a small-sized high school in South Korea with 154 students and three mathematics teachers. I analyzed the teachers' mathematics classes based on types of interaction, types of questions, and mathematical quality in instruction. Their students' responses for the National Assessment of Educational Achievement study about attitudes towards mathematics were also analyzed. The findings show that this school, over all, improved the mathematical quality and changed the types of questions and the types of interactions towards students' participation in discussing, exploring, and probing mathematical meanings. The students' attitudes towards mathematics became more positive throughout the 3-year period. However, the changes in each teacher's mathematics instruction were different. This study discusses the challenges of having an effective teacher community and researching teachers as learners. [ABSTRACT FROM AUTHOR]

This paper presents a study conducted with 83 Romanian elementary school teachers about their representations of Financial Education (FE) and the importance of teaching it in school. The teachers responded to an online survey about their perceptions and their needs to teach Financial Literacy (FL). The preliminary results show that most of the teachers recognize the importance of learning FL. Their rationale for the importance of financial education in schools range from rational arguments, to citizenships arguments with sociocultural arguments in between. [ABSTRACT FROM AUTHOR]

• Closely examining the mathematical details of classroom interaction is essential. • Engaging in details of others' mathematical ideas relates to achievement. • Productive teacher support depends on following up on invitations to students. • Interaction varies across classroom participation structures. This paper traces the development of a program of work that seeks to understand the teacher practices that promote productive dialogue and learning in mathematics classrooms. This work originated in cooperative/collaborative learning research, with a focus on understanding group dynamics effective for student learning. Over time, it layered on increasing attention to the teacher's role, and branched out to consider the multiple participation structures in the classroom (whole-class discussion, small-group collaborative work, private student-student conversations). Each phase of this work brought in a heightened focus on the details of classroom interaction around mathematics—both in the thinking that students share and in the practices teachers use to support student participation—to better understand the development of students' mathematics learning. [ABSTRACT FROM AUTHOR]

Background: Key elements of instructional quality include the teacher's ability to immediately react in domain‐specific classroom situations. Such skills – defined as action‐related skills – can only be validly assessed using authentic representations of real‐life teaching practice. However, research has not yet explained how teachers apply domain‐specific knowledge for teaching and to what extent action‐related skills are transferable from one domain to another. Aims: Our study aims to examine (1) the relationship between action‐related skills, content knowledge, and pedagogical content knowledge, and (2) the domain specificity of action‐related skills of (prospective) teachers in the two domains of mathematics and economics. Sample(s): We examined German pre‐service and in‐service teachers of mathematics (N = 239) and economics (N = 321), including n = 96 (prospective) teachers who teach both subjects. Methods: Action‐related skills in mathematics and economics were measured using video‐based performance assessments. Content knowledge and pedagogical content knowledge were assessed using established paper–pencil tests. Correlation analyses, linear regressions, and a path model were applied. Results: In mathematics and economics, we find a similar pattern of moderate correlations between action‐related skills, content knowledge, and pedagogical content knowledge. Moreover, a significant correlation between action‐related skills in mathematics and economics can be explained almost entirely by underlying relations between content knowledge and pedagogical content knowledge in both domains. Conclusions: Our findings suggest that action‐related skills empirically differ from domain‐specific knowledge and should be considered as domain‐specific constructs. This indicates that teacher education should not only focus on domain‐specific teacher knowledge, but may also provide learning opportunities for action‐related skills in each domain. [ABSTRACT FROM AUTHOR]

School systems around the world are adopting more intellectually ambitious academic content in the hopes of improving their educational productivity. In the United States, these efforts have required significant changes to teachers' instructional practices, and increased attention to teachers' formal and on-the-job professional learning opportunities. Focusing on the initial implementation of a reform-oriented approach to teaching mathematics in two local school systems in the United States, this paper examines whether – and under what circumstances – elementary teachers' professional learning opportunities predict changes in their instructional practices and beliefs related to mathematics. Our findings reveal that teachers' on-the-job interactions during the first year of reform predicted changes in their instructional practices; further, these changes were associated with the infrastructures that local school systems created to support teacher learning in mathematics. Teachers' participation in formal professional development, in contrast, predicted changes in their instructional beliefs, but not their practices. These findings have implications for future efforts to design formal and on-the-job professional learning opportunities that support ambitious educational reforms. [ABSTRACT FROM AUTHOR]

Empirical studies demonstrate that students have various difficulties in the mathematical modeling and therefore need teacher support. This research explains teacher support in mathematical modeling through the three characteristics of scaffolding (i.e., contingency, fading, and transfer of responsibility). Studies using this theoretical perspective involve open questions concerning which teacher support is suitable for effective scaffolding methods. This study aims to examine the scaffolding methods of teachers who used different participant structures during mathematical modeling activities. This paper argues that teachers' participation structures relate to their scaffolding methods. It also addresses issues that teachers may reflect on while supporting modeling activities. • Teachers' participant structures can relate to their support levels but not support areas. • The teacher who acted as a monitor provided higher support levels compared to the teacher who acted as a partner. • Guiding the understanding of the nature of a modelling task and assisting with modeling stages support modeling competencies. • Strategic and content-related strategic support can be recognized as effective scaffolding methods in modeling process. [ABSTRACT FROM AUTHOR]

• We examine the relationship between teacher meanings and conventions. • Teachers often do not dissociate conventions from logico-mathematical operations. • We provide implications for teaching in relation to conventions of graphing. In this paper, we use relevant literature and data to motivate a more detailed look into relationships between what we perceive to be conventions common to United States (U.S.) school mathematics and individuals' meanings for graphs and related topics. Specifically, we draw on data from pre-service (PST) and in-service (IST) teachers to characterize such relationships. We use PSTs' responses during clinical interviews to illustrate three themes: (a) some PSTs' responses implied practices we perceive to be conventions of U.S. school mathematics were instead inherent aspects of PSTs' meanings; (b) some PSTs' responses implied they understood certain practices in U.S. school mathematics as customary choices not necessary to represent particular mathematical ideas; and (c) some PSTs' responses exhibited what we or they perceived to be contradictory actions and claims. We then compare our PST findings to data collected with ISTs. [ABSTRACT FROM AUTHOR]

• Mathematicians may value pedagogical content knowledge but lack confidence in teaching for its development. • Mathematicians and mathematics educators may value pedagogical content knowledge for similar reasons. • Expectancy-value theory may explain a lack of focus on developing teachers' pedagogical content knowledge. Recent studies suggest that change is needed in undergraduate mathematics capstone courses for prospective secondary teachers. One promising but infrequently used strategy for improvement is to incorporate tasks that explicitly focus on pedagogical content knowledge (PCK). Expectancy-value theory provides an account for why instruction of these courses does not more regularly employ this strategy. To make this argument, this paper uses an interview-based study of 9 mathematicians that investigated the process of prioritizing tasks and goals for these courses. As the study found, these mathematicians valued developing teachers' PCK. However, they were unconfident of their ability to teach with tasks and goals focused on developing teachers' PCK relative to more purely mathematical tasks and goals. The central implication is that interventions in mathematicians' teaching must take into account the possibility that it may be just as important to improve confidence and resources as it is to change values. [ABSTRACT FROM AUTHOR]

Studies have shown that educational robotics (ER) may impact student learning, especially in relation to STEM (science, technology, engineering, and mathematics) areas. In the STEM framework, particularly for younger children, the "E" and the "T" are considered to be missing letters, because few studies have concentrated on teaching and evaluating technology and engineering through ER activities. This study aimed to develop and test the efficacy of an ER protocol to teach robotics in a sample of 389 students, hypothesizing that girls would be as successful as boys. A Robotics Questionnaire assessing the basics of robotics was developed for this study. A Wilcoxon nonparametric test was performed in order to evaluate improvements (p < 0.05). A Mann–Whitney nonparametric test was performed in order to test the presence of gender differences (p < 0.05). Data indicated significant improvements for all the age ranges considered. No gender differences were found. In order to evaluate the efficacy of a didactic intervention utilizing ER, it is important to assess the impact on children's technological and engineering (robotics, in particular) knowledge. Lay Description: What is already known about this topic: Studies have shown that educational robotics (ER) has a potential impact on student learning.In the STEM framework, the "E" and the "T" are considered the STEM missing letters.What this paper adds: This study aims at developing and testing the efficacy of an ER protocol to teach robotics.The hypothesis that girls will be equally successful than boys is explored too, and no gender differences were found.Implications for practice and/or policy: Our results suggest that ER can be utilized to learn robotics, bringing technology in the schools.ER could be considered as a tool able to contribute to girl's involvement in STEM. [ABSTRACT FROM AUTHOR]

The integration of ubiquitous technologies in the field of education has considerably enhanced our way of learning. Such technologies enable students to get a gradual feedback about their performance and to provide adapted learning materials. It is particularly important in the domain of foreign language learning which requires intense daily practice. One of the main inputs of adaptive learning systems is the user’s understanding of a reading material. The reader’s understanding can be divided into two parts: the objective understanding and the subjective understanding. The objective understanding can be measured by comprehension questions about the content of the text. The subjective understanding is the reader’s perception of his own understanding. The subjective understanding plays an important role in the reader’s motivation, self-esteem and confidence. However, its automatic estimation remains a challenging task. This paper is one of the first to propose a method to estimate the subjective understanding. We show that using the eye gaze to predict the subjective understanding improves the estimation by 13% as compared to using comprehension questions. [ABSTRACT FROM AUTHOR]

Integrated Science, Technology, Engineering and Mathematics (STEM) education is an emerging approach to improve students’ achievement and interest in STEM disciplines. However, the implementation of integrated STEM education depends strongly on teachers’ competence, which entails, among others, teachers’ attitudes. Nonetheless, not much is known about the factors that influence teachers’ attitudes toward teaching integrated STEM. Therefore this paper uses a survey method to get insight into the relationship between three groups of variables and teachers’ attitudes toward teaching integrated STEM: teacher background characteristics, personal attitudes and school context variables. The results of the multiple regression analyses reveal three variables that are positively linked with teachers’ attitudes: professional development, personal relevance of science and social context. Moreover two variables show a negative correlation: having more than 20 years of teaching experience and experience in mathematics. The results of this study provide valuable information about factors related to teachers’ attitudes toward teaching integrated STEM. Moreover, these results can be deployed by school administrators to guide them when implementing integrated STEM education in their school. [ABSTRACT FROM AUTHOR]

Abstract: Wealthy schools appoint better qualified teachers, less wealthy schools under qualified teachers. Added to this mix is a powerful teacher’s union whose policies attempt to entrench the job security of teachers in the less wealthy schools irrespective of whether they can teach their subjects or not. Can one isolate these effects from that of other socio-demographic factors that may also be affecting the performance of students when they enrol for a degree at the University of KwaZulu-Natal (UKZN)? An outcome variable that subtracts the number of courses that have been failed from the number of courses that have been passed, dividing this by the total number of years that they have spent studying for a particular degree will be used as a response variable for this paper. Objectives: The system of secondary education in South Africa is highly polarized. On the one hand, we have a group of mainly Black African students, forming about 80% of the total student population, that come from a vastly under-resourced rural or township based community. On the other hand, we have a group of predominantly White and Indian students who are able to attend a far better resourced set of private schools. Added to this mix, we have 240,000 of South Africa’s total number of 390,000 primary and secondary school teachers who belong to a powerful teacher’s union which enjoys a strong political alliance with the ruling party in South Africa. With most of their union members teaching in the less wealthy schools in South Africa, `school background’ now includes a politically motivated component that focuses on teacher self–interest rather than the education of the child. What sort of effect does school background have on the performance of students when they enter an institution of higher learning? More importantly, can one isolate the effect of school background from that of other possibly confounding factors such as gender, financial aid and the receipt of some form of residence based accommodation that will also impact on their performance while at university? Method: A total of 6,183 students enrolling for a degree at the University of KwaZulu-Natal (UKZN) over the period 2008 to 2012 were used a dataset for this study. Permission to use this dataset was given by the Teaching and Learning Office at UKZN. The database that was used for this study was obtained from the Division of Management Information (DMI) office at UKZN. The percentage based marks that students have managed to record for Mathematics, English, Biology and Accounting in their school leaving exams together with some other important but observable socio-economic factors were included in a regression model to determine how students will perform at UKZN. Socio-economic variables relating to gender, race and whether they have receivd some form of financial aid or residence based accommodation while studying at university were also included as predictor variables in our regression based model structure. Results and Conclusions: An interaction effect associated with being a Black African student who has been privileged enough to attend a quintile five school was found to be significant. A main effect associated with being able to attend a more privileged quintile 5 school however was found to be nonsignificant even after an adjustment has been made for gender, race, the receipt of some form of financial aid and residence based accommodation. Given that UKZN already has a number of bridging programs in place that target students who have come from a less privileged background, for university based policymakers, this result may help to justify the targeted selection of Black African students from the less privileged schools that is taking place. Because some of the disparity in matric performance that we are observing may also be associated with teacher competency and the protective influence of a powerful teacher’s union, this paper may also help to highlight some of the economic costs related with having under-prepared students. “A mind is a terrible thing to waste”–United Negro College Fund. [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]

The paper estimates the effect of students’ position in the classroom register on their academic performance. We use a unique dataset from Poland which contains information on the academic outcomes of students in the humanities, science and mathematics lower secondary school exams as well as the position students occupy in their classroom register. We find that students whose names are recorded near the end of the class list have lower performance than those students whose names are recorded near the beginning of the list. The effect appears to be larger for performance in the humanities exam, and for low-achieving boys who attend large classes. [ABSTRACT FROM AUTHOR]

In the present paper we propose an improved class of estimators in the presence of measurement error and non-response under stratified random sampling for estimating the finite population mean. The theoretical and numerical studies reveal that the proposed class of estimators performs better than other existing estimators. [ABSTRACT FROM AUTHOR]

Formal techniques have been devoted to analyzing whether network protocol specifications violate security policies; however, these methods cannot detect vulnerabilities in the implementations of the network protocols themselves. Symbolic execution can be used to analyze the paths of the network protocol implementations, but for stateful network protocols, it is difficult to reach the deep states of the protocol. This paper proposes a novel model-guided approach to detect vulnerabilities in network protocol implementations. Our method first abstracts a finite state machine (FSM) model, then utilizes the model to guide the symbolic execution. This approach achieves high coverage of both the code and the protocol states. The proposed method is implemented and applied to test numerous real-world network protocol implementations. The experimental results indicate that the proposed method is more effective than traditional fuzzing methods such as SPIKE at detecting vulnerabilities in the deep states of network protocol implementations. [ABSTRACT FROM AUTHOR]

Staff education is considered key to quality of early childhood education and care (ECEC) programs. However, findings about associations between staff education and children’s outcomes have been inconsistent. We conducted a systematic review and meta-analysis of associations between ECEC staff education and child outcomes. Searches of Medline, PsycINFO, and ERIC, websites of large datasets and reference sections of all retrieved articles were conducted. Eligible studies provided a statistical link between staff education and child outcomes for preschool-aged children in ECEC programs. Titles, abstracts and paper reviews as well as all data extraction were conducted by two independent raters. Of the 823 studies reviewed for eligibility, 39 met our inclusion criteria. Research in this area is observational in nature and subject to the inherent biases of that research design. Results from our systematic review were hampered by heterogeneity in how staff education was defined, variability in whose education was measured and the child outcomes that were assessed. However, overall the qualitative summary indicates that associations between staff education and childhood outcomes are non-existent to very borderline positive. In our meta-analysis of more homogeneous studies we identified certain positive, albeit very weak, associations between staff education and children’s language outcomes (specifically, vocabulary and letter word identification) and no significant association with a mathematics outcome (WJ Applied Problems). Thus, our findings suggest that within the range of education levels found in the existing literature, education is not a key driver of child outcomes. However, since we only explored levels of education that were reported in the literature, our findings cannot be used to argue for lowering education standards in ECEC settings. [ABSTRACT FROM AUTHOR]

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]

Recently, echo state network (ESN) has attracted a great deal of attention due to its high accuracy and efficient learning performance. Compared with the traditional random structure and classical sigmoid units, simple circle topology and leaky integrator neurons have more advantages on reservoir computing of ESN. In this paper, we propose a new model of ESN with both circle reservoir structure and leaky integrator units. By comparing the prediction capability on Mackey-Glass chaotic time series of four ESN models: classical ESN, circle ESN, traditional leaky integrator ESN, circle leaky integrator ESN, we find that our circle leaky integrator ESN shows significantly better performance than other ESNs with roughly 2 orders of magnitude reduction of the predictive error. Moreover, this model has stronger ability to approximate nonlinear dynamics and resist noise than conventional ESN and ESN with only simple circle structure or leaky integrator neurons. Our results show that the combination of circle topology and leaky integrator neurons can remarkably increase dynamical diversity and meanwhile decrease the correlation of reservoir states, which contribute to the significant improvement of computational performance of Echo state network on time series prediction. [ABSTRACT FROM AUTHOR]

Accurately describing the knowledge dissemination process is significant to enhance the performance of personalized education. In this study, considering the effect of periodic teaching activities on the learning process, we propose a periodic impulsive knowledge dissemination system to regenerate the knowledge dissemination process. Meanwhile, we put forward learning effectiveness which is an outcome of a trade-off between the benefits and costs raised by knowledge dissemination as objective function. Further, we investigate the optimal teaching strategy which can maximize learning effectiveness, to obtain the optimal effect of knowledge dissemination affected by the teaching activities. We solve this dynamic optimization problem by optimal control theory and get the optimization system. At last we numerically solve this system in several practical examples to make the conclusions intuitive and specific. The optimal teaching strategy proposed in this paper can be applied widely in the optimization problem of personal education and beneficial for enhancing the effect of knowledge dissemination. [ABSTRACT FROM AUTHOR]

Girls performing well in mathematics at school do not necessarily enrol for mathematics courses at South African universities. Teachers could be transferring beliefs about the nature of mathematics favouring boys. This paper compared male and female pre-service teachers’ beliefs about the nature of mathematics. A quantitative, descriptive research approach was adopted. One hundred and twenty-six mathematics pre-service teachers, enrolled for an undergraduate teaching training programme at a South African university, completed a questionnaire. While both genders hold the same Platonist and instrumentalist beliefs, females embrace lower experimentalist beliefs than males. Research on differences between male and female pre-service teachers’ beliefs about the nature of mathematics could promote gender equity in mathematics teacher training and better facilitation of the subject, which might consequently encourage more girls to opt for mathematics-related careers. [ABSTRACT FROM AUTHOR]

Thematic work that integrates different knowledge areas is considered suitable for developing young children’s knowledge and skills in early childhood education. This paper reports evidence from a survey of early childhood teachers’ work with mathematics and art integrated in thematic work. In this study, we aim to explore how teachers perceive mathematics learning and teaching integrated with art. Data for analysis were collected from a questionnaire answered by 27 early childhood teachers from Finland and Sweden. Influenced by a sociocultural theoretical framework, the analysis concerns the teachers’ expressed goals for learning and their strategies for achieving these goals. The analysis reveals qualitatively different approaches to the learning goals addressed by the teachers – process-oriented, product-oriented, development-oriented and providing awareness – which, respectively, seem to generate different meanings of mathematical learning integrated with art. This study offers an overview of teachers’ approaches to teaching mathematics and art in thematic work, and of how different approaches may influence what mathematical meaning is offered to children to explore. [ABSTRACT FROM PUBLISHER]

Background: Poor menstrual knowledge and access to sanitary products have been proposed as barriers to menstrual health and school attendance. In response, interventions targeting these needs have seen increasing implementation in public and private sectors. However, there has been limited assessment of their effectiveness. Objectives: Assess the impact of providing reusable sanitary pads and puberty education on girls’ school attendance and psychosocial wellbeing outcomes. Methods: A cluster quasi-randomised controlled trial was conducted across 8 schools, including 1124 girls, in rural Uganda. Schools were allocated to one of four conditions: the provision of puberty education alone; reusable sanitary pads alone; puberty education and reusable sanitary pads; and a control (no intervention). The primary outcome was school attendance. Secondary outcomes reflected psychosocial wellbeing. Results: At follow-up, school attendance had worsened for girls across all conditions. Per-protocol analysis revealed that this decline was significantly greater for those in the control condition d = 0.52 (95%CI 0.26–0.77), with those in control schools having a 17.1% (95%CI: 8.7–25.5) greater drop in attendance than those in any intervention school. There were no differences between the intervention conditions. High rates of school drop-out and transfer meant the trial suffered from substantial participant drop-out. Intention-to-treat analyses using two different imputation strategies were consistent with the main results, with mean differences of 5.2% attendance in best-case and 24.5% in worst-case imputations. Results were robust to adjustments for clustering. There was no impact of the interventions on girls’ self-reported shame or insecurity during menstruation. Conclusion: Results of the trial support the hypothesised positive impact of providing sanitary pads or puberty education for girls’ school attendance in a developing country context. Findings must be interpreted with caution in light of poor participant retention, intervention fidelity, and the attendance measures used. Trial Registration: Pan African Clinical Trials Registry [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]