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In the past decade, research on learning trajectories has progressed from an agenda for research on student learning to include an agenda for research on teaching. In this paper, we use a design experiment to examine a professional development program created to support teacher learning of one learning trajectory. Using a re-interpretation of Ball and colleagues' mathematics knowledge for teaching framework, we conducted a retrospective analysis to examine how a purposefully selected sample of three teachers used their knowledge to participate in discussions of the professional learning tasks designed to support teacher learning of the trajectory. Findings indicate that professional learning tasks focusing on pedagogical content knowledge present in learning trajectories also allow for teacher learning of subject matter knowledge; this learning is mediated by teachers' prior mathematics knowledge for teaching. We conclude with considerations for researchers and professional developers seeking to support teachers in learning about learning trajectories.

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]

This paper explores the nature and source of mathematics homework and teachers' and students' perspectives about the role of mathematics homework. The subjects of the study are three grade 8 mathematics teachers and 115 of their students. Data from field notes, teacher interviews and student questionnaire are analysed using qualitative methods. The findings show that all 3 teachers gave their students homework for instructional purposes to engage them in consolidating what they were taught in class as well as prepare them for upcoming tests and examinations. The homework only involved paper and pencil, was compulsory, homogenous for the whole class and meant for individual work. The main source of homework assignments was the textbook that the students used for the study of mathematics at school. 'Practice makes perfect' appeared to be the underlying belief of all 3 teachers when rationalising why they gave their students homework. From the perspective of the teachers, the role of homework was mainly to hone skills and comprehend concepts, extend their 'seatwork into out of class time' and cultivate a sense of responsibility. From the perspectives of the students, homework served 6 functions, namely improving/enhancing understanding of mathematics concepts, revising/practising the topic taught, improving problem-solving skills, preparing for test/examination, assessing understanding/learning from mistakes and extending mathematical knowledge. [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]

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]

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]

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]

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]

Comparison is a fundamental cognitive process that can support learning in a variety of domains, including mathematics. The current paper aims to summarize empirical findings that support recommendations on using comparison of multiple strategies in mathematics classrooms. We report the results of our classroom-based research on using comparison of multiple strategies to help students learn mathematics, which includes short-term experimental research and a year-long randomized controlled trial using a researcher-designed supplemental Algebra I curriculum. Findings indicated that comparing different solution methods for solving the same problem was particularly effective for supporting procedural flexibility across students and for supporting conceptual and procedural knowledge among students with some prior knowledge of one of the methods, but that teachers may need additional support in deciding what to compare and when to use comparison. Drawing from this research, we offer instructional recommendations for the effective use of comparison of multiple strategies for improving mathematics learning, including (a) regular and frequent comparison of alternative strategies, particularly after students have developed some fluency with one initial strategy; (b) judicious selection of strategies and problems to compare; (c) carefully-designed visual presentation of the multiple strategies; and (d) use of small group and whole class discussions around the comparison of multiple strategies, focusing particularly on the similarities, differences, affordances, and constraints of the different approaches. We conclude with suggestions for future work on comparing multiple strategies, including the continuing need for the development of, and rigorous evaluation of, curriculum materials and specific instructional techniques that effectively promote comparison. [ABSTRACT FROM AUTHOR]

This article discusses the relationship of measure scores to classroom teaching and student learning. It discusses the formulated assumption as well as several observable inferences about the relationship of the measures of teachers' mathematical knowledge for teaching to their actual classroom mathematical work.

In this paper, we explore the influence of the teacher on the language games being played in a Grade 3 mathematics classroom. The kinds of listening strategies used by the teacher seemed to have an impact on the kind of language game being played as a small group of students engaged in a problem-solving activity. Understanding classroom conversation from a language-games perspective is used to explore the kinds of sense-making, student engagement, and new understandings evolving through classroom discourse. Language games may also be important for encouraging students to extend and transform their understandings. We describe how learning to 'teach etcetera' as a way of helping students 'see-as' and move beyond narrowly defined predetermined content may entail playing more open-ended language games and learning how to 'listen'. [ABSTRACT FROM AUTHOR]

The use of and reflection on writing prompts in mathematics education can allow pre-service teachers to enhance their own mathematical knowledge and broaden their understanding of students’ learning needs. In this paper, we share results from a study with secondary pre-service mathematics teachers who were asked to respond to writing prompts related to various mathematical concepts, reflect on their responses, and then give the same prompts to a group of college algebra students. Our analysis of the data shows that the prompts helped the pre-service teachers to reflect on their role as learners, student thinking and needs and classroom practices. We relate these findings to a framework for looking at pedagogical content knowledge and discuss the usefulness of writing prompts with pre-service mathematics teachers for expanding such knowledge. [ABSTRACT FROM PUBLISHER]

Nurtured as a teacher and mentored as a mathematics education researcher, the reflective voice of a teacher-researcher-educator is portrayed in this paper. While drawing upon experience of creating teaching-learning environments, the author outlines the growth of praxis within her practice. She then outlines her coming upon narrative as a deployable unit of analysis with which to grasp teaching-learning practice. With narrative inquiry as strategy, she finally outlines examples of educational action research she is able to conduct. She argues in favour of empowering the praxis of teachers, recognising their language of practice and urges us to listen to their individual voice. [ABSTRACT FROM AUTHOR]

This paper focuses on the preliminary design of a multifaceted computer-based mathematics resource for undergraduate and pre-entry engineering students. Online maths resources, while attractive in their flexibility of delivery, have seen variable interest from students and teachers alike. Through student surveys and wide consultations, guidelines have been developed for effectively collating and integrating learning, support, application and diagnostic tools to produce an Engineer's Mathematics Gateway. Specific recommendations include: the development of a shared database of engineering discipline-specific problems and examples; the identification of, and resource development for, troublesome mathematics topics which encompass ideas of threshold concepts and mastery components; the use of motivational and promotional material to raise student interest in learning mathematics in an engineering context; the use of general and lecture-specific concept maps and matrices to identify the needs and relevance of mathematics to engineering topics; and further exploration of the facilitation of peer-based learning through online resources. [ABSTRACT FROM AUTHOR]

In this article, we describe preservice elementary teachers 'reactions to Liping Ma's (1999) book, Knowing and Teaching Elementary Mathematics (KTEM), from five universities. Ma's discussion of solely teaching elementary mathematics procedurally and its consequences awakens the preservice teachers 'memories of learning elementary mathematics. Ma's analysis of and solution to the problem ignites strong emotions in the preservice elementary teachers and promotes a desire to teach elementary mathematics conceptually. Through the analysis of writing assignments, we summarize how reading and reflecting on KTEM gives preservice teachers an opportunity to examine their beliefs about teaching and learning elementary mathematics conceptually. [ABSTRACT FROM AUTHOR]

This paper describes research into the beliefs and practices established over time by teachers, who had been engaged in an innovative `mathematical investigations' school program, based on the use of exploratory software. The theoretical framework perceives the teacher as an active mediator of innovation, constructing and reorganizing a personal pedagogy. Interview and detailed observa- tional classroom data were collected and analyzed, synthesizing qualitative and quantitative interpretations of teachers' comments in the classroom. The results show that teachers refer to a variety of aspects of the learning situations in which they intervene rather than just the mathematical concepts and ideas. They adopt multiple roles in the classroom and are influenced by the values of the educational system. The ways in which these issues influence teaching and learning of the mathematical concepts at hand is considered. The nature of teacher beliefs and the ways in which they may influence their practice is questioned. [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]

I present Maple Learn, one of Maplesoft's educational products. I provide examples of documents created with it, list some of its capabilities, and share my experience using it in online mathematics tutoring. Overall, I recommend it to teachers and tutors. [ABSTRACT FROM AUTHOR]

The past decade has witnessed a strong, standards-based call for improving what mathematics is taught and how it is taught. In the USA, districts have hired instructional coaches to help teachers shift their teaching from algorithm-based instruction to instruction that is more student-centered and conceptually focused. The purpose of this study was to contribute to the field's understanding of (a) the specific coaching practices that help teachers enact more conceptual-based forms of instruction; and (b) how coaches learn to enact those practices. Using a design-based implementation research approach, we trained coaches using a particular model for one-on-one coaching (Content-Focused Coaching); the coaches then worked with teachers to plan lessons aligned with the coaching model. Data consisted of videotapes of pre-lesson conferences that were transcribed and coded according to the model. Analyses of 32 coaches' practice over a 2-year period suggest that each of the three components of our coaching model (attention to student thinking, pedagogy, and mathematics) demonstrated statistically significant improvement over time. An illustrative analysis of five coaching sessions of one coach revealed a progression over five sessions from planning discussions that stayed at the level of general strategies to more specific conversations about teaching a particular task and then to deeper discussions that integrate attention to mathematical concepts, student thinking, and pedagogical moves. We view this delineation of coach learning as an important first step in laying the groundwork for the design of future coach training. [ABSTRACT FROM AUTHOR]

Games are types of natural activity of children. They enable children to get to know the world, practice various activities in which they are very successful. Children always learn something new from games. By playing mathematical games, children develop mathematical skills and knowledge. Learning through games is an easy, interesting and self-motivating activity. Games are a combination of luck and knowledge, while mathematics is one of the subjects which comprises a special place in the education of children. Mathematics is considered as a basic need for every individual. By playing mathematical games, students love mathematics more than usual, they gain self-confidence and at earliest age they submit themselves to solve mathematical problems with great confidence. The information presented below has been enabled by the conducted interviews of 123 teachers who teach from class one to three, from nine primary municipal schools of the city of Skopje and the surrounding areas. [ABSTRACT FROM AUTHOR]

Mindsets have been shown to greatly influence individuals' efforts and subsequent success in the endeavors they attempt. This is particularly true of mathematical endeavors where mindset impacts the ways in which individuals approach and persevere in learning. This exploratory study investigated the mathematical mindsets held by 242 prospective teachers in undergraduate mathematics content courses for PreK‐8 teachers as well as examined the relationships between mindset, depth of learning, challenge seeking choices, and course grades. A strong predictive nature was found to exist among these variables. Recommendations are identified for future research to investigate prospective teachers' mindsets and depth of learning. [ABSTRACT FROM AUTHOR]

In this paper, we highlight one whole-class discussion that took place in a middle school mathematics Rational Number and Proportional Reasoning course, one of the six mathematics courses teachers take to complete our state-wide middle school mathematics specialist program. Statistical measures indicate that teachers made gains in their understanding of concepts and substantial gains in their views of teaching and preparedness. We provide a microanalysis of one of the lessons, to explain, in part, how they might have made this progress. To develop our argument, we coordinate a social analysis with an analysis of the types of specialized mathematical knowledge that teachers might have considered as they engaged in these discussions. As we will illustrate, these types of classroom discussions provided teachers opportunities to consider new visions for mathematics learning and teaching. [ABSTRACT FROM AUTHOR]

This paper reports on the learning of a group of teachers engaged in an action research project to develop critical numeracy classrooms. The teachers initially explored how contexts in the media could be used as bases for activities to encourage student discernment and critical thinking about the appropriate use of the underlying mathematical concepts. As a result they found it is better to embed critical thinking in the design of whole units of study rather than just to treat it as an add-on to the mathematics curriculum. The following suggests a possible unit of study around the topic of average that aims to build students' capacities for critical thinking. [ABSTRACT FROM AUTHOR]

In this study I have investigated how alternative ways of teaching mathematics influence and affect Early Childhood Education (ECE) students' attitudes towards maths and how they understand their own subjectivities as more or less mathematical during a 10-week alternative maths course. The investigated course adopts a feminist post-structural approach based on critical pedagogy and deconstructive theory and includes an interdisciplinary approach to investigative mathematics. The data used include the memory/narrative writings and process-writings of 75 female teacher-education students, collected from three different cohorts, in which the students describe their learning processes throughout the maths course. The study shows that, in the main, the students became much more positively inclined to the subject of mathematics after the maths course and agreed that this course had changed their understanding of their own mathematical subjectivity, albeit in different and varying ways. [ABSTRACT FROM AUTHOR]

Classroom talk is regarded as essential in engaging and developing student understandings in the domain of mathematics. The processes of classroom talk may occur in quite different ways, ways that shape particular opportunities for learning mathematics. Little is known about how the talk produced in innovative approaches to education mediates the teaching/learning process and promotes student engagement in the practices of mathematics. Situated within a larger study that employed multiple forms of data collection to determine whether a sociocultural approach to teaching and learning could be employed by a sample of teachers to enrich the teaching and learning of mathematics, this paper examines how two teachers used talk to scaffold student learning and how this talk provided students with different opportunities for learning. In the analyses of talk produced in Year 7 classrooms we use Renshaw and Brown's (in press) discourse characterizations to make visible how different forms of talk were being used in the classrooms as thinking devices and as means to explain and generate understanding. We also employ Bakhtin's notion of 'voice' to consider whether the formats of talk used in each classroom facilitate learning in the domain of mathematics. We conclude that the intentional and reflective use of classroom talk affords students a range of opportunities to develop their mathematical thinking and to facilitate engagement with the practices of mathematics. [ABSTRACT FROM AUTHOR]

The use of manipulatives within a mathematical classroom environment has traditionally been offered through the use of manufactured or teacher-created concrete objects. Manufactured manipulatives are ones such as Cuisenaire rods, color tiles, Unifix cubes, pattern blocks, colored craft sticks, or other related, mass-produced objects. Teacher-created concrete objects consist of cardstock, foam, or other paper templates similar to manufactured manipulatives. These are used to provide tactile-kinesthetic learning activities to enhance mathematics conceptualization. The Information Age offers mathematics educators the opportunity to integrate the use of digital manipulatives similar to manufactured and teacher-created ones using the World Wide Web (WWW or Web) as an innovative medium to expand the learner's conceptual framework of understanding. The availability of such web-based mathematical manipulatives is an ever-expanding possibility that can be integrated into student-centered learning environments. However, it is critical for classroom teachers to develop sound rationale when choosing a technology-based resource over other resources, (i.e., manufactured or teacher-created manipulatives). This article explores necessary rationale elements to create a successful "student-centered" learning environment involving digital manipulatives. [ABSTRACT FROM AUTHOR]

For a long time, mathematics educators have shown interest in the use of history of mathematics in mathematics teaching. This article discusses some interesting reasons put forwards by the supporters of this use and their epistemological assumptions. The initial part of the article provides a short account of the setting in which the first discussions and the first experiments concerning the use of history in mathematics teaching took place. Afterwards, the article outlines the development of the community of scholars interested in the relationship between history and pedagogy of mathematics, which in 1976 was officially established as the group HPM (History and Pedagogy of Mathematics) affiliated to ICMI (International Commission on Mathematical Instruction). The materials produced in this context constitute a background and a source for researchers and for mathematics teachers wishing to explore the opportunity offered by history in their teaching. About the introduction of history of mathematics in the classroom, the article focuses on two main streams of action: – history for promoting the image of mathematics as a vivid discipline with links with reality and culture, – history for dealing with mathematical concepts. An efficient introduction of history in teaching entails adequate teachers' historical knowledge. Then a part of this article is dedicated to discuss the role of this knowledge and to present how history may be used in teacher training programs. At the end of the article, some frequent objections put forwards by teachers about the possibility of introducing history in their teaching are presented. The conclusion is that, though there are difficulties and some contexts are not favourable to this introduction, in suitable contexts, the effort required for facing this endeavour will be rewarded by significant improvements in the classroom life. [ABSTRACT FROM AUTHOR]

Given the increasing diversity of the student body, teachers are called to appropriately address students' various learning needs by means of differentiated instruction (DI). However, empirical research has yielded mixed evidence on teachers' reported use of DI. Using nationally representative data from the National Educational Panel Study in Germany, this article aimed to explore German (as native language) and Mathematics teachers' use of DI practices. In addition, this study took into consideration contextual factors, such as school track, and investigated the impact of teachers' constructivist beliefs on their DI implementation. Results from a mixed analysis of covariance indicated that teachers occasionally implement DI practices. Furthermore, between‐subject effects reported differences across school tracks. It appears that advanced secondary school teachers implement less often DI practices. The covariate of teachers' constructivist beliefs was also positively linked to overall teachers' implementation of DI. Implications of the results, as well as further lines of research are discussed. [ABSTRACT FROM AUTHOR]

Using technology to get a graphical representation of functions requires the choice of a suitable viewing window. The literature suggests teachers' knowledge as being central in this process, but does not tell us much about how the teachers should manage this. This study aims to improve understanding about the teachers' choices related to the viewing window on the study of functions. It also intends to illustrate how this analysis can be a useful way to access aspects of teachers' knowledge based on the framework of Knowledge for Teaching Mathematics with Technology (KTMT). The study adopts a qualitative methodological approach, undertaking case studies of two teachers. The findings recognize the importance of carefully sequencing the students' contact with this kind of situation and the impact of the viewing window over the teachers' choices of tasks, pointing to the relevance of considering situations where the students actually face the difficulties. This highlights the relation of teachers' choices of viewing window to their knowledge of different KTMT's domains, and specifically the relevance of knowledge of different ways to change the window; of the difficulties faced by the students; of the most suitable tasks (and required viewing window) at each moment; of the impact of the viewing window on the appearance of a graph and of the different situations associated, from the mathematical point of view. [ABSTRACT FROM AUTHOR]

Objectives: Children's additional health and developmental needs are often first identified by teachers when they begin school. This study estimates the Grade 3 literacy and numeracy outcomes of children with teacher‐identified additional needs emerging in the first year of school, including the added burden conferred by socioeconomic disadvantage. Methods: Population linked data (n = 42,619) were analysed from the Australian Early Development Census, which include teacher reports on children's health and development at school entry, and the National Assessment Program–Literacy and Numeracy, a direct assessment of reading and numeracy skills at Grade 3. Linear regression analyses were used to estimate associations between emerging needs and learning outcomes, adjusted for sociodemographic characteristics. The combined effect of emerging needs and low maternal education (an indicator of socioeconomic disadvantage) on academic outcomes was examined by estimating the relative excess risk due to interaction (RERI). Results: Emerging health and developmental needs at school entry were associated with lower reading (b = −26.86, 95% CI = −29.19, −24.52) and numeracy (b = −24.39, 95% CI = −26.43, −22.35) outcomes at Grade 3. The combined effect of emerging needs and socioeconomic disadvantage was greater than expected when their individual effects are summed (RERI = 0.38, 95% CI 0.22, 0.55 for reading and RERI = 0.27, 95% CI 0.10, 0.43 for numeracy). Conclusion: In the current study, emerging health and developmental needs identified by teachers at the outset of schooling were associated with poorer literacy and numeracy skills at Grade 3, and family socioeconomic disadvantage appeared to further amplify this effect. Meeting the needs of these children will require timely and coordinated supports across the health and education systems, particularly for those children who are also disadvantaged. [ABSTRACT FROM AUTHOR]

This study describes a teaching process that offers teachers and pupils ways of constructing the division operation through illustration based on defining the reference unit (divisor), the reference whole1 and the dividend. We introduce a computerized dynamic environment, using an Excel spreadsheet, in which both teachers and pupils can independently construct the solution process in a manner that leads to meaningful learning. Nine pairs of teachers and pupils underwent an intervention process using Excel, comparing pupils' understanding of division of fractions before and after the learning process. Findings from the pupils indicate the Excel software enabled them to portray and construct the meaning of the division process while applying accurate mathematical terms. Specifically, they could thoroughly understand the meaning of a word problem, so as to explain another student's mistake. Furthermore, teachers' analyses of the pupils' work indicate that the use of this computerized dynamic environment helped the teachers develop mathematical knowledge, pedagogical knowledge and technological pedagogical knowledge. [ABSTRACT FROM AUTHOR]

In Australia, there is increasing scrutiny of teacher education processes in learning to teach primary mathematics. In this study, mixed methods, including linear regression, are used to examine the entry mathematical content knowledge of third-year Bachelor of Education Pre-service Students and to relate this to their graduating level of content and a measure of pedagogical content knowledge based upon capacity to describe student errors and provide learning support. The data indicate low levels of mathematical content knowledge at the beginning of the course, prompting questioning of the focus of earlier mathematics curriculum courses. Over the life of the study, there was improvement in some domains, which is to be expected where knowledge of mathematics was an intended outcome. Mathematical content knowledge at the start, but particularly at the end of the study, was highly predictive of expressions of mathematical pedagogical content knowledge. The stronger predictive value of mathematical content knowledge at the end of the study for mathematical pedagogical content knowledge suggests merit in developing the two aspects of teacher knowledge in tandem, rather than in different courses. The relevance of the data to teacher preparation in the institution and more broadly is discussed. [ABSTRACT FROM AUTHOR]

This scoping review presents an overview of cognitive and social congruence in peer assisted learning (PAL), as the positive effects of PAL have been shown to rely on these critical factors. The scoping review followed the guidelines of the preferred reporting items for systematic reviews and meta-analyses (PRISMA) statement. Databases were systematically searched for articles that focus on PAL and cognitive and social congruence. Participants of the studies included were medical, health science, polytechnic, law and paramedic students. Studies that assessed cognitive and social congruence by questionnaires with a 5-point Likert scale were regarded for meta-analytic pooling. Sixteen of 786 identified articles were included in the review, whereof 9 studies were considered for meta-analytic pooling. The meta-analytic pooling showed that tutees tend to see their student tutors as cognitively (Mweighted = 3.84; range of Mweighted = 2.69–4.56) and socially congruent (Mweighted = 3.95; range of Mweighted = 2.33–4.57). Further, characteristics of student tutors are summarized. This scoping review presents an overview and operationalization of cognitive and social congruence in PAL. Based on the presented meta-analytic pooling, cognitive and social congruence were found to represent relevant key factors in the PAL context. Thus, this theoretical background should be acknowledged as a core concept for tutorials within the medical curriculum. [ABSTRACT FROM AUTHOR]

Physical education professionals aim to develop quality programmes for physical education. This study aimed to develop and validate a scale using professionals’ perceptions of Quality Physical Education QPE in Asia using twenty-four items regarding QPE quality issues. The items covered status and roles, development of educational elements and supportive features in physical education. A sample of N = 799 sport and physical education professionals from eleven Asian cities participated in this questionnaire survey. Twenty-four items relating to QPE were examined via exploratory factor analysis (EFA) using maximum likelihood extraction and direct oblimin rotation methods. Nevertheless, only 20 items were extracted following the EFA examination. Items 1, 9, 14 and 18 were excluded because of low factor loadings. The remaining items were clustered into four subscales: Development and Supportive Elements for Quality Physical Education in Schools (DSFQPE; α = .918), Core Values of Quality Physical Education (CVPE; α = .908), Curriculum Arrangement of Physical Activities (CAPA; α = .884) and Provision and Norms in Physical Education (PNPE; α = .865). The Cronbach’s alpha coefficient (α = .875) indicated excellent internal consistency for the overall measure. Furthermore, the 4 retained factors from the EFA were assessed via robust confirmatory factor analysis (CFA). The 4-factor model demonstrated a good fit with the data (CMIN/DF = 3.450, CFI = .928, TLI = .916, PCFI = .801, RMSEA = .078). The study identified a 4-factor structure with internal consistency and acceptable interfactor correlations. The structure seemed to be applicable, including the twenty items identified as useful and necessary tools for the framework of analysis in the investigation of diverse settings for the study of quality physical education. [ABSTRACT FROM AUTHOR]