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

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

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]

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

Over the years, many countries have modified their school curricula to reflect the problem-solving skills and strategies which school goers should acquire while at school. In 2018, South Africa published a document titled, “Mathematics Teaching and Learning Framework for South Africa: Teaching Mathematics for Understanding” as a means of conscientising and assisting teachers in implementing the curriculum through a problem-solving pedagogy. However, little is known about the problem-solving abilities of pre-service mathematics teachers (PSMTs) solving mathematical problems in applied topics such as financial mathematics. This study drew on Polya’s four-step problem solving heuristic to explore the problem-solving strategies used by groups of PSMTs when solving non - routine problems in financial mathematics. This paper reports on a case study of 11 PSMTs chosen from a Bachelor of Education programme at a rural-based university in South Africa. Data were generated using documents (PSMTs’ written responses), interviews and observations. Inductive analysis procedures were followed in interrogating the data. The results show that groups of PSMTs mostly used algebraic, numerical, pictorial, and verbal problem-solving strategies to solve the problems. None of the groups deployed graphical problem-solving strategy. The study recommends a five-point mathematical problem-solving framework as a tool for analysing teachers’ classroom problem solving strategies. [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]

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]

Inquiry into the teaching and learning of mathematics is a central aspect of the work of both the mathematics teacher and the mathematics education researcher, yet there are profound differences between the practices and processes underlying educational inquiries within each community. These differences are known to hinder implementation of research, yet they can also become a valuable resource. This paper explores a particular model of implementation of research: mathematics teachers adopt and adapt practices and processes of disciplined educational inquiry in a co-learning partnership with mathematics education researchers. We present a narrative inquiry of a teacher–researcher community that designed and studied classroom activities aimed at encouraging students to ask meaningful mathematical questions. The data analysis, informed by the literature on boundary objects and boundary crossing, highlights how the teachers and researchers leveraged their different processes and practices of educational inquiry as a resource in their collaborative inquiry. We conclude by suggesting that informed and thoughtful attention to the differences between teacher inquiry and disciplined inquiry may support and enhance mathematics education research implementation. [ABSTRACT FROM AUTHOR]

Globally, there is considerable investment in education technologies leading to increased attention from stakeholders (Trucano, 2017). For a deeper understanding about the implementation of various technologies, research is needed to examine how teachers are incorporating them in teaching and learning. This study focused on eight countries to examine how teachers used ICT in mathematics instruction and factors that contributed to ICT use. Results show that teachers’ education levels and cooperation amongst educators are associated with ICT use in instruction. The paper includes recommendations and implications for practice and future research. [ABSTRACT FROM AUTHOR]

The study investigated the effects of condonation on the promotion of senior phase mathematics learners into the FET phase in a high school in KwaZulu-Natal. Condoned learners were assisted to progress, despite not meeting the pass requirements. The study suggests learning support strategies teachers could use to improve condoned FET mathematics learners' performance. An exploratory case study investigated the condonation policy and its effects thereof. Interviews were conducted with two mathematics teachers, and open-ended questions were posed. The data analysis entailed collating the data, followed by a thematic data analysis approach. The literature study was done on pertinent theories, prior studies, and pragmatic research. The findings suggest that condoned learners did not master the foundational knowledge and accumulated knowledge gaps. Consequently, learners struggle to achieve good performance in FET mathematics. This may lead to condoned learners failing FET mathematics, dropping mathematics in favour of more uncomplicated mathematical literacy, or dropping out of school rather than completing Grade 12. The study recommends that condoned senior phase mathematics learners struggling to perform well in FET mathematics need to undergo an individualised learning support programme. Teachers will then employ various academic teaching and learning support strategies to help improve learners' FET mathematics performance. The success of learning support depends on a collaborative relationship between nurturing teachers and parents and positive discipline in group teaching within supplemental classes. [ABSTRACT FROM AUTHOR]

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

In response to urgent calls for teaching that is culturally affirming, scholars have developed a myriad of images of culturally sustaining (and related) pedagogies (CSPs). However, for maths teachers, CSPs remain elusive, in part because these images are typically content-neutral and their applicability to practice opaque. In this paper, I synthesize research to help conceptualize and clarify what CSPs may look like specifically in mathematics classrooms. I offer a framework for CSPs in mathematics comprised of four dimensions: (1) anti-assimilationism, (2) strengths-based teaching, (3) power and justice, and (4) affirming identities. [ABSTRACT FROM AUTHOR]

Research in mathematics education has placed significant emphasis on teacher identity, particularly during teacher education, since it plays a critical role in shaping the identity of preservice teachers with regard to teaching mathematics. However, as teacher identity is context dependent, it is essential to study preservice teachers' identities in various contexts to develop expertise in mathematics teacher education. This study explored the transformation of preservice mathematics teachers' (PMTs) teacher identity orientations after participating in a video club. Concentrating on task perceptions as the indicator of teacher identity, the change in the teacher roles that PMTs would like to adopt in the future and the student outcomes they associated with these roles were investigated. The analysis of teacher identity orientations before and after participating in the video club revealed that PMTs' teacher identity orientations were transformed by their participation because the video club increased their self-awareness and understanding of the complexity of teaching mathematics. The most noticeable transformation was observed in the didactical roles and their associated outcomes. These roles were transformed from being a didactical expert aiming to develop students' affective outcomes to being a didactical expert who prioritizes students' cognitions. Although PMTs' expertise in teaching mathematics and the content of the video cases limited their orientations, the video club can simulate alternative experiences for teacher education programs aiming to support PMTs' teacher identity orientations. [ABSTRACT FROM AUTHOR]

We give an unconventional, mythopoetic response to the question of Why teach mathematics to all learners in school? In our work with pre-service teachers, we attempt to teach how to value the vulnerability of the multispecies world in a relational, anti-colonial way through passionate immersion, and to use mathematics education towards the ends of promoting its and our own (human) flourishing through taking on relationships of curatorial care. Our contribution includes the novel theoretical assemblage and elaboration of the metaphors of plot and curating as "medicine" [Doolittle, E. (2007). Mathematics as medicine – plenary lecture. In P. Liljedahl (Ed.), Proceedings of the 2006 CMESG Annual Meeting (17–25), Burnaby, BC, Canada.] for addressing challenging ethical questions for mathematics education [Karrow, D., Khan, S., & Fleener, Y. (2017). Mathematics education's ethical relation with and response to climate change. Philosophy of Mathematics Education Journal, 32 (Special Issues on Mathematics Education and the Living World: Responses to Ecological Crisis). ISBN: 1465-2978.] of its ongoing relationship with the precarity produced by unexamined plantation commitments. [ABSTRACT FROM AUTHOR]

The study reported on here was conducted to explore four Grade 7 mathematics teachers' understanding of the relationship between the objectives indicated in the CAPS for teaching different topics/concepts and instructional time stipulated for doing so. Seven lessons were studied in 4 primary schools in the Vhembe district of the Limpopo province, South Africa. A constructivist philosophical approach was used. The data collection methods included interviews and classroom observations. The main finding indicates teachers' understanding of instructional time as either a regulatory or a teaching tool. The ability to translate instructional time into social time depends on the level of teachers' curriculum literacy. Consideration of how CAPS objectives could be fulfilled based on the topic/concept to be taught and the stipulated instructional time, influenced the learners' conceptual understanding, procedural fluency, and competency in mathematics. The conclusion underscores the importance of instructional time as both an essential authoritative regulatory tool and signal of a pedagogic device and communication required to advance the instructional objectives. [ABSTRACT FROM AUTHOR]

Teacher dashboards in mathematics classrooms tend to provide teachers with information on student performance that are often linked to classroom management systems, online course systems, or peer-tutoring software. Teacher dashboards also tend to emphasize features that support teachers using a "transition" or "direct instruction" model. In our approach, we iteratively designed, developed, tested, and refined a teacher dashboard that is linked to a student digital collaborative environment with an embedded problem-based mathematics curriculum. In this study, we investigate teacher dashboard features that support teacher enactment of problem-based mathematics curriculum embedded in a digital collaborative platform. We report on design principles that guided the development of three teacher dashboard features: (1) monitoring evidence of student thinking in real-time or after class, (2) accessing workspace for whole-class discussions of the problem, and (3) creating and sending "just-in-time" supports. The pedagogical advantages and challenges teachers face throughout the iterative development process are also discussed. Evidence from observational data and teacher interviews suggests that the organic synergism generated from the student and teacher digital platform offers several ways that teachers are provided with new and timely information from teacher dashboards that supports problem-based mathematics teaching. [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]

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]

When implementing educational innovations, teachers' approaches to integrating new teaching demands are a crucial factor in their professional development. This becomes especially important in inclusive mathematics education, where teachers are demanded to integrate two jobs: (a) create joint learning experiences for all students and (b) provide focused learning opportunities for individuals. These jobs and the orientations in which they are pursued are perceived as conflicting demands by some teachers, while others do not. Within the model of content-related teacher expertise, this qualitative study investigates teachers' practices for integrating these demands by disentangling the interplay between teachers' self-reported practices and their underlying orientations about inclusive education. The analysis reveals that only some teachers explicate conflicts between inclusive teaching demands. It also shows that teachers command a variety of different practices for dealing with the new teaching demands and that some complex practices can indeed integrate different demands simultaneously. Implications include the insight that professional development programs on inclusive education should pay careful attention to teachers' articulated jobs and orientations in order to promote the integration of teaching demands. Beyond this specific professional development content, the search for practices for integrating demands arising from an interplay of jobs and orientations might be a promising professional development research approach for increasing the scope of professional development. [ABSTRACT FROM AUTHOR]

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

This article offers an analysis of preservice mathematics teachers' knowledge and understanding of assessment literacy. We draw from Abell and Siegel's (2011) notion of assessment literacy to explain the salient component of assessment literacy among the preservice teachers who participated in this study. Semi-structured and group interviews were used to generate data from three second-year preservice teachers enrolled in a Diploma in Education program. Data were analyzed using thematic analysis. While the findings revealed that preservice teachers perceive assessment as an ongoing process aimed at gathering information about students' learning, their knowledge is grounded more on summative assessment. Furthermore, it was noted that preservice teachers view assessment as generic and not specific to mathematics teaching. In terms of conducting assessments, preservice teachers concede that time aligns with purpose and that administering assessments is solely the instructor's responsibility. Based on the findings, we concluded that preservice mathematics teachers have limited knowledge and understanding of assessment literacy. Thus, it is recommended that teacher educators pay particular attention to the evolution of preservice mathematics teachers' conception of assessment literacy. It is also recommended that preservice mathematics teachers' classroom assessment practices be investigated to ascertain how their assessment knowledge informs their classroom practices. [ABSTRACT FROM AUTHOR]

The current paper primarily aims to investigate pre-service science and mathematics teachers' personal growth initiative levels. The second aim of the study is to examine whether participants' initiative levels differ in relation to their gender, grade, department, perceived academic achievement, and willingness to attend graduate education after graduation. The study group consists of 212 pre-service teachers (156 female, 56 male). 80 of them attend science education program, whereas 79 of them attend primary mathematics education and 53 of them attend secondary mathematics education program in two different state universities located in Aksaray and Ankara, Turkey. The participants were surveyed by "The Personal Growth Initiative Scale-PGIS" developed by Robitschek (1998) and adapted into Turkish by Akın and Anlı (2011). The data collected during the spring term of 2014/15 academic year. The construct validity of the scale was verified by confirmatory factor analysis, and the reliability was examined by calculating the Cronbach alpha value of the PGIS. The results showed that (1) pre-service teachers have moderate levels of personal growth initiative, (2) their PGI levels statistically differ in relation to their willingness to attend graduate education, and (3) juniors have higher levels of personal growth initiative than freshman and sophomores. [ABSTRACT FROM AUTHOR]

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

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]

This study examined the mathematical learning opportunities provided to emergent bilinguals (EBs) through their participation in whole class discussions in an elementary classroom. Positioning theory (Harré & van Langenhove, 1999) was used to examine a third-grade monolingual teacher's positioning acts and related storylines across two years. An examination of the data revealed the teacher utilized three prevalent positioning acts with EBs (i.e., inviting EBs to share mathematical thinking, valuing EBs' mathematical contributions, and inviting peers to consider EBs' mathematical contributions) that provided multiple and varied opportunities to participate in whole class mathematical discussions while circulating two storylines: EBs are mathematically competent and EBs can explain their mathematical reasoning to others. Findings suggest that positioning acts can be used in similar ways by other teachers across contexts to strive for equitable mathematics education. [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]

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

The aim of this study is to compare students’ use of number sense strategies based on their mathematics success levels. Participants were 129 seventh graders from three elite secondary schools in Trabzon. Data were collected through a written examination with 10 problems and semi-structured interviews. Interview data were analyzed by considering students’ mathematics success and the differences and similarities among responses. Interviews were held with six students from two schools with different levels of mathematics success. The findings showed that students rarely used number sense strategies and mostly solved problems by using rules and algorithms. Even successful students seemed to have adopted the rule- and algorithm-based solution approach, making it necessary to investigate teacher criteria of mathematical competence. Another noteworthy finding from the interviews with students was teachers’ embrace of rule- and algorithm-based solutions when solving problems. The study finishes with an evaluation of the inclusion of number sense dimensions in secondary school mathematics textbooks in Turkey and recommendations for improving students’ number sense. [ABSTRACT FROM AUTHOR]

The teachers' role is to influence, engage, commit, and support the students toward a positive outlook of Mathematics as a discipline. This suggests that students' understanding, acknowledgment, and achievement in the discipline primarily depend on the teachers. Considering teachers' roles and students' achievement, the study aimed to determine the teaching competencies affecting teachers' performances and their association with the students' mathematics performance. The study utilized a survey questionnaire, and the obtained data were analyzed using descriptive and inferential analysis. The respondents involved 51 primary school teachers from Grades 4 - 6 in Tinoc District, Tinoc, Ifugao, Philippines. Results showed that the teachers always observed the teaching competencies in their Mathematics teaching. Conclusively, assessment of learning was the most observed competency, followed by personality traits, teaching pedagogy, and instructional material (IM) utilization. Results also showed no significant difference in the teaching competencies based on demographic factors. Moreover, results indicated a lower average (45.80%) Mathematics performance of the primary school students. Consequently, further analysis revealed a non-association between the teaching competencies and the students' mathematics performance. These results infer that the students' mathematical ability was at the beginning level, and mathematical concepts were not fully grasped. It also indicates that teachers were not able to affect the students' performances regardless of always observing the competencies. Nonetheless, a firm view of the teacher's ability to impact the students' understanding and achievement in mathematics is still sustained. [ABSTRACT FROM AUTHOR]

Research shows that attention to pattern and structure is fundamental to mathematical learning and attainment yet early mathematics curricula in England underplay the importance of patterning. In a critical realist notion of powerful knowledge, pattern teaching has the potential to empower children to notice patterns, mathematise their everyday experiences and engage in mathematical sense-making. This study investigated how to harness this potential. It reports on participatory research with ten teachers of three to five-year-old children in England as they developed pattern teaching in their classrooms. Findings indicate that teacher knowledge, pedagogic interactions and pattern-rich environments (all underpinned by an appropriate developmental progression and extended to form a setting-wide shared approach) support the development of patterning praxis in early childhood classrooms. These offer potential priorities for ECE teachers in developing their patterning praxis in order to support children's mathematical learning. [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]

In this study, we aimed to determine Cypriot primary mathematics teachers' perspectives and lived experiences during the transition to emergency remote teaching (ERT) in the early stage of the COVID-19 pandemic. An in-depth online survey combining closed-ended and open-ended questions was administered to sixty-two (n = 62) educators teaching mathematics in public primary schools during the first lockdown in spring, 2020. The data from closed-ended questions were analyzed using descriptive and inferential statistics, whereas, for the open-ended questions, a thematic analysis approach was employed. Our findings provide useful insights regarding teachers' self-reported technology backgrounds and levels of instruction regarding the use of technology in mathematics prior to the pandemic, as well their level of preparedness for ERT and the main challenges they faced in implementing ERT of mathematics. Our findings also indicate teachers' levels of satisfaction with their ERT practices and their beliefs concerning the extent of achievement of the curriculum learning objectives through ERT, and how these varied based on teachers' self-reported levels of familiarity with technology, their self-reported levels of preparedness for teaching at a distance, and their engagement (or non-engagement) in synchronous instruction during ERT. Teachers' suggestions, based on their experiences from the lockdown period, regarding how to transform mathematics teaching and learning in the post-COVID-19 era are also presented. [ABSTRACT FROM AUTHOR]

Throughout my career as a teacher, I encountered classes with students who had special educational needs on several occasions. I concur that including them in all activities relevant to Mathematics and natural sciences is crucial. To achieve this, an Individual Educational Plan must be created. (IEP). According to the definition provided by the author, "the INDIVIDUAL EDUCATION PLAN is a written document for the steps taken to support children with special education needs that result from the disabilities the students pose, and helps them in a special way to achieve their academic and socializing objectives." The purpose of this study was to gain a fundamental understanding of how Mathematics and natural sciences teachers implement individualized education programs for students with special needs, how these plans affect students' academic achievement, and whether or not parents are involved in the planning process. The study's findings revealed that 68% of Mathematics and natural sciences teachers in lower and higher secondary schools use individualized education plans. Also, it was discovered that there is a statistically significant correlation between student progress or achievement in these classes and the implementation of (IEP) in Mathematics and natural sciences classes. While creating a student's customized education plan for the topic of Mathematics and natural sciences, teachers, and parents don't work together at all. The teachers agreed that students with special needs should continue their education in ordinary schools or regular classes, rather than special ones, but they claimed that they lacked sufficient training and required a better understanding of the creation and implementation of the IEP PLAN. [ABSTRACT FROM AUTHOR]

This article reports on a second national survey of higher education institutions in the USA to answer the question "Who teaches mathematics content courses for prospective elementary teachers, and what are these instructors' academic and teaching backgrounds?" and addresses valuable information not collected with the first survey conducted in 2010. We surveyed 1740 institutions and a faculty member from each of 413 institutions (23.7%) participated in the survey. The survey results demonstrate that the majority of these institutions are not meeting the recommendations of the Conference Board of Mathematical Sciences (2012) and the Association of Mathematics Teacher Educators (2017) for prospective elementary teachers to take at least 12 semester-hour credits of mathematics content designed specifically for them. The data do indicate that there is movement toward more activity-based approaches for these courses as compared to the 2010 survey. Additionally, there is an increase in these courses having instructors with doctorates in mathematics education as well as an increase in instructors having grades 7–12 teaching experience. Most instructors for these courses do not have elementary teaching experience and have likely not had opportunities to think deeply about the important ideas in elementary mathematics. While most institutions still do not provide training and/or support for these instructors, formalized support and training appear to be increasing since the 2010 survey. [ABSTRACT FROM AUTHOR]

We report on a teacher development program aimed at improving mathematics teaching and learning from grades 5–9. The 18-month largely online program arose from a partnership of mathematics education researchers, mathematicians, physicists, and nine school districts. The program employed functions as a lens to reinterpret and interconnect content topics in the mathematics curriculum. It was designed to promote a deep understanding of mathematics while drawing upon students' spontaneous reasoning, generalizations, representations, and discussions about relations between physical quantities and numbers. We describe the program's foundations and activities and analyze changes in teaching and in student learning during 3 years of implementation. Results suggest that the teacher development program contributed to improved teaching in the target districts and to positive changes in the performance of target district students on state-mandated tests. [ABSTRACT FROM AUTHOR]

This article approaches the relationship between mathematics education and field education, based on the academic production of the research group on mathematics education in field education contexts (Gpemce) created in 2008 at the Federal University of Pernambuco. After presenting the repercussions and lines of research of the group, we reflect on the roots and principles of field education and some approximations of this domain with mathematics education. Then, we present a documentary study, whose corpus consists of 20 articles published in journals by researchers from Gpemce from 2009 to 2020. These articles are organised around four thematic categories that are associated with the research lines of the group: teaching and learning mathematics in field education contexts; relationships between curriculum contents, mathematical practices and productive field activities; resources in the teaching of mathematics in field schools and qualification of mathematics teachers of schools in field areas. The study highlights the diversity of educational subjects, themes, and sociocultural contexts contemplated in the research, and points out ways to conduct new investigations that contribute to deepen our understanding of the teaching and learning of mathematics in field schools and initial and continuing teacher education in field education contexts. [ABSTRACT FROM AUTHOR]

This study aims at investigating inclusive pedagogical content knowledge (IPCK) of mathematics teachers who teaches in inclusive classes including learning disabilities (LD) students or hearing impairments (HI) students in the context of angle concept. The study is a cross-case study which facilitates the comparison as one of the multiple case designs. The participants of the study are six Turkish mathematics teachers, three of them have experience of teaching to students with LD, and three of them students with HI. The data of the study is collected via semi-structured clinical interviews, and analysed using cross-case analysis. According to the findings of the study that examines the IPCK of teachers regarding the concept of angle, it can be said that teachers' definitions of angle and their teaching strategies are insufficient. Additionally, it was found that HI teachers used much more multiple presentation such as speaking, writing, drawing shapes, and gestures than LD teachers. [ABSTRACT FROM AUTHOR]

Background: Research into numerical cognition has contributed to a large body of knowledge on how children learn and perform mathematics. This knowledge has the potential to inform mathematics education. Unfortunately, numerical cognition research and mathematics education remain disconnected from one another, lacking the proper infrastructure to allow for productive and meaningful exchange between disciplines. The present study was designed to address this gap. Aim: This study reports on the design, implementation, and effects of a 16‐week (25‐hour) mathematics Professional Development (PD) model for Kindergarten to Grade 3 educators and their students. A central goal of the PD was to better integrate numerical cognition research and mathematics education. Sample: A total of 45 K‐3 educators and 180 of their students participated. Methods: To test the reproducibility and replicability of the model, the study was carried out across two different sites, over a two‐year period, and involved a combination of two different study designs: a quasi‐experimental pre–post‐research design and a within‐group crossover intervention design. Result: The results of the first implementation (Year 1), indicated that compared to a control group, both teachers and students benefited from the intervention. Teachers demonstrated gains on both a self‐report measure and a test of numerical cognition knowledge, while students demonstrated gains in number line estimation, arithmetic, and numeration. In Year 2, teachers in the intervention group demonstrated greater improvements than the control group on the self‐report measure, but not the test of numerical cognition knowledge. At the student level, there was some evidence of gains in numeration. Conclusion: The current PD model is a promising approach to better integrate research and practice. However, more research is needed to determine in which school contexts the model is most effective. [ABSTRACT FROM AUTHOR]

This study aims to describe the representation ability profile of prospective English teachers in terms of Prior Knowledge (PK) and the types of errors that are made based on the Newman procedure. The research method used is descriptive qualitative case research. The subjects of this study were 50 level IV students taking Statistics on ELT (English Language Teaching) courses in the English Language Program at a university in Cirebon. The results of the data show that the ability of the prospective teacher's mathematical representation in solving statistical questions in ELT in terms of PK, namely the upper group with an average of 76.57% lower than the average midterm score of 95.75, the middle group with an average 67.82% lower than the midterm average of 82, and the lower group with an average of 38.33% lower than the midterm average of 57%. The types of mistakes made by the SKB group were many mistakes in understanding the problem, transforming the problem, and the final answer. The SKS group had the most mistakes in the final answer and the SKA group had the most errors in understanding the problem. Based on the results of research for learning mathematics to prospective language teachers starting from basic concepts, not only memorizing but concepts, giving problems related to the ability of mathematical representation with lots of practice questions, especially in statistical tests. [ABSTRACT FROM AUTHOR]

Within a global context of more standardization of teacher preparation, programs in the USA are increasingly using standardized teacher performance assessments such as edTPA to evaluate prospective teachers' instructional effectiveness and readiness for their own classroom. This study was conducted in a state recently requiring successful completion of edTPA for initial teacher certification. Phenomenological methodology was used to examine the lived experiences of six elementary prospective teachers completing Elementary Education edTPA: Assessing Students' Mathematics Learning (i.e., Math Task 4) during student teaching. Data were collected via 24 individual, phenomenological interviews at specific phases during the student teaching semester. Whole-Part-Whole analysis revealed the prospective teachers found themselves in a state of elusiveness as they engaged in Math Task 4. Three themes provide the structure for elusiveness, including juggling Math Task 4 in student teaching classrooms, from relying on experts to standing alone, and navigating edTPA processes. Understanding prospective teachers' lived experiences with Math Task 4 provides insights into both needed supports for their successful completion of the task and some of the issues with a high stakes teacher performance assessment embedded in the student teaching semester. [ABSTRACT FROM AUTHOR]

With this article, we aim to spur a conversation on research implementation in the context of collaborations of mathematics teachers and educational researchers, with a special interest in projects situated in university mathematics education. Implementation has been often discussed in relation to the education of school teachers, and we suggest that the conceptual, theoretical, and analytical apparatus that has been developed in this research area can be re-purposed to study implementation. Specifically, we propose that in collaborative projects, implementation can be construed as an interactive change-oriented process, in which teachers and researchers develop their praxeologies through interaction and joint work on boundary objects. We illustrate the usefulness of this proposal with a teacher-mathematician and a mathematics education researcher who joined forces to introduce scriptwriting activities into an undergraduate mathematics course. Drawing on the theoretical analysis and illustration, we make suggestions for future implementation studies in the context of teacher-researcher collaborations. [ABSTRACT FROM AUTHOR]

While the perspectives and practices of many educational stakeholders in relation to STEM have been documented, research has yet to deeply explore pre-service teachers' (PST) understandings and how to support their sensemaking about STEM during pre-service teacher education. To address this, we used two STEM integration frameworks, focused on discipline-based practices and modeling with data, to inform the design of a STEM unit that brought together thirty secondary mathematics and science PSTs. With an eye on PSTs' development of a situated understanding of STEM, a qualitative analysis of pre/post surveys and STEM lesson sketches revealed that PSTs collectively shifted from initial views of STEM as blurred lines between subjects to a more nuanced understanding of where and how subjects cross and meet. PSTs also described STEM activities through a more plausible understanding of student and teacher actions and viewed data as a bridge to connect disciplines and the real-world. Furthermore, PSTs' descriptions of anticipated challenges to planning for and implementing STEM mirrored those of in-service teachers. We discuss these findings through the lens of sensemaking theory, highlighting shifts in the sum of PSTs' individual understandings to a more collective and situated understanding of STEM. We also discuss implications focused on the role of data in STEM activities and the affordances of secondary mathematics and science PSTs sensemaking together to about STEM. [ABSTRACT FROM AUTHOR]

Although trigonometry is an important section in secondary school mathematics curricula, many teachers find it challenging to teach as a result of insufficient pedagogical content knowledge (PCK). Therefore, the aim of this article was to report on how PCK on trigonometry manifests itself in teachers' practice. This exploratory case study was underpinned by the mathematics knowledge for teaching (MKT) model of Hill et al. (2008). Twelve teachers were purposefully selected from six township schools. Qualitative data were collected through semi-structured one-on-one interviews, lesson plans, assessment tasks, and lesson observations; and analyzed using content analysis. The findings show that four elements of PCK on trigonometry manifest themselves in teachers‟ practice, namely knowledge of subject matter, knowledge of teaching strategies, knowledge of students‟ conceptions and knowledge of curriculum, but varied in levels of sufficiency. Awareness of these variances forms a useful basis for planning developmental opportunities that could address shortcomings in PCK on trigonometry in teachers‟ practice. This study adds to few studies in PCK in mathematics by providing empirical evidence on how PCK on trigonometry manifests itself in teachers‟ practice. [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]

This article builds upon a systematic review of 53 articles in international research journals and makes three main contributions. First, it develops a method for identifying motives, values, and assumptions in research by analysing segments of text in journal articles. Second, it represents a reflective account of research within the field of mathematics education. Third, it captures the ongoing directions of intentionalities inherent in the diverse field of special education mathematics and, thereby, some of the characteristics of the core issues in this field. Three directions of intentionalities were identified: towards teachers and teaching competence, towards enhanced mathematical achievement, and towards every student's learning. The results indicate that each direction has specific limitations and potentials. In order to improve special education mathematics, we recommend that researchers and practitioners remain broadly informed and involved in all three directions of intentionalities. [ABSTRACT FROM AUTHOR]