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This theoretical paper focuses on how school-based continuous professional development (CPD) for mathematics teachers in schools located in disadvantaged areas can be carried out using the lesson study approach. School-based CPD is based on the notion that teachers need real-time and on-site professional training tailored to improve the instructional practices unique to their school and classroom contexts. The paper seeks to address the research question: How can a lesson study [or research lesson] be used in the school-based CPD of mathematics teachers in schools located in disadvantaged areas? Empirical evidence from lesson study research suggests that it is an effective tool for CPD activities because it is school-centred, focuses on learner learning, and draws on the collective and collaborative experiences of teachers working in the same school mathematics department. Therefore, this paper significantly contributes to theoretical and practical debates on school-based CPD activities in schools located in disadvantaged areas, using lesson study. Further research would necessitate a focus on understanding how the social learning processes within school-based CPD can be linked to school contexts. [ABSTRACT FROM AUTHOR]

As content-specific educational coaches, elementary mathematics specialists (EMSs) have emerged as school-based professionals who are needs-driven and work closely with school stakeholders in regard to mathematics teaching and learning. While leading mathematics education organizations have identified the specialized knowledge and skills required for EMS positions, how to best prepare these individuals is knowledge that the field is still exploring. This paper first presents a theoretical model for EMS preparation that aligns an emerging coaching tool, the Decision-Making Protocol for Mathematics Coaching (Baker & Knapp, 2019, [DMPMC]) with the Professional Development Design Framework (Loucks-Horsley et al. in Designing professional development for teachers of science and mathematics, Corwin Press, 2010). The paper then presents a descriptive case study that examines the application of this model in an EMS preparation course. The findings indicate that assessing the coaching situation fostered administrative partnerships, revisiting goals increased specificity of anticipated outcomes, and applying research-informed practices increased EMS self-efficacy and advanced coaching agendas. Taken together, these findings suggest that integrating the DMPMC into an EMS preparation course led to positive changes in EMS candidate learning of professional development design. Notably, this is one of the first studies that documents the influence of a coaching education tool on EMS candidates' professional development design. [ABSTRACT FROM AUTHOR]

This article shares a paper presented as the keynote for the Terry L. Wood Memorial Conference that was held virtually on May 20, 2022. This paper starts with a reference to the project, The Coordination of a Psychological and Sociological Perspective, that was funded by the Spencer Foundation. The results of the research in this project are published in the book, The Emergence of Mathematical Meaning, edited by Cobb and Bauersfeld (1995). [ABSTRACT FROM AUTHOR]

Learning styles is the idea that there are unique ways in which individuals approach learning and process information. Though refuted, the idea of learning styles has not declined in peer-reviewed reports of empirical studies or teacher/practitioner resources. Some reports have also used learning styles as a tool for improving the mathematics education of students with learning disabilities—an area of interest for mathematics education and special education communities alike. In this paper, we review articles published by the National Council of Teachers of Mathematics to investigate the perspectives of learning styles at the intersection of mathematics education and learning disabilities. Analyses highlight the relationship between mathematics education, learning disabilities, and learning styles, and the varied meanings and perspectives of the articles' authors. Of note is both the perpetuation of unfounded concepts and the lackluster response to explicit contests of the idea of learning styles. [ABSTRACT FROM AUTHOR]

This article explores the power of language to either include or exclude certain groups of students from genuine opportunities for mathematical sense-making. The substantial increase worldwide in the number of students learning mathematics through a language other than their primary language makes this a particularly urgent issue. This paper focuses on the South African situation, where, because English is widely perceived as the language of opportunity, it is, by grade 4, overwhelmingly the chosen language of learning and teaching. The epistemological and pedagogical consequences of this choice are evidenced in the poor performance of the country's students on national and international assessments of mathematical proficiency. Drawing on research literature around language immersion education models and the extent to which these align with certain key principles of second language acquisition, this position paper motivates for a stronger and more sustained commitment to providing students, particularly those from marginalized and vulnerable communities, with opportunities for becoming both bilingual and biliterate. Empirical data from two South African grade 4 mathematics classrooms are used to illuminate aspects of the mathematical sense-making challenges students and their teachers face without such commitment. [ABSTRACT FROM AUTHOR]

Copyright of Alberta Journal of Educational Research is the property of Alberta Journal of Educational Research 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.)

In recent years, the inclusion of computational thinking in education has become very important. This is a response to the needs of the evolution of our society and the skills demanded in students to obtain practical and integrated training. For this reason, the educational inclusion of these types of practices, strategies, and skills has been the subject of study in recent years. However, it is equally important to prepare and analyse the initial training of future teachers in this area. This research paper presents an empirical experience in which the degree of development of skills associated with computational thinking in preservice primary teachers is examined. For this purpose, programming practices with Scratch were carried out with a total of 149 students of primary education university degrees as part of their training in mathematics education. An experiment was designed for a control group and an experimental group with initial and final measurements using a validated diagnostic instrument consisting of 30 questions associated with computational concepts and their application: a computational thinking test. The result of the experience is positive, as a more significant improvement was observed in the experimental group, which was also accompanied by the impressions, provided by participants, that point in a positive, useful, and practical direction in terms of the development of this type of educational practice being relevant enough to introduce to the teaching and learning process of mathematics. [ABSTRACT FROM AUTHOR]

In this paper we report the results of a study in which we investigated how formal education and shadow education in Taiwan provide students opportunities to learn mathematics. Based on the conceptual framework of Opportunity to Learn (OTL), aspects specific to formal education, including mathematics curriculum, mathematics textbooks, and teachers' competence, and their teaching, were reviewed. Two national projects identified under shadow education were examined. The results revealed significant features of the mathematics curriculum, textbook design, and the quality of mathematics teachers in Taiwan that constitute a lived space where teachers with their knowledge and beliefs, curriculum, textbooks, and school settings, can generate cognitive and affective learning outcomes in students. Further analyses of the two above-mentioned projects showed how Taiwan extended learning opportunities to motivate students to learn and understand school mathematics. Based on the review, challenges were also identified. [ABSTRACT FROM AUTHOR]

Divergent thinking (DT), which involves finding new possibilities and seeing the familiar from a new perspective, has been stressed in mathematical creativity education. However, convergent thinking (CT), which involves searching for a correct single answer, has been relatively understudied in relation to developing mathematical creativity. Moreover, how to relate the two thinking modes when facilitating mathematical creativity in daily teaching has rarely been studied. In this study, we propose a framework of dynamic interplay between DT and CT, which we call DT/CT dynamics, that characterizes the creative learning process in the classroom, and to provide an example we analyze research results from two classes from our 3-year longitudinal study with an experienced teacher, in order to demonstrate the framework. Findings indicate that there were significant differences between the two classes in how DT/CT dynamics worked with respect to three aspects, namely, authority distribution, micro-level transition, and macro-level goals. This paper provides a new integrative framework that combines extant work on the psychology of DT/CT with ongoing research in mathematics education, which offers a meaningful lens to capture the way mathematical creativity is pursued effectively in everyday mathematics classrooms. In particular, the study provides a reinterpretation of the theoretical perspectives of Tan and Sriraman (2017) on creativity and provides an analytical tool that enables an understanding of creative learning processes in everyday mathematics classrooms in relation to DT/CT dynamics. [ABSTRACT FROM AUTHOR]

Mathematical problems that contain a common condition and an ordered list of tasks are traditionally called cascade problems. Problems of this type are extremely popular during teaching of mathematics. At the same time, they can be used both in the formation of knowledge, skills and abilities (competencies) of students, and to assess their academic achievements. In the paper we give a thorough theoretical analysis of possible types of cascade problems, describe methodology and provide examples of their applications on different stages of studying mathematics at school, in particular, during the final attestation of graduates. According to our statistical survey of mathematics teachers in Ukraine and Republic of Moldova, we clarify their attitude to problems of cascade type, as well as the advantages and disadvantages of using such problems. It is shown that the use of cascading problems in the school course of mathematics contributes to the adequate formation of important competencies of students in their learning process. [ABSTRACT FROM AUTHOR]

In this paper, illustrative excerpts from mathematics lessons are analysed to examine mathematical and multilingual moves between representations within Sepedi and English medium classrooms. Duval's theory of representational registers and the literature on multilingual practices help foreground similarities within and differences between the instructional practices of four teachers—two teaching in the medium of Sepedi and two in English—as they move between mathematical and multilingual representations in the teaching of numbers. The findings show patterned differences on the basis of the medium of instruction, with the Sepedi medium instruction indicating, primarily, 'restatement' moves between the oral and the symbolic modes of representation, whilst the English medium instruction incorporated a higher incidence of mathematical moves between oral, concrete, iconic and symbolic number-based modes of representation. The evidence of broader use of mathematical representational moves as observed in the English medium lessons offers insights into how and, perhaps, why learners' knowledge development and understanding of early number in English medium classrooms may emerge in ways that are different from the knowledge developed in the Sepedi medium classes. These patterned differences are important to understand in a South African context where language of instruction continues to be associated with differences in mathematical outcomes in ways that, as previously documented, relate to socio-economic disadvantage. [ABSTRACT FROM AUTHOR]

Task design is increasingly recognised as crucial for enhancing student learning of mathematics. Even so, and despite the significance of mathematical activity related to proofs and counterexamples in school mathematics, the task design principles underpinning students' success in proof-related activity remains under-explored in mathematics education research. What is more, although the affordances of using dynamic geometry environments (DGEs) have been established in the literature, task design in DGEs remains somewhat under-studied. In this paper, we address both these issues by theoretically developing, and empirically testing, task design principles for supporting students' heuristic refutation (revising conjectures/proofs through addressing counterexamples) in DGEs. We use the existing literature to elaborate three design principles: using tasks whose conditions are purposefully implicit, providing tools that enhance the production of counterexamples, and increasing students' recognition of contradictions. To test these principles empirically, we analyse two sets of task-based interviews, one with a triad of secondary school students and the other with a pair of undergraduates, where tasks designed according to the principles were implemented. Our analysis shows that using the tasks enabled the students to engage successfully in heuristic refutation. The matter of examining mathematical definitions when handling counterexamples emerged as an issue for further research. [ABSTRACT FROM AUTHOR]

The concept of flipping the classroom and flipped learning is becoming increasingly more popular in secondary schools. Although more prevalent in tertiary teaching, flipped learning has a number of affordances that may address the challenging demands of teaching secondary mathematics. While enactments of the approach vary, flipped learning requires a reconceptualization of traditional secondary mathematics instruction in that instructional content is assigned as homework before class, providing for more targeted in-class teaching. This paper reports on a study that investigated the enactment of the flipped classroom in ten different secondary mathematics classes. Findings indicated that there were essentially three different ways in which the approach was enacted, yet all enactments appeared to offer similar affordances. The study adds to the limited research that documents flipped learning in secondary mathematics classes and contributes to current understandings of teachers' and students' perceptions of their experiences of such an approach and the affordances it offers. The study has implications for secondary students and teachers of mathematics, particularly those who are teaching within the constraints of prescribed textbooks and externally imposed assessment measures. [ABSTRACT FROM AUTHOR]

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

Copyright of Scientia et Technica is the property of Scientia et Technica 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.)

Mathematics uses a wide range of representations, but the mathematical symbol is not the only way to code information. Different ways of representing mathematical concepts and relationships are used, especially in the early stages of learning. Generally, the teacher decides on the choice of representational forms to use. But in the process of solving mathematical problems, it is the pupils - not the teacher - who are engaged in the problem-solving, and the coding used should support their cognitive work. This paper analyses how different representations can influence the results of work on an untypical mathematical problem. The task was solved by a group of 7-8 year-old pupils participating in a mathematics club. The examples selected for analysis indicate a strong relationship between the choice of representations and the final result of the pupils' work. [ABSTRACT FROM AUTHOR]

Copyright of Ingeniería (0121-750X) is the property of Ingenieria 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 paper reports on a New Zealand iteration of the Encouraging Persistence, Maintaining Challenge (EPMC) project, which proposes that students learn mathematics best when they build connections between mathematical ideas for themselves. This iteration explores the actions, perceptions and learning of 12 primary teachers and their 281 students during the implementation of a set of challenging tasks related to geometric reasoning. The teachers launched the suggested tasks, ensuring that the challenge was maintained. The students explored these tasks with minimal input from the teacher, and learning was summarised and extended. The teachers were positive about the intervention. The challenging task approach enabled students' thinking became visible and, at times, the teachers' prior perceptions of their students' ability were challenged. A highly significant difference between the students' pre- and post-assessment scores was found. The students were supported to have autonomy in their learning and make mathematical connections themselves. The students became less reliant on their teachers' help and were positive about their involvement in the project. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the results of a staff survey on accessibility barriers to participation and success for disabled students in higher education in the UK and Ireland. We focus on the range and complexity of student difficulties encountered by staff involved either in the lecturing of mathematics or the provision of Mathematics Learning Support. We report on the range of supports available to both staff and students in these situations and their varying levels of awareness and implementation of these supports. We close with a brief overview of how we intend to use the results of this survey to both increase awareness of existing appropriate supports and develop additional services to improve student accessibility. [ABSTRACT FROM AUTHOR]

The paper deals with theoretical substantiation and construction of the methodological system of autonomous learning of the course "English for Specific Purposes (ESP)" for prospective teachers of Mathematics. The purpose of the study is to prove theoretically the methodological system of autonomous ESP learning for prospective teachers of Mathematics and to test empirically the current students? level of autonomous learning competence. The main components of the methodological system are observed, among them: target component (social demand, requirements, goals, and objectives); methodological component (approaches and principles); procedure component (content and technologies); assessment component (control and results). The main features such as functionality, complexity, openness and conceptual positions of the methodological system are described in the paper. It is said that the designed methodological system of autonomous learning of ESP of prospective teachers of Mathematics can be implemented in the educational process effectively in the presence of grounded pedagogical conditions, among them: training of students? autonomy, pedagogical support, and effective learning environment. The analysis of the study results reveals that during the initial phase of the implementation of autonomous ESP learning, the students have a moderate level of autonomous learning competence and it needs improvement in the process of implementation of the developed system. [ABSTRACT FROM AUTHOR]

The use of digital textbooks in mathematics is increasing. However, the implementation of digital textbooks in schools is complicated. The objective of this paper is to understand how the introduction of a digital textbook affects the activity of teaching mathematics. An intervention was conducted where six mathematics teachers, with students in aged 7-15, used a digital textbook for six weeks. This paper applies cultural-historical activity theory to consider contradictions that arose in the activity. Four contradictions were revealed: first, teachers' need for coherence and linearity vs. the digital textbook with a wide range of content and nonlinear paths; second, teachers' need for transparent learning processes vs. the digital textbook as opaque; third, teachers' beliefs about appropriate pedagogy for learning mathematics vs. the pedagogy embedded in the digital textbook; and fourth, differentiated instruction for all students vs. digital textbook supporting individualization for every student. [ABSTRACT FROM AUTHOR]

The educational reforms are emphasizing, besides other things, the importance of collaborative work among teachers to improving education in schools. Still much is unclear about how teachers in fact react within a collaborative setting, despite emphasis on collaboration by reform curriculums as by invoking uses of phrases such as "exploring ideas together", "inquiry learning", "working in teams", "learning from each other". This study presents a case study (with a teacher named Fan) under frame of qualitative research. We explore engagement of a group of primary mathematics teachers within context of teacher training sessions (as collaborative settings)for understanding and implementing principles and pedagogy proposed by the New Primary Mathematics Curriculum in Portugal (ME, 2007). Positioning Theory (PT) has been used as an analytical lens to illustrate how Fan takes particular positions (in relations to other mathematics teachers) as a way to engage in the processes of professional mathematical learning promoted through these training sessions. Furthermore, what kinds of implications these dynamic positionings of Fan can bring to unpacking the complexity of teachers' learning within collaborative settings? Here dynamic movement between "I" and "we" that Fan invokes to handle complex of moral orders within collaborative setting. The purpose of the paper is to create evidence for teacher' learning which captures dynamic shifts that occur in a collaborative professional setting. [ABSTRACT FROM AUTHOR]

In this paper, we take a semiotic/dialogic approach to investigate how a group of UK 12–13-year-old students work with hierarchical defining and classifying quadrilaterals. Through qualitatively analysing students' decision-making processes, we found that the students' decision-making processes are interpreted as transforming their informal/personal semiotic representations of "parallelogram" (object) to more institutional ones. We also found that students' decision-making was influenced by their inability to see their peers' points of view dialogically, i.e., requiring a genuine inter-animation of different perspectives such that there is a dialogic switch, and individuals learn to see the problem "as if through eyes of another," in particular collectively shared definitions of geometrical shapes. [ABSTRACT FROM AUTHOR]

This paper reports findings from a case study of the impact that teaching using guided notes has on university mathematics students' note-taking behaviour. Whereas previous research indicates that students do not appreciate the importance of lecturers' non-written comments and record in their notes only what is written on the board when taught with the traditional chalk and talk method, some students in our study recorded the non-written comments as well as some of their own links between sections of the lecture. We did not, however, find students' attitude towards those comments to be different from what previous research found. We conclude that guided notes can be an appropriate way of teaching university mathematics but on their own cannot make the pedagogical intentions of the lecturer clearer to the students. We also found that the educational environment plays a big part for all aspects of student learning, including decisions related to note-taking during lectures. [ABSTRACT FROM AUTHOR]

The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real-world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and their applications to solving problems arising in real-world situation. Clearly, it is assumed that the teachers themselves are able to make such connections. On the other hand, research shows that mathematics teachers find it difficult to make those connections. In this paper, we present the results of the study that investigated the ways in which exploring mathematics in informal sites, and in particular science museum, assist teachers with making connections between school mathematics and its applications in real world. [ABSTRACT FROM AUTHOR]

This paper presents the Mathematics Teacher's Specialised Knowledge (MTSK) model. It acknowledges earlier contributions to understanding and structuring teachers' knowledge, in particular, the special debt owed to Shulman's notion of pedagogical content knowledge and to Ball and collaborators' Mathematical Knowledge for Teaching (MKT), influential for the specialised nature of one of its sub-domains. The authors' research with teachers has led them to explore the characteristics of MKT and to refine the descriptors relating to its sub-domains, a task which has underlined the difficulty involved in unambiguously delimiting the boundaries which separate these. As a result, and taking into consideration a broader view of the specialised nature of the teacher's mathematical knowledge, the authors propose a framework which, whilst respecting the major domains of Content Knowledge and Pedagogical Content Knowledge, regards the specialisation in respect of mathematical knowledge as a property which is inherent to the model and extends across all sub-domains. [ABSTRACT FROM AUTHOR]

The notion of 'opportunities to learn in mathematics education' is open to interpretation from multiple theoretical perspectives, where the focus may be on cognitive, social or affective dimensions of learning, curriculum and assessment design, issues of equity and access, or the broad policy and political contexts of learning and teaching. In this paper, I conceptualise opportunities to learn from a sociocultural perspective. Beginning with my own research on the learning of students and teachers of mathematics, I sketch out two theoretical frameworks for understanding this learning. One framework extends Valsiner's zone theory of child development, and the other draws on Wenger's ideas about communities of practice. My aim is then to suggest how these two frameworks might help us understand the learning of others who have an interest in mathematics education, such as mathematics teacher educator-researchers and mathematicians. In doing so, I attempt to move towards a synthesis of ideas to inform mathematics education research and development. [ABSTRACT FROM AUTHOR]

This paper reports on combining semiotic and discursive approaches to reification in classroom interactions. It focuses on the discursive characteristics and semiotic processes involved in the teaching and learning of square roots in a ninth grade classroom in Japan. The purpose of this study is to characterize the development of mathematical discourses in a series of mathematics lessons in terms of the commognitive framework and the model of semiotic chaining. To achieve this objective, the notion of reification is revisited from cognitive, semiotic, and discursive points of view, and classroom activities are observed and analysed in terms of the combined theoretical framework. The results suggest that the model of semiotic chaining is not incommensurable with a strong discursive approach and the changes of meta-discursive rules-an essential aspect of the reification of new signifiers-that take place in the phases of the learning of addition on square roots. [ABSTRACT FROM AUTHOR]

This paper proposes a framework for identifying the mathematical knowledge teachers activate when using curriculum resources. We use the term knowledge of curriculum embedded mathematics (KCEM) to refer to the mathematics knowledge activated by teachers when reading and interpreting mathematical tasks, instructional designs, and representations in mathematics curriculum materials. The KCEM framework is situated within existing research on content-specific teacher knowledge. Through analysis of elementary mathematics teacher's guides from the USA, we identified elements of curriculum resources teachers interact with when using them to plan instruction. These findings were complemented by interviews of teachers using curriculum guides to plan lessons, uncovering how they interacted with different elements of their guides. From this analysis, we propose four overlapping dimensions of KCEM: foundational mathematical ideas, representations and connections among these ideas, problem complexity, and mathematical learning pathways. Using an excerpt from one elementary curriculum guide and one of the teacher interviews on using this guide to plan a lesson, we illustrate how these dimensions might be activated as teachers read and use their guides. [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]

The purpose of this study was to determine the hypothetical learning trajectory through a problem-based learning model to class VIII junior high school students. Learning mathematics requires a meaningful process and that process cannot be obtained in a relatively short time because it requires good preparation in conveying mathematical concepts to students. The preparation is designed according to the characteristics of students so that the delivery of the material goes well as expected. The preparation referred to in this case is to design a good hypothetical learning trajectory (HLT) according to the needs and subject matter. Hypothetical learning trajectory (HLT) is a temporary hypothesis about students' activities in the learning process on certain materials. This study uses a design research method with stages referring to Plomp (2013) which consists of three phases including (1) preliminary research; (2) development or prototyping phase; and (3) assessment phase. However, in this research, it is only in the first phase, namely preliminary research. In designing the HLT, it is based on a problem-based learning model which has five stages in each process. The instrument used in this study was a teacher and student interview sheet. The results obtained are the HLT design on linear equation material that is adjusted to the stages in the problem-based learning model. The results obtained from this study can be used as an initial reference for mathematics teachers in designing learning material for linear equations that are in accordance with the real context of students. [ABSTRACT FROM AUTHOR]

This research is quasi-experimental research conducted to improve students's mathematical connection skills, one of which is through the use of attention, relevance, confidence, and satisfaction (ARCS) models. The purpose of this study was to determine (a) the description of the process of students and teachers in learning mathematics using the ARCS learning model, (b) differences in the improvement of mathematical connection skills between students using the ARCS learning model and students using conventional learning, (c) student responses to mathematics learning using the ARCS learning model. The data were obtained using a test research instrument in the form of mathematical connection skills and nontest questions, namely student response questionnaires to learning using the ARCS learning model. This research was conducted at SMPN 3 Bandung City with a sample of class VIII-6 as a control class and class VIII-7 as an experimental class on statistical material. Based on the results of research and processing of n-gain data, obtained: (a) the description of the learning process of teachers and students on statistical material using the ARCS learning model is in the very good category; (b) there are differences in the improvement of mathematical connection skills between students who use the ARCS learning model and students who use conventional learning; (c) most of the students who received learning using the ARCS learning model responded positively to learning mathematics using the ARCS learning model. [ABSTRACT FROM AUTHOR]

Needs assessment is used as a base or a foundation in designing learning models based on mathematical problem posing. This research aims to identify mathematics learning that occurs and should occur. Needs assessment is carried out by literature study and field study. The participants in this study were junior high school mathematics teachers in Palu City. Of the 25 mathematics teachers who sent the mathematics learning questionnaire results, it was found that 65% of the teachers rarely applied the problem-posing task, and 35% never gave the assignment of proposing mathematics problems. The information obtained from the interviews with 4 mathematics teachers regarding problem posing was that the students understanding about the concept. The teacher argues that if students are given the task of problem posing, they would only copy in the book. They construct problems from the textbook and replace the numbers. The task of posing a problem is given when the math teacher is unable to attend. The task of constructing problem was a punishment for students for not working on the questions. The conclusion from this study results is that the teacher rarely gives the task of problem posing. There are misconceptions about the task of mathematical problem posing. [ABSTRACT FROM AUTHOR]

As a central objective, problem-solving skills are important in the mathematics curricula of many countries. However, such skills tend to receive limited and rarely systematic attention in mathematics lessons, including in the Netherlands. To address this gap, the authors adopt a specific approach that defines problem solving as integral to mathematics: Teaching mathematics Through Problem solving (TTP). In Japan, teachers often learn about TTP by performing Lesson Study (LS), an approach in which teachers work in teams to design and conduct a research lesson that allows them to learn collectively about students' learning processes. TTP offers a promising, structured, didactical approach to introducing problem solving in mathematics lessons, and LS appears to represent an effective means for teachers to learn about TTP. To test this proposition, the current study entails a TTP- and LS-based intervention implemented in two secondary schools in the Netherlands, with an explicit focus on problem-solving skills. The central research objective for this study is to determine whether this TTP-LS-intervention helps mathematics teachers incorporate problem-solving skills into their lessons and how design characteristics and mechanisms of the intervention affect the outcomes. Interviews with teachers provide insights into which characteristics of the TTP-LS intervention fostered the implementation of problem solving in their teaching practice, as well as which did not. The collected data show that the teachers regard TTP as a valuable pedagogy to teaching mathematical problem solving. They report that the joint development, implementation, and evaluation of TTP lessons in the LS cycles, and especially observations of students, has given them more tools for applying TTP pedagogy and that they use these tools to promote problem-solving skills. Elements of the TTP lessons that the teachers perceived as difficult were the lesson phases that featured discussions on solution strategies rather than finding the "right" answers. Teachers regarded LS as a suitable approach for learning about TTP. Some points for improvement also emerged from the data. For example, more support should be given to TTP-LS-teams to explain the problem-solving skills they want to target in their lessons, and to practice especially the classroom discussion and summary phase. [ABSTRACT FROM AUTHOR]

This paper reports a study of students' and teachers' perceptions of their classroom learning environment in Bhutanese eighth-grade mathematics classes. Research suggests that positive perceptions of the learning environment can have a positive influence on students' learning outcomes, interest and engagement in classroom activities. The study was conducted in 2013, using the survey samples of 608 students and 98 teachers from 22 lower- and middle-secondary schools in western Bhutan. Students' and teachers' perceptions of the classroom environment were measured using the Mathematics Classroom Learning Environment Survey (MCLES). Students and teachers mostly perceived their classroom environments favourably on the MCLES scales irrespective of gender, school level and school location. The study is significant for understanding and evaluating the implementation of new mathematics curriculum in Bhutanese schools because it could guide the development of strategies for more-productive mathematics classroom learning. It is also significant from the perspective of Bhutan's national goal of Gross National Happiness because perceptions and happiness always go hand-in-hand. [ABSTRACT FROM AUTHOR]

Student autonomy has been an important object of study for mathematics educators for many years. Over time, framings of autonomy have moved from a focus on the individual to considerations of how an individual's autonomy is entangled in classroom-level interactions. What has been less closely studied is how classroom interactions provide uneven access to autonomy for individuals. This study uses a communicational perspective to clarify Piaget's intellectual autonomy and examine students' mathematical interactions. The findings describe barriers and supports to autonomous activity for three students. Students were prevented from engaging in autonomous activity when they were seen as less capable than others, when they felt the need to manage the activities of their peers, or when they focused on being seen as knowledgeable. In contrast, students acted with autonomy when they took up the teacher's request for explanations, noticed a contrast between their answer and the right answer, and worked on making connections across different representations. [ABSTRACT FROM AUTHOR]