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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]

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]

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]

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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]

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]

Students' concerns about mathematics can significantly affect their ability to learn the subject. In particular, their anxieties and attitudes can greatly affect how they perceive their own mathematical competence, and in return, this may make them reluctant to pursue mathematical studies. Many researchers believe in the role of active learning environments in reshaping students' perception of and emotions about mathematics. This paper reports the results of an investigation on the effect of one such environment. As a result of being exposed to an active learning environment, a group of 21 cohort students showed opinion changes from a pre- to post-survey statements significantly on emotion and noticeably on confidence and perception statements. There was, however, no statistically significant change observed on the opinions of a group of 41 traditional students. [ABSTRACT FROM AUTHOR]

The aim of this study was to contribute to knowledge about classroom assessment by identifying profiles of teachers’ assessment of their students’ understanding of mathematics. For carrying out this study we used data of a nationwide teacher survey (N = 960) in the Netherlands. The data were collected by an online questionnaire. Through exploratory factor analyses the underlying structure of what is measured by this questionnaire was uncovered as consisting of five factors: Goal centeredness of assessment, Authentic nature of assessment, Perceived usefulness of assessment, Diversity of assessment problem format, and Allocated importance of assessing skills and knowledge. By using a latent class analysis four different assessment profiles of teachers were identified: Enthusiastic assessors, Mainstream assessors, Non-enthusiastic assessors, and Alternative assessors. The findings suggest that teachers with particular assessment profiles have qualitatively different assessment practices. The paper concludes with discussing theoretical implications of these assessment profiles and indications these profiles can offer both for designing material for professional development in classroom assessment and for evaluating changes in teachers’ classroom assessment practice. [ABSTRACT FROM AUTHOR]

In theories of learning that adopt a situated stance to knowledge the notion of identity is vital; how learners position themselves in relation to, and are mutually positioned by, the situation within which they are learning will have a strong bearing on the learning outcomes. One of the challenges for learning mathematics in school is that learners position themselves, and are positioned, as pupils rather than as mathematicians. This paper focuses on discussion boards designed for secondary school mathematics students, and we use Wenger's (1998) model of communities of practice, building on earlier work by the authors (Back and Pratt 2007; Pratt and Kelly 2007) in which 'idealised communities' are constructed and used, to consider a case study of one participant who engages in developing his identity as a mathematician doing mathematics, as well his identity as a learner and a teacher of mathematics. [ABSTRACT FROM AUTHOR]

Informed by an amalgam of notions drawn from constructivist, socio-cultural, metacognitive and self-regulation theory, the discourse created to describe assessment to enhance learning has gone through a number of iterations or discursive shifts. As a result, the current discourse is both ambitious and complex with the roles and responsibilities assigned to teachers and learners in learning and assessment radically transformed. Sponsored by the New Zealand Ministry of Education, the Teaching and Learning Research Initiative (TLRI) seeks to develop teachers' research capability and to build knowledge about teaching and learning with the intention of improving outcomes for learners. Using a range of qualitative data generation strategies this TLRI research project investigated secondary school teachers' and students' conceptions of assessment and feedback. This paper reports on the professional learning that accrued for these teachers using the data gained from the four mathematics teachers in the project. It also details changes in these teachers' thinking about the roles and responsibilities of teachers and learners in the assessment process and documents reported changes to their professional practice resulting from these changed views. Whilst it is argued that involvement in the project became a valuable form of professional learning whereby these teachers, to varying degrees, achieved accessibility to, and greater understanding of, the current discourse of formative assessment, the mediating influence of teachers' efficacy beliefs is also acknowledged. [ABSTRACT FROM AUTHOR]

It seems uncontroversial that the nature of classroom discourse influence learning. The Malaysian primary mathematics curriculum advocates that teachers should guide the pupils' constructions towards a conceptual understanding of mathematics that compliments the skills developed through the manipulation of concrete objects and representations prior to the introduction of symbolism and algorithms, and also ensure that the construction of understanding in mathematical concepts plays an equal part to the development of skills. Against this background, this article considers the way in which primary schools mathematics teachers' actions within their classrooms may contribute towards their pupils' achievement and understanding. Using lessons associated with determining fractions of whole numbers as an example, the paper considers the evidence to answer the question "What form of relationship exists between the teaching and learning of fractions?". Episodes from lesson observations were associated with the knowledge and skill of the pupils through their personal constructions of the substance of the lessons. Whilst the pupils' level of achievement may suggest broad understanding, in reality it is grounded within a limited frame of procedural competence construed from their teachers' emphasis in the classrooms. Although there may be differences in achievement between pupils attending urban and rural schools, there are no qualitative differences in their understanding of fractions because there are no qualitative differences in the indications given by their teachers in the classrooms. The pupils' perceptions of fraction are framed within a narrow procedural perspective derived from teacher indications which, whilst emphasizing the needs of an examination system, are at variance with the spirit and intention of the national curriculum designed to meet the nation's aspiration of becoming an industrialized nation. [ABSTRACT FROM AUTHOR]

In this paper I address the challenge of developing theory in relation to the practices of mathematics teaching and its development. I do this by exploring a notion of ‘teaching as learning in practice’ through overt use of ‘inquiry’ in mathematics learning, mathematics teaching and the development of practices of teaching in communities involving teachers and educators. The roles and goals of mathematics teachers and educators in such communities are both distinct and deeply intertwined. I see an aim of inquiry in teaching to be the ‘critical alignment’ (Wenger, 1998) of teaching within the communities in which teaching takes place. Inquiry ‘as a tool’ and inquiry ‘as a way of being’ are important concepts in reflexive developmental processes in which inquiry practice leads to better understandings and development of theory. [ABSTRACT FROM AUTHOR]

Effective mathematics teaching and learning is crucial not only for the purposes of examination and assessment but as well for the learners' empowerment so that they cope with the everchanging technology and be able to solve real-life social and economic problems of the world. The study aimed at revealing the pre-service teachers' pedagogical practices during teaching practice as well as whether they aligned their practices to the teaching approaches recommended in the mathematics syllabus. The case study involved four secondary school pre-service mathematics teachers who were purposively sampled. Documents, interviews and lesson observations were the data collection instruments. The results showed that out of the four teachers only two used both teacher-centered and learner-centered methods, whilst the other two used purely traditional teacher-centered methods. The learner-centered methods used by the two teachers were only limited to group work and pair work out of the several learner methods recommended by the syllabus. In this era of technology, none of the teachers made use of technology whilst delivering their lessons, which is also not in line with the syllabus requirements. Pre-service teachers need to be more knowledgeable in learner-centered approaches, syllabus use and interpretation as well as technology integration in the teaching and learning of mathematics. [ABSTRACT FROM AUTHOR]

This study aimed to determine how preschool teachers handle mathematics learning processes in their mathematics activity plans and which contents they include. The study used the document analysis method as a descriptive research model. The study examined 200 mathematics activity plans applied by 10 preschool teachers working in preschool education institutions in the 2020-2021 Fall and Spring academic terms. The data of the study were collected with the Mathematics Activities Assessment List (AEL), which the researchers developed. The researchers analysed the data obtained in the study separately by using the coding system without specifying the teachers' names for confidentiality. As a result, the researchers determined that preschool teachers planned mathematics activities mainly in large group activities and integrated them into their activity plans. On the other hand, they also found that teachers included concepts such as number/counting and quantity more in their mathematics activity plans and they planned mathematics activity plans as classroom activity plans. In addition, they included family participation activities in mathematics activity plans. [ABSTRACT FROM AUTHOR]

Mathematics learning achievement of elementary school students is determined by the learning method used by the teacher. The learning method needed is a method that can help maximize student memory so that students can remember the material well. The Loci method connects certain objects with specific locations so that the individual may easily recall them. The purpose of this study was to empirically test the effectiveness of the loci method on mathematics learning achievement for elementary school students. This experimental research used a quasi-experimental design, with a one-group research design. Six elementary school students participated in this study. Pretest-posttest design with mathematics achievement test and the loci method treatment module were utilized as instruments. Data were analyzed by the paired sample t-test. The results of data analysis found that there is a difference between pre-test and post-test and that the loci approach helps enhance mathematics achievement. The Cohen's d Effect Size test resulted in a score of 77.4%, indicating that the Loci Method is highly effective in boosting mathematics learning achievement for students in elementary school. The implication of this research is that schools are expected to train mathematics teachers to use the loci method to improve students' mathematics learning achievement. [ABSTRACT FROM AUTHOR]

This study examined the effect of using computer simulation on students' interest in algebra. A quasi-experimental design was employed. A sample of fifty-four students (age range: 12-14years old) drawn from two schools constituted the subjects for the study. Two JSS 2 classes in each school were assigned through balloting to experimental and control groups. The subjects were taught by their regular mathematics teachers that served as an assistant in the research. Both groups (experimental and control) were pre-and post-tested. The Algebra Interest Inventory (AII) was the instrument utilized for data collection for the study and it has a reliability coefficient of 0.76. Data collected were subjected to analysis using SPSS software. The mean and standard deviation were used for reporting the research questions and analysis of covariance (ANCOVA) was for testing the hypotheses at.05 level of significance. Analysis of the results showed that the mean interest scores of students taught algebra with computer simulation was significantly higher than those taught with the conventional method. The result also showed that there was no significant difference between the mean interest scores of male and female students taught algebra with computer simulation. The study made some recommendations and one of them is that the use of computer simulation in mathematics lessons should be encouraged in the mathematics teaching and learning process especially as it arouses students' interest. [ABSTRACT FROM AUTHOR]

In this paper we focus on variation of the design and the implementation of a specific task during three mathematics lessons in the 8th grade in a learning study (Marton & Tsui, 2004; Runesson, 2008). The theme of the lesson was division, with a denominator between 0 and 1. The teachers wanted their students to understand that when dividing with a denominator less than 1, the quotient is larger than the numerator. Four teachers collaboratively planned, analyzed and revised three lessons in a cyclic process. The study shows that the implementation of the task changed between the lessons. Although the same task was used in the lessons, the way it was enacted provided different possibilities to learn. [ABSTRACT FROM AUTHOR]

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

Game-based learning has received more focus as a way to engage students and increase interest in mathematics. Game-based learning should be integrated with effective practices for teaching mathematics, though there is a need for further research on effective implementation models. The purpose of this article is to describe two modes of game-based learning that are aligned with National Council of Teachers of Mathematics effective practices for teaching mathematics including multiple representations and meaningful discourse. Examples will be discussed from the implementation of game-based learning in a Saturday Science, Technology, Engineering and Mathematics (STEM) program for middle school students offered at a large research university. [ABSTRACT FROM AUTHOR]

The aim of the present study was to examine the effects of Technology-Assisted Learning (TAL) and Project-Based Learning (PjBL) approaches upon students' attitudes toward mathematics and their academic achievements. A quasi-experimental research design was employed including pre-tests, post-tests and a retention test. The findings of the research revealed that the TAL approach, when compared to the PjBL approach, had a higher level of effect on students' attitudes toward mathematics. However, it was revealed that the PjBL approach had a higher level of effect on academic achievement than did TAL. In light of the findings that the present study yielded, a discussion is presented on the technology-assisted project-based learning (TAPjBL) method. [ABSTRACT FROM AUTHOR]

This study conducted at the Lebanese American University in spring 2018 reports on an inquiry-oriented differential equations class where the course curriculum falls within the realm of Realistic Mathematics Education. The focus of the study is on some curriculum tasks and how they assist students reinvent successfully key mathematical notions covered in most introductory differential equations courses. While the results show remarkable cognitive gains in understanding and thinking, reinventing knowledge was demanding and in some cases required the intervention of the instructor to control and lead the discussion. Results also show that the lack of appropriate mathematical knowledge was sometimes an obstacle for the reinvention process, and the traditional view of mathematical learning a hindrance for accepting that an inquiry-oriented approach can fulfil the course outcomes. [ABSTRACT FROM AUTHOR]

• We present the results of presenting an instructional module connecting the teaching of real analysis to the teaching of secondary mathematics. • We focus on the relationship between continuity, injectivity, and invertibility and the use of the arcsine function. • Prospective teachers who completed this module were better prepared to teach inverse trigonometric functions. Prospective secondary mathematics teachers are typically required to take advanced university mathematics courses. However, many prospective teachers see little value in completing these courses. In this paper, we present the instantiation of an innovative model that we have previously developed on how to teach advanced mathematics to prospective teachers in a way that informs their future pedagogy. We illustrate this model with a particular module in real analysis in which theorems about continuity, injectivity, and monotonicity are used to inform teachers' instruction on inverse trigonometric functions and solving trigonometric equations. We report data from a design research study illustrating how our activities helped prospective teachers develop a more productive understanding of inverse functions. We then present pre-test/post-test data illustrating that the prospective teachers were better able to respond to pedagogical situations around these concepts that they might encounter. [ABSTRACT FROM AUTHOR]

Mixed-attainment mathematics teaching is not a common practice in England, despite evidence that ability grouping is not an effective strategy for improving educational outcomes. This study compares mathematics in School M (mixed-ability groupings) and School S (sets) in relation to student beliefs, and teacher beliefs and practices. Questionnaire data from 286 students and 12 teachers were triangulated with lesson observations and interviews. This article suggests grouping practices could indeed influence students' mindsets, teachers' mindsets and teachers' beliefs and practices. An above average proportion of students in both schools reported growth orientations, although these beliefs were held more strongly by students in the mixed-attainment grouping. School M teachers also held stronger growth-mindsets than School S teachers. Mathematics teachers in both schools reported connectionist beliefs, but the students' experiences differed. Most students in School M perceive typical mathematics lessons as involving a substantial problem or challenge worked on collaboratively in pairs or small groups, and having several entry points. Students in both schools valued learning from mistakes, but School M students were more likely to both believe this would help them, and have access to this type of learning opportunity. Students taught in sets experienced mathematics as procedures delivered by teachers and reproduced by students. This has implications for further research as mixed-attainment groupings may be a factor in determining the way in which students experience learning mathematics. [ABSTRACT FROM AUTHOR]

This study aims to characterise the pedagogical practices of 45 observed primary mathematics lessons taught by 24 mathematics teachers in six national primary schools (SK) and six Chinese vernacular primary schools (SJKC). The data were collected using two video cameras, one focused on the teacher while the other camera focused on the pupils' activities. The qualitative data were analysed based on two main activities in the classroom, which are teacher's activities and pupils' activities. The findings show that mathematics lessons conducted by SK teachers tended to engage the pupils in individual seatwork so as to assess pupils' understanding. Conversely, SJKC teachers were focused more on explaining mathematical concepts to help the pupils build up their conceptual understanding. By characterising the pedagogical practices of mathematics lessons in various schools, the researcher hopes that the findings of this study will contribute to better understanding of the teaching and learning process in SK and SJKC mathematics classrooms. The results serve as a documentation of pedagogical practices in Malaysia to enable implementation of suitable programmes to help in improving teachers' pedagogical practices from different types of primary schools. While the results are interesting and provide some directions, a much larger study would be needed to determine if the results are due to the teachers' enthusiasm, geographical differences, cultural or social differences, or what is known as the Hawthorne Effect. [ABSTRACT FROM AUTHOR]

Whilst research underlines the importance of early mathematics in kindergarten, practitioners need effective and innovative approaches to pedagogy. Currently, very different approaches are deployed from an instructional, educator-led approach based on training programmes to a play-based approach. This intervention study examines the effects on the mathematical competency of these two pedagogies. Thirty-five kindergarten educators and 324 six-year-old children were randomly assigned to either a training programme, a play-based approach with card and board games or to the control group. Educators’ views on the interventions were gathered in semi-structured interviews. The results indicate higher learning gains overall for the play-based approach. Differentiated effects were found as tendencies: children with low competencies tend to gain more from training programmes compared to no intervention; children with high competencies gain more from the play-based approach than the training. Educators evaluated the play-based intervention with card and board games as better suited to children’s diverse needs. [ABSTRACT FROM AUTHOR]

Computers have been available to teach and do mathematics for decades. There have been spikes of interest, energy, and results in their use over the years. However, there is little sustained use of computers as they could be used to permit students to learn and do mathematics. To be effective computers need to be embedded in the learning process. They need to be ubiquitous and part of every student's learning kit. Indeed, they should be a first tool of choice for most of what students do with mathematics; that is, plotting, algebraic manipulation, optimization, playing “what if” games, data analysis, etc. I outline a number of scenarios and experiences to show just how pervasive computer use can and should be. I put computer use in context with its most important applications for teaching mathematics—namely, modeling and inquiry or problem-based learning. [ABSTRACT FROM PUBLISHER]

This research is focused on dimensions of mathematical thinking among preservice teachers learning through the use of e-Portfolios. The data came from portfolios created and reconstructed by future mathematics teachers. Their process of reviewing and republishing pages through the Internet was constantly saved and reviewed in turn by the researchers. Seven case studies were conducted. Results stress the importance of the use of ICT by pre-service teachers as an interface to become more reflective about their learning and to improve their knowledge. Besides being a tool to recognize different dimensions (technological, conceptual and communicative) the e-Portfolios were a powerful resource for creating, publicizing ideas, and learning mathematics in different ways. The article also presents some methodological issues. [ABSTRACT FROM AUTHOR]

The article offers information on problem-based learning (PBL) in mathematics. It says that the implementation of PBL entails the redesign of curriculum and the development of effective facilitation-cum-coaching approaches. According to the author, teachers must find out where the learners are in order to challenge them with investigations and problems that have a moderate mismatch with the present status of learners.

The purpose of this article is to identify factors that statistically explain the variation and the measures on the level of motivation of a sample of mathematics students in a university. Specifically, this analysis will identify groups of similar items and reduce the number of variables used in a study. This article explains the use of exploratory factor analysis in extracting factors of personal belief and motivational factors among students in learning mathematics. The adaptation of these factors can be used for assessing academic performance in relation to motivation level. By identifying these factors, the mathematics educators or researchers will be able to find ways to improve the condition of the factors and also to further investigate the factors based on confirmatory approaches. [ABSTRACT FROM AUTHOR]

This study examines the impact of computer technology (CT) on mathematics education in K-12 classrooms through a systematic review of existing literature. A meta-analysis of 85 independent effect sizes extracted from 46 primary studies involving a total of 36,793 learners indicated statistically significant positive effects of CT on mathematics achievement. In addition, several characteristics of primary studies were identified as having effects. For example, CT showed advantage in promoting mathematics achievement of elementary over secondary school students. As well, CT showed larger effects on the mathematics achievement of special need students than that of general education students, the positive effect of CT was greater when combined with a constructivist approach to teaching than with a traditional approach to teaching, and studies that used non-standardized tests as measures of mathematics achievement reported larger effects of CT than studies that used standardized tests. The weighted least squares univariate and multiple regression analyses indicated that mathematics achievement could be accounted for by a few technology, implementation and learner characteristics in the studies. [ABSTRACT FROM AUTHOR]