Linking university mathematics classroom environments to student achievement: The mediation of mathematics beliefs

This study examined the relationships between university mathematics classroom environments, mathematics beliefs, and achievement in the context of mainland China. As a type of affect in mathematics learning, mathematics beliefs including mathematics conceptions and efficacy were examined as mediators. Based on analysis of a sample of 1443 undergraduate students from a university in northern China, the study not only found that the mathematics classroom environment was associated with both affective and cognitive mathematics outcomes, but also confirmed the mediating role of mathematics beliefs. Specifically, a desirable classroom environment was related to students’ cohesive conceptions, enhanced self-efficacy, and higher mathematics achievement. In contrast, students’ perceived difficulty of learning mathematics was connected to their fragmented conceptions, reduced self-efficacy and lower mathematics achievement. Implications of the study are discussed.     

Changing perspectives: Examining the potential for advanced mathematical studies to influence pre-service teachers' beliefs about mathematics

This study considers the potential for advanced mathematical studies to impact pre-service teachers' beliefs about mathematics. Results show that, after completing a degree which includes advanced mathematical studies, many prospective teachers' beliefs still reflect limited interpretations of key terminology and do not value the theoretical and conceptual network underpinning the rules and procedures of secondary mathematics. Many of their beliefs about the nature of mathematics also fail to recognise its capacity to stimulate analytical thought and creativity. In cases where pre-service teachers showed evidence of well-developed beliefs, the study explores the role of their advanced mathematical studies in this development.     

Ecological contexts and early learning: Contributions of child,family, and classroom factors during Head Start,to literacy and mathematics growth through first grade

The current study investigated the extent to which child, family, and classroom factors during Head Start are related to children's literacy and mathematics skills at the beginning of preschool and through first grade. Children and families (n = 945) were participating in the Family and Child Experiences Survey (FACES), a large-scale data collection effort that assessed children's developing skills as well as their family and classroom environments. Longitudinal growth models revealed that Head Start children began their academic careers well below their more advantaged peers in literacy and mathematics, although by the end of first grade, their scores were nearly on par with national averages. Demographic characteristics of children, as well as their early language and social skills, were the strongest predictors of children's initial status and growth in both early academic domains. Results highlight key foundations and specific promotive factors of early school success for the nation's most disadvantaged children.     

数学教育如何体现以学生的发展为本

随着数学教育改革的深入，数学教育主张“以学生的发展为本”。数学教育“以学生发展为本”可从以下几个方面体现：从育人观看要培养学生良好的个性品质；从课程观看要让学生学习有用的数学；从教学观看要使学生主动学习主动发展；从学习观看要对学生进行学习方法指导。它们相互联系、相互影响，在进行教学实践中应融会贯通，就能促进学生数学素质的全面发展。     

Peer relations and access to capital in the mathematics classroom: a Bourdieusian social network analysis

The aim of this article is to explore the structure of social capital in peer networks and its relation to the unequal access of educational resources within mathematics classrooms. We hypothesise that learners can gain access to mathematics through friendship networks which provide more or less help from peers that might sustain (or curtail) their mathematics learning based on a Bourdieusian framework. We report a social network analysis of mutually-recognised helping within friendship groups. This is complemented by observation and interviews that illustrate how different classrooms have different network structures, positioning learners of different ethnic minorities and genders in significantly different ways regarding access to learning. We argue that friendship networks mediate social capital and access to further cultural capital, and that this may help explain structural differences in attainment. Because ethnicity and gender, inter alia, mediate friendship networks, they also mediate access to capital in the classroom.     

Supporting novice elementary mathematics teachers’ induction in professional communities and providing innovative forms of pedagogical content knowledge development through information and communication technology

This paper reports on the needs identified as important to 27 novice elementary mathematics teachers and examines how Connect-ME, an online mathematics community, provides these supports. Qualitative data were collected using two focus groups and 16 telephone interviews. Findings validate the need for alternative teacher professional development (TPD) models and the value of professional communities and knowledge acquired through technology-facilitated learning. The results indicate that teachers actively seek formal and informal TPD experiences, opportunities for sharing and communicating, and access to quality resources. This study provides educational researchers and administrators with essential elements for effectively supporting novice elementary mathematics teachers.     

Using classroom videos to stimulate professional conversations among pre-service teachers: windows into a mathematics classroom

This paper reports on the novel use of classroom videos by 71 pre-service teachers enrolled in a one-year graduate diploma pre-service teacher education program across three Australian universities. The classroom videos were of an experienced teacher delivering a Year-6 mathematics lesson. Students observed, discussed and debated practices that were evident. Data were collected via observation protocols and through recorded focussed discussions. Pre-service teachers, even at the early phase of their course, were able to articulate theoretical explanations for events occurring in the lesson. All students, irrespective of the progression in the course, lamented the absence of prior opportunities to engage in analysis and discussion of classroom lessons. The study reinforces the value of dialectical interactions focussed on authentic teaching scenarios.     

PISA and policy-borrowing: A philosophical perspective on their interplay in mathematics education

Mathematics achievement in different education systems around the world is assessed periodically in the Programme for International Student Assessment (PISA). PISA is deemed to yield robust international comparisons of mathematical attainment that enable individual countries and regions to monitor the performance of their education systems relative to standards being achieved internationally, with a view to informing their mathematics education policy decisions. Initially, the role of PISA in instigating mathematics education policy borrowing is outlined using England as a case study, and some existing technical critiques of PISA are then reviewed. Following this, aspects of Ludwig Wittgenstein’s later philosophy of mind are used to reason that an over-reliance on the use of PISA to inform policy decisions in mathematics education may be problematic. It is suggested that, when PISA is viewed through a later Wittgensteinian lens, a potential deficiency in the underpinning psychometric model, pertaining to the inherent indeterminism in unmeasured mathematical abilities, may weaken PISA’s utility in guiding mathematics education policy decisions. It is concluded that, whilst PISA mathematics scores may give some indication of the mathematical proficiency of a nation’s students, caution is required before mathematics education policies are borrowed from other jurisdictions on the basis of PISA performance. Implications for the other PISA domains are also outlined.     

谈如何在小学数学教学中培养学生独立思考的习惯

在当今多元化教育模式下,教师侧重于培养小学生自我探索、独立思考的能力,格外重视小学生逻辑思维能力的培养,让学生在潜移默化中形成独立思考的习惯。小学阶段的数学教育教学对学生来说非常重要,教师要让学生养成独立思考的习惯,提高独立思考的能力,要学会活学活用知识,避免死板地吸收数学内容。     

大学生开展数学第二课堂活动的调查分析与思考

第二课堂既是第一课堂的有益补充,也是提高学生综合能力素质的有效途径,对于提高学生综合能力,培养学生创新意识等方面具有独特价值。经过我校不断努力,数学第二课堂建设取得了很大的进步,在培养人才方面发挥了巨大的作用。为了构建科学的数学第二课堂教育体系,我们课题组通过调查研究,旨在把握我校数学第二课堂活动开展现状,总结经验,查找不足,为进一步加强数学第二课堂教育体系的建设提供参考与借鉴。     

The development and use of an instrument to measure willingness to seek help from peers and teachers when studying college mathematics

As part of a three-phase study, 18 items were developed to measure aspects of a student’s willingness to seek help from and/or work with peers and teachers when studying college mathematics. In the first phase, 24 items were developed and administered to 165 undergraduate college students. During the second phase, 20 items, modified from the first instrument, were completed by a sample of 314 undergraduate college students. The sample was randomly divided in half and principal factor analysis with varimax rotation was performed on the first half. Two factors emerged and were interpreted as: Willingness to Work with Students (nine items); and Willingness to Seek Help from Teachers (nine items). Based on the results of the exploratory factor analysis, confirmatory factor analysis was performed on the second half of the sample. Coefficient α estimates were calculated to assess internal consistency. In the third phase, the final 18-item survey was given to 140 undergraduate college students and confirmatory factor analysis was again performed based on the results of the exploratory factor analysis from Phase II. Recommendations for future uses of these scales are given.     

Relationship to place: positioning Aboriginal knowledge and perspectives in classroom pedagogies

This project is based on research conducted with 12 schools in New South Wales, Australia. It examines how each school incorporates Aboriginal perspectives in its Kindergarten to Year 6 program with a view to identifying quality practice. As we interviewed teachers in these schools, it became clear that there is considerable confusion over the difference between Aboriginal perspectives and Aboriginal knowledge with both concepts being used interchangeably to teach syllabus content and information about Aboriginal people. We endeavour to clarify these concepts and to suggest how teachers might incorporate Aboriginal knowledge in their programs, without recreating some of the stereotypical representations that are often an effect of current pedagogies.     

Control engineering,system theory and mathematics: the teacher's challenge

The principles, difficulties and challenges in control education are discussed and compared to the similar problems in the teaching of mathematics and systems science in general. The difficulties of today's students to appreciate the classical teaching of engineering disciplines, which are based on rigorous and scientifically sound grounds, are discussed. The new demands for modern engineering education assume that the mathematical skills of the students in modelling, analysis, synthesis, simulation and validation of control problems improve significantly, which sets a major challenge to the education system. To meet that challenge new activating teaching methods are needed, which together with traditional studies bring the students closer to practical applications. In the current paper two new teaching methods are presented, which are aimed at bringing the control world near the student more easily than the traditional courses do. These example cases are control courses in the net with self-study sections, interactive repetitive questions, problems with complete solutions (both pen and paper and computer problems). Also, new ‘interactive laboratory exercises’ have been included, where the students prepare their preliminary problems first, and after that test the controller with a real process over the net (from their home or from a computer class).     

Balancing classroom ready with community ready: enabling agency to engage with community through critical service learning

Recent initial teacher education policy and regulatory frameworks privilege “classroom ready” discourses. Taking up “readiness” as technical skill requiring more “practice” leads to narrowing of teachers’ roles and efficacy with increasing pressure and regulation that marginalises ideals to equip pre-service teachers to be “community ready”. We argue that enabling preservice teacher agency to engage with community beyond notions of mastering bounded classroom practice is critical to teachers’ roles. Supporting teachers to teach in context as engaged global citizens requires a readiness of relational understanding and skills about the lived experiences of learners, and their wider community contexts. Data from a critical service learning case study highlight how preservice teacher agency to engage with community is conceptualised and experienced in simultaneously beneficial and challenging ways. These findings indicate the complex, yet necessarily significant contributions of service learning experiences to the development of preservice teacher “readiness”.     

Using a video-based curriculum to develop a reflective stance in prospective mathematics teachers

Although video cases are increasingly being used in teacher education as a means of situating learning and developing habits of reflection, there has been little evidence of the outcomes of such use. This study investigates the effects of using a coherent video-case curriculum in a university mathematics methods course by addressing two issues: (1) how the use of a video-case curriculum affects the reflective stance of prospective teachers (PTs); and (2) the extent to which a reflective stance developed while reflecting on other teachers’ practice transfers for reflecting on one’s own practice. Data sources include videotapes of course sessions and PTs’ written work from a middle school mathematics methods course that used a video-case curriculum as a major instructional tool. Both qualitative and quantitative analytical methods were used, including comparative and chi-square contingency table analyses. The PTs in this study showed changes in their level of reflection, their tendency to ground their analyses in evidence, and their focus on student thinking. In particular, they began to analyze teaching in terms of how it affects student thinking, to consider multiple interpretations of student thinking, and to develop a more tentative stance of inquiry. More significantly, the reflective stance developed via the video curriculum transferred to the PTs’ self-reflection in a course field experience. The results of this study speak to the power of using a video-case curriculum as a means of developing a reflective stance in prospective mathematics teachers.

Motivating adults to learn mathematics in the workplace: a trade union approach

ABSTRACT

The aim of this qualitative study is to explore adults’ motivation to learn mathematics in the workplace and the role that the trade union education approach promoted in the United Kingdom plays in that motivation. The findings draw on data from 20 semi-structured in-depth interviews with adults learning mathematics, organised through their trade union representatives. Trade unions promote education which uses teaching and learning approaches based on collectivist and activist principles, which is different from mainstream education, so the research explores what might be learnt from this approach. The findings show that the trade union-led approach enables even long-held negative feelings towards mathematics to become positive. The research finds a strong link between supportive social networks, including Union Learning Representative, as well as positive social and emotional encounters in the classroom that develop adult learners’ confidence, increasing their motivation to both learn and use mathematics in their everyday lives. This change in feelings and motivation is termed an Affective Mathematical Journey. These findings, while taking place in a non-traditional context, nevertheless are relevant to practitioners working with adults in both traditional (school and college) and non-traditional (workplace and community) settings. There are also indications of the positive influence this learning has on the relationship between individual members and their trade union organisations.     

Looking through the lens of a teacher's life: The power of prototypical stories in understanding teachers' instructional decisions in mathematics

The focus of this narrative inquiry was to examine how teachers describe influences on their instructional decisions in mathematics. Using a lens provided by pivotal or prototypical stories teachers told about their past experiences, connections were suggested between these past experiences and their instructional decisions. These connections helped to illustrate how instructional decisions may be shaped by priorities and beliefs established earlier in life, as well as by current contexts. Further research on the use and characteristics of prototypical stories is suggested.     

A study of the partnership between schools and universities to improve science and mathematics education in Indonesia

This paper examines what kinds of impacts a school–university partnership has on schoolteachers and university faculty members, and what types of challenges and tasks exist. The results show the following: (1) joint lesson planning, observation, and reflection, called piloting activities (PA) have succeeded in improving teaching methodologies; (2) faculty members and teachers generally regarded the students under PA as being more participative; (3) it is necessary to ensure linkages between materials and students, as well as between students; and (4) PA resulted in the development of collegiality within schools and between faculty members and teachers.