Academic continuity through online collaboration: mathematics teachers support the learning of pupils with chronic illness during school absence

Recent applications of technology to mathematics education have been designed with cognitive and constructivist theoretical perspectives in mind, viewing mathematical learning as the acquisition of knowledge through the construction of meanings and connections between concepts. With the advent of increasingly flexible communication technologies, there is both the need and opportunity to consider how they might be utilised, particularly since emergent socio-cultural theories advocate learning in mathematics as an inherently social activity where understanding is developed and negotiated collaboratively. The need to examine effective technology-facilitated learning arose in the context of a research project, currently underway in a number of secondary schools in the state of Victoria and funded by the Australian Research Council. It is investigating the learning needs of pupils who are absent from school for prolonged or intermittent periods owing to chronic illness yet continue with their school studies. An emerging understanding of the significant difference between computer-mediated contact for mere information exchange and communication for teaching and learning has led to a consideration of socio-cultural perspectives on effective mathematical learning and a focussed investigation of technologies able to facilitate them. Early data have demonstrated the potential of videoconferencing, online whiteboarding and interactive whiteboard application sharing, but which require particular resources, aligned infrastructure and teacher support. This article explores issues surrounding the use of such technologies for collaborative mathematical learning in a context where online interaction is being considered for the learning support of pupils unable to attend school.     

Characterising lesson planning: a case study with mathematics teachers

ABSTRACT

The quality of students’ learning experience depends on the learning activities that their teachers plan prior to classroom delivery. This article characterises the lesson planning practices of a group of 27 mathematics teachers. The questionnaire and the associated information coding and analysis procedures designed for that purpose may be applicable to lesson planning characterisation involving larger groups of teachers and of other disciplines. Some of the study group’s needs and difficulties are established. One of the observations discussed is that planning procedures and criteria tend to be generic rather than specific to the lesson at issue. Another is that these teachers’ vision of planning does not necessarily ensure a coordinated approach to all curricular dimensions.     

Professional development of mathematics teachers toward the facilitation of small-group collaboration

Collaborative work in small groups is often a suitable context for yielding substantial individual learning outcomes. Indeed, small-group collaboration has recently become an educational goal rather than a means. Yet, this goal is difficult to attain, and students must be taught how to learn together. In this paper, we focus on how to prepare teachers to become facilitators of small-group collaboration. The current case study monitors a group of six prospective teachers and their instructor during a one-semester course. The instructor was a skilled mathematics teacher with strong beliefs about what is entailed in establishing a mini-culture of learning to learn together and about how to facilitate student group work in problem-solving situations. We describe the learning path followed by the instructor, including the digital environment. The findings show that by the end of the course, the students became more competent facilitators of learning to learn together.     

Teacher collaboration and professional development in the workplace: a study of Portuguese teachers

This article reports on findings from research aimed at investigating teacher collaboration and professional development in the workplace. It draws upon a broader study carried out in a school in Northern Portugal. Data were collected through questionnaires, semi-structured interviews and written reflective accounts. In total, 80 teachers participated in phase 1, 11 key informants participated in phase 2 and 10 teachers participated in an intervention/training project (phase 3). Findings suggest that problems and limitations in relation to collaborative work are situated at the organisational level, such as time and working conditions. Lack of training in collaboration, and issues such as motivation and personal difficulties, also emerged from the data. Teachers tend to stress the importance of interpersonal relationships at school, but they also identified formal meetings when they described the contexts and opportunities to work collaboratively in the workplace, namely department meetings and projects driven by central government or school administration initiatives. Implications for teacher collaboration and professional development are discussed.     

Preparing mathematics and science teachers through a residency program: perceptions and reflections

The critical challenge of recruiting, preparing, and retaining high-quality mathematics and science teachers for high-need urban schools is complex. Therefore, identifying factors that support and impede a teaching residency program’s implementation may have the potential to build an effective initiative that will benefit all stakeholders. The purpose of our study was to examine preservice teachers’ perceptions about their experiences in the Teaching Residency Program for Critical Shortage Areas program, a federally funded program designed to address teacher shortages in mathematics and science in high-need schools. Three themes emerged from the data analysis: (a) the residency framework, (b) a relevant curriculum, and (c) immersion in an authentic school context. Our findings have the potential to inform policy-makers, school administrators, university directors of school partnerships, and other individuals who have direct influence on teacher recruitment and retention.     

What they notice in video: a study of prospective secondary mathematics teachers learning to teach

Most teacher preparation programs have embraced the use of video as an effective methodology for developing teachers’ noticing skills. This study focused on learning about what secondary mathematics prospective teachers (PSTs) were able to notice when viewing video of their own co-teaching, particularly in a microteaching setting that consisted of peers. PSTs documented their observations on an observation tool while re-watching their video and then identified and ranked their top three observations. The ranked noticing statements were analyzed based on a grounded theory approach. Overall, PSTs’ ranked observations were more likely to attend to students and had a strong focus on mathematics and student learning. Ranked observations equally demonstrated both broad and specific understanding of video moments and often made suggestions that something they noticed could be improved in the implementation stage, versus improvements in planning or changes in themselves. Results support PSTs’ use of video for developing noticing skills in teacher education programs.     

Preparing student teachers to use computers in mathematics classrooms through a long-term pre-service course in Turkey

Recent studies have found short in-service teacher education programs are not providing adequate technology experiences to prepare their participants for teaching mathematics with computers. As an alternative to the short-term courses the author has been teaching a two-term mandatory undergraduate course within a mathematics teacher education program since 1995 to train student teachers and to investigate their perceptions on their preparation to use computers in their own teaching. This article describes issues that emerged from the analysis of this undergraduate course. Data were gathered through questionnaires and students' writings about the course activities. Findings indicated that computer literacy appeared to be an important key factor in utilising the course activities successfully. Students who felt prepared made the link between computer-based mathematical activities and school mathematics, and had more experience of using instructional software during the course than others. Findings of this nature can also assist teacher educators as they incorporate information technology into existing pre-service programs. The implications of these results for the designing and implementing of computer-based undergraduate courses and for further research in this field are discussed.     

Pre-service teachers in mathematics: Struggling with the Standards

The purpose of this paper is to describe a two-year investigation of pre-service teachers in mathematics. Of particular interest is the degree to which the NCTM (1989) Curriculum and evaluation standards for school mathematics, the NCTM (1991) Professional standards for teaching mathematics, and other reform agendas impact pre-service teachers' thinking and practices. The beliefs, perceptions, philosophies, and classroom actions of four cohorts of student teachers (n = 44) were examined throughout this 2year study. Of particular interest were the pressure student teachers felt to implement the Standards in their teaching, their perceptions of their own teaching with respect to the Standards, the content of their lessons, and the impact of cooperating teachers on the development of the student teachers. Data was collected through a variety of sources, organized and analyzed in the spirit of ethnographic work. Data was generated through classroom observations, pre- and post-lesson conferences, lesson plans, seminar sessions, survey questionnaires, and informal conversations. A minimum of four classroom observations were made for each participant. Analysis of the data revealed general agreement among the student teachers in their regard for the Standards. Although they appeared to affirm the goals, content and recommendations contained therein, they almost uniformly suggest that they lack the tools to implement the Standards appropriately in the classroom. The consistency in the types and content of lessons observed appeared to validate this concern. An overwhelming majority of the lessons observed bore little or no resemblance to the values so highly espoused by the student teachers. Student teachers perceived notable pressure from the education program to include the Standards in their teaching practices, while feeling little pressure from cooperating teachers. They also point to cooperating teachers as the most significant influence on their teaching.     

Studying mathematics problem-solving classrooms. A comparison between the discourse of in-service teachers and student teachers

In the article we compare the approaches of 3 in-service teachers and 3 student teachers when they tried to solve a verbal arithmetic problem in the classroom. Each interaction was studied using a System of Analysis that takes into account the cognitive processes involved in the solution of a mathematic problem and describes the interaction at different levels showing what is done and to what degree teachers and/or pupils are responsible for what is done. The results of the study suggest that both groups of teachers are different in how they direct the student’s attention toward the essential aspects implied in the resolution of word problem. On the one hand, the in-service teachers guaranteed students’ understanding of the problem before dealing with the solution, while students teachers only did so when pupils committed errors. On the other hand, the in-service teachers allowed a high level of student participation, while student teachers took a more prominent role so children’s participation was lower.     

Examining the supervision of mathematics student teachers through analysis of conference communications

Student teaching is often a capstone experience in the preparation of mathematics teachers. Thus, it is essential to better understand key aspects of the experience. We conducted a qualitative study of post-lesson conferences led by supervisors (classroom cooperating teachers and a university supervisor) working with mathematics student teachers. Analysis of conference communications revealed differences in the types and content of communications in conferences led by the cooperating teachers and by the university supervisor. Cooperating teachers tended toward evaluative supervision that lacked a focus on the mathematics of the lessons while the university supervisor tended toward educative supervision, guiding student teachers to reflect on and learn from their own classroom experiences including the mathematics of their lessons. Differences are discussed, and suggestions concerning the supervision of student teachers are made along with recommendations for further research.     

Developing complex understandings: On the relation of mathematics education research to mathematics

This article explores some of the intellectual bases of the apparent cultural divide between the fields of mathematics and mathematics education research. The chasm is in part attributable to epistemologies or theoretical `paradigms', fashionable in education, that dismiss or deny the integrity of fundamental aspects of mathematical and scientific knowledge. The solution offered is for the next generation of mathematics education researchers to knowledgeably and thoughtfully abandon such `isms' in favor of a unifying scientific and eclectic approach to research.     

Peer collaboration: the relation of regulatory behaviors to learning with hypermedia

Peer collaboration is a pedagogical method currently used to facilitate learning in classrooms. Similarly, computer-learning environments (CLEs) are often used to promote student learning in science classrooms, in particular. However, students often have difficulty utilizing these environments effectively. Does peer collaboration help students learn with these environments? Little research looking closely at face-to-face peer collaboration with computer learning environments exists. Utilizing a social-cognitive theoretical framework, this study investigated the relation between the conceptual-knowledge learning and the collaborative regulatory behaviors of students working with a peer as they studied about the human circulatory system using a hypermedia CLE. Fifty-four high-school students from the East Coast of the United States were audiotaped to identify the collaborative regulatory behaviors they evidenced as they studied. Results revealed significant correlations among students’ proportion of categories of regulatory behaviors and their learning gains (from pretest to posttest). Moreover, qualitative analyses revealed particular behaviors that larger-gain collaborative pairs engaged in to a greater extent than smaller-gain pairs as they learned with the hypermedia environment.     

Advisory teachers of mathematics: the ESG initiative

This paper traces the development of the education support grant provision for mathematics teaching. The rationale behind this DES initiative is discussed, and the paper provides evidence of the range of activities undertaken by ESG teams in various local authorities. An analysis of the variety of working models is provided across five LEAs. Results of interviews conducted with advisory teachers and teachers in participating schools are reported in an attempt to portray the nature of the support work. In the concluding section, it is argued that LEAs should consider basing their in‐service policy for mathematics teachers around projects of this nature, which have provided a much needed catalyst for curriculum change in the post‐Cockcroft era.     

Data-based individualization in mathematics to support middleschool teachers and their students with mathematics learning difficulty

Project STAIR (Supporting Teaching of Algebra: Individual Readiness) aims to develop and iteratively refine a framework for using data-based individualization (DBI) to support the readiness for algebra of middle-school students with mathematics learning difficulty. Project STAIR was tested in four middle schools in the United States to assess the impact of intensive professional development, ongoing coaching, and frequent student progress monitoring on teachers’ DBI practices, school-level culture and climate, and students’ algebra readiness. Findings from this exploratory research point to the promise of Project STAIR for improving teacher perceptions of school culture and climate related to support of students experiencing mathematics learning difficulty as well as increasing specific DBI practices, including teachers’ ratings of importance, understanding, and confidence with assessment practices. Students’ mathematics outcomes improved on several algebra-readiness progress monitoring measures, along with a diagnostic measure, but not on a more distal measure of mathematics performance.     

Synergies between theoretical approaches to mathematics education with technology: A case study through a cross-analysis methodology

Mathematics education as a research domain is characterized by a plurality of theoretical approaches. Acknowledging the existence of such diversity and the risks of an excessive theoretical fragmentation does not mean to search for a unifying theory but to urge the community to develop strategies for coping with this diversity. This article is meant to show the potential of a “cross-analysis” methodology for establishing connections between different theoretical approaches to mathematics education with technology. Within the frame of the ReMath European Project, two Teaching Experiments were realized, centred on the use of a same ICT tool—Casyopée. Two distinct theoretical approaches shaped both the Teaching Experiments design and their enactments: the Theory of Didactical Situations and the Theory of Semiotic Mediation. The two Teaching Experiments have then been analysed from both theoretical points of view. In this article we will provide some examples drawn from this cross-analysis that show the synergy which can be established between the aforementioned theoretical approaches. Beyond contributing to a deeper understanding of the observed “didactical phenomena”, that synergy allows establishing connections between the two approaches that lead to their reciprocal enrichment.     

浅谈教学中增强学生数学应用意识的意义及途径

长期以来 ,受传统教育思想的影响 ,数学教学存在严重缺陷。课堂上不讲知识的实际来源和应用方法 ,“掐头去尾烧中段” ,把能力培养局限于解答考题 ,造成学生动手能力差 ,应用意识弱的现状。随着科技的发展、技术的进步 ,数学的应用日益广泛 ,教学中如何增强学生的数学应用意识是一个迫切需要解决的问题。1　增强学生数学应用意识的意义1 1　符合数学学科自身特点数学的特点之一是应用广泛性 ,这是数学生命力之所在 ,也是数学内容虽然高度抽象却仍能蓬勃发展的基础。马克思就曾预言 :“一门科学只有成功地运用数学后 ,才能达到完善的地步。…     

Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge

Preservice teachers’ pedagogical content knowledge (PCK) development was investigated with respect to integrating technology. Four components of PCK were adapted to describe technology-enhanced PCK (TPCK). The study examined the TPCK of student teachers in a multi-dimensional science and mathematics teacher preparation program that integrated teaching and learning with technology throughout the program. Five cases described the difficulties and successes of student teachers teaching with technology in molding their TPCK. Student teachers view of the integration of technology and the nature of the discipline was identified as an important aspect of the development of TPCK.     

Britain's contribution to the training of mathematics teachers in other countries

Despite differences in both the nature and scale of the problems facing teacher trainers in developing countries compared to those in Britain, British collaboration is still widely sought in mathematics teacher education in such countries. Various forms that such assistance may take are described, with reference to specific examples from a number of countries. Three mathematics projects in which British aid has been involved ‐ in the West Indies, Southern Africa and India ‐ illustrate how in‐service teacher education is an integral component of such projects.