Using wikis to promote quality learning in teacher training

This paper discusses writing as a social practice and speculates on how wikis might be used to promote higher quality academic writing and support collaborative learning. This study of undergraduate teacher trainees’ online learning activities focuses on how shared spaces – wikis – might be used to communicate ideas and generate course‐specific content. The study also explored how students, through such activities, were able to improve their academic writing skills and engage more critically in learning. Data captured from student discussion boards and a post‐module email questionnaire (n = 35) were used to map student perceptions of the usefulness of wikis in support of their academic studies. The data indicate that most students raised their skill level in writing directly to the publicly viewable wiki space, in sharp contrast to the more informal content they posted on the discussion boards. The scope of collaborative writing was limited due to students’ reluctance to edit each others’ work, but students appreciated the shared environment as a means of discussing their work and the content of the course. Students reported that their academic writing skills had improved through their formal participation in the wiki.     

Designing Curriculum-Based Mathematics Professional Development for Kindergarten Teachers

This study examines the influence of a year-long mathematics professional development program on Kindergarten teachers’ beliefs, content knowledge, instructional practices, and their students’ achievement. The professional development program is grounded in the theoretical construct of learner-centered professional development and focuses on supporting teachers’ integration of standards-based pedagogies aligned with the Common Core State Standards in Mathematics. Data analysis included examining 15 Kindergarten teachers’ mathematics content knowledge, their beliefs about mathematics, their enactment of student-centered pedagogies, and student achievement on curriculum-based assessments. Findings indicated that teachers adopted more student-centered pedagogies and embraced more student-centered beliefs about mathematics teaching during their time in the project. Further, Kindergarten teachers also demonstrated gains in their mathematical content knowledge, and those content knowledge gains were linked to gains in student achievement.     

EXPLORING TEACHERS’ KNOWLEDGE AND PERCEPTIONS ACROSS MATHEMATICS AND SCIENCE THROUGH CONTENT-RICH LEARNING EXPERIENCES IN A PROFESSIONAL DEVELOPMENT SETTING

This paper examines upper elementary and middle school teachers’ learning of mathematics and science content, how their perceptions of their disciplines and learning of that discipline developed through content-rich learning experiences, and the differences and commonalities of the teachers’ learning experiences relative to content domain. This work was situated within a larger professional development (PD) program that had multiple, long-term components. Participants’ growth occurred in 4 primary areas: knowledge of content, perceptions of the discipline, perceptions about the learning of the discipline, and perceptions regarding how students learn content. Findings suggest that when embedded within an effective professional development context, content can be a critical vehicle through which change can be made in teachers’ understandings and perceptions of mathematics and science. When participants in our study were able to move beyond their internal conflicts and misunderstandings, they could expand their knowledge and perceptions of content and finally bridge to re-conceptualize how to teach that content. These findings further indicate that although teachers involved in both mathematics and science can benefit from similar overall PD structures, there are some unique challenges that need to be addressed for each particular discipline group. This study contributes to what we understand about teacher learning and change, as well as commonalities and differences between teachers’ learning of mathematics and science.     

数学教育与大学生就业能力发展

大学生就业难与缺乏就业能力有重要关系,当前一部分师生看不到二者的紧密联系。通过数学教育可以培养学生诚实正直,崇尚真理;勤于思考、坚忍不拔;爱岗敬业、勇于创新;热爱生活、团结协作等三个方面的就业能力。在数学教育中把握好转变教育观念、建立和谐师生关系这个关键因素,通过基本知识的挖掘和渗透;解题的提炼和反思;作业、练习的概括...     

An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge

The importance of students’ problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students’ mathematical content knowledge could be highly related to creativity in mathematics, too. This paper reports on a study that investigated USA and Chinese high school students’ mathematical content knowledge, their abilities in mathematical problem posing, and the relationships between students’ mathematical content knowledge and their problem-posing abilities in mathematics.     

How Does Ongoing Task-Focused Mathematics Professional Development Influence Elementary School Teachers’ Knowledge, Beliefs and Enacted Pedagogies?

This study examined how a task-focused, year-long mathematics professional development program influenced elementary school teachers’ knowledge, beliefs, and practices. Participants completed 84 h of professional development over 13 months that were focused on exploring, modifying and implementing cognitively-demanding mathematical tasks. Using a multi-methods approach, teacher-participants completed pre- and post-measures of mathematical knowledge for teaching, teachers’ beliefs about teaching and learning mathematics, and teachers’ self-reports of enacted instructional practices. Further, three teacher-participants were randomly selected to be observed 3 times over the course of the school year. Data analyses indicated that the professional development had a statistically significant positive impact on participants’ mathematical knowledge for teaching, use of student-centered instructional practices, and beliefs towards mathematics as a subject area. Further, the observed teachers enacted some high-level mathematical tasks and questions, but these were more visible at the end of the study compared to the beginning of the study. Implications for future work are also shared.     

“变教为学”,小学生数学逻辑思维能力的培养

随着素质教育在我国教育工作中的普及,学校培养学生的逻辑思维能力成为重中之重,能使学生思维更加完善,对其今后的想象力、创新力以及审美力的发展至关重要。小学数学教学可以有效提升学生思维核心能力,通过让学生对数学规律进行掌握以及归类,能让学生的思维逻辑更加清晰、有条理性,不仅能巩固学生小学数学基础知识,还能使学生的思维更加敏捷与灵活。     

Towards a theory of mathematics homework as a social practice

This article presents a theoretical conceptualization of mathematics homework as a social practice. Rather than considering homework as a task or an artifact, this approach frames homework in terms of the social contexts in which students participate and how students participate in those contexts. This perspective has long been suggested by homework researchers but has not been developed as a framework for understanding homework. Drawing from Wenger’s (1998) social theory of learning and research grounded in sociocultural theory, this conceptualization makes central meaning making and identity development, and puts forth meaning and identity as lenses for understanding students’ participation in the practice of mathematics homework. To further develop this conceptualization of homework, I draw on data from an ethnographic study of the role and meaning of mathematics homework in the lives of middle school students. Case studies of two students are presented to demonstrate the relationships among the meaning of homework, students’ identities, and their participation in the practice of homework. One student’s experiences support him in identifying as a capable mathematics student who is bound for continued academic success through high school to college. Thus, he comes to take on mathematics homework as a means to learn and succeed. The other student’s experiences support him in building an identity that leads him to reject homework. This conceptualization of homework and the case study data have implications for the practice of homework and for theories of students’ motivational dispositions in the context of mathematics homework and learning in general.     

Elementary mathematics teachers’ judgment accuracy and calibration accuracy: Do they predict students’ mathematics achievement outcomes?

In this study we investigated whether elementary mathematics teachers’ knowledge of their students, as reflected in both the accuracy and confidence with which they are able to estimate their students’ task-specific performance on sets of mathematics problems, predicted students’ overall mathematics achievement. Thirty-nine teachers made predictions about the performance of a random sample of target students (n = 150) in their classrooms on sets of “easy” and “difficult” multiplication and division problems. Teachers also provided confidence ratings for those judgments. From these data, indicators of teachers’ judgment accuracy, judgment confidence and calibration accuracy (a measure of metacognitive monitoring) were then related to all of their students’ (n = 834) performance on year-end standardized mathematics achievement tests. Multilevel analyses indicate that teachers’ calibration accuracy, but not their task-specific judgment accuracy, significantly predicted students’ mathematics achievement. Implications for future research on teacher knowledge as well as professional development programs are discussed.     

Integrating mathematics,science, and technology: effects on students

Few studies have examined the student learning effects of integrating science with mathematics and technology. We compared a school that integrated mathematics, science and technology in grade 9 to a school in the same district that taught the three courses separately. The distinguishing feature of the integrating school was the reorganization of instruction in the three subjects to prepare students for seven group projects (involving a total of 25 h) that required the application of knowledge and skill that were shared by the three subjects, as well as learning outcomes that were unique to each. The study detected benefits for students in the integrated setting in terms of their ability to apply shared learning outcomes, student motivation, ability to work together and attitudes to appraisal of group work. Female students in the integrated school had a better understanding of selected science learning outcomes. Attitudes toward mid‐term exams were higher in the control school.

     

Talking about mathematics

Students in a grade 3 class in a primary school in an outer suburb of Melbourne were encouraged to talk about, and ultimately reflect on, the work they had learnt in mathematics. Four lessons, each of approximately 50 minutes duration, were videotaped. Key excerpts were subsequently replayed to the children in a one-to-one setting. The data presented focussed on a lesson aimed to extend the children’s knowledge of fractions beyond a half and a quarter. By tracing the responses of four students in particular, two low and two average achievers, substantial individual differences in the ways children constructed meaning out of shared mathematical experiences were identified. The investigation confirmed that listening to students talk about their own mathematical experiences provides a rich data base for investigating students’ learning, error analysis, and subsequent teaching.     

Preservice elementary school teachers’ knowledge of fractions: a mirror of students’ knowledge?

This research analyses preservice teachers’ knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed literature regarding students’ knowledge of fractions. We did so because assessments of required content knowledge for teaching require review of the students’ understanding to determine the mathematics difficulties encountered by students. The preservice teachers were tested on their conceptual and procedural knowledge of fractions, and on their ability in explaining the rationale for a procedure or the conceptual meaning. The results revealed that preservice teachers’ knowledge of fractions indeed is limited and that last-year preservice teachers did not perform better than first-year preservice teachers. This research is situated within the broader domain of mathematical knowledge for teaching and suggests ways to improve instruction and student learning.     

Comparing theoretical perspectives in describing mathematics departments: complexity and activity

We draw on two studies of mathematics departments in 11–18 comprehensive maintained schools in England to compare and contrast the insights provided by differing theoretical perspectives. In one study, activity theory was used to describe common features of the work of three departments. In the other, a mathematics department was viewed and analysed as a complex system. In both cases, it was the learning of the departments as systems rather than of individuals that was of interest. The affordances and limitations of the analytical perspectives are discussed. Taken as a whole, this paper opens up the workings of school mathematics departments in a country which has a strong department culture.     

Exploring prospective teachers’ noticing of students' understanding through micro-case videos

This paper explores the nature of prospective teachers’ noticing of students’ understanding as they analyze and discuss middle school students’ understandings of trapezoids in micro-case videos in the context of geometry. In this exploratory study, the data were obtained from eight prospective middle school mathematics teachers through individual video analysis, reflection papers, and group discussions. The results indicated that the use of purposeful micro-case video designs based on prospective teachers’ background knowledge of quadrilaterals allowed them to be productive in video analyses and discussions. In individual video analyses, prospective teachers attended to various mathematical elements to identify students’ responses but did not always use them to make interpretations of each student’s understanding of trapezoid. In the group discussions of the micro-case videos, in contrast, prospective teachers could provide alternative interpretations of students’ understanding by identifying links between the mathematical elements in students’ responses and the characteristics of students’ understandings. In the group discussions, they provided more detailed and specific instructional actions to support each student’s understanding of trapezoid than their individual video analyses. This study suggests practical implications for teacher education programs on how to use video cases (e.g., firstly, working individually and then having group discussions about the videos) to explore prospective teachers’ professional noticing skills. Considering prospective teachers’ background knowledge of related mathematical contents, this study can also inspire future studies on how to design effective videos about students’ mathematical understanding.

     

Collaborative learning and the construction of common knowledge

In collaborative learning, students not only have to acquire knowledge, they also have to learn to regulate the process of acquiring knowledge. In the traditional classroom, the function of regulation rests with the teacher. In the collaborative classroom, however, the responsibility for learning has in part been handed over to the students. We examine how students, who work as members of a community of learners, construct shared understanding. in particular, we want to explore what interactive and discursive tools students use in their collaboration. We present observations made during a series of innovative mathematics lessons in an 8th grade classroom at a Dutch primary school in which children (between 11 and 13 years of age) worked as “researchers” who were encouraged to formulate questions for exploration and to collaborate in answering them. Both in small group discussions and in discussions involving the whole class, students worked on the construction of arguments and the creation of shared knowledge. The construction and diffusion of knowledge occurred in “cycles of argumentation” to which many children contributed and in which ideas were repeated and elaborated upon. Because, in students’ collaboration, learning is made dependent on proposing and critically discussing arguments, the character of knowledge, acquired under these circumstances, is different from knowledge acquired in a more traditional classroom setting.     

核心素养下的初中数学教学策略

随着新的教育理念的更新发展,对于数学教学的要求也不再是让学生学习基础的数学知识,而是要求培养学生的核心素养,切实培养学生应用数学知识解决实际问题的能力,为学生的全面发展奠定良好的教育基础。为此,初中教师需要结合学生的特点,主动转变教育理念,坚持以学生为主体,相信学生并且在教学时以核心素养为标准科学选择教学方法。     

Learning mathematics—letting the pupils have their say

Pupil voice is an emerging force for change and improvement in many UK schools, but what is not fully understood is how best to access pupil voice within the specific context of secondary mathematics departments. This paper presents a research project designed to use pupils as co-researchers in increasing knowledge about how to improve learning in mathematics. Pupils within the school were selected and trained as “Ambassadors” to understand and disseminate innovative ways of learning mathematics into their school environment and to act to allow the voice of all the pupils in their year group to be heard. The project was intended both to raise the pupils’ awareness of how learning mathematics could be different and to enable them to voice their newly informed opinions about how best they learned mathematics. The pupils’ current feelings about the way that they were taught mathematics were explored, but the focus of the project was on enabling the pupils to make informed decisions about how they felt their learning could be improved. The pupils’ awareness of different ways of learning mathematics was raised by introducing them to alternative teaching approaches. The data generated were initially analysed by the pupils themselves in order to inform their teachers about their views and subsequently constant comparison analysis resulted in the outcomes reported here. The outcomes indicate that the students could have an important role in enabling schools to develop their teaching and improve their pupils’ mathematical learning when that voice is both informed and authorised.     

Learning inter-professional teamwork during university studies: a case study of student-teachers’ and social work students’ shared professional experiences

This paper explores ways of enhancing inter-professional skills as part of professional development during university studies. From a socio-psychological viewpoint, inter-professional teamwork can be regarded as an interface between the group and individual levels, where collective commitment, efficiency, shared processes and outcomes, as well as tensions and dilemmas, are brought together. Inter-professional skills, which are already practised in university, may enable professionals to work in inter-professional contexts during their careers. In this case study, the participants (three student-teachers, two social work students and four supervisors) reflected on their shared experience of participating in a shared practicum at a primary school. The data-set comprises two group interviews conducted separately with the students and supervisors following the practicum. The results indicate that it is possible to develop inter-professional competencies during one’s university studies and that this has the potential to promote students’ reflective skills as they reframe their expertise and the expertise in other professions.