The ability to understand and use conceptual change pedagogy as a function of prior content learning experience

This research examined the relationship between content instruction and the development of elementary teacher candidates' understanding of conceptual change pedagogy. Undergraduate students (n = 27) enrolled in two sections of a science methods course received content instruction through either traditional or conceptual change methods, followed by instruction about conceptual change pedagogy. Candidates were interviewed pre- and postinstruction about their content and pedagogical knowledge and also wrote conceptual change lessons. Twelve of the 27 subjects were videotaped teaching in the field. Results indicate that prior to instruction, most candidates had weak content knowledge and held traditional pedagogical conceptions. After instruction, students in the conceptual change group had significantly larger gains in their content knowledge than those in the traditional group, gave qualitatively stronger pedagogical responses, and used conceptual change strategies more consistently in practice. These results indicate that personal experience of learning science content through conceptual change methods facilitated the development of understanding and use of conceptual change pedagogy in teaching practice. Thus if conceptual change methods are to be incorporated into teacher candidates' repertoire, science content courses that students take prior to teacher education should be taught using conceptual change pedagogy. In addition, courses in science education should use pedagogy more in line with that taught in methods courses.     

Designing and implementing authentic investigative proportional reasoning tasks: the impact on pre-service mathematics teachers’ content and pedagogical knowledge and attitudes

In this study we created, implemented, and evaluated the impact of proportional reasoning authentic investigative tasks on the mathematical content and pedagogical knowledge and attitudes of pre-service elementary and middle school mathematics teachers. For this purpose, a special teaching model was developed, implemented, and tested as part of the pre-service mathematics teacher education programs conducted in Israeli teacher colleges. The conclusion of the study is that application of the model, through which the pre-service teachers gain experience of and are exposed to authentic investigative proportional reasoning tasks with incorporation of theory (reading and analyzing relevant research reports) and practice, leads to a significant positive change in the pre-service teachers’ mathematical content and pedagogical knowledge. In addition, improvement occurred in their attitudes and beliefs towards learning and teaching mathematics in general, and ratio and proportion in particular.     

高师《小学数学课程教学概论》课的教学探索

《小学数学课程教学概论》是研究小学数学教学理论及其应用的一门教育学科,是高师院校小学教师教育专业的一门必修课.但是有些师范生对这门课的重要性认识不够,学习兴趣不大.在教学中让师范生提前感知小学和小学数学、感知新课标下的课堂教学,学习小学数学教育理论,进行说课、讲课训练和比赛等实践活动是行之有效的.     

The effect of teacher education programs on future elementary mathematics teachers’ knowledge: a five-country analysis using TEDS-M data

This article addresses the problem of how opportunities to learn in teacher education programs influence future elementary mathematics teachers’ knowledge. This study used data collected for the Teacher Education and Development Study in Mathematics (TEDS-M). TEDS-M measured the mathematics content knowledge (MCK) and the mathematics pedagogical content knowledge (MPCK) of future teachers in their final year in teacher preparation programs. The purpose of this study is to explore whether elementary teaching candidates’ MCK and MPCK are associated with their opportunities to learn in mathematics courses and mathematics methods courses in five countries. The results showed that opportunities to learn in some teacher preparation components are more important than in other components.     

The role of university-based induction in beginning elementary teacher enactment of effective mathematics teaching

The purpose of this paper is to describe the school-based contextual constraints perceived by beginning elementary teachers as they attempted to enact their visions of effective mathematics teaching and the components of a mathematics-specific, university-based induction program designed to support elementary teachers in their teaching of mathematics. A significant number of beginning teachers in the program indicated that curriculum pacing guides and grade level teachers often discouraged their enactment of effective mathematics teaching. We describe the components of the induction program in general and then discuss the specific ways that program mentors, who were elementary teachers with expertise in mathematics teaching, supported beginning teachers in navigating the constraints identified. Data suggest that supporting teachers’ pedagogical agency to navigate local school contexts should be an additional consideration in teacher preparation and induction programs.     

The Development of Diploma in Education Student Teachers’ Mathematics Pedagogical Content Knowledge

Mathematics pedagogical content knowledge (MPCK) of teachers cannot be easily defined but is a complex concept integrating generic pedagogical knowledge, mathematics teaching methodology as well as knowledge of the discipline of mathematics. It is the objective of mathematics methodology courses in teacher preparation programmes to begin the development of MPCK in their pre-service teachers. As part of a research study on the development of MPCK in primary school beginning teachers, a 16-item instrument was developed to measure some aspects of the MPCK for teaching mathematics at primary level. The instrument was administered to the 2003 Intake of the Diploma in Education student teachers at the National Institute of Education, Singapore just at the beginning of their programme. As they completed their methodology course in February 2005, the instrument was administered again. This paper will discuss the findings concerning their performance in these two tests, with reference to the overall performance as well as topic-specific and MPCK construct-specific performance. The findings indicate that student teachers at the beginning of their programmes are generally quite weak in their mathematics pedagogical content knowledge, as might be expected. There was significant improvement in some aspects of their MPCK on completion of their mathematics pedagogy course.     

Preservice elementary teachers' views of pedagogical and mathematical content knowledge

In broad terms, this study describes preservice elementary teachers' beliefs, conceptions, and practices during the mathematics methods course and teaching practica of a teacher education program. In particular, the study employs qualitative data to investigate preservice teachers' views of mathematical and pedagogical content knowledge. The study reveals symbiotic relationships between their views of content knowledge and their instructional actions which remain problematic. With unwavering beliefs and practices, and without reconceptualizing their roles as future elementary teachers, at the end of the semester the preservice teachers emerge as poor duplicators of mathematics methods instead of initiators of learning.     

Exploring the role of TPACK and teacher self-efficacy: an ethnographic case study of three iPad language arts classes

This ethnographic research study investigated three elementary teachers’ perceived self-efficacy beliefs and their attitudes toward mobile technology-enhanced instruction. Using technological pedagogical content knowledge (TPACK) as a guiding theory, the authors sought to determine whether and how the three knowledge components that form the foundation of the TPACK framework– technological, pedagogical or content knowledge – have similar levels of influence on teachers’ language arts teaching practices. They also examined how each teacher incorporated iPad technologically enhanced pedagogical practices and made connections to their beliefs about the role of technology and education. Data collection consisted of classroom observation field notes, teacher interviews and teacher blogs. Findings reveal that the teachers’ attitudes toward the integration of iPad technology formed a basis for how they approached their pedagogy. Compared to their technological and content knowledge, teachers’ pedagogical knowledge and years of teaching experience strongly influenced their decisions regarding mobile technology integration. By the end of the study, all teachers identified stronger connections and awareness in relation to the components of TPACK. The implications of these findings will provide insight relevant to the development of professional development opportunities for teachers regarding TPACK that could ultimately lead to more successful technology integration by teachers.     

Holistic school pedagogy and values: Finnish teachers’ and students’ perspectives

The purpose of the study was to identify the components of holistic school pedagogy as identified by a sample of Finnish secondary school teachers and students from two schools. Holistic pedagogy concerns the development of the whole student and acknowledges the cognitive, social, moral, emotional and spiritual dimensions of education. The data were gathered in spring 2008 and include 19 interviews of Finnish secondary school teachers of different subjects and 37 interviews of their students. The teachers and students came from two schools that both emphasize mathematics in their curricula. Analysis of the teachers’ and students’ interviews revealed three different components in holistic school pedagogy. These components were values and worldviews, field-invariant pedagogical components (which are important regardless of the content or the subject) and field-dependent pedagogical components (subject- or context-specific issues, such as pedagogical content knowledge of mathematics or the type of school). Holistic school pedagogy also emphasized the importance of the whole school community for the best pedagogical practices in schools.     

Early childhood mathematics teaching: challenges,difficulties and priorities of teachers of young children in primary schools in Ireland

Issues of pedagogy are critical in all aspects of early childhood education. Early childhood mathematics is no exception. There is now a great deal of guidance available to teachers in terms of high‐quality early childhood mathematics teaching. Consequently, the characteristics of high‐quality early childhood mathematics education are clearly identifiable. Issues such as building on young children’s prior‐to‐school knowledge; engaging children in general mathematical processes; and assessing and documenting children’s learning are some of the key aspects of high‐quality early childhood mathematics education. The extent to which teachers of four‐ and five‐year‐old children in primary schools in Ireland incorporate current pedagogical guidance in early childhood mathematics education was explored in 2007 in a nationally representative questionnaire survey of teachers of four‐ and five‐year‐old children attending primary schools. This paper presents some of the findings of the study in relation to teachers’ self‐reported challenges, difficulties and priorities in teaching early childhood mathematics. Implications are drawn for professional development, curriculum guidance and educational policy.     

Developing a Pedagogy of “Making” through Collaborative Self-Study

We believe that the ideas associated with the Maker Movement have profound implications for teacher education. We have isolated the pedagogical principles of hack, adapt, design, and create as central to exploring how they work with teacher candidate participants in a maker pedagogy lab. We frame these ideas as Maker Pedagogy, which is the enactment of the principles inspired by the maker movement in the classroom to foster learners who operate as innovators, creators, sharers and givers of knowledge, tools and technologies. The purpose of our self-study research is to describe, interpret and analyze how our pedagogies of teacher education and our critical friendship have changed and developed as a result of providing experiences for teacher candidates in our maker pedagogy lab. In this project we use self-study methodology to investigate our teaching and practices, and we dialogue about our tacit and personal knowledge as it contributes to the knowledge and understanding of our teaching through Maker Pedagogy. In particular, the emphasis is on critical collaborative inquiry through critical friends and on dialogue as a valued component of our research. Of particular interest were data in the video recordings of each lab that indicated that one or both of us had reframed our understanding of maker pedagogy. The findings are framed as three themes that document what we are learning about Maker Pedagogy through teaching teacher candidates. These are (1) the value of self-study methodology, (2) Maker Pedagogy as distinct and (3) deepening our pedagogies of teacher education.     

Reconstructing elementary teacher candidates' understanding of mathematics and science content

This paper examines the mathematics and science content knowledge of elementary teacher candidates. Data are presented which demonstrate that many elementary teacher candidates enter teacher education seriously deficient in their understanding of the subject matter they will teach to elementary students. The authors argue that these candidates are weakly prepared in content because of deficiencies in the pedagogy practiced in traditional didactic mathematics and science courses. They describe a conceptual approach to teaching mathematics and science content and contrast this with a didactic approach. Data are presented which demonstrate that these conceptual approaches significantly improved novice teachers understanding of content.     

Connecting with the horizon: developing teachers’ appreciation of mathematical structure

A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior secondary mathematics is the context for this study of teachers’ mathematical and pedagogical knowledge. The analysis of teachers’ reflections on their learning explored teachers’ understanding of mathematical connections and their appreciation of mathematical structure. The findings indicate that a professional learning program about senior secondary mathematics can enable practicing teachers to deepen and broaden their knowledge for teaching junior secondary mathematics and develop their practice to support their students’ present and future learning of mathematics. Further research is needed about professional learning approaches and tasks that may enable teachers to imbed and develop awareness of structure in their practice.     

Pre-Service Elementary Teachers'' Perceptions of Factors in an Holistic Methods Course Influencing their Confidence in Teaching Science

Lack of confidence towards science is a major factor in the avoidance of teaching science at elementary school. This paper reports the results of a survey that asked 28 pre-service elementary teachers what they believed contributed to their confidence towards science and the teaching of science during a second year science unit where an holistic teaching/learning approach was taken. The holistic nature of the unit was based on a model that considered six major factors to be important influences on the confidence of the pre-service teacher. Using median values, and ranking from the most to least important factor influencing their confidence, the pre-service teachers identified practicum, teacher educator, pedagogical content knowledge, learning environment, assessment and reflection. Factors within pedagogical content knowledge, ranked from most to least important, were science pedagogy, science activities, children's views of science, science content knowledge and investigating scientifically. The wide variability in responses highlighted that no single factor was perceived to be a major contributor to the pre-service teachers' confidence, but rather a balanced mix was necessary. Implications for pre-service elementary science education units are discussed.     

Contribution of mathematics in-service training course to the professional development of elementary school teachers in Israel

The present study aimed to explore the contribution of a mathematics in-service training course to elementary school teachers (1st–6th grades) in Israel. The study was conducted among 449 educators. They were required to respond to background questions. Moreover, they were asked to indicate their expectations from the in-service training course and, at its end, point out to what extent they benefitted from that course. The research findings illustrate that educators who teach mathematics at elementary school and attended the course are generally women in their 40s, holding a BEd degree and a teaching certificate not in mathematics, with an average 13-year seniority. The participating teachers indicated their wish to enrich their didactic knowledge in order to acquire varied tools for teaching mathematics to the entire pupil population as well as to gifted pupils and pupils with learning difficulties. Nevertheless, their demand to expand their mathematics knowledge was very limited. Based on the fact that most teachers have no mathematics education, this is a surprising finding as, in order to be a good teacher, one must be versed not only in Pedagogical Content Knowledge but also in Subject Matter Knowledge.     

A review of pedagogy related to information and communications technology

Abstract

This article reviews research on pedagogies associated with the use of information and communications technology (ICT) in primary and secondary schools. We propose a framework for examining pedagogical practices based on an analysis of the nature of pedagogy as revealed in the literature. In the light of this framework we discuss empirical evidence of the use of different types of ICT in different subjects and phases of education. We identify pedagogical issues associated with ICT use and their implications for teachers' pedagogical reasoning and practices. The evidence suggests that new affordances provided by ICT-based learning environments require teachers to undertake more complex pedagogical reasoning than before in their planning and teaching that incorporates knowledge of specific affordances and how these relate to their subject-based teaching objectives as well as the knowledge they have always needed to plan for their students' learning. In addition the research shows that teachers' beliefs about the value of ICT for learning and the nature of successful learning environments are important in teachers' pedagogical reasoning     

History of mathematics: illuminating understanding of school mathematics concepts for prospective mathematics teachers

The use of the history of mathematics in teaching has long been considered a tool for enriching students’ mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of research conducted over four semesters in which I sought to characterize what prospective mathematics teachers (PMTs) understand about the topics that they will be called upon to teach in the future and how that teaching might include an historical component. In particular, I focus on how the study and application of the history of solving quadratic equations illuminates what PMTs know (or do not know) about this essential secondary school algebraic topic. Additionally, I discuss how the results signal important considerations for mathematics teacher preparation programs with regard to connecting PMTs' mathematical and pedagogical knowledge, and their ability to engage in historical perspectives to improve their own and their future students' understanding of solving quadratic equations.     

Pedagogical content knowledge and the teaching of outdoor education

This theoretical paper examines the concept of pedagogical content knowledge (PCK) and explores how it might contribute to conversations around quality teaching and learning in outdoor education. This paper begins by summarizing the historical and contemporary literature, including issues of definitions, curriculum, content, and pedagogy in outdoor education. We then review the concept of PCK, its history, and contributions to other subject areas, including mathematics. We present a framework for PCK from the field of mathematics education and propose a 'modified' PCK framework for outdoor education. We postulate that this framework might help articulate knowledge areas needed by a teacher of outdoor education, and how these differ from and are similar to those required in other subject areas. We conclude by exploring how the idea of PCK and the modified framework might add to existing understandings of what it means to provide high quality outdoor education teaching and learning experiences.     

美国数学教师学科知识研究的概述和启示

我们对美国近五十年有关教师学科知识及其应用的研究方式和发展途径进行了概述和评论,在职教师培训重视教学专题学习以提升教学内容知识,职前培训重视教学论和教学方法课的学习,以积累总的分析和理解教学内容知识的观念和方法,是对我国数学教师学科知识教育最有益的借鉴和启示。