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.     

On Enhancing Teachers' Knowledge by Constructing Cases in Classrooms

This study was designed to enhance teachers' knowledge by constructing cases as part of a school-based professional development project in Taiwan. Cases, involving episodes and issues from real classroom events, were constructed collaboratively by a school-based team consisting of the researcher and four classroom teachers. The process of constructing cases, characterization of teachers' understanding of cases, and their skills for case writing were developed in the course of the study. In the process of constructing these cases, teachers improved their awareness of and their competence in dealing with the difficulties students encountered in the learning of mathematics; they enhanced their pedagogical content knowledge and their ability to reflect on classroom practices.     

信息技术支持下的学科教学知识:缘起、演化、结构模型及其教育意蕴

信息技术支持下的学科教学知识(TPACK)是学科教学知识(PCK)在信息化时代的发展。技术知识(TK)、教法知识(PK)和内容知识(CK)是TPACK结构模型中的基础成分;学科教学知识(PCK)、技术支持下的内容知识(TCK)、技术支持下的教学知识(TPK)和技术支持下的学科教学知识(TPACK)是TPACK结构模型中的互动成份。TPACK框架在理论上、在教师教育、在教学实践上等诸方面为信息技术与学科课程整合提供了新思路,将有助于我们推动学科教学知识发展,将为学科教育的信息化提供有力的教学知识基础。     

Student teachers’ patterns of reflection in the context of teaching practice

This study clarifies the basic structure of student teachers’ reflective thinking. It presents a constructivist account of teacher knowledge through a detailed analysis of various patterns of reflection in student teacher portfolios. We aim to gain a greater understanding of the process and outcomes of portfolio writing in the context of teaching practice. By closely analysing portfolio texts, we defined six main starting points for reflective episodes and several patterns under each of them. Also, the patterns of reflective episodes were analysed according to their deductive and inductive dimensions, together with their static and dynamic features. According to our results, it is possible that student teachers can reflect beyond solely practical issues on teaching, articulate multiple concerns about practice and elaborate them in an integrative manner as well as learn both from theory and from practice as a result of reflection for their future profession.     

Student teachers’ perceptions of reading and the teaching of reading: the implications for teacher education

This article reports on research which identified perceptions of reading and the teaching of reading held by trainee teachers and the impact on my provision as a teacher educator. It found that students’ past and present experiences of learning to read and being a reader influenced their perceptions of what reading is and of what it means to teach reading. As a teacher educator, I am not able to give students long experience of seeing children becoming readers, but I am able to give them richer experiences of reading in personally and culturally relevant contexts. This has implications for the nature of subject knowledge required by a student teacher of reading and the curriculum and practice of teacher education.     

Geography pre-service teachers’ pedagogical content knowledge

This paper reports on an exploratory study that investigated the pedagogical content knowledge (PCK) of four Geography pre-service teachers as they completed their final practicum of their Bachelor of Secondary Education programme. It uses Shulman’s (1986, 1987) two categories of PCK as a conceptual framework to identify the participants’ PCK of their Geography teaching. The first type of PCK is teachers’ representations of content that is pedagogically powerful for students; the second type of PCK refers to teachers’ understanding of what makes the learning of specific topics easy or difficult for students. Historically, researchers have tended to focus on the teachers’ representations component of PCK while little evidence-based research has been reported on the second category of PCK. Findings from this study show that all participants demonstrated both types of PCK. This study sheds light on the importance of teacher-educators modelling both types of PCK as both are equally important for pre-service teachers.     

Promoting higher levels of reflective writing in student journals

This paper traces the development over several years of an initiative involving student journals that was introduced into a tertiary science education course for pre‐service teachers to promote enhanced learning of how to teach science. Very soon after introducing the journals into course work the lecturer began engaging in ‘unplanned’ informal reflection (reflection‐in‐action and reflection‐on‐action) when she witnessed the shallow, often trivial nature of her students’ reflective writing and the lack of pedagogical insights they were gaining from the exercise. Motivated by her own ongoing scholarship the lecturer introduced purposeful coaching of reflective skills into her pedagogy to scaffold students’ learning and promote more useful reflection. The impact of these interventions on students’ reflective capabilities and learning were investigated using a formal action research cycle. Findings indicate that student teachers’ reflective skills improved and resulted in deeper and more focused thinking about how to teach science for learning.     

数学特级教师学科教学知识的个案研究

运用文本分析法,发现特级教师在深刻理解数学的基础上形成了文化取向的学科知识;课程的知识体现了数学知识的发生发展和结构特点,并考虑了学生的认知特点;学情的知识切合了学生心理发展的特点,并能以具体内容为载体推动学生心理的发展;教学的知识拟合了做数学的过程。提高教师的学科素养能促进教师对教学理论、课程编排及学生认知心理的认识;充分考察认知的文化性,也能促进教师对上述三者的认识,从而有效地发展学科教学知识。     

Pre-service mathematics teachers’ learning and teaching of activity-based lessons supported with spreadsheets

In this study, 12 pre-service mathematics teachers worked in teams to develop their knowledge and skills in using teacher-led spreadsheet demonstrations to help students explore mathematics concepts, stimulate discussions and perform authentic tasks through activity-based lessons. Pre-service teachers’ lesson plans, their instruction of the lessons designed, experiences and lesson enactment outcomes were examined. The pre-service teachers in the study were able to develop and demonstrate their knowledge and skill adequately in designing and enacting activity-based mathematical lessons supported with spreadsheets. The results also showed that the pre-service teachers’ use of the spreadsheet as an instructional tool promoted student in-depth mathematical concept formation and an activity-based learning approach to make lessons less teacher centred and more interactive.     

Prospective teachers' initial conceptions about pupils' understanding of science and mathematics

Earlier reports have shown that prospective teachers' conceptions about teaching science to a high degree are resistant and do not change substantially during the teacher‐training programme. In our investigation we elucidate the prospective teachers' initial conceptions about pupils' understanding of science and mathematics. We applied ‘The Lesson Preparation Method' and used a phenomenographic approach in order to reveal the range of conceptions that the prospective teachers hold. A third of the prospective teachers did not consider pupils' conceptions when planning lessons. The rest of the 32 participants expressed awareness; some of the prospective teachers even referred to subject‐specific teaching experience. Also regarding the prospective teachers' conceptions about pupils' knowledge and beliefs, as well as about pupils' difficulties, there was a significant diversity. By raising these issues about pedagogical content knowledge the prospective teachers' conceptions can be extended and developed during the education.     

教育实习调查报告

本文从师范学校小教大专中文和数学专业的实习中取样132份,对他们的实习反思心得文章进行定性分析,发现师范生教育实习存在问题主要有实习前的心理适应性弱;教学中存在基本功准备不足、教育机智缺乏、课堂教学设计能力和语言表达能力不够要求和课堂纪律管理困难;师范院校的课程设置和管理存在缺乏;指导教师的指导不统一有效,较随意等。并针对性分析了原因和提出了相应的对策。     

The Role of Mathematics Teachers' Content Knowledge in their Teaching: A Framework for Research applied to a Study of Student Teachers

The authors develop and explain a framework toguide research on the relationship betweenmathematics teachers' knowledge of content andtheir teaching. The framework istwo-dimensional. The dimensions are (a) theelements of teaching and (b) the processes ofteaching in which knowledge of content is ofconsequence. The interplay between the elementsof teaching and the processes of teaching isdiscussed theoretically, consideringconnections to existing literature about therole of teachers' subject matter knowledge.Three vignettes from the authors' work withpre-service secondary mathematics teachersinvestigate further the relationship betweencontent knowledge and effective mathematicsteaching. The vignettes also serve toillustrate the complexity of investigationsinto this relationship. Direction is offeredfor use of the framework in future research.     

数学教师专业发展的新视角——数学教学内容知识(MPCK)

数学教学内容知识(MPCK)是关于某一特定的数学内容该如何进行表述、呈现和解释,以使学生更容易接受和理解的知识.它作为数学教师知识结构的核心,是区别数学教师与数学家、数学教师与其它学科教师的重要特征,是数学教师专业成长的重要体现.依据我国数学教师的特点,通过数学知识向数学教学内容知识的转化不失为一条发展教师MPCK的直接而有效的途径.     

Spanish preservice primary school teachers’ pedagogical knowledge of numbers: results from TEDS-M / Conocimiento didáctico de los estudiantes españoles de magisterio sobre números: resultados en TEDS-M

Abstract

This paper describes and characterises Spanish preservice primary school teachers’ pedagogical knowledge on school mathematics, particularly in the number subdomain. The study conducts a conceptual analysis of the TEDS-M survey items on this type of knowledge and interprets the responses. We found that preservice teachers were able to recognise variables that affect the difficulty of arithmetic and proportionality problems, but showed difficulties in diagnosing errors committed by students and in graphically representing mathematical concepts and procedures and applying them to the teaching process. These results will be useful for the design of syllabi in the new Primary School Teaching degree.     

学科教学知识：一个教师专业发展的新视角

学科教学知识概念的提出,对教师教育的理论与实践产生了重大影响。文章在探讨了学科教学知识的内涵、特征、建构等问题,并分析了学科教学知识对教师专业发展的意义的基础上,进而提出以学科教学知识概念指导我国教师教育改革的若干对策。