高中数学教师专业知识研究--基于吉林省数学教师的调查

教师专业发展必然需要教师专业知识的有力支撑。对高中数学教师专业知识进行的问卷调查和访谈发现：目前高中数学教师基本上较好地掌握了常用的教师专业知识,但也存在一些问题：对数学学科知识的关注范围过于狭窄;运用数学教学知识进行教学时偏向于被动;对数学课程标准的理解存在偏差。另外,研究还发现：数学教学知识的增长并非是持续的;不同层级的教师之间、不同类别学校中的教师之间,其差异主要体现在数学学科知识与数学教学知识。进而对数学教师教育提出相应建议：数学教师应适当拓展数学学科知识的关注范围;应依据调查数据加强数学教师教育培养计划的针对性;关于教师一般教育学知识的评价方式亟需改进等。     

Content knowledge and pedagogical content knowledge in Taiwanese and German mathematics teachers

In comparing content knowledge (CK) and pedagogical content knowledge (PCK) of Taiwanese and German inservice mathematics teachers, the present study examines whether the two-dimensional structure of teachers' subject matter knowledge is cross-culturally invariant and whether differences in teacher education and in teacher selection are reflected in teachers' subject matter knowledge. The results confirm that CK and PCK represent two distinct, but correlated dimensions, even in teachers from completely different backgrounds. Taiwanese inservice teachers showed considerably higher CK and also higher PCK scores than German teachers. Teacher education and teacher selection should be considered important levers for reform in mathematics education.     

An Ode to Imre Lakatos: Quasi-Thought Experiments to Bridge the Ideal and Actual Mathematics Classrooms

This paper explores the wide range of mathematics content and processes that arise in the secondary classroom via the use of unusual counting problems. A universal pedagogical goal of mathematics teachers is to convey a sense of unity among seemingly diverse topics within mathematics. Such a goal can be accomplished if we could conduct classroom discourse that conveys the Lakatosian (thought-experimental) view of mathematics as that of continual conjecture-proof-refutation which involves rich mathematizing experiences. I present a pathway towards this pedagogical goal by presenting student insights into an unusual counting problem and by using these outcomes to construct ideal mathematical possibilities (content and process) for discourse. In particular, I re-construct the quasi-empirical approaches of six!4-year old students’ attempts to solve this unusual counting problem and present the possibilities for mathematizing during classroom discourse in the imaginative spirit of Imre Lakatos. The pedagogical implications for the teaching and learning of mathematics in the secondary classroom and in mathematics teacher education are discussed.     

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.     

Rate your course! Student teachers’ perceptions of a primary pre-service mathematics education programme

Although research suggests that many pre-service mathematics education programmes are weak interventions having a negligible effect on student teachers’ knowledge, beliefs and attitudes, there is consensus that programmes that model and engage student teachers in reform teaching and learning approaches have the potential to effect positive change in attitudes and knowledge of mathematics. This paper focuses on the perceptions of 345 student teachers regarding their mathematics education programme. The authors consider that in order to further our understanding of the characteristics of an effective pre-service mathematics education programme, the opinions of participating student teachers are fundamental. Participants reported improved mathematical subject matter knowledge and pedagogical content knowledge in addition to greater confidence and decreased anxiety towards mathematics. Programme features such as small group tutorials and interactive engagement were identified as impacting this positive change.     

Mathematics‐teachers’ Knowledge Bases: implications for teacher education

Understanding the knowledge bases of mathematics teachers is an important task in working towards the construction of adequate models for: (i) teacher education and development, and (ii) teacher operations in the classroom. To date, little systematic attention has been focused on this task. The primary aim of this study is to obtain a view from the field of mathematics teacher knowledge with respect to content knowledge in mathematics, content‐specific pedagogical knowledge in mathematics and curriculum knowledge relevant to teaching tasks. This study has used data obtained from a survey of primary teachers and secondary mathematics teachers. Analysis of the results has indicated that less than half of the teachers in the study believed that they were sufficiently prepared in mathematics content, and that almost two‐thirds of the teachers in the sample believed that their level of knowledge in contemporary teaching methodologies in mathematics is not sufficient for their role as school teachers. Key differences emerge between the primary and secondary sectors and also within the secondary sector. Implications for preservice and in‐service mathematics teacher education are drawn.     

A longitudinal study of effects of a developmental teacher preparation program on elementary prospective teachers’ mathematics beliefs

The universal emphasis in mathematics education on teaching and learning for understanding can require substantial paradigmatic shifts for many elementary school teachers. Consequently, a pressing goal of teacher preparation programs should be the facilitation of these changes during program experiences. This longitudinal, mixed methods study presents a thorough investigation of the effects of a distinctive teacher preparation program on important constructs related to prospective teacher preparedness to teach mathematics for understanding, including mathematics pedagogical and teaching efficacy beliefs, mathematics anxiety, and specialized content knowledge for teaching mathematics. The results indicate that the programmatic features experienced by the prospective teachers in this study, including a developmental two-course mathematics methods sequence and coordinated developmental field placements, provided a context supporting teacher change. These shifts are interpreted through the nature and timing of the experiences in the program and a model of teacher change processes. The findings provide insights for mathematics educators as to the outcomes of these programmatic features.     

关于教育系在综合大学发展的若干问题思考

对综合大学教育系面临并急需要解决的地位、特色和功能三个问题进行了初步探讨，提出要真正提高教育系在综合大学中的地位，必须做到改革要到位、政策有保障、学术有位置；教育系要在综合大学得到生存和发展，就必须选择特色，设计特色，创造特色，保持特色，强化特色。综合大学教育系的特色应集中反映在培养模式、办学模式、教育研究等方面；综合大学教育系应充分利用综合大学多学科的优势，充分发挥辅助他系培养师资、培养职业技术教育和成人教育以及各种继续教育机械师资和教育管理干部、培养和培训各级各类学校所需的教育学科师资、影响学校实践、提供决策支持、影响社会、发展教育学术等功能。     

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.     

Comparing Pre-Service Teachers’ PCK Through 9E Instructional Practice: A Case of Mathematics and Technology Pre-Service Teachers

Instructional practice plays a significant role in understanding teachers’ pedagogical content knowledge (PCK). The aim of the study reported on was to compare mathematics and technology pre-service teachers’ knowledge of PCK. The study used a case study approach of five mathematics and five technology pre-service teachers with a total of ten. Data was collected in seven public schools around Gauteng province in South Africa. The observation technique was employed in order to understand students’ classroom practice, using a video camera to capture the setting. One lesson of 45 minutes presented by each pre-service teacher, rendering a total of ten lessons, was observed. The study adapted the theoretical framework of PCK (Shulman 1987). The study scrutinised the data based on the qualitative content analysis method and found that most pre-service teachers in both mathematics and technology possess a limited knowledge of PCK. In both subjects, most of the pre-service teachers’ classroom practice did not exhibit comprehensive knowledge of the subject matter or knowledge of the learners. However, the difference is that only mathematics pre-service teachers have some knowledge of assessment. The data also indicate that “9E” instructional practice can be a valuable tool to enhance field-specific PCK within the field of mathematics and technology education subjects. Therefore, the study proposes further investigation of the “9E” instructional model that could be used as field-specific PCK within the fields of mathematics, science and technology.     

法国中学数学教材的特色及启示

法国中学数学教材具有鲜明的特色.如:以现代数学内容及方法为统领;注意与多学科联系,突出数学的文化价值和应用意识;以实验、探究等活动方式展示“活生生的数学”,等.这对我国中学数学教材编写具有一定的启示作用:中学几何内容应融入现代数学内容及其方法;应注意数学与其他学科的联系;妥善处理信息技术与数学教育的关系.     

Novice mathematics teachers create themselves

This study presents a qualitative research based on three narratives written by novice mathematics teachers. We examine their unique professional world during their first year of work. The methodology of narrative framework, on which this article is based, helps to gain better understanding of the need for novice mathematics teachers to have pedagogical knowledge. Findings reveal three themes of pedagogical knowledge: the attitude of novice teachers toward students with difficulties in mathematics; parents’ expectations of and involvement with novice mathematics teachers; teacher–student relations. The implications of the findings show that novice mathematics teachers are required to have not only content knowledge of mathematics but also, and above all, pedagogical knowledge. The implications of this study enable reassessment of emphases required in training mathematics teachers, as well as the assistance and support they need, especially as they launch their careers.     

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.     

Fachdidaktisches Wissen von Lehrkräften und multiple Ziele im naturwissenschaftlichen Sachunterricht

Recent investigations in the field of mathematics have demonstrated that teachers’ pedagogical content knowledge, as a central component of teachers’ professional knowledge, plays a significant role in high-quality instruction and students’ learning gains. The study presented here explores the significance of teachers’ pedagogical content knowledge for gains in pupils’ understanding of scientific concepts and for motivational and self-related outcome criteria in primary science education in Germany. It reports on findings from a study with a pre-post-design comprising 60 primary school teachers and their 1326 pupils. Teachers’ pedagogical content knowledge and pupils’ learning gains as well as motivational and self-related outcome criteria were directly assessed with paper-and-pencil tests. Two-step models controlling for several relevant variables at the individual and the class level were specified. Results revealed a substantial positive effect of the measured pedagogical content knowledge on pupils’ achievement gains as well as on pupils’ situational interest and perceived competence.     

The Lesson Preparation Method: a way of investigating pre-service teachers’ pedagogical content knowledge

Teacher education should build on the knowledge base that pre-service teachers already have on account of their lifelong learning in and outside of school. An international team of mathematics and science teacher educators developed a method of investigating the pedagogical content knowledge parts of this knowledge base. They asked pre-service teachers to prepare a lesson about a topic, e.g. area, as if they had to teach that lesson the next day. In this article the main aspects of the research environment are described and their effects on the research outcomes are evaluated.     

Forms of Knowing Mathematics: What Preservice Teachers Should Learn

What important ideas about forms of knowing mathematics should be included in mathematics methods courses for preservice teachers? Ideas are proposed that are related to categories in Shulman's (1986) framework of teacher knowledge. There is a brief discussion of the implications each idea holds for teaching mathematics, and some suggestions are given about experiences that may help preservice teachers appreciate these notions. One portion of Shulman's pedagogical content knowledge construct is knowing what makes a subject difficult and what preconceptions students are apt to bring. Three of the ideas offered for inclusion in a methods course are related to this aspect of pedagogical content knowledge: (1) Understanding students' understanding is important, (2) Students knowing in one way do not necessarily know in the other(s), and (3) intuitive understanding is both an asset and a liability. The last two ideas, are related to the other portion of pedagogical content knowledge, knowing how to make the subject comprehensible to learners. These ideas are (4) certain characteristics of instruction appear to promote retention, and (5) providing alternative representations and recognizing and analyzing alternative methods are important. Readers are asked to consider if the suggestions offered are appropriate and how they might best be taught.     

School–University Action Research: Impacts on Teaching Practices and Pupil Learning

The aim of this article is to describe a design and implementation of a school–university action research project about teaching and learning biology and mathematics in primary school. Nine teachers in grades 1 to 6, in collaboration with two researchers, were using content representation (CoRe) in learning study (LS)-inspired cycle as pedagogical tools when planning, implementing, and reflecting on lessons and pupil learning. By using pre- and post-tests, the teachers acquired knowledge about pupil subject-specific knowledge and learning. Some examples are given on how the tools in the project influenced the teaching practices and pupil learning. This research design brought together university and school practitioners to work collaboratively in a professional learning community, which developed teaching and learning in biology and mathematics.     

Resolving the chicken-or-egg causality dilemma: The longitudinal interplay of teacher knowledge and teacher beliefs

To examine the longitudinal relation between knowledge and beliefs and to determine cause and effect, 183 mathematics teachers were assessed three times during their first years of teacher education on their mathematics pedagogical content knowledge (MPCK) and their beliefs about teaching and learning. The data revealed that prior MPCK predicted later achievement. Prior beliefs also determined later ones. In addition, MPCK affected later beliefs: Higher MPCK at the first measurement resulted in more constructivist beliefs at later time points. By contrast, beliefs did not predict later MPCK. If constructivist teacher beliefs are to be fostered, teacher education should strengthen MPCK.