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1.
解题是中学数学教师的基本功之一,但目前职前中学数学教师在解题方面的能力比较弱。因此,需要有效地、全面地提高职前中学数学教师解题的能力。具体来说,需要系统地、有计划地培养职前中学数学教师解题能力。在第一学年研读中学数学课标和教材,强化中学数学的概念性知识;在第二学年熟练掌握中学数学解题中的解题思想和方法;在第三、四学年对解题中的有意识控制的知识进行训练。同时,将解题的书面表达、口头表达的训练融入每一个阶段当中。 相似文献
2.
Olivia Fitzmaurice Niamh O’Meara Patrick Johnson Sean Lacey 《Asia-Pacific Journal of Teacher Education》2019,47(4):361-382
This paper reports on an exploratory study designed to determine and enhance the conceptual understanding of a group of pre-service mathematics teachers at one Irish university utilizing an established framework for understanding mathematics. 23 students on a one year Professional Diploma in Mathematics Education participated in the study, which involved the distribution of a pre- and post-test and engagement in a ten week intervention designed to enhance their subject matter knowledge (SMK) and pedagogical content knowledge (PCK). The findings highlight that although there was an improvement in overall conceptual understanding across the entire cohort at the end of the intervention, within certain mathematical topics there was a statistically insignificant improvement and many deep-rooted issues remain. In this paper we focus on the pre-service teachers’ understanding of elementary algebra, in particular, how to solve a linear equation. 相似文献
3.
The aim of this mixed methods study was to investigate the difficulties prospective elementary mathematics teachers have in solving the Programme for International Student Assessment (PISA) 2012 released items. A mathematics test consisting of 26 PISA items was administered, followed by interviews. Multiple data were utilized to provide rich insights into the types of mathematical knowledge that a particular item requires and prospective teachers’ difficulties in using these knowledge types. A sample of 52 prospective teachers worked the mathematics test, and 12 of them were interviewed afterwards. The data-sets were complementary: the quantitative data showed that PISA items could be categorized under contextual, conceptual, and procedural knowledge and indicated the most frequent difficulties in the combined contextual, conceptual, and procedural knowledge items. The qualitative data revealed that few prospective teachers could give mathematical explanations for conceptual knowledge items, and that their contextual knowledge was fragmented. Educational implications were discussed. 相似文献
4.
A Study Of Mathematics Anxiety in Pre-Service Teachers 总被引：1，自引：0，他引：1
Gina Gresham 《Early Childhood Education Journal》2007,35(2):181-188
The study investigated the changes in levels of mathematics anxiety among pre-service teachers in six different sections of
a mathematics method courses for early childhood/elementary education pre-service teachers. The changes were a function of
using Bruner’s framework of developing conceptual knowledge before procedural knowledge and using manipulatives and other
activities to make mathematics concepts more concrete and meaningful. Data were collected using quantitative and qualitative
measures. Two hundred forty-six pre-service teachers completed a 98-item Likert-type survey. Informal discussions, informal
interviews, and questionnaire-guided narrative interviews were conducted with pre-service teachers. Data revealed a statistically
significant reduction in mathematics anxiety in pre-service teachers (p < .001) who completed a mathematics methods course that emphasized Bruner’s model of concept development. Results of the
study have implications for teacher education programs concerning how future teachers are trained, the measurement of mathematics
anxiety levels among pre-service teachers, and the determination of specific contexts in which mathematics anxiety can be
interpreted and reduced. 相似文献
5.
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. 相似文献
6.
Tonya Gau Bartell Corey Webel Brian Bowen Nancy Dyson 《Journal of Mathematics Teacher Education》2013,16(1):57-79
This study examined prospective teachers’ (PSTs) ability to recognize evidence of children’s conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. It also investigates the role PSTs’ content knowledge plays in their ability to recognize children’s mathematical understanding. Results of content knowledge assessments administered at the beginning of the study revealed that content knowledge did seem to support PSTs’ analyses of children’s understanding when the child’s response demonstrated understanding or demonstrated a misconception. Content knowledge did not seem to support PSTs’ analyses of children’s procedural responses, as many PSTs with good content knowledge initially characterized procedural solutions as evidence of conceptual understanding. Similarly, content knowledge did not seem to support PSTs’ analyses of children’s responses with features commonly associated with understanding but not evidence of understanding. After the instructional intervention consisting of three multifaceted lessons in which PSTs examined many examples of student thinking, they showed improved ability to analyze responses with conceptual features and no evidence of conceptual understanding and responses demonstrating procedural knowledge. Results suggest that content knowledge is not sufficient for supporting PSTs’ analysis of children’s thinking, and that building activities such as the intervention into content courses may help develop this ability. Implications for teacher education programs and future research are considered. 相似文献
7.
In this study, we report on what types of mathematical knowledge for teaching teachers (MKTT) mathematics teacher educators (MTEs) use and develop when they work together and reflect on their teaching in a Community of Practice while helping prospective primary teachers (PTs) generate their own mathematical knowledge for teaching in learning mathematics via problem solving. Two novice MTEs worked with an experienced MTE and reflected on the process of learning to teach via problem solving and supporting PTs in developing deep understandings of foundational mathematical ideas. Taking a position of inquiry as stance, we examined our experiences teaching mathematics content courses for PTs via problem solving. We found that all of the MTEs used and developed some MKTT through (a) understanding and deciding on the mathematical goals of both the individual lessons and the two-course sequence as a whole, (b) choosing and facilitating tasks, and (c) using questions to scaffold PTs learning and engage them in mathematical processes such as making conjectures, justifying their reasoning, and proving or disproving conjectures. 相似文献
8.
Lisa Berger 《PRIMUS》2018,28(8):772-784
In this article we address the Common Core State Standard for Mathematical Practice: Attend to Precision. We describe work in mathematics content courses for pre-service and inservice teachers focused on developing teachers’ understanding of mathematical definitions. We discuss teachers’ work in developing definitions for students at various levels of mathematics, in generalizing a definition in order to extend the domain to which it may be applied, and in correcting teachers’ misconceptions. The work discussed in this article is consistent with the recommendations of the Conference Board of the Mathematical Sciences for the mathematics education of teachers. In explicit response to contemporary mathematics education research, the author presents constructive assessment prompts which lend themselves to formal study by mathematics education researchers. 相似文献
9.
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. 相似文献
10.
Research on identity has been a growing domain in the contexts of teacher education and mathematics education; however, identity work has been explored to a much lesser extent, with a future orientation overlooked. In addition, earlier studies have not provided sufficient knowledge on how different elementary teacher education programs might facilitate pre-service teachers’ identity work. In this study, we compare future-oriented mathematical identity work through a narrative framework considering six pre-service teachers undergoing two different teacher education programs. All pre-service teachers reported having had negative experiences with mathematics during their school years. Based on the results we conclude that despite the striking similarities in pre-service teachers’ mathematical backgrounds, the ways in which these cases are conducting their identity work differ substantially. It seems that the main reasons for these differences are different emphases and pedagogical practices in mathematics education courses. Additionally, we further elaborate on our earlier conceptualisation of identity work. 相似文献
11.
David Ben-Chaim Yaffa Keret Bat-Sheva Ilany 《Journal of Mathematics Teacher Education》2007,10(4-6):333-340
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. 相似文献
12.
The research interest underpinning this paper concerns the type of mathematical knowledge engineering students may acquire during their specialised education in terms of the conceptual and procedural dimensions of doing and using mathematics. This study draws on interviews with 25 qualified engineers from South Africa and Sweden regarding their views on the role of mathematics in engineering education, with special focus on the conceptual and procedural aspects of mathematical knowledge. A thematic analysis of the interview data led to the identification of two main themes. According to the conceptual view a predominantly conceptual approach is needed and valued more than procedural skills, while the balanced view emphasises a balance of conceptual understanding and procedural fluency as well as links between them. It is suggested that the mathematical education of engineers would need to be more conceptually oriented to prepare for the demands at the workplace. 相似文献
13.
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. 相似文献
14.
借鉴Kahan等的教学过程和基本要素研究框架,以情意原理、序进原理和活动原理作为解析课堂教学的框架,调查师范生融合内容的教学知识的实然水平。师范生的教学水平大致分布在三个等级上,师范生对学与教的理解有明显的缺失。如果师范生对知识的发生发展过程认识较为深刻,那么知识教学的序列安排就与知识发生的历史过程拟合得较好;如果师范生对做数学的一般机制有一定的体会,那么学生思维过程的设计就与历史上人们做数学的活动经验较为相似。数学发生发展的知识是影响师范生课堂教学水平的重要因素之一。 相似文献
15.
César Sáenz 《Educational Studies in Mathematics》2009,71(2):123-143
This paper analyses the difficulties which Spanish student teachers have in solving the PISA 2003 released items. It studies
the role played by the type and organisation of mathematical knowledge in the activation of competencies identified by PISA
with particular attention to the function of contextual knowledge. The results of the research lead us to conclude that the
assessment of the participant’s mathematical competencies must include an assessment of the extent to which they have school
mathematical knowledge (contextual, conceptual and procedural) that can be productively applied to problem situations. In
this way, the school knowledge variable becomes a variable associated with the PISA competence variable.
This paper is based on a research project funded by a grant awarded in 2003 by the General Directorate for Research of the
Spanish Ministry of Education and Science (BSO-2003-7133). 相似文献
16.
In this article the ‘lesson preparation method’ was used to investigate pre-service teachers’ pedagogical content knowledge, in particular their knowledge of pupils’ conceptual difficulties on temperature and heat. A relation is found between the conceptual difficulties pre-service teachers expect their pupils to have and the conceptual difficulties they themselves have or have had. The discussion considers what pedagogical content knowledge teacher educators should include in the initial or inservice teacher education curriculum. 相似文献
17.
小学数学教师职前培养应重视的几个方面 总被引：1，自引：0，他引：1
数学教师的职前培养是数学教师专业化发展的重要环节,小学数学教师职前培养应重视以下几个方面:更新职前教师的数学教育观念;改进小学教育专业数学类相关课程的教学方法;深入研究高观点下的小学数学内容知识。 相似文献
18.
教师教育中数学知识的获得是影响职前小学教师数学知识的主要因素之一,以我国上海师范大学和美国纽约城市大学小学教育专业本科培养的数学课程计划为个案,从数学内容类课程和数学方法类课程两方面研究发现,两国职前小学教师教育中各数学课程在学分要求、教学目标、教学内容和教学方法等方面存在差异。美国职前小学教师本科培养的经验,对我国职前小学教育专业本科培养的数学课程设置与实施应该如何加强联系小学数学课程与教学实际具有一定借鉴。 相似文献
19.
William W. Cobern David Schuster Betty Adams Brandy Ann Skjold Ebru Zeynep Muğaloğlu Amy Bentz 《International Journal of Science Education》2013,35(13):2265-2288
A critical aspect of teacher education is gaining pedagogical content knowledge of how to teach science for conceptual understanding. Given the time limitations of college methods courses, it is difficult to touch on more than a fraction of the science topics potentially taught across grades K-8, particularly in the context of relevant pedagogies. This research and development work centers on constructing a formative assessment resource to help expose pre-service teachers to a greater number of science topics within teaching episodes using various modes of instruction. To this end, 100 problem-based, science pedagogy assessment items were developed via expert group discussions and pilot testing. Each item contains a classroom vignette followed by response choices carefully crafted to include four basic pedagogies (didactic direct, active direct, guided inquiry, and open inquiry). The brief but numerous items allow a substantial increase in the number of science topics that pre-service students may consider. The intention is that students and teachers will be able to share and discuss particular responses to individual items, or else record their responses to collections of items and thereby create a snapshot profile of their teaching orientations. Subsets of items were piloted with students in pre-service science methods courses, and the quantitative results of student responses were spread sufficiently to suggest that the items can be effective for their intended purpose. 相似文献
20.
Ailish Hannigan Olivia Gill Aisling M. Leavy 《Journal of Mathematics Teacher Education》2013,16(6):427-449
The development of statistical literacy is fast becoming the focus of a large part of mathematics instruction at primary, secondary and tertiary levels. This broadening of the mathematics curriculum to encompass a focus on statistics makes considerable demands on teachers. Most mathematics teachers acknowledge the practical importance of statistics and are willing to give more relevance to the teaching of statistics; however, many mathematics teachers do not consider themselves well prepared to teach statistics. The aims of this study were to investigate the conceptual understanding of statistics of prospective secondary mathematics teachers; the nature of their attitudes towards statistics and if there was a relationship between attitude towards statistics and conceptual understanding of statistics. Conceptual understanding was measured using a standard assessment instrument (comprehensive assessment of outcomes in a first statistics course) which allows comparison across other disciplines. Despite being very mathematically able and confident, the prospective mathematics teachers in this study do no better in the assessment than students from other (mostly non-quantitative) disciplines. This, perhaps, gives further evidence that statistical thinking is different from mathematical thinking and that a strong background in mathematics does not necessarily translate to statistical thinking. Conceptual knowledge was poor in some fundamental areas of statistics such as being able to properly describe the distribution of a quantitative variable and data production. The attitudes of these teachers towards statistics were measured using a widely used instrument (survey of attitudes towards statistics). The results indicate generally positive attitudes but an acknowledgement that statistics is not a subject quickly learned by everyone and requires discipline to learn. No strong correlation was found between attitudes and conceptual knowledge. It is recommended that in order to improve teacher knowledge, teacher education programmes must include tailored modules in statistics and highlight the differences between mathematical and statistical thinking. 相似文献