Becoming a Teacher Educator: A Self-Study of the Use of Inquiry in a Mathematics Methods Course

This article details the self-study of a beginning teacher educator in her first experience in teaching a mathematics methods course. The transition from teacher to teacher educator is explored through the experience of a course focused on inquiry. Inquiry is embedded within the course from two perspectives: mathematical inquiry and teaching as inquiry. The framework of teaching as inquiry is an important part of both the self-study and the mathematics methods course. Implications of the transition from teacher to teacher educator as well as the role of inquiry in mathematics teacher education are discussed.     

Study of Self: The Self as Designer in Online Teacher Education

In this article we describe our engagement in self-study as part of an examination of design-based research for education. We focus on graduate-level online teacher education as an example of how self-study provided a means of examining deeply our teaching and our roles as teacher and designer in the learning environment. We posit that online learning environments are particularly well suited for self-study to enhance design perspectives because the interactions between teacher and students are informed by personal context and mediated by technological tools. The graduate students in our courses were teacher leaders in literacy or mathematics who were learning how to support professional development for other teachers. Throughout our self-study research we found ourselves drawing upon our previous design research experiences, which aided our ability to engage in self-study: We were part of the classroom system, focusing on our roles within the teaching and learning process as designers of the online learning environment. Three key design principles resulted from our self-study process: focusing on systems of learning and teaching, designing pedagogical tools and products, and using iterative processes. Engaging in self-study enhanced our understanding and implementation of synchronous online instruction, particularly regarding our use of technological tools to enhance student learning and support learning communities.     

Self-Study of a Teacher's Journey toward Standards-Based Mathematics Teaching

The authors describe a journey of self-study during which one author shifted from traditional, teacher-driven approaches to a more problem-based inquiry approach to teaching mathematics. He videotaped a series of lessons taught to sixth-grade students over a semester and analyzed his teaching during discussions with his mentor at the university. The shared analysis helped him learn to involve his students more directly in their own learning. A major lesson learned was that understanding the potential value of a problem-solving approach to teaching mathematics does not guarantee corresponding changes in the classroom. Two vital elements of lesson development emerged as focal points for self-study. After first learning how to prepare worthwhile mathematical tasks, the teacher also learned the importance of implementing effective questioning strategies to help students think more deeply about the mathematics they were learning.     

Foreseeing the Unforeseen through Collaborative Self-Study by a Teacher Educator and Two Teacher Candidates

This article reports the collaborative self-study of a teacher educator and two teacher candidates, focusing on the unforeseen negativity of experiences encountered by the three researchers in both a university methods course and student teaching settings. The implication of this study helped the researchers foresee new hypothetical learning trajectories for their respective students. Throughout the study, the university teacher educator and two teacher candidates tried to maintain a collegial relationship while analyzing their teaching and learning experiences. The researchers analyzed the effectiveness of their mathematics teaching strategies over an extended period of time. The changing roles of the researchers throughout the study encouraged them to examine not only their own teaching processes but also those of the other researchers. As critical colleagues they positioned themselves in different contexts. This study generates several insights for the improvement of the researchers' future teaching practices. The results suggest that collaborative self-study by a teacher educator and teacher candidates can generate effective learning experiences for all participants.     

“慕课+翻转课堂”教学模式下的《中学数学教学设计》课程建设及实践

为使高师院校数学师范专业的教学适应基础教育数学课程改革的需要,提升师范生教学技能,《中学数学教学设计》实现了线上教育和线下教育相结合的“慕课+翻转课堂”教学模式。课程关注有效学习,落实先学后教,在完善网上课程资源、构建立体化教材的基础上,对教学方法、教学场所、评价模式等方面进行改革。从学生在线互动、课堂反馈、微格教学、教师资格证考试及教学技能竞赛中可知课程实施效果明显。     

Understanding the Theoretical Framework of Technological Pedagogical Content Knowledge: A collaborative self-study to understand teaching practice and aspects of knowledge

This paper describes a self-study research project that focused on our experiences when planning, teaching, and evaluating a course in initial teacher education. The theoretical framework of technological pedagogical content knowledge (TPACK) was used as a conceptual structure for the self-study. Our understanding of the framework in relation to our teaching practice was in focus. The principal educational goal of the course was to develop the pedagogical use of web 2.0 resources to support learning in the preschool/school context. As a result, the focus, content, form of distribution, teaching, and assessment of the course went beyond what is common in initial teacher training in Sweden. The potential of the different digital tools was explored by situated use in the design and teaching of the course. Analysis highlights the challenges and opportunities that teacher educators and student teachers may encounter while working with, and learning about, information and communication technologies to support learning. Some of the findings discussed are related to the identified challenges and opportunities for both teachers and students to integrate content knowledge, pedagogical knowledge, and technological knowledge into a TPACK. Taken-for-granted organizational and institutional assumptions about teaching, learning, and assessment in teacher education were identified in the study.     

大学英语听力教学有效性的再思考

对目前制约大学英语听力教学有效性的因素做了分析和讨论,并基于有效教学理论的视角从教学理念、教学内容选择、学习任务设置、教学环节的设计以及多元化评价机制的建立等五个方面探讨了如何组织与实施有效的大学英语听力教学.主张应将现阶段单纯依靠教材、教学软件、教师全面讲、学生被动听的教学模式转变为互联网、多媒体设备、课堂教学、课外自主学习、合作学习五位一体、综合运用的个性化、主动式学习模式.     

Using TPCK as a scaffold to self-assess the novice online teaching experience

How does one evaluate one’s own online teaching? Do novice online instructors depend on end-of-semester course evaluations or a Quality Matters rubric? Perhaps their professional development is driven by a personal belief that seeking multiple perspectives from different lenses is core to reflective practice. This work explores one way to interrogate one’s own online teaching practices through a systematic reflection on technological pedagogical content knowledge (TPCK). It involved identifying and reflecting upon instances in which TPCK was evident in the design and facilitation of the online learning environment in an undergraduate online course. Ways to improve online teaching based on increased meta-cognitive awareness of TPCK are considered. Implications of this self-study for distance learning professional development are discussed.     

Listening to Students,Listening to Myself: Addressing pre-service teachers' fears of mathematics and teaching mathematics

This paper describes a self-study in which I, as a teacher educator, seek to understand how to respond effectively to my pre-service students' fears about learning and teaching primary mathematics. I studied my students' response to a new mathematics methods course that is tied to practicum. Results include the importance of listening closely to students' feelings about learning and teaching math, responding with opportunities to re-learn primary math concepts in a collaborative and hands-on environment, and providing opportunities for pre-service teachers to experience success with math teaching in primary school settings. What I did not realize at the outset was that the students and I would be on a parallel journey. While I endeavored to listen to their voices, I struggled with my limited voice as a sessional instructor. While they struggled to feel like “real” math teachers, I struggled to feel like a “real” math professor. Fear of teaching math to young children was mirrored by my fear of pioneering a new course. Examination of a key incident in the first year of the course and of the role of a critical friend helped me to see and understand these parallel paths.     

Integrating Learning Technologies with Experiential Learning in a Postgraduate Teacher Education Course

This paper discusses how a postgraduate certificate course in third-level learning and teaching for academic staff in the Republic of Ireland has adopted a particular approach in teacher education. An important aspect of the successful integration and use of learning technology is the way in which it effectively reflects and articulates a given learning model; this course has its theoretical basis in the Kolb Experiential Learning Cycle. The work illustrates that no one technology can support all types of tertiary-level learning and teaching; an effective approach is to combine a range of technologies. The self-study focuses on analyzing key experiences regarding the integration of a variety of learning technologies in an effort to determine how the teacher educator can integrate technology into the curriculum effectively. What I learned from this self-study will assist the course participants with some of the integration issues that they, in turn, will be dealing with as they move towards incorporating more learning technology into their own subject disciplines. Course tutors deliberately set out to model what we advocate to our own participants.     

普通高校高等数学基础课程面向学生学习的教学设计

本文结合高等数学教学实践,阐述了教师根据不同教学内容,对高等数学基础课程进行教学设计.实践证明,学生学习的教学设计是激发学生学习兴趣、提高学生自主学习能力的较好方法.     

Learning by Exploration in Mathematics Courses: a programme for student teachers

In order to adapt teacher education to new demands in mathematics classrooms, it is necessary to change the courses in mathematics at the university. Teachers’ beliefs about mathematics, learning and teaching has great impact on their teaching. At the University of Göteborg, a co‐operative project has been conducted in order to design a programme based on problem solving in courses taken by prospective Comprehensive School teachers (grade 4‐‐9). The main purpose of the project has been to make student teachers more reflective about mathematics as such, about learning and teaching. Another purpose of the project has been to use a teaching method in a university course‐‐a method which could be applied in a school classroom. The student teachers have worked co‐operatively in small groups of 3‐4 students and the educators role has been that of a facilitator. A preliminary evaluation indicates that student teachers have developed an insight into the complexity of learning and teaching, even though there are variations in this respect. However they still have difficulties in applying the method to teaching mathematics at school.     

Perceptions of Reform-Based Teaching and Learning in a College Mathematics Class

This study investigated, from the students',professor's, and researchers' perspectives, the effects of a reform-based introductory undergraduate mathematics course, and the efforts of a mathematics professor to teach such a course. The class had been designed for teacher candidates of middle school mathematics and science (Grades 4 to 8) but was open to all qualified students. We addressed the following research question: What perceptions about learning and teaching mathematics emerged through the participants' experiences in a reform-based mathematics course? Results of the analysis of the data suggested that the teacher candidates and the professor took an important first step toward enculturation into a reform-based vision of mathematics learning and teaching. Implications for mathematics faculty and teacher education faculty interested in promoting reform-based mathematics are presented.     

调动学习数学的“发动机”,促进学生自我学习

数学的逻辑性很强,如果不认真去学习,就会无效学习。所以必须调动学生身上的＂发动机＂,促进学生自我学习。为此,可以采取以下策略教学：创设数学生活情境,使枯燥的数学有趣化;借助现代教育技术,让数学动起来;分层次教学,挖掘学生自我学习的潜力;采取激励措施,长效调动学生的积极性;激发学生主体意识,调动其学习积极性;授之以渔,教给学生自我学习的方法。     

在线学习课程设计与实施的关键环节研究(下)

本研究对北京师范大学研究生在线课程教学的一些典型案例做提炼分析,总结归纳了在线课程教学设计的8个关键环节的设计理念和应对策略.研究观点聚焦于教学模式的5个核心要素、教学内容的4个重组方法、教学问题的4种设计取向、小组学习活动的认知冲突建构/解构的2个设计理念、资源设计开发的3项原则、教学交互质量提升的4种实施策略、学习...     

Communicating to Learn Multivariable Calculus: Students' Blackboard Presentations as a Means for Enhancing Mathematics Learning

This paper reports observations and reflections from a pedagogic intervention intended to enhance mathematics students' learning of course content in a course in multivariable calculus. The intervention design required students to structure, practice, and deliver an oral presentation that was a synthesis of the teacher's weekly lectures, for the benefit of themselves and their peers. The intervention appears to have incentivized students to engage with and learn mathematics contents in an effective way, and it also helped the mathematics teacher to reflect on, adapt, and develop his teaching strategies. To conclude, it would seem that both students and teachers in mathematics have much to gain from giving students opportunities to develop their own voice in learning contexts otherwise relying on books and lectures.     

高等数学"目标导向+阅读自学指导"教学模式的设计

针对高职高专《高等数学》教材及学生特点,采用“目标导向 阅读自学指导”教学模式可取得良好的教学效果。该模式以建构主义、主体性学习及人本主义为理论基础,具体设计时要抓好教学目标、教学方法、教学评价等环节的设计。     

关注学习起点 构建数学高效课堂

在创新数学教学手段的过程中,教师要关注学生学习起点,合理设计课程内容,积极营造轻松活跃的课堂学习氛围,为构建高效课堂奠定基础。文章从数学教学实践出发,指出在日常教学过程中寻找学生学习起点的方式,并提出基于学习起点思想的数学高效课堂构建的有效途径。     

A Self-Study of the Role of Technology in Promoting Reflection and Inquiry-Based Science Teaching

   This self-study examined the 1st-year science teacher educator's integration of instructional technology into a science methods course and modeled the reflective practice of her own teaching. Elementary science methods students participated in a series of inquiry-based activities that utilized various instructional technologies. Data sources included daily reflections, formative assessments, concern-based surveys, and class assignments. Findings from this self-study revealed that the teacher educator's own reflections and practical inquiry influenced and paralleled her students’ development of learning how to teach scientific inquiry using instructional technology. Results suggest that inviting preservice teachers into reflective practice and modeling for them the development of professional practical knowledge allow them to address the uncertainties in their own learning about using technology for inquiry-based science teaching.     

调动学习数学的“发动机”,促进学生自我学习

数学的逻辑性很强,如果不认真去学习,就会无效学习。所以必须调动学生身上的"发动机",促进学生自我学习。为此,可以采取以下策略教学:创设数学生活情境,使枯燥的数学有趣化;借助现代教育技术,让数学动起来;分层次教学,挖掘学生自我学习的潜力;采取激励措施,长效调动学生的积极性;激发学生主体意识,调动其学习积极性;授之以渔,教给学生自我学习的方法。