A call to come together: why it matters and why it works

This letter to the editor is in response to Barbara Hotelling's column, "Tools for Teaching - The Power of Numbers: Transforming Birth Through Collaborations," published in the Volume 19, Number 2 (Spring 2010) issue of The Journal of Perinatal Education. Hotelling's brief overview of the history of birth activism in the United States and of current collaborations among diverse groups and individuals provides inspiration to continue efforts that improve maternity care and promote natural, safe, and healthy childbirth practices.     

Teaching teachers to teach Boris: a framework for mathematics teacher educator pedagogical content knowledge

The notion of pedagogical content knowledge (PCK) was posited in the context of school teaching and the knowledge used by teachers teaching school students. It has been examined for a number of discipline areas, notably mathematics. There are, however, other teaching contexts, including those of teacher educators, whose students are pre-service teachers (PSTs). The content these teacher educators teach is not subject discipline knowledge (or not solely), but the PCK for teaching a subject discipline. What knowledge do teacher educators use as they teach PCK? This paper presents a framework for the PCK required of mathematics teacher educators as they work to develop PSTs’ PCK for teaching mathematics. The framework builds on existing research into PCK and categorises aspects of the work of teacher education. The framework’s usefulness is examined by studying the PCK used by the first author in building PSTs’ understanding of mathematics teacher PCK.     

我们应该怎样教数学 --从三个案例说开去

对儿童来说,数学究竟是什么?我们究竟应该怎样来组织儿童的数学学习?长期以来,我们总是将儿童的数学学习当作是认符号、记公式、背定义、练计算、做习题的一种过程,而并不关注儿童在生活中发现了什么?对什么感兴趣?从最根本的价值追求来看,小学数学教育的最基本任务应当是发展儿童的数学素养.好奇、好探究永远是儿童主动学习的内在动力,而数学就在儿童的生活之中.因此,对儿童来说,学数学就应该是一个"做数学"的过程.显见,儿童亲历数学的发现、探究与问题解决过程的体验是小学数学教学的基本目标之一.     

Mathematical knowledge for teaching teachers: knowledge used and developed by mathematics teacher educators in learning to teach via problem solving

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.     

Preparing teachers to teach science and mathematics with technology: Developing a technology pedagogical content knowledge

Preservice teachers’ pedagogical content knowledge (PCK) development was investigated with respect to integrating technology. Four components of PCK were adapted to describe technology-enhanced PCK (TPCK). The study examined the TPCK of student teachers in a multi-dimensional science and mathematics teacher preparation program that integrated teaching and learning with technology throughout the program. Five cases described the difficulties and successes of student teachers teaching with technology in molding their TPCK. Student teachers view of the integration of technology and the nature of the discipline was identified as an important aspect of the development of TPCK.     

Troubling teacher identity: preparing mathematics teachers to teach for diversity

This paper reports on an action research project designed to explore the complexities of pre‐service mathematics teacher resistance to social justice issues. Research on equity and mathematics education has indicated that such resistance seems particularly strong for mathematics teachers. Twelve pre‐service mathematics teachers participated in a course‐based research project to explore this issue. Participants completed a classroom discourse analysis and a self‐study narrative as part of their secondary mathematics methods course. The findings suggest that attention to issues of identity construction within school mathematics can be successfully embedded in methods courses in order to better prepare mathematics teachers to teach for diversity.     

Assessment in deaf education: Perspectives and experiences linking it all together

This article serves as an overview and introduction to the topics within the Special Issue: Deaf Education Assessment. This issue strives to establish the recognition of the importance of continued dialogue among stakeholders to support the diverse needs of Deaf and hard of hearing (DHH) students as it relates to assessments. The articles recognize that academic success in all areas and performance on assessments is related to many complex factors and variables. These are significant factors that influence the assessments of DHH and how those involved in the assessment process need to consider each of the factors. Deaf students are assessed for various reasons and numerous individuals look at the results to determine success, progress, additional disabilities, or interests.     

Learning mathematics and learning to teach: Learning cycles in mathematics teacher education

The reconceptualization of mathematics teacher education based on current mathematics education reform efforts necessitates the elaboration of theoretical frameworks to guide both the practice of and research on teacher education. The author presents a framework which has been useful in shaping two major mathematics teacher education research and development projects. This framework for mathematics teacher learning builds recursively on a framework for mathematics learning which derives from a social constructivist view of learning and incorporates aspects of French didactical theory using the organizing structure of the Karplus Learning Cycle. The framework can be used to think about the content and organization of a particular lesson or of an entire course or program for teachers. Further, it describes the interconnection between different domains of teacher knowledge.     

Effects on the technological pedagogical content knowledge of early childhood teacher candidates using digital storytelling to teach mathematics

This study aimed to present early childhood teacher candidates' experiences preparing digital stories and to reveal the resulting changes, if any, in self-reported technological pedagogical content knowledge (TPACK). This study was quasi-experimental and indicated that teacher candidates' evaluations of digital storytelling were affected by their preparation experiences. Moreover, results showed a shift from dual intersections of technology, pedagogy, and content knowledge to the triple intersection of TPACK.     

怎样上好高等数学辅导课

辅导课是高等数学课程教学的必要补充。本文在对在对高等数学辅导课教学必要性分析的基础上,结合自己的教学体会从辅导教师应当做好的几项工作,辅导课的主要形式,辅导课要注意的几个问题三个方面对辅导课的教学内容、教学模式和作用进行了阐述,为推动高等数学的教学效果和改革提供了一定的借鉴。     

Using social semiotics to prepare mathematics teachers to teach for social justice

In this article, we propose that guiding teachers to examine the regulative/discursive norms of school mathematics with tools derived from social semiotics can serve two related goals: (1) to deconstruct the “math is math period!” disposition in prospective teachers by promoting their critical understanding of the symbolic domination work they often unknowingly perform and (2) to reconstruct a more socio-political disposition by equipping them with tools for decoding the dominant discursive practices of school mathematics. After reviewing research on the social semiotics of mathematics education, we discuss two sample teacher education tasks designed with the above goals in mind.     

Digital technologies to teach and learn mathematics: Context and re-contextualization

The central assumption of this paper is that, especially in the field of digital technologies to teach and learn mathematics, the influence of the context in which research is carried out has not been given enough attention, so that research results are not really useful outside this context. We base our discussion on the work of a group of European teams carrying out research with a special methodology of “cross-studies” and carrying out “cross-analyses” of particular studies. A context for a research study is described as a dynamic construction by researchers, connecting relevant contextual characteristics in the settings (empirical and academic) where research activity takes place and helping to gain insight from the outcomes of the study. Analyzing the design of two “Didactical Digital Artefacts,” and the associated cross-studies involving teams of three countries, we identify more or less conscious influences of characteristics in the researchers' contexts upon research outcomes. Cross-studies and cross-analysis help to go further by making researchers more aware of their context and of its characteristics. It also helps researchers to “re-contextualize,” that is to say to identify new contextual characteristics in the settings they are acting in, to gain insight from research outcomes that emerged in other contexts.     

Learning to teach mathematics specialists in a synchronous online course: a self-study

This article uses a self-study research methodology to explore teaching an online course for mathematics specialists. The course included weekly videoconferencing sessions and focused on supporting their development as mathematics coaches working with K-8 teachers to enhance mathematics teaching and learning. The central question for the self-study was about the design of the course and the characteristics of the learning environment that resulted from the design. The study included journal reflections and survey data. Three themes emerged in the analysis of the instructional decision making for the course: student autonomy and engagement, authenticity and practicality, and fostering community.     

Learning to teach science for all in the elementary grades: What do preservice teachers bring?

Implicit in the goal of recent reforms is the question: What does it mean to prepare teachers to teach “science for all”? Through a teacher research study, I have encountered characteristics that may assist prospective elementary teachers in developing effective, inclusive science instruction. I describe these strengths, link them to requirements for teaching, and suggest how science teacher educators might draw on the strengths of their own students to support teaching practices aimed at universal scientific literacy. My conceptual framework is constructed from scholarship concerning best practice in elementary science education, as well as that which describes the dispositions of successful teachers of diverse learners. This study is based on a model of teacher research framed by the concept of “research as praxis” and phenomenological research methodology. The findings describe the research participants' strengths thematically as propensity for inquiry, attention to children, and awareness of school/society relationships. I view these as potentially productive aspects of knowledge and dispositions about science and about children that I could draw on to further students' development as elementary science teachers. © 2002 Wiley Periodicals, Inc. J Res Sci Teach 39: 845–869, 2002