Beginning the Process of Rethinking Mathematics Instruction: A Professional Development Program

This article describes a professional development program that introduces middle school teachers to an inquiry approach to mathematics instruction as a vehicle to reform their teaching of mathematics. The program is characterized by the use of a few illustrative units that provide an integrated context for experiences as learners and experiences as teachers. Project participants consisted of mathematics and special education teachers in school-based support teams led by school facilitators. Results suggest that the illustrative units were of considerable value in promoting reform. The benefits of including an heterogeneous group of teachers in the same professional development program and of involving teachers from the same school are also discussed.     

Examining change in K-3 teachers’ mathematical knowledge,attitudes, and beliefs: the case of Primarily Math

This study examines the impact of the Primarily Math Elementary Mathematics Specialist program on K-3 teachers’ mathematical content knowledge for teaching, attitudes toward learning mathematics, and beliefs about mathematics teaching and learning. Three cohorts of teachers participating in the program were compared to a similar group of non-participating teachers. Teacher outcomes were measured longitudinally across 5 years. Participating teachers showed changes in their knowledge, attitudes, and beliefs in line with program goals immediately after completion of coursework. Moreover, these changes were sustained in subsequent years, following program completion. Relative to the comparison group, participants demonstrated greater gains in knowledge as well as greater improvements in attitudes and beliefs. Implications of these results for professional development design, implementation, and evaluation are discussed.     

Factors affecting teachers’ continuation of technology use in teaching

This study was conducted to investigate the continuation of technology use in science and mathematics teaching of the teachers who attended a professional development program between 2010 and 2012. Continuation of technology use was hypothesized to be affected by the professional development program and by personal, institutional, and technological factors. Twelve teachers and three school leaders participated in the study. Data was collected through interviews. Findings showed that the continuation of technology use differed for the teachers involved in the professional development program. While all teachers reported to have gained knowledge and skills through the professional development program and were positive about technology use in education, only some teachers continued the use of technology. The data revealed that despite the challenges that all teachers in the sample encountered when using technology in their teaching (such as large classrooms, problems with electricity supply, lack of time and lack of technology tools), the encouragement of school management was a critical factor in teachers’ continuation of technology use. Implications of the findings are discussed.     

高职院校教师培训的比较研究——澳大利亚高职教师资格证书（TAA）培训的研究与探索

澳大利亚高等职业教育TAFE对师资有严格的规定和要求,在澳大利亚高等职业院校TAFE学院执教的老师必须经过TAA培训并获得证书。本文对澳大利亚TAA证书培训进行研究和探索,力争对国内高职教师培训起到对比和借鉴的作用。本文分为部分：1．澳大利亚TAA证书培训的概述;2．澳大利亚TAA证书培训的主要内容;3．澳大利亚TAA证书培训对教学所起到的作用。4．结论。     

Professional Conversations and Professional Growth

A professional development program for 18 teachers was conducted over a two-year period. The participating teachers taught in intermediate schools (students aged 11–13) and secondary schools. The teachers worked collaboratively to improve their mathematics teaching, with encouragement to reflect on their practice but with minimal instruction from the researchers. Results, as defined by change in teaching practices, beliefs, and reflections, and student achievement, indicated that the collaborative program was particularly useful for experienced secondary school teachers but less useful for intermediate school teachers. We concluded that this type of professional development was most useful for teachers who had sufficient knowledge of mathematics; these teachers were able to focus on pedagogy and to draw connections between aspects of the mathematics they taught, without recourse to a specialist's advice. This revised version was published online in August 2006 with corrections to the Cover Date.     

The Work of Providers of Professional Development for Teachers of Mathematics: Two Case Studies of Experienced Practitioners

This paper is an initial investigation into the practice of providers of professional development for teachers of mathematics. The study examines the work of two providers of professional development for teachers of mathematics. Both provided professional development while working with teachers on implementing a new mathematics curriculum for seventh grade. Although their work conditions were quite different from each other the study reveals that there were similar characteristics in their practices. The most salient ones were acting out lessons, analyzing principles of the new curriculum, encouraging the teachers to explicate their concerns, and asking teachers to solve concrete practical problems related to the reservations they have about specific components of the new curriculum. The role of a program that prepared the two participants to be providers of professional development for teachers is also discussed.     

TAFE模式在高职课程改革中的应用

TAFE课程的灵活性体现在培养方式、教学方式、课程安排等诸多方面,以最新的职业技术来影响学校的教学工作。高职高专课程改革也提出了新的专业知能结构,课程改革与教师发展是整合一致的,课程改革是在教师发展中推进的,教师发展是在课程改革中达成的。我们在课程改革中要借鉴TAFE课程在培养方式、教学方式、课程安排等诸多方面的灵活性,为学生提供社会变革和职业转变过程中所需的各种知识和技能。     

Designing Curriculum-Based Mathematics Professional Development for Kindergarten Teachers

This study examines the influence of a year-long mathematics professional development program on Kindergarten teachers’ beliefs, content knowledge, instructional practices, and their students’ achievement. The professional development program is grounded in the theoretical construct of learner-centered professional development and focuses on supporting teachers’ integration of standards-based pedagogies aligned with the Common Core State Standards in Mathematics. Data analysis included examining 15 Kindergarten teachers’ mathematics content knowledge, their beliefs about mathematics, their enactment of student-centered pedagogies, and student achievement on curriculum-based assessments. Findings indicated that teachers adopted more student-centered pedagogies and embraced more student-centered beliefs about mathematics teaching during their time in the project. Further, Kindergarten teachers also demonstrated gains in their mathematical content knowledge, and those content knowledge gains were linked to gains in student achievement.     

The Impact of a Professional Development Program on Teachers' Mathematical Knowledge for Teaching,Instruction, and Student Achievement

In this paper, we describe findings from a three-year evaluation of a well-developed mathematics professional development program that is commercially available on a wide scale. The professional development is designed to improve teachers' mathematical knowledge for teaching and to enable them to elicit more student thinking and reasoning during mathematics lessons. Specifically, it focused on helping teachers (a) learn more mathematics, (b) understand how children learn math, (c) use formative assessment to develop insight into what specific students know and do not know, and (d) develop effective classroom instructional strategies that enable student problem solving. Participants included 105 fourth- and fifth-grade teachers teaching in 19 low-income schools within a single district. Teachers were randomly assigned within schools either to a “business as usual” control group or to receive the professional development. The training consisted of a week-long summer institute and four to six in-service days during the school year. The training was run by full-time trained associates. We find some limited evidence of positive impacts on teachers' mathematical knowledge for teaching, but no effects on instructional practice or student outcomes.     

基于学习进阶的幼儿教师数学核心经验模型建构

幼儿教师数学核心经验主要是指教师在教学实践中形成的数学领域至关重要的概念、能力或技能,对于幼儿的数学学习和教师的数学教学具有至关重要的作用。幼儿教师作为基本的学习者,其专业发展过程符合学习进阶的各项准则,不同职业发展阶段的幼儿教师有着各自不同的进阶轨迹。学习进阶强调学习是一种不断积累和发展的过程,并倡导为不同阶段的学习者设计不同的进阶框架,这为有效推动幼儿教师数学核心经验的发展提供了充分的理论参考。本研究在厘清幼儿教师数学核心经验内涵与结构的基础上,依据学习进阶的主要观点,建构幼儿教师数学核心经验的经验模型,并提出相应的教师培养策略,主要包括加强数学核心经验的学习共同体建设、制订数学核心经验的阶梯式成长方案和完善数学核心经验的质量监测指标。     

Less experienced mathematics teachers report what is wrong with their professional support system

Teachers with seven years of teaching experience or less (n = 10) participating in a large‐scale mathematics professional development program in the United States were interviewed. The goal of this qualitative study was to better understand less experienced teachers' reactions to professional development and professional support in the teaching profession. The interview data ­indicate that these less experienced mathematics teachers are not satisfied with their mentors orcollaboration in their department and would welcome opportunities for classroom observations. In addition, these teachers were disappointed and surprised at their more experienced peers' lack of mathematics content knowledge. The results of this study have direct implications for the structure and philosophy for professional development to better serve incoming and less experienced teachers.     

数学教师专业化新课程实施的必然要求

数学教师专业化的标准主要包括数学教师的素质结构与成长环境两个方面,而数学新课程从这两个方面都对数学教师专业化发展提出了严峻的挑战,首先,新课程实施要求数学教师具备良好的数学专业基础、教育教学观念和数学教学能力等素质结构;其次,新课程实施又迫切需要相关部门在教师职前教育、教师在职培训,教育教学研究以及教师聘任机制等方面为数学教师建立专业化成长环境。     

Fostering a “head start” in math: observing teachers in early childhood mathematics engagement

ABSTRACT

Studies show that early engagement with mathematics leads to increased math achievement later in life. Yet, early childhood teachers do not regard mathematics as critical to young learners’ development and lack confidence with helping children learn mathematics. Early childhood teacher comfort and engagement with mathematics is a critical element to promoting intentional math instruction. Research was conducted to examine the effects of an innovative professional development program for Head Start preschool teachers with the goal of increasing pedagogical content knowledge and confidence in teaching mathematics. The findings in this article focus on classroom observations that concentrated on teacher engagement with mathematics.     

Essential Characteristics for a Professional Development Program for Promoting the Implementation of a Multidisciplinary Science Module

Teachers involved in the implementation of a curriculum innovation can be prepared for this task through a professional development program. In this paper, we describe essential characteristics (identified empirically and theoretically) for such a professional development program that promotes the acquisition of competences by these teachers. The innovation deals with the introduction of modules from a new multidisciplinary subject, in which elements from physics, chemistry, biology, mathematics, and physical geography are integrated. A 3-step approach was used to identify the essential characteristics: (a) evidence from classroom practice, (b) characteristics of the new subject, and (c) theoretical and empirical evidence from curriculum implementation studies. Analysis of the data showed that 5 characteristics need particular attention in a professional development program.     

Primary special school teachers' knowledge and beliefs about supporting learning in numeracy

This paper presents findings from a qualitative study of a group of 12 teachers in primary special schools in Scotland for children with moderate learning difficulties. It sets out an analysis of classroom observations and interviews that explored teachers' knowledge and beliefs about teaching and learning in mathematics with children with moderate learning difficulties. The teachers were interviewed pre‐ and post‐intervention; this was a research‐based professional development programme in children's mathematical thinking (Cognitively Guided Instruction) which teachers then developed in their classrooms. The findings showed that prior to the professional development, the teachers had a limited knowledge of children's mathematical development with teaching frequently informed by intuitive beliefs and dated and sometimes discredited practices. Most teachers had low expectations of children with learning difficulties. Post‐intervention, the teachers reviewed this stance and affirmed that a deeper understanding of children's mathematical thinking provided a more secure knowledge base for instruction. They also recognised the extent to which learners were constrained by existing classroom practices. The paper argues for the commonality of this knowledge base and considers the problematic nature of viewing such knowledge as sector specific.     

From preschool teachers’ professional development to children’s knowledge: comparing sets

Recently, there have been increased calls for enhancing preschool children’s mathematics knowledge along with increasing calls for preparing preschool teachers to meet the demands of new preschool mathematics curricula. This article describes the professional development program Starting Right: Mathematics in Preschools. Focusing on four episodes that revolve around the topic of equivalent sets, it demonstrates how engaging preschool teachers with challenging tasks may promote their subject matter knowledge as well as their pedagogical content knowledge, leading to an interweaving of knowledge and practice. Assessment of the program included assessing the children’s knowledge. Results indicated that students of participating teachers learned to be more flexible and to give more possible answers than students of non-participating teachers.     

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。     

STEMulate Engineering Academy: Engaging Students and Teachers in Engineering Practices

Informal science opportunities provide authentic experiences to stimulate students’ interests in science and engineering and foster their curiosity through problem-based investigations. STEMulate Engineering Academy was designed to provide children (Grades 3–5) engineering opportunities and offer teachers a unique professional development experience. The program serves as a practicum experience for teachers seeking a gifted and talented add-on license and the camp also offers free professional development to area teachers. Using a co-teaching approach, students gained firsthand experiences from an engineer in the field, and teachers collaborated with engineers to make the content more relevant. Despite a limited number of contact hours, students and teachers demonstrated growth on pre and post engineering assessments. Informal learning opportunities provided by programs such as STEMulate Engineering Academy could possibly spark student interest in science, technology, engineering, and mathematics (STEM)––leading them to a promising career in a STEM field.     

How Does Ongoing Task-Focused Mathematics Professional Development Influence Elementary School Teachers’ Knowledge, Beliefs and Enacted Pedagogies?

This study examined how a task-focused, year-long mathematics professional development program influenced elementary school teachers’ knowledge, beliefs, and practices. Participants completed 84 h of professional development over 13 months that were focused on exploring, modifying and implementing cognitively-demanding mathematical tasks. Using a multi-methods approach, teacher-participants completed pre- and post-measures of mathematical knowledge for teaching, teachers’ beliefs about teaching and learning mathematics, and teachers’ self-reports of enacted instructional practices. Further, three teacher-participants were randomly selected to be observed 3 times over the course of the school year. Data analyses indicated that the professional development had a statistically significant positive impact on participants’ mathematical knowledge for teaching, use of student-centered instructional practices, and beliefs towards mathematics as a subject area. Further, the observed teachers enacted some high-level mathematical tasks and questions, but these were more visible at the end of the study compared to the beginning of the study. Implications for future work are also shared.     

Connecting with the horizon: developing teachers’ appreciation of mathematical structure

A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior secondary mathematics is the context for this study of teachers’ mathematical and pedagogical knowledge. The analysis of teachers’ reflections on their learning explored teachers’ understanding of mathematical connections and their appreciation of mathematical structure. The findings indicate that a professional learning program about senior secondary mathematics can enable practicing teachers to deepen and broaden their knowledge for teaching junior secondary mathematics and develop their practice to support their students’ present and future learning of mathematics. Further research is needed about professional learning approaches and tasks that may enable teachers to imbed and develop awareness of structure in their practice.