Promoting teacher learning: a framework for evaluating the educative features of mathematics curriculum materials

Educative curricula, curriculum materials that intentionally foster teacher professional development, can serve as a site for teacher learning through their use in daily instructional practices. The present article introduces a framework, Teacher Learning Opportunities in Mathematics Curriculum Materials (TLO-Math), for designing and evaluating mathematics curriculum materials’ educative features according to seven theoretically based variables: (1) mathematics content knowledge for teaching, (2) teacher knowledge of student thinking in mathematics, (3) teacher knowledge of disciplinary discourse in mathematics, (4) teacher knowledge of assessment in mathematics, (5) teacher knowledge of differentiated instruction in mathematics, (6) teacher knowledge of technology use in mathematics, and (7) teacher knowledge of mathematical community. Each variable is illustrated with a definition, guiding questions, discipline-specific literature, and examples from two sets of elementary mathematics curriculum materials. The development of the TLO-Math framework is a critical first step for further study of the use of mathematics curriculum materials as sites for teacher learning.     

Levels of use of Interactive Whiteboard technology in the primary mathematics classroom

Despite the availability of Interactive Whiteboard (IWB) technology in a large number of Australian primary schools, many teachers focus only on technical issues as opposed to pedagogical engagement in an attempt to incorporate the technology. Previous research suggests that the technology is being used for sophisticated transmission-style teaching as opposed to constructivist approaches. This article presents findings of a project that considered the implementation of IWB technology in three Victorian primary mathematics classrooms (5 to 12 years of age). The study analysed the teaching strategies adopted by three teachers as they embarked on the use of IWB technology as an integral component of mathematical activities with the support of professional development. Teacher use of IWB technology in the primary mathematics classroom was aligned against Beauchamp’s generic transitional framework for viewing the development of teacher use of IWB technology. Through this alignment, a transitional framework emerged which is specific to the introduction of IWB technology in the mathematics classroom.     

韩国职前数学教师教育的评介与分析

韩国的数学教师职前教育体制有如下特点:类型多样的教师职前培养机构、严格的公立学校数学教师聘任制度、定期的教师教育机构评估制度.小学数学教师教育课程具有综合性、多样化特点;中学数学教师教育课程更重视学科知识.韩国数学教师职前教育对中国的数学教师教育有如下启示:建立多元的办学体制,致力于专业化的数学教师培养;以教师聘任制度和教师教育机构评估制度促进数学教师培养质量的提高;在学科课程和教学法课程之间寻求恰当平衡.     

Effects of teacher professional learning activities on student achievement growth

The authors examined the effects of six types of teacher professional learning activities on student achievement growth over 4 years using statewide longitudinal survey data collected from 467 middle school mathematics teachers in 91 schools merged with 11,192 middle school students' mathematics scores in a standardized assessment in Missouri. The data showed that teacher-centered collaborative activities to learn about mathematics teaching and learning (teacher collaboration and informal communication) seem to be more effective in improving student mathematics achievement than learning activities that do not necessarily involve such teacher-centered collaborative opportunities (professional development programs, university courses, individual learning activities). Teacher-driven research activities through professional conference presentation and participation were also found to be associated with student achievement growth in mathematics. The districts and schools may benefit from investing their professional development funds and resources in facilitating teacher-centered collaborative and research-based learning activities in order to improve student learning.     

Classroom assessment tools and uses: Canadian English teachers’ practices for writing

Classroom assessment of writing is considered from an anthropological perspective as practitioners’ tool use. Pan Canadian data from a 2002 English teacher questionnaire (N = 4070) about self-reported assessment practices were analyzed in terms of tool choice and use by secondary teachers of different experience and qualification levels. Four underlying variables were identified in their choice of assessment tools: whether affective traits such as attendance, effort, motivation or participation were factors; whether self-assessment and peer evaluation were considered; whether portfolios or examples of student work were variables in grading practices; and whether multiple choice or short response tasks were chosen. In terms of tool use, the three salient variables were: the nature of the feedback cycle with students; whether homework contributed to grades; and whether homework served in large group instruction. A number of significant differences by career stage and credential level were revealed in assessment instrument choice and use. Implications for teacher pre-service and in-service professional development are outlined.     

The nature and development of middle school mathematics teachers’ knowledge

In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers’ knowledge identified by Shulman (1987) refined by Ball et al. (2008) and extended to include teachers’ confidence to use and teach various topics in the middle school mathematics curriculum and their beliefs about mathematics teaching and learning. Based on a hierarchical coding of items, the application of the partial credit Rasch model revealed that the profile items were measuring a single underlying construct and suggested that the various facets of teacher knowledge develop together. We describe the characteristics of four levels of the hierarchical construct measuring teacher knowledge and understanding for teaching mathematics in the middle years of schooling, and discuss the unique affordances of a holistic view of teacher knowledge in contrast to considerations of multiple knowledge categories.     

Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teachers affords identifying corresponding needs for teacher education. However, specific empirical research is scarce. Taking into account the possible role of culture, this study consequently focuses on views about using multiple representations held by more than 100 English and more than 200 German preservice teachers. The results indicate that there are culture-dependent aspects of preservice teachers’ views, but also that there are common needs for professional development.     

Student perceptions of the classroom environment: Relations to motivation and achievement in mathematics

This study examined the relationship of 979 middle school students’ perceptions of their mathematics classroom environment to their motivation and achievement. Structural equation modeling indicated that motivational variables (utility, personal achievement goals, efficacy) mediated the influence of perceived teacher expectations, teacher support and use of reform practices on mathematics standardised test scores. Our study provides empirical evidence that students’ perceptions that their teachers believe that they are capable of learning and understanding mathematics positively relate to their Mastery and Performance Goal orientations and mathematics Utility. Further, we found an interaction between students’ perceptions of the frequency of reform practice use in their mathematics classroom and mathematics efficacy. For students with lower mathematics efficacy, their perceptions of more frequent use of reform practices in their mathematics class related to higher standardised test performance. For students with higher mathematics efficacy, perceived use of reform practices did not significantly relate to standardised test performance. These data suggest that frequent exposure to reform practices is especially critical for students who judge themselves as being less capable in mathematics and who are lower performers. This finding differs from prior research that has suggested that reform practice use benefits higher achievers but not lower achievers. An important implication of our study is the need for coordinated, ongoing professional development that highlights reform pedagogy and beliefs while also focusing on student motivation theories and strategies.     

Unravelling continuous assessment practice: Policy implications for teachers’ work and professional learning

Assessment policy in some countries continues to promote the use of continuous assessment (CA) within classrooms. Several policy claims have been made about the potential of CA to improve education. Using data from a 2010 evaluation of the Trinidad and Tobago Continuous Assessment Programme (CAP), canonical correlation analysis (CCA) was used to unravel the pattern of relationships between institutional variables, professional learning, teacher beliefs, and CA components. The CA components measured were (1) overall use, (2) multiple assessment formats use and (3) formative feedback use. Each CA component was shown to be associated with different variables, with overall use related to several teacher belief factors such as extra-role behaviour. However, multiple assessment formats use added only a small amount of unique variance to the CCA solution. Moreover, the canonical variate for formative feedback use was not statistically significant. These findings have implications for CA as a policy tool. Successful implementation of CA may require high quality professional learning as well as teacher workforce remodelling. Even when implemented successfully, however, CA may not be a useful vehicle for promoting high quality formative assessment or use of multiple assessment formats.     

We can,we know how. But do we want to? Teaching attitudes towards ICT based on the level of technology integration in schools

Teachers’ attitudes towards technology are crucial to foster its use in schools and to improve its educational affordances and this is still a topic for research. This article relates the attitudes school teachers have towards information and communication technologies (ICT) with the different levels of technology integration in schools. A multiple case-study research methodology was applied, and in which the school was the unit of sampling used. Thirty-five schools from eight Spanish regions were selected, and 1222 questionnaires were collected, representing 78.9% of the sample. Three combined variables were utilised to classify schools in four different levels of technology integration. Results suggest level 4 school teachers exhibit better attitudes towards ICT, which results in creating a positive circle which improves the learning process. This becomes relevant for teacher education and professional development, as effective ICT integration in the classroom can perform as a catalyst for educational innovation.     

Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice teachers affords identifying corresponding needs for teacher education. However, specific empirical research is scarce. Taking into account the possible role of culture, this study consequently focuses on views about using multiple representations held by more than 100 English and more than 200 German preservice teachers. The results indicate that there are culture-dependent aspects of preservice teachers’ views, but also that there are common needs for professional development.

     

信息技术支持的教师专业发展:从应然走向实然

全面认识信息技术在教师专业发展中的作用,对于广大教师学习并且利用信息技术促进自身专业发展具有重要意义。作者基于多年来的研究与实践,论述了信息技术在促进教师专业素养提升、加快教师专业发展进程、推动教师专业发展方式变革、提高教师绩效、引发教育变革和促进教育观念转变等五个方面的作用,并且指出,在教育信息化纵向推进的今天,研究者必须尽快完成四个转变——从应然走向实然,从描述性研究走向关系研究和过程与机制研究,从实证研究走向质性研究,从验证性研究走向设计研究。     

IMPROVING MATHEMATICS TEACHER EDUCATION IN GERMANY: EMPIRICAL RESULTS FROM A LONGITUDINAL EVALUATION OF INNOVATIVE PROGRAMS

Innovative programs for restructuring the entry phase of mathematics teacher education programs have been implemented at various German universities within the last few years. This article reports about the design and the results of a longitudinal evaluation study of the effectiveness of two of these programs aiming to improve mathematics teacher education by altering the conditions in university teaching (the so-called Teacher Education and Development Study TEDS-Telekom). The development of prospective teachers’ professional knowledge in academic mathematical content knowledge, knowledge in elementary mathematics from an advanced standpoint, and mathematical pedagogical content knowledge from the innovative programs were compared to traditional university programs. The study points out that the innovative programs only partially succeeded in improving the acquisition of professional knowledge for prospective mathematics teachers.     

Learning to Lead: an Approach to Mathematics Teacher Leader Development

This paper describes a partnership between a university and an urban school district, formed with a goal of preparing mathematics teacher leaders to conduct professional development (PD) at their schools. The university and district partners worked together to achieve the district’s mission of providing every student with high-quality instruction and equitable learning opportunities in mathematics by building the district’s capacity to conduct school-based PD for mathematics teachers. Given the power of school-based subject-specific PD for improving instructional quality, we worked with Teacher Leaders from participating schools to prepare and support them to lead PD workshops at their schools. In this paper, we examine how Teacher Leaders learn and adapt key elements of a PD model over three school years through the lenses of Prediger et al.’s Three-Tetrahedron-Model (2019) and the university’s Learning to Lead model. Over 3 years, we see that Teacher Leaders use the key structures of the PD model; make adaptations in response to school goals, interests, and priorities; and gain confidence in their work with colleagues. By viewing the adaptations through the lens of pedagogies of practice as well as the relationships illustrated by the 3-T model, this work offers insights into the complexities of teacher leadership development.

     

Teachers’ use of their mathematical knowledge for teaching in learning a mathematics learning trajectory

In the past decade, research on learning trajectories has progressed from an agenda for research on student learning to include an agenda for research on teaching. In this paper, we use a design experiment to examine a professional development program created to support teacher learning of one learning trajectory. Using a re-interpretation of Ball and colleagues’ mathematics knowledge for teaching framework, we conducted a retrospective analysis to examine how a purposefully selected sample of three teachers used their knowledge to participate in discussions of the professional learning tasks designed to support teacher learning of the trajectory. Findings indicate that professional learning tasks focusing on pedagogical content knowledge present in learning trajectories also allow for teacher learning of subject matter knowledge; this learning is mediated by teachers’ prior mathematics knowledge for teaching. We conclude with considerations for researchers and professional developers seeking to support teachers in learning about learning trajectories.     

Using an Exploratory Professional Development Initiative to Introduce iPads in the Early Childhood Education Classroom

The purpose of this study was to investigate the incorporation of iPads into the early childhood classroom through an exploratory teacher professional development initiative. Eighteen early childhood educators participated in a 6-month study targeting teacher professional development and pedagogical innovation. This study included built-in opportunities for teacher collaborative discussions and support in their team meetings, as well as basic technology training on the use of an iPad in a classroom. A thematic analysis was conducted using constructed codes from teacher interviews and focus groups, as well as artifact collections of notes from teacher bi-monthly meetings. Results indicate that teachers used technology in three innovative ways: as an efficiency solution, as a bridge in virtual parent communication, and as curriculum enhancement or replacement. The researchers of this study argue that using the iPad as curriculum is the next area of professional growth for early childhood teachers.