Two negatives don't always make a positive: Exploring how limitations in teacher knowledge and the curriculum contribute to instructional quality

This paper examines the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the implementation of lessons on integer subtraction. In particular, it investigates the instruction of three teachers with differing MKT levels using two editions of the same set of curriculum materials that provided different levels of support. This variation in MKT level and curriculum support facilitated exploring the distinct and joint contribution of MKT and the curriculum materials to instructional quality. The analyses suggest that MKT relates positively to teachers' use of representations, provision of explanations, precision in language and notation, and ability to capitalize on student contributions and move the mathematics along in a goal-directed manner. Curriculum materials set the stage for attending to the meaning of integer subtraction and appeared to support teachers' use of representations, provision of explanations, and precision in language and notation. More critically, the findings suggest that less educative curriculum materials, coupled with low levels of MKT, can lead to problematic instruction. In contrast, educative materials can help low-MKT teachers provide adequate instruction, while higher MKT levels seem to enable teachers to compensate for curriculum limitations.     

Teacher knowledge,curriculum materials,and quality of instruction: Lessons learned and open issues

This paper draws on four case studies to perform a cross-case analysis investigating the unique and joint contribution of mathematical knowledge for teaching (MKT) and curriculum materials to instructional quality. As expected, it was found that both MKT and curriculum materials matter for instruction. The contribution of MKT was more prevalent in the richness of the mathematical language employed during instruction, the explanations offered, the avoidance of errors, and teachers' capacity to highlight key mathematical ideas and use them to weave the lesson activities. By virtue of being ambitious, the curriculum materials set the stage for engaging students in mathematical thinking and reasoning; at the same time, they amplified the demands for enactment, especially for the low-MKT teachers. The analysis also helped develop three tentative hypotheses regarding the joint contribution of MKT and the curriculum materials: when supportive and when followed closely, curriculum materials can lead to high-quality instruction, even for low-MKT teachers; in contrast, when unsupportive, they can lead to problematic instruction, particularly for low-MKT teachers; high-MKT teachers, on the other hand, might be able to compensate for some of the limitations of the curriculum materials and offer high-quality instruction. This paper discusses the policy implications of these findings and points to open issues warranting further investigation.     

Teaching transformation under centralized curriculum and teacher learning community: Two Chinese chemistry teachers' experiences in developing inquiry-based instruction

The establishment of centralized curriculum standards and school-based teacher learning communities are presumably necessary to reform science teaching towards inquiry-based instruction in many countries. Drawing on interview, document, and unit plan data from two high school chemistry teachers in China, this study examines these assumptions. Findings indicated that both teachers developed different kinds of science teaching practices despite working under the centralized science curriculum and school-based teacher learning communities. Different teaching experiences of the two teachers and their school cultures of teaching interacted with the centralized curriculum and teacher teaching community to consequently shape their teaching practices in different ways.     

A Flexible Plan of Supervised Study

ABSTRACT

The authors examined the characterization of mathematical knowledge of teachers using educative curriculum materials. In particular, they investigated knowledge of change and rate of change (in the context of algebra and functions) of 12 teachers with differing levels of experience. Participants used a same set of curriculum materials that embed features that had potential to be educative for teachers. Data were collected using a mathematical task-based interview. The analyses suggest that context played an important role with regard to teachers’ ability to explore complex situations. Teachers with a high level of experience teaching the educative curriculum materials showed greater success in dealing with complex problems and recognizing similar and contrasting characteristics of different types of representations across contexts. The findings suggest that curriculum materials can be designed to assist teachers’ learning in ways that contribute to establishing contexts where teacher learning takes place.     

Relationships between mathematical knowledge for teaching and teaching practice: the case of proof

Teachers of mathematics orchestrate opportunities for interactions between learners and subject matter. Therefore, mathematics teachers need rich, multidimensional content knowledge for teaching mathematics, which incorporates knowledge of the subject matter, students, and teaching. Studying this mathematical knowledge for teaching (MKT) necessitates more than a unidirectional assessment. In this study, the mathematical knowledge for teaching reasoning and proving of two secondary mathematics teachers was investigated through classroom observations and clinical assessments. Results indicate that using MKT as a frame for examining classroom practice, in addition to assessing the MKT a teacher possesses in a clinical setting, provides an in-depth and innovative method for investigating MKT. The comparison of the two cases also identifies student positioning as a key mediating factor between MKT and opportunities to learn. Implications for using MKT as a lens for examining practice in teacher education are discussed.     

河北省新建地方本科院校师资队伍建设研究

师资队伍建设是影响新建地方本科院校教学质量提升最为重要的因素。目前河北省各新建地方本科院校在师资队伍建设方面仍存在以下问题:生师配比矛盾,骨干教师缺乏;教师专业化程度较低,教学质量有待提升;教学理念缺乏更新,教学模式局限;教师培养途径单一,课程建设进程缓慢。对此,新建地方本科院校应进一步完善人才引进机制,优化教师队伍结构;加深教师职业认同,提高教师专业素质;改善教学管理体制,拓展教师培养模式。     

The Impact of High School Science Teachers’ Beliefs,Curricular Enactments and Experience on Student Learning During an Inquiry-based Urban Ecology Curriculum

Inquiry-based curricula are an essential tool for reforming science education yet the role of the teacher is often overlooked in terms of the impact of the curriculum on student achievement. Our research focuses on 22 teachers’ use of a year-long high school urban ecology curriculum and how teachers’ self-efficacy, instructional practices, curricular enactments and previous experience impacted student learning. Data sources included teacher belief surveys, teacher enactment surveys, a student multiple-choice assessment focused on defining and identifying science concepts and a student open-ended assessment focused on scientific inquiry. Results from the two hierarchical linear models indicate that there was significant variation between teachers in terms of student achievement. For the multiple-choice assessment, teachers who spent a larger percentage of time on group work and a smaller percentage of time lecturing had greater student learning. For the open-ended assessment, teachers who reported a higher frequency of students engaging in argument and sharing ideas had greater student learning while teachers who adapted the curriculum more had lower student learning. These results suggest the importance of supporting the active role of students in instruction, emphasising argumentation, and considering the types of adaptations teachers make to curriculum.     

课堂教学文化重建困境探析

通过对一所小学问题式教学实践的现实考察发现,尽管教师接受了许多新课程培训,但教师内心对传统教学观念的高度认同和坚守使得问题式教学实践缺乏实效性,同时也表明课堂教学文化的重建之路困难重重。课堂教学文化的重建关键在于教师教学观念的重塑,然而要改变教师的教学观念,并不能仅靠对教师的知识培训和技能训练来实现,必须确立一种整体观,改变教师生存于其中的学校场景和生活场景,为教师观念的转变提供外部支持。     

Teachers’ use of educative curriculum materials to engage students in science practices

New reform documents underscore the importance of integrating science practices into the learning of science. This integration requires sophisticated teaching that does not often happen. Educative curriculum materials – materials explicitly designed to support teacher and student learning – have been posited as a way to support teachers to achieve these ambitious goals, yet little is known about how elementary teachers actually use educative curriculum materials to support student engagement in science practices. To address this gap, this study investigated how five upper elementary teachers supported students to engage in science practices during an enactment of two curriculum units. Three of the teachers had units enhanced with educative features, informed by current research and reforms, while two of the teachers had units without these features. The teachers varied in how they supported students in the science practices of justifying predictions, constructing evidence-based claims, recording observations, and planning investigations. For example, some of the teachers with the educative features supported students in constructing evidence-based claims and justifying predictions in ways called for by the educative features. Implications for curriculum developers and teacher educators are discussed based on the patterns found in the teachers’ use of the educative curriculum materials.     

Changes in science classrooms after experiencing an international professional staff development program

This professional development program was designed to prepare science teachers to be more student-centered and to implement newer goals for science instruction. These goals are to improve science teaching in ways that promote broader and longer-lasting learning. Secondary school science teachers in Korea are expected to follow a rigid national curriculum with large classes - often with more than 50 students. This study focuses on feedback and follow-up interaction with teacher participants who were enrolled in a month-long workshop in the U.S. before returning to Korea to implement the new ideas. Assistance was offered to help teachers develop teaching modules which were more constructivist while also assisting with assessment efforts that provided further evidence of use of the new teaching practices and their effect on student learning. Student mastery of concepts and improvement in student creativity were two aspects of the summer workshop experiences and these were evaluated to illustrate workshop effects on teacher participants in their actual classrooms. An erratum to this article is available at .     

Revisiting curriculum inquiry: the role of visual representations

Curriculum materials and knowledge about curricular purposes and structures are valuable tools that teachers often draw upon to organize instruction and facilitate student learning. Careful analysis of teachers’ curriculum implementation and the decision-making that undergirds their curriculum use is critical for fully understanding enactment. This paper compares how integrity analyses of implementation of curriculum materials and actor-oriented analysis of teachers’ curriculum use can help researchers, teacher educators, and curriculum designers interpret teachers’ decisions about what aspects of new materials to use and how to use such materials. Drawing on evidence from teacher interviews and observations, we compare two teachers’ enactments of a new elementary-level environmental biology unit. Our analyses of integrity point to differences in teachers’ adaptations with respect to their consistency with the purposes and structures of curriculum materials as construed by designers. By contrast, our actor-oriented analysis explain how the teachers’ different approaches to interpreting the goals and structures of the curriculum unit partly account for patterns in their enactment in ways that can inform refinements to materials and the design of professional development supports for teachers. In so doing, we show how implementation integrity and actor-oriented analyses offer complementary perspectives to inform curriculum research and development.     

Teacher knowledge,curriculum materials,and quality of instruction: Unpacking a complex relationship

The set of papers presented in this issue comprise a multiple-case study which attends to instructional resources—teacher knowledge and curriculum materials—to understand how they individually and jointly contribute to instructional quality. We approach this inquiry by comparing lessons taught by teachers with differing mathematical knowledge for teaching who were using either the same or different editions of a US Standards-based curriculum. This introductory paper situates the work reported in the next four case-study papers by outlining the analytic framework guiding the exploration and detailing the methods for addressing the research questions.     

Faithfully following,adapting, or rejecting mandated curriculum: teachers’ curricular enactments in elementary writing instruction

The qualitative study shows how 20 teachers from 4 districts in the same state enacted mandated school-wide writing curricula. Analyses of the observations and interviews revealed that 4 teachers were faithfully following the district-adopted curriculum, 4 rejected it, and 12 teachers adapted the curriculum to meet their students’ needs. The teachers who followed the curriculum had positive views of it but were inexperienced or uncomfortable teaching writing and had less access to professional development (PD) than teachers in other groups. Most of the teachers who adapted the curriculum were experienced teachers and felt supported in making changes due to the quality of PD. The teachers who rejected the curriculum were unhappy with the existing curriculum and drew from a number of different resources; however, their writing instruction lacked coherence and an underlying philosophy of writing. The findings show that factors such as policies, PD, and personal factors including previous writing experiences and philosophies influenced teachers’ enactments. While previous studies have found that overarching policies including NCLB increase pressure on teachers resulting in a lack of autonomy, our findings explore the ways that teachers were able to navigate their school contexts.     

Extending students’ mathematical thinking during whole-group discussions

Studies show that extending students’ mathematical thinking during whole-group discussions is a challenging undertaking. To better understand what extending student thinking looks like and how teachers’ mathematical knowledge for teaching (MKT) supports teachers in their efforts to extend student thinking, the teaching of six experienced elementary school teachers was explored. During group discussions, all six teachers created opportunities for extending student thinking about important mathematical ideas and solution methods. Findings on the nature of these episodes include identification of individual instructional actions and the ways in which teachers’ MKT was connected to these actions.     

Teachers and science curriculum materials: where we are and where we need to go

Curriculum materials serve as a key conceptual tool for science teachers, and better understanding how science teachers use these tools could help to improve both curriculum design and theory related to teacher learning and decision-making. The authors review the literature on teachers and science curriculum materials. The review is organised around three main questions: What do teachers do when using science curriculum materials?, What happens when teachers use science curriculum materials? and Why do teachers make the decisions they do? For each question, the authors first summarise the findings of two key reviews from the mathematics education literature, then situate the findings from science education in juxtaposition with those findings. The review uncovers that relatively little is understood about the mechanism underlying how teachers interact with curriculum materials. To try to address this gap, complementing and extending the field’s existing understandings of the teacher–curriculum relationship, the authors make four propositions, grounded in the literature on self-regulation. The propositions reflect a mechanism for teacher curricular decision-making. The self-regulation perspective also helps to develop more targeted support for science teachers aimed at the uptake, adaptation and enactment of curriculum materials in ways that are intended, and that teachers themselves experience as an improvement in their teaching. The authors conclude with a call for research that further explores the ways in which individual science teachers’ decision-making is situated within the wider sociocultural context.     

How Mathematical Knowledge for Teaching May Profit from the Study of History of Mathematics

In this theoretical article, we aim at theorizing the old statement that mathematics teachers might profit from studying the history of mathematics. We do this by drawing upon the theoretical framework of mathematical knowledge for teaching (MKT). A selection of international studies on the history and pedagogy of mathematics is used as starting points for discussing how the different domains of teachers’ MKT—to a larger or smaller degree—can profit from the history of mathematics.     

ENACTED TYPES OF ALGEBRAIC ACTIVITY IN DIFFERENT CLASSES TAUGHT BY THE SAME TEACHER

The aim of this study was to examine how teachers enact the same written algebra curriculum materials in different classes. The study addresses this issue by comparing the types of algebraic activity (Kieran, 2004) enacted in two 7th grade classes taught by the same teacher, using the same textbook. Data sources include lesson observations and an interview with the teacher. The findings show that students in the two classes were offered somewhat different algebraic experiences. At one school, more emphasis was placed on global/meta-level activities (activities that are not exclusive to algebra and suggest general mathematical processes), whereas at the other school, more emphasis was placed on transformational activities (“rule-based” algebraic activities). Analysis of the sources of the differences related to the ways in which the teacher used and enacted the curriculum materials in the two classes revealed that these were linked to the teacher’s attempts to be attentive to the students in the class and to the nature of the students’ work.     

A Spiral Task as a Model for In-service Teacher Education

The spiral approach has long been used by curriculum designers to deepen students’ knowledge of scientific and mathematical concepts and to bring students to higher levels of abstraction. The benefits of a spiral approach, however, can also be extended to teacher education. This paper describes a spiral activity employed by the Kidumatica program not only to raise the level of teachers’ content knowledge, but also to promote discussion and collaboration among teachers teaching at different grade levels. The activity was designed to take a single problem situation and develop it in ways appropriate to the different grade levels. At each stage, the teachers are encouraged to discuss teaching approaches required by the students at each grade level and the relationships between the different stages of the development.