The relationship among elementary teachers’ content knowledge,attitudes, beliefs,and practices

This study investigated 481 in-service elementary teachers’ level of mathematical content knowledge, attitudes toward mathematics, beliefs about the effectiveness of inquiry-based instruction, use of inquiry-based instruction and modeled the relationship among these variables. Upper elementary teachers (grades 3–5) were found to have greater content knowledge and more positive attitudes toward mathematics than primary teachers (grades K-2). There was no difference in teachers’ beliefs about effective instruction, but primary level teachers were found to use inquiry-based instruction more frequently than upper elementary teachers. Consistent with Ernest’s [Ernest (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33] model of mathematics teaching, content knowledge, attitudes, and beliefs were all found to be related to teachers’ instructional practice. Furthermore, beliefs were found to partially mediate the effects of content knowledge and attitudes on instructional practice. Content knowledge was found to be negatively related to beliefs in the effectiveness of inquiry-based instruction and teachers’ use of inquiry-based instruction in their classrooms. However, overall, teachers with more positive attitudes toward mathematics were more likely to believe in the effectiveness of inquiry-based instruction and use it more frequently in their classroom. Teacher beliefs were found to have the strongest effect on teachers’ practice. Implications for the goals and objectives of elementary mathematics methods courses and professional development are discussed.

“建构——合作”模式在自然科学课堂教学中的探索

通过对当前自然科学课堂教学的分析与教学实践 ,提出了“建构—合作”教学模式来重构自然科学课堂教学。该模式包含六个环节 ,即结合内容查找资料 ;研究资料提出问题 ;合作探究问题的解决方案 ;交流反馈拓展延伸 ;小组评价 ;应用解决新问题。通过这六个环节的循环操作 ,唤起课堂活力 ,培养创新精神 ,使学习者达到知、能统一。     

The effect of block scheduling high school mathematics courses on student achievement and teachers' use of time: implications for educational productivity

Block scheduling involves the reallocation of instructional time into longer class sessions to encourage more active teaching strategies, reduce fragmentation inherent in single-period schedules, and improve student performance. To the degree that such policies reallocate existing resources to realize higher levels of desired educational outcomes, the goal of productivity can be served. Despite widespread experimentation with various forms of block scheduling, there is conflicting evidence on the impact of these innovations on student achievement, and little evidence of their effect on classroom practice. This study explores these relationships. More specifically, the study draws on data from the National Education Longitudinal Study: 1988 to estimate the impact of block-scheduled mathematics courses on tenth-grade student achievement and teachers' use of class time. Findings suggest that while block scheduling is positively associated with teachers' use of multiple instructional methods and more individualized instruction, this scheduling reform has a negative impact on students' tenth-grade mathematics scores, controlling for other factors. Implications for educational productivity are discussed.     

INSTRUCTIONAL COHERENCE IN CHINESE MATHEMATICS CLASSROOM—A CASE STUDY OF LESSONS ON FRACTION DIVISION

In this study, we examined the instructional coherence in a Chinese mathematics classroom by analyzing a sequence of four videotaped lessons on the topic of fraction division. Our analysis focused on the characteristics of instructional coherence both within and across individual lessons. A framework was developed to focus on lesson instruction in terms of its content and process and the teacher's use of classroom discourse. The analyses of lesson instruction were further supplemented with the analyses of teaching materials and interviews with the teacher. The findings go beyond previous studies that mainly focused on a single lesson to provide further evidence about Chinese teachers' instructional practices and their possible impact on students' learning. In particular, the teacher tried to help students build knowledge connections and coherence through lesson instruction. Results also suggest that coherent curriculum and the teacher's perception of the knowledge coherence facilitated the teacher's construction of coherent classroom instruction.     

��Good�� mathematics teaching for students of color and those in poverty: the importance of relational interactions within instruction

In considering ??good teaching?? in mathematics, scholars usually refer to teacher knowledge and instructional practices that promote understanding. However, researchers have found that these two elements of instruction are often not as prevalent in urban contexts, a space where high percentages of students of color and the poor are educated. Additionally, recent work calls for understanding other classroom mechanisms that impact the mathematics learning of students of color. Using video, field notes, and an interview, this research examines a case study of one urban classroom of Latino and African American students. Their teacher engages them in substantive mathematics and reform-minded pedagogical strategies, but a number of relational interactions raise issues of how these micro-interactions can mediate access to mathematics. The study found four dimensions in which relational interactions mediated access to mathematics: addressing behavior, framing mathematics ability, acknowledging student contributions, and attending to culture and language. The paper ends with raising questions for future research and calling for a broader framing of instruction that incorporates relational dimensions of the classroom.     

Diversity and High Academic Expectations Without Tracking: Inclusively Responsive Instruction

This article presents an instructional model (inclusively responsive instruction) that takes advantage of student diversity in order to differentiate student learning while maintaining high expectations. In the history of U.S. education, diversity and academic rigor were often considered at odds, and educators tried to emphasize one at the expense of the other. This article uses a detailed set of examples from Japanese mathematics education to illustrate how diverse ideas, as important resources, can drive classroom instruction. Teaching and learning supports are described that are essential to helping all teachers balance group and individual learning in classrooms. Current U.S. instructional approaches and the model of inclusively responsive instruction are compared in terms of balancing diversity and academic expectations.     

Reading teachers’ knowledge of children’s literature and English phonology

We investigated relationships among elementary teachers’ reading-related content knowledge (knowledge of literature and phonology), their philosophical orientation toward reading instruction, their classroom practice, and their students’ learning. Correlations showed little relationship between instructional philosophy and content knowledge, and little relationship between instructional philosophy and classroom practice. However, relationships emerged between content knowledge and instruction, and between kindergarten teachers’ phonological knowledge and their students’ reading achievement. We recommend that the recent focus on teacher’s disciplinary knowledge be broadened to include teachers of beginning reading and that teachers be afforded opportunities to develop the necessary knowledge base to teach reading effectively.     

Self-regulated learning: Implications for the design of instructional media

This paper describes the implications of principles derived from cognitive social learning theory and Vygotsky's socially oriented developmental perspective for the design of technology-based instructional materials. Vygotsky's ideas about the kinds of experience that facilitate intellectual growth in the “zone of proximal development” suggest that contemporary mathematics instruction (usually characterized by presentations to large groups, or by individualized instruction dominated by worksheets) deny students opportunities for individual interaction with and supportive guidance by adult experts or competent peers. It is proposed that such instruction fails to support the transfer of regulatory responsibility from teacher to student. The derivation of design specifications for the use of instructional technologies to overcome these limitations of contemporary instruction in mathematics is described. Instructional materials designed to promote self-regulation strategies as well as procedural and declarative knowledge in mathematics are presented.     

Teachers’ enactment of policy in classrooms: making students accountable through inscriptions from the curriculum in classroom interactions

The purpose of this paper is to examine the complex relationships between educational policy and classroom practice. By employing a sociocultural perspective, we examine formulations inscribed in socio-material artifacts about what students should learn and how they should engage with knowledge. We explore how these formulations are mobilized in instructional work and the implications this activity has for student participation. To address this issue, we analyzed video data of how teachers invoke competence aims from the national curriculum in their instructional work in six classrooms. The analytical procedures were derived from interaction analysis. The analysis focuses on how such formulations explicitly mediate social interaction as it unfolds on a micro level. The findings show that competence aims gain different functions as they are mobilized in classroom practice; in other words, they serve different purposes in teachers’ instructional work and anticipate different modes of student participation. In this study, the competence aims were (a) invoked as a source of authority, (b) translated into instructions, and (c) mobilized to obtain social order in the classroom. More rarely, the competence aims were used in meta-level discussions, where they functioned to reach agreements on how to pursue work toward joint goals. We discuss the implications of these ways of invoking competence aims for student participation.

     

Toward a constructivist perspective: The impact of a mathematics teacher inservice program on students

A constructivist-oriented inservice program provided teachers of mathematics (K-12) with intensive two-week summer institutes and weekly classroom follow-up. Pre- and post-program data on student outcomes indicate that, along with transformations in the nature and quality of mathematics activity in the classroom, students' beliefs about learning mathematics changed and elementary students' attitudes toward mathematics improved. Although the instruction they now received focused more on conceptual understanding and less on computational skill, students' scores on standardized tests assessing routine knowledge were maintained.An earlier version of this paper appeared in R. Underhill (ed.),Proceedings of the Thirteenth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education 1, 43–49, Backsburg, VI.     

Exploring the impact of written reflections on learning in the elementary mathematics classroom

The authors examined the implementation of written reflections in a Grade 4 mathematics classroom over the course of 8 weeks. Students in this case study engaged in a workshop modeled after Calkin's Writers' Workshop and within this workshop the use of writing as a reflective tool in mathematics was introduced. The authors explore how students used writing to evaluate their learning and how the teacher used the students' written reflections as a formative assessment for instructional purposes. Students' written reflections were coded and these codes were used to conduct an inductive thematic analysis. Analysis of written reflections via constant-comparison analysis was used for further differentiation. The findings show students' ability to accurately self-evaluate their problem-solving skills and highlighted students' confidence level with certain mathematical concepts. Teachers were able to use students' reflections as a place to begin conferring with a student for further clarification. The written reflections aided in instructional decisions and increased individual instruction when needed. The authors include implications for teacher practice and areas for future research.     

Use of comics to enhance students’ learning for the development of the twenty-first century competencies in the mathematics classroom

Abstract

This paper discusses the use of comics in teaching mathematics in the secondary mathematics classroom. We explicate how the use of comics in teaching mathematics can prepare students for the twenty-first century competencies. We developed an alternative teaching package using comics for two lower secondary mathematics topics. This alternative teaching package consists of (1) several sets of comic strips expounding all related mathematical concepts in a lively way; (2) tiered practice questions for learning reinforcement; and (3) a set of proposed lesson outlines with suggestions on how to use the comics for mathematics teaching. We also report how one of the teachers in our study used this teaching package in her mathematics lessons. Her lessons were video-recorded and 11 students were interviewed to help us understand how the mathematics comics lessons were enacted and the students’ perception of comics as instruction. We identified instances in which the teacher tweaked the provided resource to further enhance student learning and incorporated elements of the twenty-first century competencies during her lessons. Through selected student interviews, we also identified instances in which students commented on their gain from the new approach from the perspective of the twenty-first century competencies.     

The meaning of mathematics instruction in multilingual classrooms: analyzing the importance of responsibility for learning

In the multilingual mathematics classroom, the assignment for teachers to scaffold students by means of instruction and guidance in order to facilitate language progress and learning for all is often emphasized. In Sweden, where mathematics education is characterized by a low level of teacher responsibility for students’ performance, this responsibility is in part passed on to students. However, research investigating the complexity of relations between mathematics teaching and learning in multilingual classrooms, as well as effect studies of mathematics teaching, often take the existence of teachers’ responsibility for offering specific content activities for granted. This study investigates the relations between different aspects of responsibility in mathematics teaching and students’ performance in the multilingual mathematics classroom. The relationship between different group compositions and how the responsibility is expressed is also investigated. Multilevel structural equation models using TIMSS 2003 data identified a substantial positive influence on mathematics achievement of teachers taking responsibility for students’ learning processes by organizing and offering a learning environment where the teacher actively and openly supports the students in their mathematics learning, and where the students also are active and learn mathematics themselves. A correlation was also revealed between group composition, in terms of students’ social and linguistic background, and how mathematics teaching was performed. This relationship indicates pedagogical segregation in Swedish mathematics education by teachers taking less responsibility for students’ learning processes in classes with a high proportion of students born abroad or a high proportion of students with low socio-economic status.     

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.     

Prospective teachers’ skills of attending,interpreting and responding to content-specific characteristics of mathematics instruction in classroom videos

This study explores prospective teachers’ skills of attending, interpreting and responding to content-specific characteristics of mathematics instruction in classroom videos. Prospective teachers analyzed the mathematics instruction of two teachers through four video clips and proposed alternative instructional ways to support the teaching and learning of mathematics. The results indicated that as prospective teachers examined the teachers’ instructional practices, they increased their level of attending and interpretation to content-specific aspects of instruction rather than focusing on generic dimensions of the instruction. When they watched and compared different characteristics of teachers’ mathematics instruction, they provided more detailed and mathematical instructional suggestions.     

The influence of video clubs on teachers’ thinking and practice

This article examines a model of professional development called “video clubs” in which teachers watch and discuss excerpts of videos from their classrooms. We investigate how participation in a video club influences teachers’ thinking and practice by exploring three related contexts: (a) teachers’ comments during video-club meetings, (b) teachers’ self-reports of the effects of the video club, and (c) teachers’ instruction across the year. Data analysis revealed changes in all three contexts. In the video-club meetings, teachers paid increased attention to student mathematical thinking over the course of the year. In interviews, teachers reported having learned about students’ mathematical thinking, about the importance of attending to student ideas during instruction, and about their school’s mathematics curriculum. Finally, shifts were also uncovered in the teachers’ instruction. By the end of the year, teachers increasingly made space for student thinking to emerge in the classroom, probed students’ underlying understandings, and learned from their students while teaching.     

Alignment, cohesion, and change: Examining mathematics teachers’ belief structures and their influence on instructional practices

This collective case study reports on an investigation into the relationship between mathematics teachers’ beliefs and their classroom practices, namely, how they organized their classroom activities, interacted with their students, and assessed their students’ learning. Additionally, the study examined the pervasiveness of their beliefs in the face of efforts to incorporate reform-oriented classroom materials and instructional strategies. The participants were five high school teachers of ninth-grade algebra at different stages in their teaching career. The qualitative analysis of the data revealed that in general beliefs were very influential on the teachers’ daily pedagogical decisions and that their beliefs about the nature of mathematics served as a primary source of their beliefs about pedagogy and student learning. Findings from the analysis concur with previous studies in this area that reveal a clear relationship between these constructs. In addition, the results provide useful insights for the mathematics education community as it shows the diversity among the inservice teachers’ beliefs (presented as hypothesized belief models), the role and influence of beliefs about the nature of mathematics on the belief structure and how the teachers designed their instructional practices to reflect these beliefs. The article concludes with a discussion of implications of teacher education.     

Associations between Fine Motor and Mathematics Instruction and Kindergarten Mathematics Achievement

Research Findings: This study investigates the role of fine motor and mathematics instruction in mathematics achievement in an international sample of kindergarteners from the United States and China. Multilevel modeling was used to assess the interaction between students’ entering skills and classroom time spent on basic math, higher-order math and fine-motor instruction. For American children, the effect of basic math and higher-order math instruction on student achievement depended on entering skills; however, fine motor instruction had negative average effects on student achievement and did not depend on students’ entering skills. Instruction time was not a significant predictor of achievement for Chinese students. Practice or Policy: Though fine motor skills have a robust correlation with mathematics achievement, a causal link has not been established. Our study indicates that time spent in fine motor instruction does not advance mathematics achievement in kindergarten and in fact may weaken mathematics achievement, given the limited time in the instructional day. American teachers in our sample who spent more time in fine-motor instruction tended to spend less time on basic math and higher-order mathematics instruction. Educators should weigh instructional trade-offs carefully and work to tailor instruction to students’ skill levels.     

A Conceptual Model (The Six Mirrors of the Classroom) and It’s Application to Teaching and Learning About Microorganisms

In this paper a conceptual model of instruction “the six mirrors of the classroom” used as a frame for teaching a learning topic, the microorganisms are depicted. The paper consists of four sections: (a) the six mirrors of the classroom model (SMC); (b) the SMC as implemented in the expository and cooperative modes of instruction in classrooms and results; (c) a “Journey of Inquiry into the Wonderful World of Microorganisms” (JIWWM), developed according to the Science–Technology–Environment–Peace–Society (STEPS) approach; and (d) teaching and learning the JIWWM, in ninth-grade classes, within the SMC model. The results show that science topic can be taught in the frame of the mirrors of the classroom. When the instructional goals of the teachers used the mirror “1, classroom organization” and mirror “6, pupils’ social behavior” and the third ring around the all six mirrors cooperative skills were practiced, academic outcomes were achieved, and attitudes toward environmental preservation and peace improved. The SMC model can serve as a valuable tool for teachers, since it can design their teaching and learning settings in a more controlled environment, in terms of objectives, teachers’ and students’ social behaviors, and academic outcomes.