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This article reports on the last of a series of iterative research studies involving students with learning disabilities in reform mathematics classrooms at the intermediate grade levels. This study reports the findings from a larger, year‐long case study that focused on ways to include students with learning disabilities and other students who are at risk for special education services in classwide discussions of problem solving. The data reported in this article detail the changes in teacher and student discourse over a nine‐week period in one classroom. Sources of data for this study included videotapes, audiotapes, and informal interviews with the teacher, a paraprofessional, and students. A quantitative analysis of the results indicates clear patterns of change in teacher and student discourse. Nonetheless, intentional efforts to include target students in the whole‐class discussions yielded instructional dilemmas that are underdescribed in the mathematics reform literature. Findings from this study have implications for special educators interested in mathematical problem solving, as well as math reformers who value the role of classroom discourse in daily instruction.  相似文献   

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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.  相似文献   

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Considering the rising proportion of English learners (ELs) in general education, little is known about how this change in classroom composition relates to the frequency of instructional activities and skills. This study uses a multimodal perspective on learning mathematics in a multilingual context, which recognizes the diverse modes of communication that students draw on in mathematics classrooms. We examined national data using quantitative analyses and investigated the mathematics practices that were more likely to occur in kindergarten classrooms that did and did not have ELs. We found teachers reported greater frequency of manipulatives and count/calendar activities in mathematics instruction when there were EL students in the classroom. Teachers in classrooms with ELs also reported a greater frequency of mathematics content that involved teaching shapes and practical skills. The findings indicate that teachers tended towards a supportive multimodal approach to instruction when ELs were present.  相似文献   

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In his 1976 book, Proofs and Refutations, Lakatos presents a collection of case studies to illustrate methods of mathematical discovery in the history of mathematics. In this paper, we reframe these methods in ways that we have found make them more amenable for use as a framework for research on learning and teaching mathematics. We present an episode from an undergraduate abstract algebra classroom to illustrate the guided reinvention of mathematics through processes that strongly parallel those described by Lakatos. Our analysis suggests that the constructs described by Lakatos can provide a useful framework for making sense of the mathematical activity in classrooms where students are actively engaged in the development of mathematical ideas and provide design heuristics for instructional approaches that support the learning of mathematics through the process of guided reinvention.  相似文献   

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Abstract. This article presents three in‐depth case studies focused on supporting students with learning challenges to learn math strategically. Participants were three eighth‐grade students enrolled in a learning assistance classroom who were of at least average intelligence but who were performing significantly below grade level in mathematics. These case studies document the processes by which these students were supported to self‐regulate their learning in mathematics more effectively. We begin by outlining important instructional foci in mathematics education for intermediate or secondary students with learning disabilities, along with what research indicates are effective instructional processes. In that context, we introduce the theoretical principles underlying the instructional model used here—Strategic Content Learning (SCL). Based on analyses of case study data, we describe how SCL instruction was structured to promote strategic learning. Throughout the discussion, intervention processes are described in sufficient detail to be of use to practitioners.  相似文献   

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Increasingly, instructional improvement efforts include teacher communities as part of their overall strategy, yet the relationship between teachers’ talk and professional learning remains underspecified. Using a discourse perspective on learning, this article compares opportunities to learn (OTLs) in the collaborative conversations of 3 mathematics teacher workgroups. We examined the differences in OTLs in 17 hr of videotaped meetings from 3 groups at different levels of instructional accomplishment in secondary mathematics. Using mixed methods, we uncovered differences in the groups’ interactions and found that OTLs were not equally distributed. Instead, teacher groups whose active participants demonstrated the greatest facility with ambitious instruction also had the richest conversational OTLs. We interpret this as an accumulated advantage developmental story: Because collaborative work in teaching involves problem posing and the articulation of practice, teachers’ conceptions get built into the framing and discussion of pedagogical problems. Accomplished teachers are thus positioned to learn more from talking with colleagues. This analysis contributes to understanding of how OTLs are constituted in teacher workgroups, with implications for making better use of teacher collaboration for professional learning.  相似文献   

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Emotions are central to how students experience mathematics, yet we know little about how specific instructional practices relate to students’ emotions in mathematics learning. We examined how dialogic instruction, a socially dynamic form of instruction, was associated with four learning emotions in mathematics: enjoyment, pride, anger, and boredom. We also examined whether these associations differed by student gender and prior mathematics achievement. The sample consisted of 1307 sixth through eighth grade students (51.6% female, 59.0% White, 30.8% African American, and 10.3% other race; 42.3% receive free/reduced price lunch) from 70 mathematics classrooms. Results indicated that teachers who used more dialogic mathematics instruction had students who reported more enjoyment and pride, and less anger and boredom. Males and low-achieving students reported more positive and fewer negative emotions with greater dialogic instruction compared to their female and high-achieving counterparts.  相似文献   

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Creating a classroom learning environment that is suitably designed for promotion of learners’ performance in geometry, a branch of mathematics that addresses spatial sense and geometric reasoning, is a daunting task. This article focuses on how grade 8 teachers’ action learning changed the learning environment for the promotion of geometry teaching. This was an exploratory study in which a sample of 13 grade 8 mathematics teachers from the rural schools of a district in the Eastern Cape Province in South Africa participated in a project aimed at creating mathematical learning environments through action learning while supporting and promoting the teaching of geometry. The study was qualitative and data was collected using questionnaires, classroom observations and semi-structured interviews with the teachers on a participatory action research conducted in two cycles. Results indicated that 92% of teachers changed their classroom environments by modifying instructional strategies, learner -interactions, and engagements, but could not change how they managed the classrooms due to some factors related to power dynamics andthe education policy. It is recommended that teachers be workshopped on modifying their classroom learning environments while they undergo learning in action on the promotion of teaching and learning geometry in their school defining contexts.  相似文献   

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ABSTRACT

The author examined whether mathematics instruction provided by kindergarten teachers is related to children's mathematics learning during the kindergarten year based on the children's socioeconomic status and race. Hierarchical linear modeling was employed using a large sample of kindergarten students to estimate relationships between the teacher's instructional approach (e.g., concrete-spatial, interpersonal, linguistic) and children's mathematics skills. Results showed that the teacher's instructional approach was selectively related to children's mathematics learning. Students in classrooms where teachers frequently employed a concrete-spatial instructional approach learned more during the kindergarten year. Students from lower socioeconomic backgrounds benefitted more from teachers who often employed an interpersonal approach, and Black/African American students benefitted less from classrooms where teachers relied more on a linguistic approach. The findings suggest that kindergarten teachers’ instruction needs to employ varied methods that take into account students’ mathematics skills and background characteristics.  相似文献   

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This study explored the design and implementation of the Cover-up and Un-cover games, two manipulative-based fraction games, in 14 fifth-grade classrooms. We examined how the fraction concepts were integrated into the game design and explored the nature of teacher-student interactions during games using lesson videos. Our examination showed that interactions focused on game progress, rules, and turn taking with little exploration of strategies or the underlying mathematics. To compare the quality of teacher-student interactions during games with interaction quality during other instructional activities, we coded 5 videotaped lessons from each of the 14 classrooms. Statistical results from a dependent t test indicated that teacher-student interactions were of statistically significant lower quality during games than during non-game segments with similar instructional purpose. Teachers might benefit from additional curriculum support and training to implement games as rich mathematical learning opportunities.  相似文献   

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漆跻遥 《天津教育》2021,(9):110-111
目前大多数小学开始注重学生的学习质量问题,尤其是在核心素养的指引下,小学的数学教学方式需要突破传统,关注学生的学习状态和方法,在课堂上教师要激发学生对数学学习的兴趣和爱好。本文主要是从小学数学教学创新的重要性,然后探讨了在当前小学数学教学呈现的问题,提出了相应的解决措施和方法,为小学的数学课堂创建更好的学习氛围。  相似文献   

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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.  相似文献   

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Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture-oriented mathematics instruction to inquiry-based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision-making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi-dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms.  相似文献   

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Abstract

The effects of 3 instructional methods on mathematical reasoning were investigated. The methods are (a) cooperative learning embedded within multilevel metacognitive training (MMT), (b) cooperative learning embedded within unilevel metacognitive training (UMT), and (c) learning in the whole class with no metacognitive training. MMT was implemented in mathematics and English classrooms; UMT was used only in mathematics classrooms; and the whole class with no metacognitive training served as a control group. Results indicated that students who were exposed to MMT significantly outperformed their counterparts who were exposed to UMT who, in turn, significantly outperformed the control group. Effects of MMT were observed on students while they solved mathematical problems. Theoretical and practical implications of the study are discussed.  相似文献   

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ABSTRACT

Proving a child has been adequately educated is manifest through assessments evaluating the recall of facts or the deciphering of codes. How this information is taught and learned is the issue. Webb's depth of knowledge (DOK) and Bloom's taxonomy are cognitive models that drive instruction in today's classrooms. According to these models, creativity is a higher-order learning process. Although creativity has gained a renewed prominence in theoretic academic arenas, on the battleground of the typical classroom, creativity takes a back seat to instructional strategies with the goal of successful standardization of knowledge. Creativity, however, is the cornerstone of arts instruction. Creative learning principles (CLPs) is a system of instructional tasks developed in the arts and used to facilitate the metacognitive act of learning through creativity to solve problems. This article discusses how the CLPs create rhizomatic learning by facilitating connections between art and other disciplines and how they are used in planning.  相似文献   

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This article explores how individualized teaching methods, such as the use of work plans, create new student strategies in Norwegian lower secondary classrooms. Work plans, which are frequently set up as instructional tools in Norwegian classrooms, outline different types of tasks and requirements that the students are supposed to do during a specific period of time, normally two or three weeks. The current analyses shed light on what strategies girls and boys use when they approach work plans. Analyses of video observations and interviews with 93 students indicate that while girls tend to complete their plan during the first week or distribute the tasks evenly throughout the period, boys either finish the plan during the first week or postpone their work until the last few days. These findings suggest that the use of work plans might give some students, often low-achieving boys, too much responsibility for their own learning.  相似文献   

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Integrating state-of-the-art computer technologies with pedagogically sound practice provides interesting challenges and potentially significant opportunities to simultaneously promote and examine learning in context. This paper unfolds in 3 parts. We begin by introducing the reader to contemporary theories of self-regulation. We present a 4-phase model of self-regulating and a sparse literature on instructional design for SRL. Second, we build on this theory to describe features of CoNoteS2 (a prototype electronic notebook) that support self-regulation through tacit and explicit scaffolding. And finally, we describe the role of CoNoteS2 in researching about how students self-regulate their own learning. Our intent is to illustrate how contemporary learning theory can be used to drive instructional innovation and technological enhancement for the classroom.  相似文献   

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