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1.
Improving mathematics education in the United States has taken many forms. Our work has focused on two aspects: the content knowledge of teachers and a well-articulated coherent curriculum. Our aim was teacher “capacity building” that is enabling teachers to teach to coherent and significant mathematical curricular goals and describe the implementation in a large-scale project based at Michigan State University. We highlight the design, structure and use of mathematics teacher learning tasks that were intended to improve teachers’ capacity to teach to these goals and note how the teachers’ perceptions of the structure and sequencing of mathematics itself affect the ways they organize mathematics in their teaching and the ways they teach.  相似文献   

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Research has shown improvements in science, mathematics, and language scores when classroom discussion is employed in school-level science and mathematics classes. Studies have also shown statistically and practically significant gains in children’s reasoning abilities as measured by the Raven’s Standard Progressive Matrices test when employing the practice of “exploratory talk”. While these studies suggest that transfer of learning had taken place, a number of dialog-intensive designs have failed to find positive results, only reported delayed transfer, or have been criticized in terms of methodological rigor, small sample sizes, or because they have only shown small effect sizes. In this study, the claim is made that a particular set of studies which focused on exploratory talk and reasoning abilities, and which used designs that are better positioned to meet the standards mentioned above when presenting data in support of far transfer, provides robust evidence of far transfer within the framework of Barnett and Ceci’s taxonomy of transfer. Possible relationships between exploratory talk, argumentation, and key domains in the science of learning are considered in an attempt to explain the apparent far transfer effects when children engage in exploratory talk.  相似文献   

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We report on the development of an after-school and summer-based science, technology, engineering, and mathematics curriculum infused with the arts and social emotional learning content (STEAM SEL). Its design was motivated by theory and research that suggest that STEM education is well-suited for teaching empathy and other emotion-related skills. In this paper, we describe the activities associated with the development and design of the program and the curriculum. We provide expert-ratings of the STEAM and social emotional elements of the program and present instructor and participant feedback about the program’s content and its delivery. Our results revealed that infusing the arts and social emotional learning content into science education created a holistic STEM-related curriculum that holds potential for enhancing young children’s interest in and appreciation for science and its applications. The data also suggested that the program was well-developed and, generally well-executed. However, experts rated the STEAM elements of the program more positively than the SEL elements, especially with regard to sequencing of lessons and integration among the lessons and hands-on activities, indicating that program revisions are warranted.  相似文献   

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Children's informal and formal learning experiences with geometric shapes currently result in misconceptions that persist into adulthood. Here, we combine research from mathematics education as well as cognitive science pertaining to concepts, categories, and learning strategies to propose a more optimal progression that is better specified and justified than the current standards. To do so, we reframed what constitutes a “simple” shape from perceptual simplicity to simplicity of properties. Our Property-Based Shape Sequence uses property-based criteria of what makes shapes “simple” and progresses in a way that affords opportunities for learners to develop hierarchical conceptions of two-dimensional and three-dimensional shapes. Our goals are threefold: (1) recommend an optimal, mathematically-correct shape learning sequence, (2) correct misconceptions that adults and children harbor about shapes, and (3) encourage cross-disciplinary collaborations between mathematics education and psychology researchers to validate the proposed learning sequence.  相似文献   

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We illustrate and exemplify how the idea of reflection is framed by the enactive concept of “deliberate analysis”. In keeping with this frame, we do not attempt to define reflection but rather work on the question of “how do we do reflecting?” within such a frame. We set out our enactivist theoretical stance, in particular pointing to implications for how we can learn from experience and showing the role of “deliberate analysis”. We then describe, drawing on education literature, what is generally seen as the purpose of reflection and review some existing conceptualizations in mathematics education, pointing out where we draw distinctions. To illustrate how we do reflecting, we offer excerpts from two lessons of an expert teacher and the writing of a prospective teacher. We exemplify how reflecting as deliberate analysis leads to a way of working with teachers supporting them in handling multiple views and ambiguity, their actions being contingent upon their students’ actions in learning mathematics.  相似文献   

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Although skilled mathematics teachers and teacher educators often “know” when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students’ mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are key to instruction that builds on student thinking about mathematics. Video of beginning secondary school mathematics teachers’ instruction was analyzed to identify and characterize PTMs in mathematics lessons and to examine the relationships among the PTMs, the teachers’ decisions in response to them, and the likely impacts on student learning. These data were used to develop a preliminary framework for helping teachers learn to identify and respond to PTMs that occur during their instruction. The results of this exploratory study highlight the importance of teacher education preparing teachers to (a) understand the mathematical terrain their students are traversing, (b) notice high-leverage student mathematical thinking, and (c) productively act on that thinking. This preparation would improve beginning teachers’ abilities to act in ways that would increase their students’ mathematical understanding.  相似文献   

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We discuss contemporary theories in mathematics education in order to do research on research. Our strategy consists of analysing discursively and ideologically recent key publications addressing the role of theory in mathematics education research. We examine how the field fabricates its object of research by deploying Foucault’s notion of bio-politics—mainly to address the object “learning”—and ?i?ek’s ideology critique—to address the object “mathematics”. These theories, which have already been used in the field to research teaching and learning, have a great potential to contribute to a reflexivity of research on its discourses and effects. Furthermore, they enable us to present a clear distinction between what has been called the sociopolitical turn in mathematics education research and what we call a positioning of mathematics education (research) practices in the Political.  相似文献   

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Instructional practice plays a significant role in understanding teachers’ pedagogical content knowledge (PCK). The aim of the study reported on was to compare mathematics and technology pre-service teachers’ knowledge of PCK. The study used a case study approach of five mathematics and five technology pre-service teachers with a total of ten. Data was collected in seven public schools around Gauteng province in South Africa. The observation technique was employed in order to understand students’ classroom practice, using a video camera to capture the setting. One lesson of 45 minutes presented by each pre-service teacher, rendering a total of ten lessons, was observed. The study adapted the theoretical framework of PCK (Shulman 1987). The study scrutinised the data based on the qualitative content analysis method and found that most pre-service teachers in both mathematics and technology possess a limited knowledge of PCK. In both subjects, most of the pre-service teachers’ classroom practice did not exhibit comprehensive knowledge of the subject matter or knowledge of the learners. However, the difference is that only mathematics pre-service teachers have some knowledge of assessment. The data also indicate that “9E” instructional practice can be a valuable tool to enhance field-specific PCK within the field of mathematics and technology education subjects. Therefore, the study proposes further investigation of the “9E” instructional model that could be used as field-specific PCK within the fields of mathematics, science and technology.  相似文献   

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分析了新时期德育工作实效性不强问题出现的原因,提出了“做为人师表的表率,起好示范带头作用”、“走进学生的心灵世界,进行师生间精神对话”、“加强班级文化建设,铸造班级灵魂”等三个方面的做法,以提高德育工作的实效性。  相似文献   

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Teacher education is in the grip of change. Due to the new Australian Curriculum, no longer is it possible to plan and implement lessons without considering the inclusion of Information and Communication Technologies. Simply knowing about the latest technology gadgets is not enough. Information literacy is essential in today’s information-rich learning and working environment. Students and teachers must be able to engage with diverse learning technologies efficiently and effectively in the search for the “right information” at the “right time” for the “right purpose”. Key information literacy and inquiry skills have been recognised as vital learning goals by the Australian Curriculum Assessment and Reporting Authority and the International Society for Technology in Education and are thus critical in science teacher education. This paper examines the overlap of technology, pedagogy and science content in the Technological Pedagogical and Content Knowledge (TPACK) framework and its affordances for science educators, at the intersection between technology knowledge, science pedagogy (information literacy and inquiry) and science content knowledge. Following an introduction of the TPACK framework for science education, the paper reports the research findings, which illustrate that 90% of pre-service teachers thought the experimental unit improved their understanding of the inquiry process, 88% reported more confidence in their understanding of science concepts and 94% of students reported an increase in their knowledge and confidence of Web 2.0 tools in supporting scientific inquiry in science. The implications of this study are that the online inquiry improved students’ knowledge and confidence in the skills and processes associated with inquiry and in science concepts.  相似文献   

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The current reform movement in mathematics education urges teachers to support students as they make sense of mathematics, while also ensuring that they gain specific mathematical skills and knowledge. The tension between these two expectations gives rise to what we call the dilemma of telling: how to ensure that students come to certain mathematical understandings, without directly telling them what they need to know or do. Our study focused on how two middle school mathematics teachers who were incorporating many aspects of reform mathematics into their instruction responded to this dilemma. Data sources include classroom observations and videotapes of lessons over a three-year period. We found that both teachers devoted the majority of class time to student conversations, both small group and whole class; however, the teachers strategically entered the student-dominated conversations by “telling” to meet specific curricular goals.  相似文献   

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In several of his works, Alfred North Whitehead (1861–1947) presents mathematics as a way of learning about general ideas that increase our understanding of the universe. The danger is that students get bogged down in its technical operations. He argues that mathematics should be an integral part of a new kind of liberal education, incorporating science, the humanities, and “technical education” (making things with one’s hands), thereby integrating “head-work and hand-work.” In order to appreciate the role mathematics plays in modern science, students should understand its diverse history which is capable of bringing abstract ideas to life. Moreover, mathematics can discern the alternating rhythms of repetition and difference in nature constituting the periodicity of life. Since these same rhythms are to be found in his theory of learning as growth, there appears to be a pattern linking Whitehead’s approach to mathematics and his educational philosophy.  相似文献   

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This mixed methodology action research study examined the impact of a curricular innovation designed to provide an authentic science inquiry learning experience for 15 secondary science teacher candidates enrolled in a master’s level initial certification program. The class investigated the question “How can peak autumn color in New England be determined?” The project goals were to help teacher candidates acquire the skills, knowledge, and dispositions necessary to foster learning through inquiry in their respective content areas as defined by teacher preparation professional standards. Though the teacher candidates were successful at identifying a likely answer to the question, the project failed to achieve its learning goals. Reasons for the project’s failure and implications for the science education community are discussed.  相似文献   

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A questionnaire was issued to 18 girls undertaking their Year 12 studies at an Australian private Catholic boys’ day school of 700 students. The questionnaire encompassed several factors in regard to gender issues and differentiation in education — subject choices, career ambitions, interaction between the sexes, female friendships, perception of gender differentiation and stereotyping in teaching styles and school structures. The girls were also asked to consider various feminist principles in relation to personal future goals. The theoretical framework within which the study was conducted was Schutz's notion of the “stranger” attempting to interpret and accommodate to the “cultural patterns” of the “approached group”; of the “thinking‐as usual” of the “foreign group” confronting that of the “approached group” and its “unquestioned and unquestionable reality”. The results indicate the girls’ high level of awareness of gender differentiation amongst peers, teachers and in‐school structures; criticism of and unwillingness to accept the new “cultural pattern”; and a modelling of their future lives along liberal feminist principles.  相似文献   

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Children’s growth and fixed intelligence mindsets in mathematics are noted as important sources of mathematics motivation and achievement. Nuanced beliefs about the malleability of mathematics intelligence that lie between fixed and growth mindsets may also be important to consider for children’s mathematics learning, yet little is known about whether children endorse these in-between beliefs and how they fit in the popular growth and fixed mindset framework. In this study, we investigated nuanced mindsets in mathematics, which we term “mixed” intelligence mindsets, alongside fixed and growth mindsets in a sample of 698 third-grade students in the United States. Factor analyses using data from a newly developed mathematics intelligence mindset scale indicated good and similar fit of three multidimensional models. Two of these models included mixed mindset items, one with a combined growth and mixed mindset factor and another with a separated mixed mindset factor. Strong positive correlations were found between the growth and mixed mindset factors. Mathematics achievement had a moderate positive correlation with mixed mindset and a moderate negative correlation with fixed mindset. These correlations were both significantly stronger than the small correlation between mathematics achievement and growth mindset. Our findings suggest mathematics intelligence mindset is multidimensional and the addition of a mixed mindset aspect could improve the adequacy and precision of the conceptualization and measurement of the growth mindset dimension. In practice, mixed mindsets may provide teachers and parents with more flexible messages to present to children when encouraging them to engage in adaptive achievement behaviors in mathematics.  相似文献   

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维特根斯坦在《逻辑哲学论》中关于“自我”概念的讨论,集中于5.6命题及其子命题,主要论述他所说的“哲学的我”或“形而上学主体”概念。通过考察各命题之间的逻辑关系以及当代解释者提出的各种观点,我们看到,只能在逻辑形式框架下讨论“世界”和“语言”概念,确认两者之间的逻辑链接点,才能真正理解维特根斯坦的真实思想。根据维特根斯坦在5.6命题表达的核心观点,自我处于一个界限上,自我本身就是界限,它规定了我们可以用语言去谈论和言说的范围。由于逻辑规定了可说与不可说的界限,逻辑概念与自我概念就是同一个概念,逻辑即自我。因此,维特根斯坦在书中所讨论的自我概念应当是一个逻辑自我概念。  相似文献   

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