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1.
As a key objective, secondary school mathematics teachers seek to improve the proof skills of students. In this paper we present an analytic framework to describe and analyze students' answers to proof problems. We employ this framework to investigate ways in which dynamic geometry software can be used to improve students' understanding of the nature of mathematical proof and to improve their proof skills. We present the results of two case studies where secondary school students worked with Cabri-Géeomèetre to solve geometry problems structured in a teaching unit. The teaching unit had theaims of: i) Teaching geometric concepts and properties, and ii) helping students to improve their conception of the nature of mathematical proof and to improve their proof skills. By applying the framework defined here, we analyze students' answers to proof problems, observe the types of justifications produced, and verify the usefulness of learning in dynamicgeometry computer environments to improve students' proof skills.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
2.
Various studies suggest that French students (grades 7 to 10) may solve geometric problems within a paradigmatic framework
that differs from that assumed by teachers, a situation prone to misunderstandings. In this paper, we study the extent to
which secondary school teachers recognise the conflicting paradigms and how they handle the geometric work conducted, in sometimes
unintended ways, by their students. This is done by analysing teachers’ reactions to specific answers students offered to
the Charlotte and Marie problem, an “ambiguous” problem with various solutions depending on the paradigm adopted. As a result
of the study, we found that, beyond similarities due to a shared mathematical background, the way secondary schoolteachers
handle students’ answers varies with their conceptions of geometric work. Implications are drawn regarding the teaching of
geometry and the training of teachers. 相似文献
3.
Fostering students' spatial thinking skills holds great promise for improving Science, Technology, Engineering, and Mathematics (STEM) education. Recent efforts have focused on the development of classroom interventions to build students' spatial skills, yet these interventions will be implemented by teachers, and their beliefs and perceptions about spatial thinking influence the effectiveness of such interventions. However, our understanding of elementary school teachers' beliefs and perceptions around spatial thinking and STEM is in its infancy. Thus, we created novel measures to survey elementary teachers' anxiety in solving spatial problems, beliefs in the importance of spatial thinking skills for students' academic success, and self-efficacy in cultivating students' spatial skills during science instruction. All measures exhibited high internal consistency and showed that elementary teachers experience low anxiety when solving spatial problems and feel strongly that their skills can improve with practice. Teachers were able to identify educational problems that rely on spatial problem-solving and believed that spatial skills are more important for older compared to younger students. Despite reporting high efficacy in their general teaching and science teaching, teachers reported significantly lower efficacy in their capacities to cultivate students' spatial skills during science instruction. Results were fairly consistent across teacher characteristics (e.g., years of experience and teaching role as generalist or specialist) with the exception that only years of teaching science was related to teachers' efficacy in cultivating students' spatial thinking skills during science instruction. Results are discussed within the broader context of teacher beliefs, self-efficacy, and implications for professional development research. 相似文献
4.
Martin Stanisstreet Dominic Dickson Edward Boyes 《International Journal of Science Education》2013,35(7):787-803
Studies exploring school students' views about science have not always distinguished between different branches of science. Here, the views of 1395 secondary school students aged 11–16 about physics and, as a science comparator, biology were determined using a closed‐form questionnaire. Over the period of secondary schooling a decreasing proportion of students expressed a liking for physics, fewer thought it was interesting and more thought it was boring. These changes did not apply to biology. There was an increasing view that the study of physics, but not biology, required mathematical skills. Fewer students thought that physics, compared with biology, could contribute to the solution of medical or environmental problems. Suggestions that physics might offer good employment prospects did not influence students' liking of physics. Factor analysis suggested that the oldest group of students distinguished between physics and biology in terms of their general characteristics – to the detriment of physics. 相似文献
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6.
Inquiry instruction often neglects graphing. It gives students few opportunities to develop the knowledge and skills necessary to take advantage of graphs, and which are called for by current science education standards. Yet, it is not well known how to support graphing skills, particularly within middle school science inquiry contexts. Using qualitative graphs is a promising, but underexplored approach. In contrast to quantitative graphs, which can lead students to focus too narrowly on the mechanics of plotting points, qualitative graphs can encourage students to relate graphical representations to their conceptual meaning. Guided by the Knowledge Integration framework, which recognizes and guides students in integrating their diverse ideas about science, we incorporated qualitative graphing activities into a seventh grade web-based inquiry unit about cell division and cancer treatment. In Study 1, we characterized the kinds of graphs students generated in terms of their integration of graphical and scientific knowledge. We also found that students (n = 30) using the unit made significant learning gains based on their pretest to post-test scores. In Study 2, we compared students' performance in two versions of the same unit: One that had students construct, and second that had them critique qualitative graphs. Results showed that both activities had distinct benefits, and improved students' (n = 117) integrated understanding of graphs and science. Specifically, critiquing graphs helped students improve their scientific explanations within the unit, while constructing graphs led students to link key science ideas within both their in-unit and post-unit explanations. We discuss the relative affordances and constraints of critique and construction activities, and observe students' common misunderstandings of graphs. In all, this study offers a critical exploration of how to design instruction that simultaneously supports students' science and graph understanding within complex inquiry contexts. 相似文献
7.
Dealing with representations is a crucial skill for students and such representational competence is essential for learning science. This study analysed the relationship between representational competence and content knowledge, student perceptions of teaching practices concerning the use of different representations, and their impact on students' outcome over a teaching unit. Participants were 931 students in 51 secondary school classes. Representational competence and content knowledge were interactively related. Representational aspects were only moderately included in teaching and students did not develop rich representational competence although content knowledge increased significantly. Multilevel regression showed that student perceptions of interpreting and constructing visual-graphical representations and active social construction of knowledge predicted students' outcome at class level, whereas the individually perceived amount of terms and use of symbolic representations influenced the students' achievement at individual level. Methodological and practical implications of these findings are discussed in relation to the development of representational competence in classrooms. 相似文献
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9.
Chan-Choong Foong Esther G.S. Daniel 《International Journal of Science Education》2013,35(14):2331-2355
This paper argues the possible simultaneous development and transfer of students' argumentation skills from one socio-scientific issue to another in a Confucian classroom. In Malaysia, the Chinese vernacular schools follow a strict Confucian philosophy in the teaching and learning process. The teacher talks and the students listen. This case study explored the transfer of argumentation skills across two socio-scientific issues in such a Form 2 (8th grade) classroom. An instructional support to complement the syllabus was utilised. The teaching approach in the instructional support was more constructivist in nature and designed to introduce argumentation skills which is uncommon in a Confucian classroom. The two socio-scientific issues were genetically modified foods and deforestation. This paper presents a part of the bigger case study that was conducted. Data collected from written arguments were analysed using an analytical framework built upon Toulmin's ideas. The whole class analysis indicated progression in students' argumentation skills in their ability to give more valid grounds and rebuttals during the transfer. The individual analysis suggests progression in the majority of students' performance, while several students demonstrated non-progression when they faced a different socio-scientific issue. 相似文献
10.
While proof is central to mathematics, difficulties in the teaching and learning of proof are well-recognised internationally. Within the research literature, a number of theoretical frameworks relating to the teaching of different aspects of proof and proving are evident. In our work, we are focusing on secondary school students learning the structure of deductive proofs and, in this paper, we propose a theoretical framework based on this aspect of proof education. In our framework, we capture students’ understanding of the structure of deductive proofs in terms of three levels of increasing sophistication: Pre-structural, Partial-structural, and Holistic-structural, with the Partial-structural level further divided into two sub-levels: Elemental and Relational. In this paper, we apply the framework to data from our classroom research in which secondary school students (aged 14) tackled a series of lessons that provided an introduction to proof problems involving congruent triangles. Using data from the transcribed lessons, we focus in particular on students who displayed the tendency to accept a proof that contained logical circularity. From the perspective of our framework, we illustrate what we argue are two independent aspects of Relational understanding of the Partial-structural level, those of universal instantiation and hypothetical syllogism, and contend that accepting logical circularity can be an indicator of lack of understanding of syllogism. These findings can inform how teaching approaches might be improved so that students develop a more secure understanding of deductive proofs and proving in geometry. 相似文献
11.
《Teaching and Teacher Education》1995,11(5):445-460
This research examined the context in urban high school physical education classes that influenced 10 teachers' conceptualizations of realistic educational goals for their students. Ethnographic data in the form of field notes and interviews were analyzed using constant comparison. Teachers reported that many students were unwilling to participate and were becoming progressively more difficult to teach. Teachers actively sought explanations for this behavior both in the students' backgrounds and their lack of interest in school. They identified inconsistencies between the school's educational mission and the students' aspirations for the future. Teachers reported substantial changes in their programs over their careers. Although they had begun their careers teaching skills and other knowledge-based curricula, the diversity and difficulties associated with teaching urban students had forced them to move from a curriculum of skills to a “curriculum” of motivation and order. Many of these programs exhibited characteristics of an elitist, discriminatory, and decontextual approach to curriculum. 相似文献
12.
Joanna Oldham 《English in Education》1999,33(1):36-46
This article concerns the ways in which moving image media enable secondary school students to improve their print literacy standards. It examines productive ways of using moving image media with literary texts to support and enhance the literacy skills of students. It contends that informed use of media enhances students' abilities in critically evaluating, consuming and producing texts and that engaging with print and media texts develops the literacy practices of students. 相似文献
13.
Iolie Nicolaidou Eleni A. Kyza Frederiki Terzian Andreas Hadjichambis Dimitris Kafouris 《科学教学研究杂志》2011,48(7):711-744
Assessing the credibility of evidence in complex, socio‐scientific problems is of paramount importance. However, there is little discussion in the science education literature on this topic and on how students can be supported in developing such skills. In this article, we describe an instructional design framework, which we call the Credibility Assessment Framework, to scaffold high school students' collaborative construction of evidence‐based decisions and their assessment of the credibility of evidence. The framework was employed for the design of a web‐based reflective inquiry environment on a socio‐scientific issue, and was enacted with 11th grade students. The article describes the components of the Credibility Assessment Framework and provides the details and results of an empirical study illustrating this framework in practice. The results are presented in the form of a case study of how 11th grade students investigated and evaluated scientific data relating to the cultivation of genetically modified plants. Multiple kinds of data were collected, including pre‐ and post‐tests of students' conceptual understanding and their skills in assessing the credibility of evidence, and videotapes of students' collaborative inquiry sessions. The analysis of the pre‐ and post‐tests on students' conceptual understanding of Biotechnology and their skills in assessing the credibility of evidence revealed statistically significant learning gains. Students' work in task‐related artifacts and the analysis of two groups' videotaped discussions showed that students became sensitive to credibility criteria, questioned the sources of data and correctly identified sources of low, moderate, and high credibility. Implications for designers and educators regarding the application of this framework are discussed. © 2011 Wiley Periodicals, Inc. J Res Sci Teach 48: 711–744, 2011 相似文献
14.
Eadaoin K.P. Hui 《Educational research; a review for teachers and all concerned with progress in education》2013,55(3):279-294
This paper is based on research investigating Hong Kong Chinese teachers' and students' perceptions of junior secondary students' concerns and of the causes of students' difficulties. Responses from 2,045 secondary students and 214 teachers revealed that both students and teachers had similar systems of beliefs about students' concerns and the causes of students' difficulties. As dimensions of most students' concerns, both groups referred to study and educational future; friendship; physical appearance; relationships at home, with peers and at school; and psychological well-being and maladjusted behaviour. Both groups in various degrees attributed students' difficulties to students themselves, the family, school or peers. Employing Moscovici's theory of social representation as a conceptual framework, the findings illustrated that students' concerns and causal attribution are social representations shared by both student and teacher groups. Mismatch between students' and teachers' perceptions was more a divergence of views than a disparity. Students' and teachers' different social identities and their protection of group self-esteem are offered as an explanation for the mismatch in perception. 相似文献
15.
This study investigated mathematics teachers' professional knowledge among elementary school teachers exposed to a professional training program that either supported self-regulated learning (SRL) or offered no SRL support (no-SRL). The SRL support was based on the IMPROVE metacognitive self-questioning method that directs students' attention to understanding when, why, and how to solve problems (Kramarski and Mevarech, Am Educ Res J 40:281–310, 2003). Sixty-four Israeli elementary teachers participated in a month-long professional development program to enhance mathematical and pedagogical knowledge. The course was part of a 3-year professional development program sponsored by the Israeli Ministry of Education. This mixed-method study included quantitative assessments of teachers' professional knowledge in mathematical problem solving for an authentic task based on Program for International Student Assessment's framework (Program for International Student Assessment, 2003) and in lesson planning, as well as qualitative interviews and videotaped observations of two teachers. Results indicated that teachers in the SRL program outperformed those in the no-SRL program on various problem solving skills (e.g., reflection and conceptual mathematical explanations) and lesson planning (e.g., task demands and teaching approach). Videotaped observations of actual teaching indicated that the SRL-trained teacher demonstrated more teaching practices that aimed to promote students' understanding and better supported students' regulation of their own learning, compared to the no-SRL-trained teacher. We discuss educational and practical implications. 相似文献
16.
夏咏梅 《上海教育评估研究》2016,5(3):64-69
在数学教学中,从农村初中学生的生活实际出发,通过挖掘和利用马鞍山市博望区的数学资源与教材资源进行有效整合研究,列出区域性数学资源与沪科版数学教材有效整合细目表。通过图片、例题、典型课例的形式,达到激发学生学习数学的兴趣,提高学生学习数学的积极性,体验数学与现实生活的紧密联系,鼓励学生能在生活中大胆地学数学、用数学,提高学生运用数学知识解决实际问题的能力,从而全面提高学生的数学素养。 相似文献
17.
Ana M. Correia Chris Forlin Eva Sio 《Journal of Research in Special Educational Needs》2022,22(3):288-296
The research explores the perceptions of five secondary school students with special education needs (SEN) about their participation in learning, group membership, and agency within an inclusive school in Macau SAR. This goal is achieved by using students' voices documented in open-ended interviews and is underpinned by the conceptual framework of heutagogy. The aim is to shed light on students' perceptions on school effectiveness in supporting their needs through successful participation and agentic possibilities. Findings showed that students were more prone to social rejection and being isolated or bullied than their peers. They were struggling to feel included or participate, their needs were only partially being met, and they had few opportunities to exert influence on their educational trajectories. Recommendations are provided to assist educators and schools in enhancing students with SEN to connect to the learning process and community, with the provision of appropriate learning adjustments and more active approaches to ensure their acceptance by mainstream students, including the formation of coaching peers to assist in developing social and academic skills under teacher's scaffolding practices. This study highlights the contribution of the heutagogical perspective to advance research on the participation and agency of students with SEN in mainstream schools. 相似文献
18.
Interactive dialogue within feedback episodes is essential for developing primary school students' mathematical reasoning competence. Our goal was to better understand the nature of the associations between observed dialogue, teachers' formative feedback, and students' mathematical reasoning. We applied a two-step approach, first constructing a video-analysis instrument for assessing the quality of interactive dialogues and then combining the interaction data with student and teacher questionnaire data from 804 students in 44 fifth and sixth grade primary school classes. The quality of the observed dialogues predicted class differences in students’ self-efficacy for explaining but not in their reasoning competence, which was predicted by perceived formative feedback. 相似文献
19.
Miroslav Lovric 《PRIMUS》2018,28(7):683-698
We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs, etc.), offers simulation and experimentation, invites discussions about structure, requires logic and testing strategies, and handles mathematics objects with an added feeling of reality. Focusing on novice and inexperienced programmers, we look for answers to the practice-oriented question, “How do students reason through their difficulties when using programming to explore a mathematics problem?” Following literature review and methodology, we build the programming model, which we use to study students' experiences as they approach a mathematical problem by writing computer code. Our research is based on analyzing students' in-class work and class notes, author's observations of students working on their computers, and his interactions with students in class and elsewhere. In the four case studies that we present we touch upon students' difficulties in working with complex conditional statements and recurrence relations. As well, we discuss cases where resolving a programming issue demands posing and answering mathematical questions. 相似文献
20.
中专信息技术课程的教学目的是让学生掌握信息技术的基础知识和基本技能,提升学生的信息技术素养。但中专计算机教学存在教学理念落后、教学模式单一、教材和新技术脱轨等问题。为有效提高中专学生的计算机应用能力,教师应在计算机教学中激发学生的学习兴趣,因材施教,弥补教材和新技术相脱轨的不足。 相似文献