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1.
要教好线性代数课程,其核心问题就是要通过课堂教学,使学生理解相关的数学知识;训练和培养学生的思维能力以及数学交流能力;帮助学生寻找新旧知识之间的内在联系,使知识系统化;在巩固已有知识的基础上,让学生自己去发现新知识.要实现这一教学目标,训练学生掌握"数学证明"的概念和在实践中的应用至关重要.传统的做法往往是通过"定义一引理一证明一定理一证明一推论"这种复杂的、程序化方法来进行训练的.由于在初等代数课程中,学生很少接受严格数学证明的训练,所以这种俗套的做法成效甚微.相反,如果把线性代数的主题和概念用一种完全合理的探究式方法来引入,那么数学证明的概念和架构将牢固植根于学生的头脑,并且这种思维习惯将对他们后续课程的学习和掌握公理化推理方法都会有很大帮助. 相似文献
2.
Markku Kankkunen 《Learning Environments Research》2001,4(3):287-324
This article grapples with the problem of how to track a student's real progress in learning, which cannot be absolutely quantified
at any given point as a result of a particular intervention. Results are presented for a long-term qualitative and quantitative
classroom study, during which the method of concept mapping was applied and interpreted in light of the semiotic paradigm
developed by Charles Sanders Peirce (1931–1958). Peirce's semiotic paradigm was thought to have sufficient intellectual rigour
and flexibility to give new access to the multiplicity of processes at work in the learning environment.
A natural learning environment was built over a four-year period in a Finnish primary school. The students, ranging in age
from 9–12 years, were encouraged to use qualitative judgement (intuition, tacit knowledge) to give them greater intellectual
access to the meanings of the concepts taught. The goal was to bring them to Vygotsky's stage of ‘conceptual learning’, and
to evaluate the effectiveness of concept mapping as an ‘advance organiser’ used in conjunction with Peirce's semiotic paradigm.
This article evaluates the success of concept mapping in constructing a conceptually-meaningful learning environment. The
qualitative results - and certain quantitative evidence - show that concept mapping provided a means for students to discover
tentative meanings for the concepts taught. In parallel, Peirce's semiotic paradigm provided a pragmatic framework for tracking
the process of ‘updating meanings’ which is intrinsic to learning.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
Perry den Brok Sibel Telli Jale Cakiroglu Ruurd Taconis Ceren Tekkaya 《Learning Environments Research》2010,13(3):187-204
The purposes of this study were to examine how Turkish students perceived their biology classroom environment, how their perceptions
compared to those of students in other countries, and what classroom learning environment profiles could be discerned in Turkish
high school biology classrooms. Data were gathered from 1,474 high school students in four inner city schools, in Bursa, Turkey.
A total of 11 biology teachers participated in the study with 52 of their classes. Data on students’ perceptions of their
learning environment were collected with the What Is Happening In this Class? (WIHIC) questionnaire. Results indicated that
Turkish classrooms were perceived as being low in terms of Teacher Support and high in terms of Task Orientation. Six distinct
classroom learning environment profiles were found: the ‘self-directed learning classroom’, ‘task-oriented cooperative learning
classroom’, ‘mainstream classroom’, ‘task-oriented individualised classroom’, ‘low-effective learning classroom’ and ‘high-effective
learning classroom’. The most common profile was the ‘mainstream classroom’ for which all WIHIC scales had medium–high scores. 相似文献
4.
Michael Fullan in 1991 made the comment that little was known about how students viewed educational change, as no one had
thought to ask them. There is a small but growing literature seeking the views of students on a range of issues associated
with schooling. This paper reports the findings of a study of students’ perceptions of top–down educational change, involving
school amalgamations, closures and creation of middle schools. The policy process was purportedly to involve consultation
with students. The study interviewed students to explore the nature and extent of their participation in the policy enactment
and their views about the changes. Several meta level themes emerged from the students’ ‘voices,’ including issues associated
with disempowerment, and competing social justice and economic discourses. The findings foreground the often messy and contradictory
tensions evident in policy processes. The study found that despite the policy intent to include students, they continued to
be the ‘objects’ of policy initiatives, submerged in what Freire labelled a ‘culture of silence.’ It was the macro level policy
elite who exerted the most influence, using their power, privilege and status to propagate particular versions of schooling.
The paper concludes that students are deeply impacted by educational change and they want to participate in restructuring
agendas. Therefore policy makers at all levels need to make spaces for the active engagement of students in policy processes. 相似文献
5.
Vasilios Grammatikopoulos Nikolaos Tsigilis Athanasios Koustelios Yannis Theodorakis 《International Review of Education/Internationale Zeitschrift für Erziehungswissenschaft/Revue internationale l'éducation》2005,40(5):427-438
The aim of this study was to develop an instrument for evaluating how an education program has been implemented. Such evaluation
can provide insight into the effectiveness of a program. Examined here was the Olympic Education Program used in Greek schools
since 2000. In it, students learn the history of the Olympic games and the importance of exercise for health along with the
principles and values of sports and volunteerism. The evaluation instrument underlying this study addressed the following
six factors: ‘facilities’, ‘administration’, ‘educational material’, ‘student–teacher relationships’, ‘educational procedures’,
and ‘training’. Results indicate that the instrument, while adequate for assessing effectiveness, should be combined with
advanced statistical methods. 相似文献
6.
This study investigates the mechanisms of scaffolding in a synchronous network-based environment – the ‘collaborative virtual
workplace’. A theoretical ‘multi-actor’ scaffolding model was formulated. The study itself focused on the role and inter-relations
of verbal scaffolding by tutor and peers during a collaborative process of making decisions about environmental issues. The analysis drew on data from the decision-making
discussions of 31 groups – material that was saved automatically by the learning environment software. The age of the 62 students
ranged from 14 to 17. Discourse act categories were devised to describe the tutor’s and the students’ task-related, supportive
and social communicative acts. The scaffolding situation was characterized through a causal discourse act interaction approach.
Tutor and students appeared to be elaborating and replacing each other’s process scaffolding acts in the collaborative decision-making
situation. The influence of certain tutor’s and students’ inter-related scaffolding patterns on students’ decision-making
provided empirical support for the ‘multi-actor’ scaffolding model.
in final form: 12 May 2005 相似文献
7.
8.
In an era of rapid global economic and social change, educational institutions like schools and universities are struggling
to keep their curricula and programs relevant. Singapore’s schools are no exception, especially when education is viewed as
the essential element for maintaining the nation’s global competitiveness in ways that are totally disproportionate to its
size. The current shift from an ‘efficiency-’ to an ‘ability-’ driven paradigm in education, however, is increasing uncertainty
and raising the stakes in an already pressurized system where schools, educators and students constantly compete for top academic
awards and rewards. The concept of “partnership” in Singapore education is a significant, relatively new, trend that has caught
on among local schools only since the late-1990s, with the focus on creating better “total” learning environments for students.
This paper analyses the challenges of matching rhetoric with professional practice with regard to school–home partnerships
in Singapore, and concludes that the key to authentic collaboration lies in the mutual appreciation and valuing of diversity
as well as a deep sense of shared responsibility by all parties concerned. 相似文献
9.
The theory of dialogism, developed by the Russian linguist Mikhail Bakhtin (1895–1975) with regard to literature and everyday
communication, can be used to improve the teaching of science. Some of Bakhtin's conceptual instruments are helpful in analysing
the teaching process, and it is interesting to compare them with former ideas about teaching and learning, especially with
the points of view of other constructivists. Together with Lev Vygotsky's analysis of thought and language, Bakhtin's dialogism
shows how teachers can support students effectively by addressing them as producers of a meaningful picture of the world.
The differences between ‘dialogic’ teaching and the well-known ‘Socratic’ method are shown and analysed, as are Bakhtin’s
discussions of a
‘carnivalistic’ approach to the students. 相似文献
10.
Stuart Rowlands 《Science & Education》2010,19(1):55-73
There appears to be a widespread assumption that deductive geometry is inappropriate for most learners and that they are incapable
of engaging with the abstract and rule-governed intellectual processes that became the world’s first fully developed and comprehensive
formalised system of thought. This article discusses a curriculum initiative that aims to ‘bring to life’ the major transformative
(primary) events in the history of Greek geometry, aims to encourage a meta-discourse that can develop a reflective consciousness
and aims to provide an opportunity for the induction into the formalities of proof and to engage with the abstract. The results
of a pilot study to see whether 14–15 year old ‘mixed ability’ and 15–16 year old ‘gifted and talented’ students can be meaningfully
engaged with two such transformative events are discussed. 相似文献
11.
Juan Pablo Mejia-Ramos Evan Fuller Keith Weber Kathryn Rhoads Aron Samkoff 《Educational Studies in Mathematics》2012,79(1):3-18
Although proof comprehension is fundamental in advanced undergraduate mathematics courses, there has been limited research
on what it means to understand a mathematical proof at this level and how such understanding can be assessed. In this paper,
we address these issues by presenting a multidimensional model for assessing proof comprehension in undergraduate mathematics.
Building on Yang and Lin’s (Educational Studies in Mathematics 67:59–76, 2008) model of reading comprehension of proofs in high school geometry, we contend that in undergraduate mathematics a proof is
not only understood in terms of the meaning, logical status, and logical chaining of its statements but also in terms of the
proof’s high-level ideas, its main components or modules, the methods it employs, and how it relates to specific examples.
We illustrate how each of these types of understanding can be assessed in the context of a proof in number theory. 相似文献
12.
Economic success is an aim of governments around the world. Their ‘human capital’ stance towards higher education implies
the need to develop graduates’ capabilities to the full. The concept of graduate ‘employability’, currently being developed
in the light of theory and empirical data, is beginning to find acceptance in the UK. One of the keys to its acceptability
in higher education has been the alignment of employability with good learning – that is, learning that is manifested in complex
outcomes. However, the achievement of complex outcomes requires a programme-level focus, rather than a focus on individual
study units. This article reports on the way such a programme-level approach was adopted in four different universities in
the UK, and how relatively small-scale actions have the potential to augment students’ employability. The implications for
policy at the levels of the system, the higher education institution and the academic department are discussed. 相似文献
13.
Current reform-driven mathematics documents stress the need for teachers to provide learning environments in which students
will be challenged to engage with mathematics concepts and extend their understandings in meaningful ways (e.g., National
Council of Teachers of Mathematics, 2000, Curriculum and evaluation standards for school mathematics. Reston, VA: The Council). The type of rich learning contexts that are envisaged by such reforms are predicated on a number
of factors, not the least of which is the quality of teachers’ experience and knowledge in the domain of mathematics. Although
the study of teacher knowledge has received considerable attention, there is less information about the teachers’ content
knowledge that impacts on classroom practice. Ball (2000, Journal of Teacher Education, 51(3), 241–247) suggested that teachers’ need to ‘deconstruct’ their content knowledge into more visible forms that would
help children make connections with their previous understandings and experiences. The documenting of teachers’ content knowledge
for teaching has received little attention in debates about teacher knowledge. In particular, there is limited information
about how we might go about systematically characterising the key dimensions of quality of teachers’ mathematics knowledge
for teaching and connections among these dimensions. In this paper we describe a framework for describing and analysing the
quality of teachers’ content knowledge for teaching in one area within the domain of geometry. An example of use of this framework
is then developed for the case of two teachers’ knowledge of the concept ‘square’. 相似文献
14.
Concept maps consist of nodes that represent concepts and links that represent relationships between concepts. Various studies
have shown that concept mapping fosters meaningful learning. However, little is known about the specific cognitive processes
that are responsible for such mapping effects. In a thinking-aloud study, we analyzed the relations between cognitive processes
during concept mapping as well as the characteristics of the concept maps that the learners produced and learning outcomes
(38 university students). To test whether differences in learning outcome are due to differences in general abilities, verbal
and spatial abilities were also assessed. In a cluster-analysis two types of ineffective learners were identified: ‘non-labeling
mappers’ and ‘non-planning mappers’. Effective learners, in contrast, showed much effort in planning their mapping process
and constructing a coherent concept map. These strategies were more evident in students with prior concept-mapping experience
(‘advanced beginners’) than in those who had not used this learning strategy before (‘successful beginners’). Based on the
present findings, suggestions for a direct training approach (i.e., strategy training with worked-out examples) and an indirect
training approach (i.e., supporting the learners with strategy prompts) were developed. 相似文献
15.
Raed Zedan 《Learning Environments Research》2010,13(1):75-88
The focus of this study was the classroom climate for Grades 4, 5 and 6 students during mathematics classes in elementary
schools in the Arab sector in Israel. The study included 3,786 Arab students. The use of a questionnaire indicated that five
major factors related to classroom climate were Satisfaction and Enjoyment, Teacher–Student Relationships, Gender Inequality
and Tension, Student–Student Relationships, and Competitiveness. Students were found to be happy, satisfied and to have a
sense of unity. Discipline was a ‘sacred’ value that could not be disregarded. Rules and regulations, obedience and respect
were integral components of satisfaction and enjoyment. The teacher–student relationship was positive, warm and supportive.
The student–student relationship was fairly satisfactory. A feeling of social cohesion and belonging, mutual help and consideration
pervaded the classroom. Students were polite to each other and disputes were rare. Low levels were perceived for Competitiveness
and the desire for students to be first, achieve high marks and compete for teacher attention. 相似文献
16.
Kyeong Hah Roh 《Educational Studies in Mathematics》2010,73(3):263-279
This study explored students’ understanding of a logical structure in defining the limit of a sequence, focusing on the relationship
between ε and N. The subjects of this study were college students who had already encountered the concept of limit but did not have any experience
with rigorous proofs using the ε–N definition. This study suggested two statements, each of which is written by using a relationship between ε and N, similar to the ε–N definition. By analyzing the students’ responses to the validity of the statements as definitions of the limit of a sequence,
students’ understanding of such a relationship was classified into five major categories. This paper discusses some essential
components that students must conceptualize in order properly to understand the relationship between ε and N in defining the limit of a sequence. 相似文献
17.
Andrew Marks 《Higher Education》2005,50(4):613-630
This paper argues that the conceptions of ‘space’ (and increasingly ‘time’) in the discussion of ‘the university’ (in its
most transcendent sense) have gone through four distinct phases in the UK. Using a Heideggerian conception of ‘space’ where
usefulness is more important than proximity, the ‘ancient’ universities were ‘useful’ to the gentry and thus were ‘closer’
to them than to the excluded ‘local’ poor in the institutions’ vicinities. The ‘civic’ universities on the other hand stressed
‘localism’ as part of their mandate – to educate the people of their locality (but only those of the new industrial middle
class). The ‘Robbins’ universities were a partial return to the ‘ancient’ notion of learning as a ‘lived’ activity, providing
scenic landscapes on green-belt campuses where students could ‘retreat’ from the ‘real world’ for the duration of their studies.
The ‘spatial’ quality of these places was thus part of a conception of higher education as ‘lifestyle choice’ where young
people moved away from their locality to study. As such ‘proximity’ was an issue only insofar as the greater the distance
from one’s point of origin the better for successful immersion in the growing student ‘culture’. The ‘new/post-1992’ universities
partially retained their polytechnic mandate to educate local people, but embraced a colonialist impulse regarding local space
usage. ‘
‘The discussion can be further refined to argue that these four stages are merely two phases which have repeated themselves:
from ancient ‘exclusivity’ to civic ‘localism’ and back to Robbins era ‘exclusivity’ and thence to post-1992 ‘localism’ once
more’. The opening up of higher education via the Internet in the late 20th and early 21st centuries provides for the possibility
of the growth of entirely non-spatial and asynchronous learning experiences, and as such we may well be on the verge of the
fifth stage of university development. 相似文献
18.
Conceptions of,and approaches to,teaching online: a study of lecturers teaching postgraduate distance courses 总被引：1，自引：0，他引：1
Carlos Gonzalez 《Higher Education》2009,57(3):299-314
This paper presents the outcomes of a study into online teaching. It builds upon previous research and conceptual frameworks
produced by Kember and Kwan (Instr Sci 28(5):469–490, 2000) and Roberts (Instr Sci 31(1–2):127–150, 2003). It advances research
on conceptions of, and approaches to, teaching by examining teaching in a novel context: distance-taught courses at the postgraduate
level. Lecturers were interviewed from a Faculty of Health Sciences in a research-intensive Australian University. Relationships
between conceptions and approaches found in previous research were confirmed in this study. However, it was found that the
conceptions of online teaching proposed by Roberts (Instr Sci 31(1–2):127–150, 2003) did not adequately distinguish between
the conceptions held by the lecturers interviewed in this study. Three modified conceptions of online teaching are proposed:
‘for individual access to learning materials and information; and for individual assessment’; ‘for learning related communication
(asynchronous and/or synchronous)’; and ‘as a medium for networked learning’. Some of the dimensions developed by Roberts
to describe approaches to online teaching were not applicable in this study setting and needed further modification. Two broad
approaches emerged: ‘informative/individual learning focused’ and ‘communicative/networked learning focused’. Contextual influences
on teaching reported by Kember and Kwan (Instr Sci 28(5):469–490, 2000)—that is, institutional influence, nature of students
and subject and curriculum—were revealed in this study to have different levels of influence over approaches to online teaching:
the first two being the more relevant ones. 相似文献
19.
The ‘Green Classroom’ in the Botanical Garden of Ulm is an experiential learning forum outside school. Its educational concept
is based on experimental learning and is geared towards expanding biological knowledge and developing positive attitudes towards
small animals such as invertebrates and insects. The attitudes of 68 school students towards small animals, before and after
they visited the ‘Green Classroom’, were assessed and the answers they gave in their questionnaires were compared with those
of 60 students froma control group that was not yet exposed to this learning environment. Although the students spent only
one morning in the ‘Green Classroom’, some of their attitudes towards small animals improved after their visit. These studies
underscore the necessity for direct observation and familiarization of the environment including small animals such as invertebrates
and insects for appreciating issues related to biodiversity and conservation. 相似文献
20.
Muammer ?alik Ali Kolomu? Zafer Karag?lge 《Journal of Science Education and Technology》2010,19(5):422-433
This paper reports on an investigation of the effect of conceptual change pedagogy on students’ conceptions of ‘rate of reaction’
concepts. The study used a pre-test/post-test non-equivalent comparison group design approach and the sample consisted of
72 Turkish grade-11 students (aged 16–18 years) selected from two intact classrooms. The ‘Rate of Reaction’ Concept Test comprising
9 lead and 10 sub-questions (total 19 items) was employed. The results suggest that the teaching intervention helped the students
to overcome their alternative conceptions and to store their newly structured knowledge in their long-term memories. It is
suggested that combining different conceptual change methods such conceptual change text/refutation text, argumentation with
the intervention used here may be more effective in reducing student alternative conceptions. 相似文献