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Frank Uhlig 《Educational Studies in Mathematics》2002,50(3):335-346
We describe how elementary Linear Algebra can be taught successfully while introducing students to the concept and practice
of ‘mathematical proof’.This is done badly with a sophisticated Definition–Lemma–Proof–Theorem–Proof–Corollary(DLPTPC) approach;
badly – since students in elementary Linear Algebra courses have very little experience with proofs and mathematical rigor.
Instead, the subjects and concepts of Linear Algebra can be introduced in an exploratory and fundamentally reasoned way. One
seemingly successful way to do this is to explore the concept of solvability of linear systems first via the row echelon form
(REF). Solvability questions lead to row and column criteria for a REF that can be used repeatedly to: compute subspaces,
settle linear (in)dependence, find inverses, perform basis change, compute determinants, analyze eigensystems etc. If these
subjects are explained heuristically from the first principles of linear transformations, linear equations, and the REF, students
experience the power of a concept–built approach and reap the benefit of deep math understanding. Moreover, early ‘salient
point’ proofs lead to an intuitive understanding of ‘math proof’. Once the basic concept of ‘proof’ is ingrained in students,
more abstract proofs, even DLPTPC style expositions, on normal matrices, the SVD etc. become accessible and understandable
to sophomore students. With the help of this gentle early approach, the concept and construct of a ‘math proof’ becomes firmly
embedded in the students' minds and helps with future math courses and general scientific reasoning.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
3.
Solvejg Jobst 《International Review of Education/Internationale Zeitschrift für Erziehungswissenschaft/Revue internationale l'éducation》2005,6(4):385-402
EUROPEAN CONSCIOUSNESS: TOWARDS DEFINING A COMPLEX CONCEPT AND ITS EDUCATIONAL SIGNIFICANCE – The present study aims at a
definition of ‘European consciousness’. In particular, it draws on Henri Tajfel’s theory of social identity as well as Roland
Wakenhut’s and Jutta Gallenmüller’s moral determination of national consciousness. European consciousness is then defined
as a sense of belonging which, depending on certain identification structures and social perspectives, can take such distinct
forms of moral consciousness as ‘Eurocentrism’, ‘European patriotism’, or ‘reflective European consciousness’. Making reference
to Wolfgang Klafki’s notion of general education, it is finally argued that the emancipatory contribution of schooling to
greater European integration consists in mediating precisely this last way of thinking. 相似文献
4.
Lilia Halim Mohd Ali Samsudin T. Subahan M. Meerah Kamisah Osman 《International Journal of Science and Mathematics Education》2006,4(4):727-739
The complexity of science teaching requires science teachers to encounter a range of tasks. Some tasks are perceived as stressful while others are not. This study aims to investigate the extent to which different teaching situations lead to different stress levels. It also aims to identify the easiest and most difficult conditions to be regarded as stressful conditions by science teachers. An occupational stress inventory of 25 items developed by Okebukola (1988) validation of the occupational stress inventory for science teachers. Science Teacher, was used to measure the science teachers’ stress level in science teaching. A four point Likert scale ranging from 1 – ‘no stress at all’ to 4 – ‘extreme stress’ was used. Fifty-eight Malaysian secondary science teachers participated in the survey in which six volunteered to participate in the interview study. The data was then analyzed using the Rasch model to measure the level of stress caused by different kinds of stressful conditions. Even though ‘overloaded science syllabus’ was identified to be the basis of multiple stressful conditions, it was, however, difficult for the respondents to regard it as a stressful condition. On the other hand, the respondents found that ‘having to teach difficult science topics’ is easiest to be regarded as a stressful condition. It was shown that even though ‘overloaded science syllabus’ is the starting point for stress caused by multiple conditions, due to the availability of coping strategies which can be employed by the respondents, the stressor is minor in causing stress among teachers. On the other hand, when teachers lack the availability of coping strategies dealing with teaching difficult science topics, they easily feel stressful. One of the main recommendations to overcome stressful conditions is to provide the science teachers ‘topic specific pedagogy’ during in-service training. 相似文献
5.
Scaffolding practices that enhance mathematics learning 总被引：1，自引：0，他引：1
Julia Anghileri 《Journal of Mathematics Teacher Education》2006,9(1):33-52
It is over 25 years since Wood, Bruner and Ross (1976, Journal of Child Psychology and Psychiatry, 17, 89–100) introduced the idea of ‘scaffolding’ to represent the way children’s learning can be supported. Despite problems,
this metaphor has enduring attraction in the way it emphasises the intent to support a sound foundation with increasing independence
for the learner as understanding becomes more secure. It has resonance with the widely accepted notion in teaching of construction
and the constructivist paradigm for learning. The discussion that follows will characterise some teaching approaches that
can be identified as scaffolding, revisiting some of the original classifications, and identifying further scaffolding strategies
with particular reference to mathematics learning. Examples will be given from studies relating to geometry learning with
four to 6 year olds and to arithmetic learning with older pupils. 相似文献
6.
In this article, we study the conditions and constraints of the integration of the dynamic geometry software ‘Cabri’ in the
teaching of geometry in ordinary primary school classes (10 years old pupils). We focus our attention on the way the dialectic
between old and new is working during this integration, looking at the types of tasks and techniques proposed in class by
the teachers. The ‘good equilibrium’ between old and new ways of doing appears as one of the main conditions of integration
as it allows to reconcile innovating and usual activities in the everyday life of the class.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
7.
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
8.
This paper examines the experiences and understandings of primary (K6) school pupils with regards to managing issues of risk
and safety during their everyday use of information and communication technologies (ICTs). The paper is based on survey and
interview data with pupils aged 7 to 11 years old in five English primary schools (n = 612). Analysis of these data shows that whilst most pupils recognised a general need to be mindful of ICT-related risks
and dangers, their actual experiences of risk tended to be described in terms of operational problems encountered when using
ICTs. Conversely, pupils’ understandings of potential risk were often based upon exaggerated fears deriving from a number
of moral panics relating to child safety. These data suggest that official notions of ‘e-safety’ remain abstract and poorly
understood concepts for many children. In considering what implications these data have for the ongoing ‘e-safety’ agenda
in UK schools the paper concludes by suggesting three possible areas of change: (1) re-orientating the topic and tone of the
official discourses surrounding e-safety; (2) increasing pedagogical interventions in primary schools aiming at enhancing
pupils’ critical literacy skills; and (3) establishing a meaningful and sustained dialogue between pupils, teachers and parents
about safety and risk when using ICTs. 相似文献
9.
The ethnography presented by van Eijck and Roth focuses on the activities of people involved in a government funded internship
program in conservation and restoration, which was offered by a ‘multidisciplinary research center’ through a local First
Nation adult education center. The internship was designed, in partnership with a local non-profit conservation society (OceanHealth),
to appeal to First Nation men and women considering career change, returning to school, or re-entering the work place. The
primary aim of the internship was to ‘provide authentic science for diverse student populations (and their teachers), with
particular attention to the needs of students from First Nations, to become scientifically literate to the extent that it
prepares them for participating in public debates, community decision-making, and personal living consistent with long-term
environmentally sustainable forms of life’. The authors report that at least one of the two interns was not interested in
science and a WSáNEC elder expressed dissatisfaction with the efforts to establish the nature park and its current approved
uses. Van Eijck and Roth argue that the divergence between the project aims and the goals of the participants are a result
of how ‘place’ is viewed in place-based education and that disagreements like these can be resolved if place is theorized
as chronotope. There are many interesting ideas raised and directions taken in the article by van Eijck and Roth. After several
discussions during the review process, we decided to focus our forum response on the meaning of ‘place’ in place-based education,
the utility of theorizing place as a chronotope, the implications for teaching–learning (‘education’), and musings on what
remains unclear. 相似文献
10.
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
11.
Felicity McArdle 《The Australian Educational Researcher》2012,39(1):91-106
It would be a rare thing to visit an early years setting or classroom in Australia that does not display examples of young
children’s artworks. This practice serves to give schools a particular ‘look’, but is no guarantee of quality art education.
The Australian National Review of Visual Arts Education (, 2009) has called for changes to visual art education in schools. The planned new National Curriculum includes the arts (music,
dance, drama, media and visual arts) as 1 of the 5 learning areas. Research shows that it is the classroom teacher that makes
the difference, and teacher education has a large part to play in reforms to art education. This paper provides an account
of one foundation unit of study (Unit 1) for first year university students enrolled in a 4-year Bachelor degree program who
are preparing to teach in the early years (0–8 years). To prepare pre-service teachers to meet the needs of children in the
twenty-first century, Unit 1 blends old and new ways of seeing art, child and pedagogy. Claims for the effectiveness of this
model are supported with evidence-based research, conducted over the 6 years of iterations and ongoing development of Unit
1. 相似文献
12.
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
13.
This paper presents findings on a hybrid guidance curriculum in Hong Kong, a place where East meets West in education and
in many other spheres. A qualitative case study method is applied that uses questions for understanding the ‘self’ in guidance
but incorporates Confucian cardinal human relationships of parent–child, brother–sister, husband–wife, superior–subordinate,
teacher–pupil and friend–friend in understanding the ‘other’ relationships. The study of ‘self–other relationship’ is combined
with Lawton’s (Social change, educational theory and curriculum planning, Hodder, London, 1973) model of curriculum development in Western traditions. Data obtained from stakeholders in schools include traditional Chinese
ideas as well as modern Western ideas. Implications of this framework to the study of other societies with a mix of Western
and traditional cultures are discussed.
相似文献
| Pattie Yuk Yee Luk-FongEmail: |
14.
The purpose of this article is to introduce ‘a new analysis’ to students of mathematics at the undergraduate and postgraduate levels, which in turn introduces a geometry very different from our Euclidean geometry and Riemannian geometry. Some strange things happen: for instance, ‘every triangle becomes isosceles!’. 相似文献
15.
Joan Abbott-Chapman 《The Australian Educational Researcher》2011,38(1):57-71
Research studies of post-school education and training conducted in Australia and internationally have revealed a mosaic of students’ education and employment experiences, with a multiplicity of nonlinear pathways. These tend to be more fragmentary
for disadvantaged students, especially those of low socio-economic background, rural students, and mature aged students seeking
a ‘second chance’ education. Challenges faced by students in their transitions to higher education are made more complex because
of the intersection of vertical stratification created by institutional and sectoral status hierarchies and segmentation,
especially relating to ‘academic’ and ‘vocational’ education and training, and the horizontal stratification of regional,
rural and remote locations in which students live. If we are to achieve the equity goals set by the Bradley Review (Bradley
et al., Review of Australian Higher Education Final Report, 2008) we need to acknowledge and work with the complex realities of disadvantaged students’ situations, starting at the school
level. Interrelated factors at the individual, community and institutional level which continue to inhibit student take-up
of higher education places are discussed in the context of discursive constructions of ‘disadvantage’ and ‘choice’ in late
modernity. Research highlights the need to facilitate students’ post-school transitions by developing student resilience,
institutional responsiveness and policy reflexivity through transformative education. 相似文献
16.
Selahattin G?nen 《Journal of Science Education and Technology》2008,17(1):70-81
The aims of this study were considered under three headings. The first was to elicit misconception that science and physics
student teachers (pre-service teachers) had about the terms, ‘‘inertial mass’’, ‘‘gravitational mass’’, ‘‘gravity’’, ‘‘gravitational
force’’ and “weight”. The second was to understand how prior learning affected their misconceptions, and whether teachers’
misconceptions affected their students’ learning. The third was to determine the differences between science and physics student
teachers’ understanding levels related to mass and gravity, and between their logical thinking ability levels and their attitudes
toward physics lessons. A total of 267 science and physics student teachers participated in the study. Data collection instruments
included the physics concept test, the logical thinking ability test and physics attitude scale. All instruments were administered
to the participants at the end of the 3rd semester of their university years. The physics test consisting of paper and pencil
test involving 16 questions was designed, but only four questions were related to mass and gravity; the second test consisted
of 10 questions with two stages. The third test however, consisted of 15 likert type items. As a result of the analysis undertaken,
it was found that student teachers had serious misconceptions about inertia, gravity, gravitational acceleration, gravitational
force and weight concepts. The results also revealed that student teachers generally had positive attitudes toward physics
lessons, and their logical thinking level was fairly good. 相似文献
17.
An Instrument for Assessing Students' Mental State and the Learning Environment in Science Education
The purpose of this research was to develop and validate a new instrument, the Mental State in Learning Environment Questionnaire (MSLEQ), to assess student's mental state in a given learning environment. The MSLEQ has high internal consistency reliability
values between 0.70–0.92 as well as good construct validity and predictive validity. After conducting a factor analysis, four
main factors were extracted and were described as ‘emotion’, ‘intention’, ‘internal mental representation’ and ‘external mental
representation’. The important feature of this study is the construction of an economical questionnaire on the mental state
in a given learning environment. The questionnaire yielded important information that can be concretely applied to science
teaching and learning. 相似文献
18.
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
19.
Elizabeth Warren 《Educational Studies in Mathematics》2006,62(2):169-189
This paper examines the change in young children’s understanding of ‘equal’, ‘more’, ‘less’, and ‘between’, words commonly
used in equivalent and non-equivalent situations, over a 3-year period. Seventy-six children participated in the longitudinal
study. Each year they were asked to share their understanding of these four words. Past research has indicated that many children
have limited understanding of ‘equal’ as quantitative sameness. The results of this research suggested that many children
also have limited understanding of ‘more’ and ‘less’ and that these understandings did not significantly change over the 3-year
period. 相似文献
20.
Sulaiman M. Al-Balushi 《International Journal of Science and Mathematics Education》2011,9(3):571-601
The purpose of the current study was to explore learners’ evaluation of the credibility of scientific models that represent
natural entities and phenomena. Participants were 845 students in grades 9 – 11 (aged 15 – 17 years) and 108 prospective science
teachers in Oman, totaling 953 students. A survey called Epistemologies about the Credibility of Scientific Models was designed
to explore participants’ epistemological positions regarding the credibility of scientific models. This instrument was based
on a credibility taxonomy proposed by the author. This taxonomy was composed of four epistemological levels: certainty, imaginary,
suspicious, and denial; thus, it was called the CISD taxonomy. Findings revealed that natural entities and phenomena were
assigned to CISD levels according to their level of abstractness. This level of abstractness is usually constructed by the
most frequently used models to represent each natural entity or phenomenon. For instance, entities, which were usually represented
by photographs or micrographs, such as meteors and meteorites, blood cells and bacteria, fell at the certainty level. On the
other hand, theoretical entities such as electron cloud and photons had a high suspicious–denial combinational level. Some
entities, with possible competing concrete–abstract parallel nature of the scientific models that represent them, had both
high certainty and suspicious–denial levels. The overall students’ epistemological perceptions across grade levels showed
a decrease in the certainty level and an increase in the imaginary level. It might also be plausible to conclude that new,
detailed microscopic and more abstract knowledge raised the suspicious and denial levels of some entities. Further research
based on qualitative research methodologies is needed to explore these findings. 相似文献