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1.
In recent years, semiotics has become an innovative theoretical framework in mathematics education. The purpose of this article
is to show that semiotics can be used to explain learning as a process of experimenting with and communicating about one's
own representations (in particular ‘diagrams') of mathematical problems. As a paradigmatic example, we apply a Peircean semiotic
framework to answer the question of how students develop a notion of ‘distribution' in a statistics course by ‘diagrammatic
reasoning' and by forming ‘hypostatic abstractions', that is by forming new mathematical objects which can be used as means
for communication and further reasoning. Peirce's semiotic terminology is used as an alternative to concepts such as modeling,
symbolizing, and reification. We will show that it is a precise instrument of analysis with regard to the complexity of learning
and communicating in mathematics classrooms. 相似文献
2.
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
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.
This paper explores the nature and source of mathematics homework and teachers’ and students’ perspectives about the role
of mathematics homework. The subjects of the study are three grade 8 mathematics teachers and 115 of their students. Data
from field notes, teacher interviews and student questionnaire are analysed using qualitative methods. The findings show that
all 3 teachers gave their students homework for instructional purposes to engage them in consolidating what they were taught
in class as well as prepare them for upcoming tests and examinations. The homework only involved paper and pencil, was compulsory,
homogenous for the whole class and meant for individual work. The main source of homework assignments was the textbook that
the students used for the study of mathematics at school. ‘Practice makes perfect’ appeared to be the underlying belief of
all 3 teachers when rationalising why they gave their students homework. From the perspective of the teachers, the role of
homework was mainly to hone skills and comprehend concepts, extend their ‘seatwork into out of class time’ and cultivate a
sense of responsibility. From the perspectives of the students, homework served 6 functions, namely improving/enhancing understanding
of mathematics concepts, revising/practising the topic taught, improving problem-solving skills, preparing for test/examination,
assessing understanding/learning from mistakes and extending mathematical knowledge. 相似文献
5.
Assessment for learning in Singapore: unpacking its meanings and identifying some areas for improvement 总被引：2，自引：1，他引：1
Kelvin Tan 《Educational Research for Policy and Practice》2011,10(2):91-103
This article examines the meanings and impact of ‘Assessment for Learning’ initiatives in schools against the back drop of
assessment reform in Singapore since 1997. It is argued that Assessment for Learning’ is understood in different ways, and
these different meanings do not always benefit students’ learning. The different meanings of ‘Assessment for Learning’ in
Singapore are unpacked, and three areas for improvement for Assessment for Learning are suggested—clear standards for effective
feedback practices, assessment for sustainable learning and assessment for integrating holistic learning. 相似文献
6.
7.
Brian L. Jones 《Research in Science Education》1990,20(1):161-170
The term ‘concept’ is used in different ways within educational literature and has at least two different, although related,
referents in relation to science knowledge, namely, public knowledge and private understandings. A taxonomic structure for
‘science concepts’ (public knowledge) has been developed to provide a rationale for the choice of phenomena to be used in
the investigation of students’ ‘concepts’ and also to act as a frame of reference for generating insights about the data to
be collected. Furthermore, it may be a useful heuristic to predict other science concepts likely to be highly problematic
in school teaching situations and thus worthy of detailed research. The taxonomy, called a ‘Scale of Empirical Distance’ (SED),
enables science concepts to be mapped according to their degree of closeness to concrete realities. The scale shows a recognition
of the empirical basis of science concepts and the role of human senses in the perception of the material world even though
“absolute objectivity of observation is not a possible ideal of science” as Harre (1972) has noted. The scale uses two binary
variables, namely, ‘visual’ and ‘tactile’, to generate four categories of science concepts ranging on a continuum from concrete
to abstract. Some concepts related to ‘matter’ will be classified and discussed.
Specializations: science teacher education, primary science curriculum and methods, students’ personal meanings of phenomena. 相似文献
8.
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
9.
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
10.
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
11.
Marida Ergazaki Konstantina Saltapida Vassiliki Zogza 《Research in Science Education》2010,40(5):699-715
This paper is concerned with highlighting young children’s ideas about the nature, location and appearance of germs, as well
as their reasoning strands about germs’ ontological category and biological functions. Moreover, it is concerned with exploring
how all these could be taken into account for shaping a potentially fruitful learning environment. Conducting individual,
semi-structured interviews with 35 preschoolers (age 4.5–5.5) of public kindergartens in the broader area of Patras, we attempted
to trace their ideas about what germs are, where they may be found, whether they are good or bad and living or non-living
and how they might look like in a drawing. Moreover, children were required to attribute a series of biological functions
to dogs, chairs and germs, and finally to create a story with germs holding a key-role. The analysis of our qualitative data
within the “NVivo” software showed that the informants make a strong association of germs with health and hygiene issues,
locate germs mostly in our body and the external environment, are not familiar with the ‘good germs’-idea, and draw germs
as ‘human-like’, ‘animal-like’ or ‘abstract’ entities. Moreover, they have significant difficulties not only in employing
biological functions as criteria for classifying germs in the category of ‘living’, but also in just attributing such functions
to germs using a warrant. Finally, the shift from our findings to a 3-part learning environment aiming at supporting preschoolers
in refining their initial conceptualization of germs is thoroughly discussed in the paper. 相似文献
12.
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
13.
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
14.
David Billing 《Higher Education》2007,53(4):483-516
This article is a result of a completed survey of the mainly cognitive science literature on the transferability of those
skills which have been described variously as ‘core’, ‘key’, and ‘generic’. The literature reveals that those predominantly
cognitive skills which have been studied thoroughly (mainly problem solving) are transferable under certain conditions. These
conditions relate particularly to the methods and environment of the learning of these skills. Therefore, there are many implications
for the teaching of key skills in higher education, which the article draws out, following a summary of the main findings
of the research literature. Learning of principles and concepts facilitates transfer to dissimilar problems, as it creates
more flexible mental representations, whereas rote learning of facts discourages transfer. Transfer is fostered when general
principles of reasoning are taught together with self-monitoring practices and potential applications in varied contexts.
Training in reasoning and critical thinking is only effective for transfer, when abstract principles and rules are coupled
with examples. Transfer is promoted when learning takes place in a social context, which fosters generation of principles
and explanations. Transfer improves when learning is through co-operative methods, and where there is feedback on performance
with training examples. The specificity of the context in which principles are learned reduces their transfer. Transfer is
promoted if learners are shown how problems resemble each other, if they are expected to learn to do this themselves, if they
are aware of how to apply skills in different contexts, if attention is directed to the underlying goal structure of comparable
problems, if examples are varied and are accompanied by rules or principles (especially if discovered by the learners), and
if learners’ self-explanations are stimulated. Learning to use meta-cognitive strategies is especially important for transfer. 相似文献
15.
Salem A. Al khawaldeh Ali M. Al Olaimat 《Journal of Science Education and Technology》2010,19(2):115-125
The present study conducted to investigate the contribution of conceptual change texts, accompanied by concept mapping instruction
to eleventh-grade students’ understanding of cellular respiration concepts, and their retention of this understanding. Cellular
respiration concepts test was developed as a result of examination of related literature and interviews with teachers regarding
their observations of students’ difficulties. The test was administrated as pre-test, post-test, and delayed post-test to
a total of 70 eleventh-grade students in two classes of the same high school in an urban area, taught by the same teacher.
The experimental group was a class of 34 students who received conceptual change texts accompanied by concept mapping instruction.
A class of 36 students comprised the control group who received traditional instruction. Besides treatment, previous understanding
and logical thinking ability were other independent variables involved in this study. The results showed that logical thinking,
treatment, previous understanding of cellular respiration concepts each made a statistically significant contribution to the
variation in students’ understanding of cellular respiration concepts. The result also showed that conceptual change texts
accompanied by concept mapping instruction was significantly better than traditional instruction in retention of this understanding. 相似文献
16.
This paper shows how the patterns of variation created in the teaching were critical in helping a class of Primary 3 students
in Hong Kong to learn about the colour of light, so that the students attained conceptual rather than procedural knowledge.
A ‘Learning Study’ approach was adopted, which is a Lesson Study grounded in a particular learning theory to improve teaching
and learning. This study, based on the learning theory of Variation advanced by Marton and Booth, was premised on three types
of variation: variation in students’ ways of experiencing what is to be taught/learnt (V1), variation in teachers’ ways of
dealing with the ‘object of learning’ (V2), and the use of ‘pattern of variation’ as a guiding principle of pedagogical design
to enhance students’ learning (V3). In planning the lesson, a conscious effort was made to create relevant patterns of variation,
i.e. varying certain critical aspect(s) while keeping other aspects of the object of learning invariant in order to help students
to discern those aspects. Comparison between the results of the pre- and post-test shows that there was significant gain in
the students’ learning outcomes with respect to the intended object of learning. The findings contribute knowledge to how
the Theory of Variation can be used in practice. It also illustrates how teachers can make use of this theoretical framework
to analyze their own teaching and thereby, develop an analytical awareness of teaching and learning. 相似文献
17.
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
18.
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
19.
David Guile 《Vocations and Learning》2011,4(2):93-111
The paper analyses a form of interprofessional working and learning (IPWL)—the fleeting spatial and temporal constitution
of project teams with little prior history of working together—that is an increasing feature of work in the global economy.
The paper argues firstly: (i) this form of working and learning is relatively under-researched in professional, vocational
and workplace learning (PVWL); and, (ii) the research traditions—Cultural-Historical Activity Theory (CHAT) and Cultural Anthropology/Symbolic
Interactionist (CA/SI)—that some researchers in PVWL have drawn on to investigate IPWL do not allow them to capture the cognitive
and symbolic complexity of this activity. Secondly, it is possible to reveal the nature of this complexity when the concepts
and methods associated with CHAT and CA-SI-based approaches are supplemented with the concepts of ‘inference’, ‘space of reasons’,
‘restructuring and ‘recontextualisation’ (Guile, 2010). The paper demonstrates this claim by reinterpreting a classic study of the aforementioned form of working and learning
undertaken by Hall, Stevens and Torolba that drew on concepts and methods from CA and SI (2002). 相似文献
20.
The purpose of this paper is to contribute to the debate about how to tackle the issue of ‘the teacher in the teaching/learning
process’, and to propose a methodology for analysing the teacher’s activity in the classroom, based on concepts used in the
fields of the didactics of mathematics as well as in cognitive ergonomics. This methodology studies the mathematical activity
the teacher organises for students during classroom sessions and the way he manages1 the relationship between students and mathematical tasks in two approaches: a didactical one [Robert, A., Recherches en Didactique
des Mathématiques 21(1/2), 2001, 7–56] and a psychological one [Rogalski, J., Recherches en Didactique des Mathématiques 23(3),
2003, 343–388]. Articulating the two perspectives permits a twofold analysis of the classroom session dynamics: the “cognitive
route” students are engaged in—through teacher’s decisions—and the mediation of the teacher for controlling students’ involvement
in the process of acquiring the mathematical concepts being taught. The authors present an example of this cross-analysis
of mathematics teachers’ activity, based on the observation of a lesson composed of exercises given to 10th grade students
in a French ‘ordinary’ classroom. Each author made an analysis from her viewpoint, the results are confronted and two types
of inferences are made: one on potential students’ learning and another on the freedom of action the teacher may have to modify
his activity. The paper also places this study in the context of previous contributions made by others in the same field. 相似文献