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1.
Kyeong Hah Roh 《Educational Studies in Mathematics》2008,69(3):217-233
There are many studies on the role of images in understanding the concept of limit. However, relatively few studies have been
conducted on how students’ understanding of the rigorous definition of limit is influenced by the images of limit that the
students have constructed through their previous learning. This study explored how calculus students’ images of the limit
of a sequence influence their understanding of definitions of the limit of a sequence. In a series of task-based interviews,
students evaluated the propriety of statements describing the convergence of sequences through a specially designed hands-on
activity, called the ɛ–strip activity. This paper illustrates how these students’ understanding of definitions of the limit of a sequence was influenced
by their images of limits as asymptotes, cluster points, or true limit points. The implications of this study for teaching
and learning the concept of limit, as well as on research in mathematics education, are also discussed. 相似文献
2.
《International Journal of Educational Research》2003,39(7):677-694
Nunes and Bryant (Children doing mathematics, Blackwell, Oxford, 1996) proposed that an understanding of the additive composition of number could be a precursor to an understanding of the decimal structure. If this is so, children should achieve an understanding of additive composition before they can handle the decimal structure. The aim of our study was to determine the developmental timing of these two forms of mathematical understanding. 5- and 6-year-old children each completed both an addition task and Terezinha Carraher's (In: Streefland, L. (Ed.), Proceedings of the Ninth International Conference for the Psychology of Mathematics Education, vol. 1. Research Group on Mathematics Education and Computer Centre, State University of Utrecht, Utrecht, The Netherlands, 1985, pp. 288–303) shop task, with concrete materials. The addition task tested an understanding of additive composition by measuring whether children used a counting-all or counting-on strategy to add two quantities. The shop task tested an understanding of the decimal structure by investigating whether or not children could successfully combine tens and ones in producing a given amount of money. Our results suggest that learning about the decimal structure enhances children's understanding of the general principle of additive composition. 相似文献
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Bertrand Troadec Benaissa Zarhbouch Valérie Frède 《European Journal of Psychology of Education - EJPE》2009,24(4):485-498
The non-computational brand of cognitivism is based on the premise that performances, including those of children, are generated
by mental models or representations, i.e., “internal” resources. The sociocultural approach, on the other hand, regards context,
i.e., an “external” resource, as the chief means of elaborating knowledge. The results of empirical research on how Moroccan
children develop their understanding of the shape and properties of the Earth highlight some of the limitations not only of
the representationalist paradigm but also of the more “radical” socioculturalist approach. They show that, while the sociocultural
context does indeed play a vital role in the development of understanding, the latter in turn helps to increase children’s
autonomy of mind. 相似文献
4.
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
5.
《Africa Education Review》2013,10(2):344-359
Abstract This study investigated educators’ understanding of the mediation role in the classroom. A quantitative research approach was used in a survey of a sample of 261 participants. To this end, a questionnaire was used for collecting data. The Chi-square test was used to analyse data and to test the hypotheses of the study. The findings indicated that educators differed significantly in the extent to which they understand the concept mediation. The findings also indicated that gender and teaching phase had a significant influence on educators’ understanding of the concept mediation. The findings further indicated that educators differed significantly in their understanding of the processes and competences involved in mediation. The findings also revealed that teaching phase had a significant influence on educators’ understanding of the processes and competences involved in mediation. 相似文献
6.
Aragón-Méndez María del Mar Acevedo-Díaz José Antonio García-Carmona Antonio 《Cultural Studies of Science Education》2019,14(3):525-555
Cultural Studies of Science Education - This article presents a qualitative study of the understanding of various epistemic and non-epistemic aspects of the nature of science (NOS), based on... 相似文献
7.
《Teaching and Teacher Education》2001,17(7):857-869
Play is a characteristic behaviour of young children. It is a vital way through which children reconcile their inner lives with the outside world. It is a central activity in kindergarten and nurseries. ‘Learning through play’ is recommended as the mode of learning and teaching for young children. In Hong Kong, it was documented in an official education report in 1986 and is the key guideline for the implementation of the aims of early childhood education for the next millennium. A case study of two kindergarten teachers in Hong Kong was conducted to investigate the understanding and implementation of play in the kindergarten curriculum. The findings showed immense difficulties in understanding the concept ‘learning through play’ and a gap between the practitioners’ espoused theories and practice. The study reflected the complex nature of learning and teaching and highlighted the core issue for reform, namely, the need for bridging the gap between theory and practice. 相似文献
8.
This study utilized discourse-based instruction as an alternative method of instruction that emphasizes the teaching of mathematics by actively engaging students in mathematical discourse practices. A quasi-experimental study was employed to determine the effectiveness of mathematical discourse-based instruction in enhancing eleventh-grade students’ conceptual and procedural understanding of probability and statistics. A researcher-constructed test instrument was used for data collection from the experimental and control groups. The data analysis performed using the Kruskal-Wallis test showed that the experimental group outperformed the control groups in terms of conceptual and procedural knowledge. Furthermore, the results suggest that discourse-based instruction when appropriately designed and implemented can increase students’ understanding of mathematical topics. 相似文献
9.
This paper investigates how the use of Pupil Views Templates (PVTs), a tool designed to elicit, record and analyse the development of students’ awareness of their own learning processes, supports teachers’ professional learning. This paper reports on a three‐year collaborative practitioner enquiry project involving more than 30 primary and secondary schools in England. The data set includes practitioners’ case studies, interviews, questionnaires and cross‐project analysis completed by the university team. Analysis focuses on the role of feedback, stimulated through the use of PVTs, in teachers’ learning through three dimensions: the influence of student feedback on teachers as part of the pedagogical encounter; the influence of student feedback on schools within the context of the practitioner enquiry projects; the influence of feedback on the lead teacher researchers. Links between the tools used, the source of the feedback, and teachers’ learning are mapped from a ‘second order perspective’ derived from the diverse data sources. 相似文献
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Xenia VamvakoussiKonstantinos P. Christou Lieve MertensWim Van Dooren 《Learning and Instruction》2011,21(5):676-685
It is widely documented that the density property of rational numbers is challenging for students. The framework theory approach to conceptual change places this observation in the more general frame of problems faced by learners in the transition from natural to rational numbers. As students enrich, but do not restructure, their natural number based prior knowledge, certain intermediate states of understanding emerge. This paper presents a study of Greek and Flemish 9th grade students who solved a test about the infinity of numbers in an interval. The Flemish students outperformed the Greek ones. More importantly, the intermediate levels of understanding—where the type of the interval endpoints (i.e., natural numbers, decimals, or fractions) affects students’ judgments—were very similar in both groups. These results point to specific conceptual difficulties involved in the shift from natural to rational numbers and raise some questions regarding instruction in both countries. 相似文献
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Alonso Lorena Kohen Raquel C. 《European Journal of Psychology of Education - EJPE》2023,38(3):929-944
In the aftermath of the financial and economic recession of 2008, 130 Spanish students of five age groups (8 to 17 years) and two socioeconomic backgrounds were individually interviewed about unemployment and lower wages. The participants were presented with two hypothetical situations, and their responses were qualitatively and quantitatively analyzed. The results indicated that children bring their conceptions of work when attempting to explain those phenomena. Specifically, it was found that the explanations were closely associated with the comprehension of the notion of surplus value (i.e., the idea that workers create more value than the cost of their salaries), and that the development of this notion proceeds in three levels. Younger children were simply unaware of the capacity of workers to create value (Level 1), which gave rise to some alternative conceptions (e.g., the idea that money for salaries comes from external sources). The children within the age range of 12–13 began to understand that workers create some value (Level 2). At this level, however, the notion of surplus value was not fully understood, and the idea that money for salaries comes from external sources persisted in a variety of ways. From the ages of 13–14, the children begin to understand that a wage is the price of labor and that the employer earns a profit because workers create more value than the cost of their wages (Level 3). The article presents a discussion of the possible reasons behind the slow progress observed and highlights some suggestions for educational practice.
相似文献15.
In order to corroborate and grow teacher educator knowledge (TEK) scholarship, this paper describes an in-depth-focused exploration of a group of teacher educators providing professional development. Our grounded data analysis allowed us to define different major elements, sub-elements, and components that comprise TEK, as well as make explicit how the use of this knowledge—in the context of teaching professional development—draws upon multiple components at any given moment. These findings hold implications for TEK scholarship and practice. Specific to scholarly efforts, while current models for TEK are useful for explicating common understandings amongst the research community, the most functional representations should be fluid and dynamic, in part by balancing both breadth and depth in their scope. Specific to the development of teacher educators, teacher educator preparation should recognize, emphasize, and develop future teacher educators’ layered understandings (i.e. knowledge of students and teachers) and robust knowledge of contexts. 相似文献
16.
Background: Feedback is one of the most significant factors for students’ development of writing skills. For feedback to be successful, however, students and teachers need a common language – a meta-language – for discussing texts. Not least because in science education such a meta-language might contribute to improve writing training and feedback-giving.
Purpose: The aim of this study was to explore students’ perception of teachers’ feedback given on their texts in two genres, and to suggest how writing training and feedback-giving could become more efficient.
Sample: In this study were included 44 degree project students in biology and molecular biology, and 21 supervising teachers at a Swedish university.
Design and methods: The study concerned students’ writing about their degree projects in two genres: scientific writing and popular science writing. The data consisted of documented teacher feedback on the students’ popular science texts. It also included students’ and teachers’ answers to questionnaires about writing and feedback. All data were collected during the spring of 2012. Teachers’ feedback, actual and recalled – by students and teachers, respectively – was analysed and compared using the so-called Canons of rhetoric.
Results: While the teachers recalled the given feedback as mainly positive, most students recalled only negative feedback. According to the teachers, suggested improvements concerned firstly the content, and secondly the structure of the text. In contrast, the students mentioned language style first, followed by content.
Conclusions: The disagreement between students and teachers regarding how and what feedback was given on the students texts confirm the need of improved strategies for writing training and feedback-giving in science education. We suggest that the rhetorical meta-language might play a crucial role in overcoming the difficulties observed in this study. We also discuss how training of writing skills may contribute to students’ understanding of their subject matter. 相似文献
17.
Mari Murtonen 《Teaching in Higher Education》2013,18(7):684-698
University research education in many disciplines is frequently confronted by problems with students’ weak level of understanding of research concepts. A mind map technique was used to investigate how students understand central methodological concepts of empirical, theoretical, qualitative and quantitative. The main hypothesis was that some students have a confused conception of empirical. The mind maps revealed that in the beginning of the course, 75% of the students hold a problematic conception of research, and after the half year course, still half of the participated students had problems with expressing a scientifically sound conception of research. In addition to general undevelopedness of the maps, a severe confused conception of drawing a link from empirical to qualitative or quantitative, but not to both, was found. This finding indicates that some students have problems with understanding the very basic and central concept of empirical. 相似文献
18.
Damian Maher 《Learning, Media and Technology》2011,36(3):235-250
The purpose of the study reported on here was to explore ways in which the interactive whiteboard (IWB) can support students’ understanding of texts. A Year 3 and a Year 4 primary school class in New South Wales, Australia, is the focus of the research. A qualitative case study was carried out using multimodal analysis focusing on the use of an e‐book displayed via the IWB. The results of the study indicate that the IWB can support students’ understanding of a narrative to prepare them to write a whole‐class response through providing increased access to a range of resources that are multimodal in nature. The way the interactive features of the IWB can facilitate access to multimodal resources to cater for student needs is also discussed. 相似文献
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《Africa Education Review》2013,10(2):288-303
Abstract The New Assessment Policy was introduced in 2003. Teachers were expected to implement this policy in the various fields that they were teaching. It is more than four years since the implementation of this policy. We explored selected teachers’ understanding of the policy, including factors that influenced their understanding. We were particularly interested in what Grade 7 and 9 Mathematics and Natural Sciences Learning Areas teachers’ understanding of this policy was and when, how and why this understanding was influenced. A naturalistic, qualitative case study approach was used. Three teacher education students were trained to collect data from a convenient, small sample of twelve Grade 7 and Grade 9 teachers. The findings suggest that many of the participating teachers’ understanding is still linked to assessing learners’ knowledge only. Some teachers included skills in their understanding of assessment, but only one Grade 7 teacher mentioned values. Furthermore, it was possible to draw a distinction between the teachers’ personal understanding and their policy understanding of the Assessment Policy. We conclude that, after more than four years, many teachers’ understanding of assessment is still restricted mainly to the assessment of knowledge. We suggest that teachers’ knowledge, skills, attitudes and values of assessment as well as of the assessment process should be given due consideration for effective implementation of the Assessment Policy. 相似文献