Students’ images and their understanding of definitions of the limit of a sequence

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.     

Exploring the use of concept chains to structure teacher trainees’ understanding of science

This paper reports on a paper and pencil concept‐sorting strategy that enables trainee teachers to restructure their knowledge in any one domain of science. It is used as a self‐study tool, mainly to enable them to break down and understand the progression of concepts beyond the level at which they have to teach. The strategy involves listing key ideas in an increasingly complex and inclusive fashion such that a ‘chain’ is developed where the initial statements are simple and the final ones more complex. Evaluation of the strategy with trainees over a five‐year period revealed promising potential for the strategy as a self‐study tool, as well as an audit tool, enabling tutors to more easily identify misconceptions. There was some evidence that trainees found the strategy useful in preparing themselves to teach in the classroom, possibly by enabling meaningful learning to take place according to the Ausubel–Novak–Gowin theory.     

Students’ understanding of voltage in simple parallel electric circuits

This paper reports an investigation of the performance of school students at age 15 on written diagnostic questions involving the prediction of meter readings in simple electric circuits with parallel branches. Results show that these students tend to perceive such questions in resistance‐current terms, with a primary focus on resistor addition, rather than in voltage terms, with two loads being driven from the same source. Common errors in predicting voltages across parallel branches suggest that few students use a mental model of voltage in approaching parallel circuit problems but instead attempt to solve problems by mechanical use of the V=IR equation. Implications for the teaching of electric circuits at this level are identified.     

Students’ understanding of the number line / Estudiantes pensando en la recta numérica

We studied the conceptions of students coming from secondary education and university regarding the number line as a representation of real numbers. In the context of a wider questionnaire, 307 students were presented with a task consisting of two verbal items and one graphic item related to the number line. The students were all at different levels in their study of mathematics (in the third, fourth or fifth year of secondary education, or at the beginning or advanced stage of a university degree in mathematics, biology or physical education). A gradient in the depth of the students’ conceptions, associated with the level of their studies in mathematics, was found. This gradient extends from the estrangement of facing the problem or a conception of a drawn or physical matter line, which was associated with students with a lower level of mathematical studies, passing through a vision centred around potential numeric density or a line containing points (discrete), up to an instrumental conception of the line as supportive of magnitudes in advanced students of biology and focusing on continuity sustained by advanced students of mathematics.     

Multilayered knowledge: understanding the structure and enactment of teacher educators’ specialized knowledge base

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.     

Three concepts or one? Students’ understanding of basic limit concepts

In many mathematics curricula, the notion of limit is introduced three times: the limit of a sequence, the limit of a function at a point and the limit of a function at infinity. Despite the use of very similar symbols, few connections between these notions are made explicitly and few papers in the large literature on student understanding of limit connect them. This paper examines the nature of connections made by students exposed to this fragmented curriculum. The study adopted a phenomenographic approach and used card sorting and comparison tasks to expose students to symbols representing these different types of limit. The findings suggest that, while some students treat limit cases as separate, some can draw connections, but often do so in ways which are at odds with the formal mathematics. In particular, while there are occasional, implicit uses of neighbourhood notions, no student in the study appeared to possess a unifying organisational framework for all three basic uses of limit.     

Diagnosing Students’ Understanding of the Nature of Models

Students’ understanding of models in science has been subject to a number of investigations. The instruments the researchers used are suitable for educational research but, due to their complexity, cannot be employed directly by teachers. This article presents forced choice (FC) tasks, which, assembled as a diagnostic instrument, are supposed to measure students’ understanding of the nature of models efficiently, while being sensitive enough to detect differences between individuals. In order to evaluate if the diagnostic instrument is suitable for its intended use, we propose an approach that complies with the demand to integrate students’ responses to the tasks into the validation process. Evidence for validity was gathered based on relations to other variables and on students’ response processes. Students’ understanding of the nature of models was assessed using three methods: FC tasks, open-ended tasks and interviews (N?=?448). Furthermore, concurrent think-aloud protocols (N?=?30) were performed. The results suggest that the method and the age of the students have an effect on their understanding of the nature of models. A good understanding of the FC tasks as well as a convergence in the findings across the three methods was documented for grades eleven and twelve. This indicates that teachers can use the diagnostic instrument for an efficient and, at the same time, valid diagnosis for this group. Finally, the findings of this article may provide a possible explanation for alternative findings from previous studies as a result of specific methods that were used.     

Educators’ understanding of the mediation role in the classroom

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.     

Students’ conceptions and the learning of science

This introductory article to the Special Issue of the International Journal of Science Education attempts to review the theoretical contexts for research into children's conceptions in science and to identify future directions for research programmes in this field.     

The relationship between biology teachers’ understanding of the nature of science and the understanding and acceptance of the theory of evolution

ABSTRACT

Despite the importance of the theory of evolution (TE) to scientific knowledge, a number of misconceptions continue to be found among biology teachers. In this context, the first objective of this study was to identify the impact of professional development programme (PDP) on teachers’ understanding of nature of science (NOS) and evolution and on the acceptance of this theory. Its second objective was to study the relationship among these variables. Three instruments were used to quantify these variables: the Views of the Nature of Science Version D (VNOS D+), the Assessing Contextual Reasoning about Natural Selection (ACORN), and the Measure of Acceptance of Theory of Evolution (MATE). The results indicate that the PDP had a positive impact on teachers, significantly improving their understanding of the NOS and natural selection, as well as their acceptance of the TE. Furthermore, a positive correlation between the understanding of the NOS obtained by teachers in the first part of the PDP and the understanding and acceptance of evolution that these teachers showed at the end of the programme was determined. However, no relationship between an understanding of the NOS and gains in the understanding and acceptance of evolution was found.     

Students’ navigation of the uncharted territories of academic writing

Abstract

Many students enter tertiary education unfamiliar with the ‘norms and conventions’ of their disciplines. Research into academic literacies has shown that in order to succeed in their studies, students are expected to conform to these norms and conventions, which are often unrecognized or seen as ‘common sense’ by lecturers. Students have to develop their own ‘map’ of their programme's expectations in order to make sense of the seemingly mysterious practices they are expected to take on. This study, undertaken at a University of Technology in South Africa, details students’ perceptions of their writing difficulties and their attempts to navigate their way through various writing tasks. The findings reveal that students experience a range of difficulties and that the students often feel unsupported in their travails with academic writing.     

On the Cultivation of College Students’ Ability of Translating

Translation is a kind of communicative function of language behavior.In English teaching,translation capabilities must be one of the purposes of our teaching.As a teaching activity it aims to lay a good foundation in English for students and effective teaching methods,but also comprehensive language skills,students study the benchmark one.     

Variation in Students’ Experiences of the ‘Oxford Tutorial’

This paper examines Oxford University students’ conceptions of the role of the tutorial in their learning. An analysis of interviews with 28 students constituted four qualitatively different conceptions of the ‘Oxford Tutorial’. These ranged from the tutorial involving the tutor explaining to the student what the student did not know, to the tutorial involving the tutor and the student in exchanging different points of view and both coming to a new understanding of the topic under discussion. These different conceptions also appeared to be related to variations in students’ views of the role of the work done in preparation for the tutorial, their view of the student’s and tutor’s roles in the tutorial, and the conception of knowledge that students adopted in relation to the tutorial. The implications of this study are discussed in terms of the relations between students’ conceptions of tutorials and their anticipated learning outcomes and its implications for contexts outside of Oxford in terms of students’ conceptions of academic tasks.     

About the Investigation of Art Students’English Study

English study is becoming more and more important.However,art students have weak English level on average.Thus,it’ s a problem for students and teachers to improve the quality of English study.In this article,it analyses the reason for the weak English level and the responding strategy.What’ s more,it encourages students to study actively and advocates teach ing based on art knowledge.     

Students’ spontaneous ideas about the speed of light

The answers given by a group of physics graduate students to two problems on the speed of light are analysed. The results seem to confirm the use of spontaneous ideas which are very similar to those which form the ‘spontaneous’ kinematics proposed by Saltiel (1980). Some consequences related to the teaching of physics and special relativity are discussed.     

Children's understanding of the additive composition of number and of the decimal structure: what is the relationship?

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.     

Students ’ perceptions of science classes in the Philippines

This study used a modified version of the Perception of Science Classes Survey (Kardash & Wallace, 2001) to survey 7,885 grade school and high school students in different provinces in the Philippines regarding their perceptions of their science classes. Factor analysis revealed five dimensions of the students ’ perceptions that relate to different aspects of the teacher ’s pedagogy and the learning environment created by the teachers: (a) Learner-Centered Pedagogy, (b) Science Inquiry Activities, (c) Positive Affect and Attitudes, (d) Grades as Feedback, and (e) Support for Self-Learning and Effort. Factor scores were compared across grade levels and genders. The results indicate a decrease in science inquiry activities and the use of grades as feedback in the higher grades, but an increase in support for self-learning and effort, and also positive affects and attitudes. These trends were discussed in relation to possible problems related to teacher practices that may contribute to low student achievement levels in science. This research was part of a research project commissioned by the Japan International Cooperation Agency-Philippines.     

Students’ understanding of a groundwater system and attitudes towards groundwater use and conservation

The purpose of this study was to investigate students’ understanding of groundwater as a system, and to further examine whether and how their understanding is related to attitudes towards groundwater use and conservation. A total of 676 junior high school students completed a groundwater survey including a drawing activity and a questionnaire. An additional group of university students with environmental science majors were recruited for the survey for the purpose of determining reasonable expectations and validating interpretations of the results. Analysis of student drawings indicated that students generally held an incomplete and unconnected understanding of the groundwater system. Correlation analysis showed that student levels of understanding were associated with their perceptions of environmental impacts as well as environmental concern regarding groundwater problems. These findings re-emphasised the importance of promoting students’ understanding of environmental systems, as well as their ability to think systemically.