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.     

Students’ images of mathematics

Students’ judgments about “what counts” as mathematics in and out of school have important consequences for problem solving and transfer, yet our understanding of the source and nature of these judgments remains incomplete. Thirty-five sixth grade students participated in a study focused on what activities students judge as mathematical, and how they make their judgments. Students completed a photo sorting activity; took, viewed, and captioned their own photos of mathematics; viewed and commented on classmates’ photos; and participated in a small group discussion. Across multiple sources of data, findings showed that students attended to two major features of photos and activities when making judgments: surface cues present in the photos, such as numbers and money, and the possibility for mathematical action. Some students looked for the possibility of mathematics, while others asked if mathematics was necessary. Students also gave higher ratings to activities with which they had personal experience. The article concludes with possible implications for practice.     

Students’ perceptions of parental bonding styles and their academic burnout

This study investigated how parental bonding style affects academic burnout in Korean adolescents. Participants were 447 middle school students, who completed the Parental Bonding Instrument and the Maslach Burnout Inventory-Student Survey. MANCOVA results confirmed that adolescents reporting the optimal bonding parental style, for both mother and father, have lower scores on three subscales of academic burnout (Exhaustion, Cynicism, and Inefficacy) than do their counterparts who report the affectionless control parental style. We discuss the possible implications for reducing students?? academic burnout rates.     

Preservice Students’ Perceptions and Level of Satisfaction with their Field Experiences

This paper reports on a study of students’ perceptions and level of satisfaction with the teaching‐learning process while participating in the field‐experience component of the four‐year Bachelor of Education course at the Australian Catholic University Signadou Campus in Canberra. It is argued that successful student‐teacher field‐experience programmes provide opportunities for ongoing renewal and growth. Essential to this process is the implementation of appropriate evaluative procedures which involve all the participating members of the programme. The success of the process is evidenced in the ongoing modification of the programme to accurately reflect the interests and needs of the participants. Such a process leads to higher levels of communication, satisfaction and reflection on practice by all interested parties. Through an analysis of students’ questionnaire responses, this paper provides insights into the changing nature of student perceptions about the quality of their field experiences and their level of satisfaction with the various components of the programme. The results indicate that as the focus moves from the university itself to independent student responsibility the levels of satisfaction increase.     

The Mismatch between Students’ Mental Models of Acids/Bases and their Sources and their Teacher’s Anticipations thereof

The aim of this study is to compare the characteristics and sources of students’ mental models of acids and bases with a teacher’s anticipations and, based on this comparison, to explore some possible explanations why motivated students might fail to learn from a subject‐knowledgeable chemistry teacher. The study involves a chemistry teacher and her 38 ninth graders and focuses on the mental models of three high achievers and three low achievers who were interviewed in depth. Four students’ mental models of acid and base are identified. The mental models and sources of students’ conceptions of acids and bases that influenced the high achievers are compared to those of the low achievers. We find that the teacher in the study made accurate anticipations of her students’ mental models in the case of the high achievers but inaccurate anticipations of the low‐achievers’ mental models and the diverse sources influencing their mental models. In addition, the teacher incorrectly attributed the poor achievement of the low‐achieving students to their intuition and underestimated the effects of her teaching on the achievement of these students. As a result, the teacher’s instruction reinforced the low‐achievers’ incorrect mental models. Finally, the different approaches for teaching students with different achievements are emphasized according to the empirical data in this study.     

Students’ conceptions about a fair assessment of their learning

The objective of this study is to know the conceptions of primary and secondary school students about what constitutes a fair assessment. To achieve this aim, a phenomenographic study was carried out with 32 students. In a broad sense, the results showed that there were two types of conceptions. On one hand, a conception of fair assessment related to equality, transparency, objectivity, and evaluation of class content; that is, an egalitarian conception of fair assessment. On the other hand, a conception associated with ideas such as adaptation, diversification of tests, and qualitative assessment, even taking into account students' effort and attitudes, which define a conception of fair assessment linked to equity. These conceptions are associated with the concepts of legal justice and social justice, respectively and they contrast with the nature of external evaluations currently carried out.     

Students’ assessment preferences, perceptions of assessment and their relationships to study results

The purposes of this study are to gain more insight into students’ actual preferences and perceptions of assessment, into the effects of these on their performances when different assessment formats are used, and into the different cognitive process levels assessed. Data were obtained from two sources. The first was the scores on the assessment of learning outcomes, consisting of open ended and multiple choice questions measuring the students’ abilities to recall information, to understand concepts and principles, and to apply knowledge in new situations. The second was the adapted Assessment Preferences Inventory (API) which measured students’ preferences as a pre-test and perceptions as a post-test. Results show that, when participating in a New Learning Environment (NLE), students prefer traditional written assessment and questions which are as closed as possible, assessing a mix of cognitive processes. Some relationships, but not all the expected ones, were found between students’ preferences and their assessment scores. No relationships were found between students’ perceptions of assessment and their assessment scores. Additionally, only forty percent of the students had perceptions of the levels of the cognitive processes assessed that matched those measured by the assessments. Several explanations are discussed.     

Improving the judgment of task difficulties: prospective teachers’ diagnostic competence in the area of functions and graphs

To teach adaptively, teachers should be able to take the students’ level of knowledge into account. Therefore, a key component of pedagogical content knowledge (PCK) is the ability to assume the students’ perspectives. However, due to the so-called expert blind spot, teachers tend to misestimate their students’ knowledge, such as when estimating the difficulty of a given task. This empirically well-documented estimation bias is predicted by Nickerson’s anchoring and adjustment model, which generally explains how people take on other people’s perspectives. In this article, we present an intervention study that aims to improve the accuracy of prospective teachers’ judgments of task difficulty in the area of functional thinking. Two types of treatments are derived from Nickerson’s model. In the first condition (PCK group), participants acquire knowledge about task characteristics and students’ misconceptions. The second condition (sensitizing group) serves to control the idea that potential improvements in the PCK group are not merely based on a pure sensitization of the expert’s estimation bias. Accordingly, these participants are only informed about the general tendency of overestimating task difficulties. The results showed that the PCK group improved both in terms of the accuracy of the estimated solution rates and the accuracy of rank order, whereas the sensitizing group only improved in regard to the former. Thus, the study shows that prospective teachers’ diagnostic judgments can be improved by teaching them relevant PCK in a short amount of time.     

Future Perfect?: Teachers’ Expectations and Explanations of their Latino Immigrant Students’ Postsecondary Futures

Teacher expectancy research has demonstrated the greatest effects for members of racialized groups. Most research has focused on students’ near-term abilities; missing are understandings of how teachers perceive their students’ future trajectories. Drawing on social mirroring and attribution theories, this study investigates how 14 elementary, middle, and high school teachers of Latino immigrant students described and explained their students’ post-high school futures. Most teachers described their students as non-college-bound, with employment likely in the service sector. They attributed their students’ futures to family related explanations more often than to structural factors. The study’s implications emphasize the need to develop deeper understanding of structural inequalities that mediate students’ trajectories including schooling factors.     

Students’ opinions on blended learning and its implementation in terms of their learning styles

The purpose of this article is to examine students’ views on the blended learning method and its use in relation to the students’ individual learning style. The study was conducted with 31 senior students. Web based media together with face to face classroom settings were used in the blended learning framework. A scale of Students’ Views on Blended Learning and its implementation, Kolb’s Learning Style Inventory, Pre-Information Form and open ended questions were used to gather data. The majority of the students’ fell into assimilators, accommodators and convergers learning styles. Results revealed that students’ views on blended learning method and its use are quite positive.     

Students’ beliefs and experiences of interdisciplinary learning

This study explored senior secondary students’ beliefs and experiences of learning an interdisciplinary curriculum, Liberal Studies, in Hong Kong. Through the analysis of focus-group interviews with 168 students, most of the students were found to enjoy or at least not resist interdisciplinary learning, and preferred to study real-world contemporary issues. More than half of the students, however, expressed their relative lack of confidence in interdisciplinary learning because of the difficulties they encountered in Independent Enquiry Studies and the public examination. The students were also found to have undertaken examination-oriented activities when the public examination approached. The study sheds light on the realization of interdisciplinary learning in secondary education in contexts where teacher-centred pedagogy and an accountability agenda remain influential.     

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.     

Students’ Preconceptions and Perceptions of Science-Oriented Studies

Do non-science, technology, engineering, and mathematics (STEM) students’ views about STEM studies correspond with how STEM students actually perceive these studies? This paper deals with this issue by comparing higher education students’ attitudes towards STEM studies between those who actually did a STEM study and those who did not. The attitudes of the first category of students have been referred to as perceptions and the attitudes of the second category as preconceptions. The study included 1,935 students in higher education. The results confirm both small and large differences between the preconceptions and perceptions, and show significant differences between suitably qualified students (i.e. eligible for STEM studies) and other students. At the end of this paper, we will discuss the implications of this study for future research and offer some suggestions for practice.     

Teachers’ and Students’ Conceptions of Good Science Teaching

Capitalizing on the comments made by teachers on videos of exemplary science teaching, a video-based survey instrument on the topic of ‘Density’ was developed and used to investigate the conceptions of good science teaching held by 110 teachers and 4,024 year 7 students in Hong Kong. Six dimensions of good science teaching are identified from the 55-item questionnaire, namely, ‘focussing on science learning’, ‘facilitating students’ understanding’, ‘encouraging students’ involvement’, ‘creating conducive environment’, ‘encouraging active experimentation’ and ‘preparing students for exam (PSE)’. Significant gaps between teachers’ and students’ conceptions on certain dimensions have been revealed. The inconsistency on the dimension ‘PSE’ is particularly evident and possible reasons for the phenomenon are suggested. This study raises the important questions of how the gap can be addressed, and who is to change in order to close the gaps. Answers to these questions have huge implications for teacher education and teacher professional development.     

The positioning of students in newly qualified secondary teachers’ images of their ‘best teaching’

Asking newly qualified teachers (NQTs) to provide images of their ‘best teaching’, and encouraging subsequent reflection on these images, has the potential to enhance their understanding of themselves as teachers as they explore their often unconsciously held assumptions about students and classrooms. This paper reports aspects of a study of 100 New Zealand secondary NQTs as they constructed and explained images of themselves when ‘teaching at their best’ at three points over the first 18 months of full-time teaching. The article shows how these images of ‘best teaching’ may represent the NQTs’ pedagogical creed, and explores the nature of relationships and ways of working with students described within this developing pedagogy. It concludes by indicating implications from this study for teacher education pedagogies and programmes.     

Analyzing prospective teachers’ images of scientists using positive,negative and stereotypical images of scientists

Background and purpose : This study details the use of a conceptual framework to analyze prospective teachers’ images of scientists to reveal their context-specific conceptions of scientists. The conceptual framework consists of context-specific conceptions related to positive, stereotypical and negative images of scientists as detailed in the literature on the images, role and work of scientists.

Sample, design and method : One hundred and ninety-six drawings of scientists, generated by prospective teachers, were analyzed using the Draw-A-Scientist-Test Checklist (DAST-C), a binary linear regression and the conceptual framework.

Results : The results of the binary linear regression analysis revealed a statistically significant difference for two DAST-C elements: ethnicity differences with regard to drawing a scientist who was Caucasian and gender differences for indications of danger. Analysis using the conceptual framework helped to categorize the same drawings into positive, stereotypical, negative and composite images of a scientist.

Conclusions : The conceptual framework revealed that drawings were focused on the physical appearance of the scientist, and to a lesser extent on the equipment, location and science-related practices that provided the context of a scientist’s role and work. Implications for teacher educators include the need to understand that there is a need to provide tools, like the conceptual framework used in this study, to help prospective teachers to confront and engage with their multidimensional perspectives of scientists in light of the current trends on perceiving and valuing scientists. In addition, teacher educators need to use the conceptual framework, which yields qualitative perspectives about drawings, together with the DAST-C, which yields quantitative measure for drawings, to help prospective teachers to gain a holistic outlook on their drawings of scientists.     

The Relationship between Students’ Views of the Nature of Science and their Views of the Nature of Scientific Measurement

The present study explores the relationship between students’ views of the nature of science (NOS) and their views of the nature of scientific measurement. A questionnaire with two‐tier diagnostic multiple‐choice items on both the NOS and measurement was administered to 179 first‐year physics students with diverse school experiences. Students’ views on the NOS were classified into four NOS ‘profiles’, and views on measurement were classified according to either the point or set paradigms. The findings show that students with a NOS profile dominated by a belief that the laws of nature are to be discovered by scientists are more likely to have a view of the nature of scientific measurement characterised by a belief in ‘true’ values. On the other hand, students who believe that scientific theories are inventions of scientists, constructed from observations that are then validated through further experimentation, are more likely to have a view of the nature of scientific measurement that is underpinned by the uncertain nature of scientific evidence. The implications for teaching scientific measurement at tertiary level are discussed.