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.     

Self-Regulation of Learning within Computer-based Learning Environments: A Critical Analysis

Computer-based learning environments (CBLEs) present important opportunities for fostering learning; however, studies have shown that students have difficulty when learning with these environments. Research has identified that students’ self-regulatory learning (SRL) processes may mediate the hypothesized positive relations between CBLEs and academic performance. In this review, we identified 33 empirical studies of SRL and CBLEs. We address three research questions: (1) How do learner and task characteristics relate to students’ SRL with CBLEs? (2) Can various learning supports or conditions enhance the quality of students’ SRL as they learn with CBLEs? (3) What conceptual, theoretical, and methodological issues exist for this growing area of research? We found evidence that specific SRL processes are more often associated with academic success than others and that SRL skills can be supported. We also identified a number of issues that researchers should aim to address in future investigations, including a more comprehensive measurement of facets of SRL and the quality of SRL processes, the seeming disconnect between SRL processes and learning outcomes, and the distinction between self- and other-regulation. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

One Science Teacher’s Professional Development Experience: A Case Study Exploring Changes in Students’ Perceptions of Their Fluency with Innovative Technologies

The purpose of this case-study is to narrate a secondary science teacher’s experience of his professional development (PD) education and training in innovative technologies (IT) in the context of engaging students in environmental research projects The sources from which the narrative is derived include (1) the science teacher’s reflective reports during three summer institute programs and (2) the science teacher’s reflective reports while subsequently engaging students in IT-embedded environmental research projects in his classroom. The science teacher’s explanations for changes in students’ perception of their IT fluency illuminate his personal narrative. The science teacher attributed his growth and significant changes in students’ perceptions of their IT fluency to the following mechanisms: (a) a personal commitment to developing his own and his students’ IT abilities in the context of doing environmental research projects, and (b) an increase in class time devoted to science education due to school-time scheduling policy. The study implies that immersive professional development opportunities have the potential to produce significant increases in students’ perceptions of their IT fluency.     

Inquiry-Based Learning and Undergraduates’ Professional Identity Development: Assessment of a Field Research-Based Course

Innovative strategies in inquiry-based learning are recognized as improving the quality of higher education learning, but there is a need to explore whether and how these strategies promote the development of professional identity among undergraduates. In this article we describe an inquiry-based course, situated in a European context, which is designed to support students’ professional identity development through reflective practice; and we present the assessment of students’ learning outcomes. Results highlight the key roles of field research, peer groups, and a narrative approach in promoting positive student attitudes toward reflecting on their production of knowledge and in developing their professional identity.     

Teachers attending to students’ mathematical reasoning: lessons from an after-school research program

There is a documented need for more opportunities for teachers to learn about students’ mathematical reasoning. This article reports on the experiences of a group of elementary and middle school mathematics teachers who participated as interns in an after-school, classroom-based research project on the development of mathematical ideas involving middle-grade students from an urban, low-income, minority community in the United States. For 1 year, the teachers observed the students working on well-defined mathematical investigations that provided a context for the students’ formation of particular mathematical ideas and different forms of reasoning in several mathematical content strands. The article describes insights into students’ mathematical reasoning that the teachers were able to gain from their observations of the students’ mathematical activity. The purpose is to show that teachers’ observations of students’ mathematical activity in research sessions on students’ development of mathematical ideas can provide opportunities for teachers to learn about students’ mathematical reasoning.     

The Role of Intragroup Marginalization in Latino College Student Adjustment

The purpose of this article is to examine how intragroup marginalization has a potential impact on Latino college students’ psychological adjustment. The concept of intragroup marginalization in this context relates to the perceived rejection of students by persons of their heritage culture group in response to the students’ acculturation efforts in regard to the college culture. Counselors can facilitate college success of Latino students by addressing acculturative stressors. Intragroup marginalization and its relationship to Latino college student adjustment is illustrated and discussed through a vignette.     

Uncovering students’ thinking about thinking using concept maps

A method for uncovering students’ thinking about thinking, specifically their meta-strategic knowledge, is explored within the context of an ongoing, multi-year intervention designed to promote the development of students’ thinking dispositions. The development of a concept-map instrument that classroom teachers can use and an analytic framework for interpreting students’ responses is presented. In a preliminary study, the concept map instrument is piloted to evaluate changes in students’ conceptions of thinking after a year’s participation in classrooms where their teachers actively sought to make thinking more visible by noticing and naming the thinking observed as well as introducing and using thinking routines (Ritchhart and Perkins. Educational Leadership, 65(5), 57–61 2008). Concept maps from 239 students from grades 3 through 11 were analyzed. Results suggest that students’ conceptions of thinking do improve with age but also can be substantially developed through a classroom culture where thinking is modeled and rich opportunities for thinking are present. The concept map instrument itself proved to be a robust instrument for uncovering students’ thinking about thinking.     

Components of Conceptual Ecologies

The theory of conceptual change is criticized because it focuses only on supposed underlying logical structures and rational process processes, and lacks attention to affective aspects as well as motivational constructs in students’ learning science. This is a vast underestimation of the complexity and diversity of one’s change of conceptions. The notion of conceptual ecology provides a context for understanding individuals’ conceptual change learning, as it is the environment through which all information is interpreted. This research investigated how high school students’ statements, made in answering questions, reflect selected components of their conceptual ecologies. Data for this study was collected from six interviews in which seven students took part. The data also include the science teacher’s profiles of each student, the students’ personal journals, their assignments, and their examinations and answers in class. The analysis presented will here include only those components that were represented in the discourse of the seven high school students who were interviewed. When students were asked questions, there was evidence of the engagement of the various components of conceptual ecologies. These components include: epistemological commitments, metaphysical beliefs, the affective domain and emotional aspects, the nature of knowledge, the nature of learning, the nature of conceptions, and past experience. Evidence from this study suggests that these components might function as constraints to learning. This study contributes to the field by expanding our knowledge of the components of high school students’ conceptual ecologies through its definition of the categories and themes associated with those components. In examining across the range of components, the study illustrates the variety and sources of science conceptions within high school students’ conceptual ecologies.     

The Interrelation of First-Year College Students’ Critical Thinking Disposition, Perceived Academic Control, and Academic Achievement

While a great deal of research has examined students’ critical thinking skills, less is known about students’ tendencies to use these skills. Specifically, little is known about what factors contribute to students developing a disposition to think critically or what impact this disposition has on college students’ academic achievement. Perceived control, which has been found to be an important factor in college students’ academic success, may be an important factor in developing this disposition. The current longitudinal study examined the reciprocal-effects between critical thinking disposition and perceived academic control, and their comparative influences on academic achievement in 1196 first-year college students. Using a two-wave, two-variable cross-lag structural equation model, a reciprocal-effect was found whereby students’ perceived academic control predicted their subsequent critical thinking disposition, and students’ critical thinking disposition predicted their subsequent perceived academic control. Furthermore, after controlling for high school academic performance, perceived academic control was found to have a stronger impact on students’ GPAs than critical thinking disposition. Implications of fostering a critical thinking disposition and perceived academic control among college students are discussed.

Delayed Understanding and Staying in Phase: Students’ Perceptions of their Study Situation

Findings are presented from a study of undergraduate students’ experiences of understanding in first-year engineering. At the end of their first year of study 86 Swedish students of electrical engineering and computer science were asked to reflect in writing on their experiences of studying and learning. Fifteen of them also took part in interviews which explored in some detail their experiences of understanding in relation to perceived constraints of the teaching-learning environment. The analyses of the students’ written accounts and the interview data focused on the students’ experiences of studying and of understanding in relation to course work in engineering. The majority of the students reported problematic first-year experiences and testified to a sensation of ‘falling out of phase’ with their studies. This sensation was frequently coupled with a lag in coming to understand course material, which may be characterised in terms of delayed understanding. The notion of delayed understanding is discussed in relation to ideas about students’ perceptions of the learning environment and the impact that those perceptions might have on students’ opportunities to reflect on learning material and develop a solid understanding of course material in engineering education. In conclusion, it is suggested that the the notion of delayed understanding captures the complications of a study situation in which a perceived lack of time to reflect on learning material obstructs students’ understanding of course material in engineering, and also points up a more general aspect of learning observing that time to reflect on previous experiences is an essential component of the process of coming to understand learning material in a particular educational setting.     

Engaging Students in Science Across the Primary Secondary Interface: Listening to the Students’ Voice

Most studies indicate primary students’ attitudes towards and interest in science decline as they progress into the secondary years. Longitudinal qualitative research exploring this phenomenon is rare as is research which focuses on the students’ voice as they cross the interface. In this study multiple qualitative data sources, supported by a ‘science interest’ composite scale, followed 20 students over 2 years. In contrast to baseline data on their peers these students, in general, maintained their interest in science. Apart from identifying the teacher’s pedagogical approach and classroom environment as two key issues in understanding these students’ journeys, the importance of listening to and heeding the students’ voice may be an even more critical concern in addressing the decline in students’ attitudes and interest in science.     

Tacit models,treasured intuitions and the discrete—continuous interplay

We explore conditions for productive synthesis between formal reasoning and intuitive representations through analysis of college students’ understanding of the limit concept in the definition of the derivative. In particular, we compare and contrast cognitive processes that accompany different manifestations of persistence of intuitions and tacit models that coexist with students’ logical reasoning. The students are highly trained in mathematics. We encounter expressions of the persistence and impact of intuitions and tacit pictorial models as described by Fischbein. But we also observe some new characterization of persistence of tacit models in which the tacit pictorial model continues to interfere in the student’s reasoning process, coexists with a logical reasoning but does not prevent the student from reaching a feeling of logical consistency. The empirical analysis and the theoretical discussion offered in the present paper permit us to highlight this very special integration of the formal and the intuitive components of the reasoning process.     

中美中学生学科知识结构的比较研究——基于概念图评价技术的实验研究

A concept map is a schematic device for representing a set of concept meanings embedded in a framework of propositions. It can be used to evaluate students’ knowledge structure. This article introduces the comparative study of Chinese and American secondary school students’ knowledge structure. They are compared quantitatively and qualitatively in terms of mean score, individual proposition scores, proposition choice and map structure. The results indicate that students’ knowledge structures in the two countries are remarkably different. Compared with American students, Chinese students’ ability to take an exam is stronger and their mean score is higher. However, Chinese students need to improve their general knowledge and creativity although their basic knowledge is solid and they are better in mastering discipline knowledge and knowledge application. __________ Translated from Bijiao Jiaoyu Yanjiu 比较教育研究 (Comparative Education Review), 2008, (2): 12–16     

Students’ Learning with the Connected Chemistry (CC1) Curriculum: Navigating the Complexities of the Particulate World

The focus of this study is students’ learning with a Connected Chemistry unit, CC1 (denotes Connected Chemistry, chapter 1), a computer-based environment for learning the topics of gas laws and kinetic molecular theory in chemistry (Levy and Wilensky 2009). An investigation was conducted into high-school students’ learning with Connected Chemistry, based on a conceptual framework that highlights several forms of access to understanding the system (submicro, macro, mathematical, experiential) and bidirectional transitions among these forms, anchored at the common and experienced level, the macro-level. Results show a strong effect size for embedded assessment and a medium effect size regarding pre-post-test questionnaires. Stronger effects are seen for understanding the submicroscopic level and bridging between it and the macroscopic level. More than half the students succeeded in constructing the equations describing the gas laws. Significant shifts were found in students’ epistemologies of models: understanding models as representations rather than replicas of reality and as providing multiple perspectives. Students’ learning is discussed with respect to the conceptual framework and the benefits of assessment of learning using a fine-tuned profile and further directions for research are proposed. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Urban Educators’ Voices: Understanding Culture in the Classroom

This article discusses urban educators’ views of their teaching experiences. The article is based upon survey research conducted with teachers in two poor, urban districts during the 2005–2006 academic year. The teachers reported a variety of positive and negative views regarding their classrooms, their students, and the students’ social worlds. The data illustrate the importance of classroom processes for the teachers, and how they believed that their students’ social locations, behaviors, and attitudes impede the delivery of educational content. We believe this research raises interesting challenges regarding the need for urban educators to incorporate students’ perspectives into both instructional processes and curriculum content. Furthermore, this research should contribute to the empirical foundation needed for the creation of better teacher preparation programs.     

Students’ Adaptation of Study Strategies When Preparing for Classroom Tests

According to theories of students’ test preparation, students may optimize their test performance by paying special attention to important information and processing this information in ways that are appropriate to the type of questions included in the forthcoming test. However, research is unclear about the conditions under which students adapt study strategies to the demands of test preparation tasks. Moreover, little is known about the processes and abilities involved. In this article, we present a theoretical model that integrates various factors that seem relevant to strategy adaptation in test preparation, including the teacher’s intended task demands, students’ perceptions of these demands, students’ personal goals for studying, and their ability to adapt and implement strategies. The aim of our model is to stimulate further research on strategy adaptation, which may eventually provide evidence-based guidelines that could help teachers support the development of students’ strategy adaptability and use tests as learning tools.     

Development of student inquiry skills in a computerised classroom environment

This paper discusses a study in progress which involves the use of a computerised research science database (Birds of the Antarctica) and specially designed curriculum materials. The purpose of the study is to investigate the extent to which students’ inquiry skills can be facilitated by the materials. Much attention is given in the programme to developing both students’ inquiry skills and their subject-matter knowledge. Year 11 and 12 students’ knowledge and skills development are interpreted as they interact with the computerised database and the curriculum materials. Preliminary findings about students’ abilities and perceptions are discussed and, in particular, constraints to the development of inquiry skills and construction of understanding are explored. Specializations: Science education, computers in education, learning environment.     

Exploration of the contribution of teachers’ knowledge about reading to their students’ improvement in reading

Recent studies of elementary teachers’ knowledge about reading have been built on the premise that teachers need thorough knowledge about language and reading processes, but these studies have provided only limited evidence that teachers’ performance on tests of such knowledge contributes to their students’ reading achievement. The present study was designed to examine the contribution of first- through third-grade teachers’ knowledge about early reading to their students’ improvement on tests of word analysis and reading comprehension, controlling for socio-demographic characteristics of students, their prior reading achievement, and teachers’ educational attainment, professional experiences, and socio-demographic characteristics. Preliminary analyses indicated that the test of teachers’ knowledge had adequate psychometric characteristics. However, performance on this measure of teachers’ knowledge did not significantly explain students’ improvement on the two reading subtests. The complexity of the factors that influence teachers’ knowledge acquisition and the context in which the study was carried out offer possible explanations for these results. In addition, teachers’ content knowledge about reading might not be closely associated with the practices they use in reading instruction, and therefore might not be significantly related to their students’ improvement in reading over a year.