An empirical study of students’ understanding of a logical structure in the definition of limit via the <Emphasis Type="Italic">ε</Emphasis>-strip activity

This study explored students’ understanding of a logical structure in defining the limit of a sequence, focusing on the relationship between ε and N. The subjects of this study were college students who had already encountered the concept of limit but did not have any experience with rigorous proofs using the ε–N definition. This study suggested two statements, each of which is written by using a relationship between ε and N, similar to the ε–N definition. By analyzing the students’ responses to the validity of the statements as definitions of the limit of a sequence, students’ understanding of such a relationship was classified into five major categories. This paper discusses some essential components that students must conceptualize in order properly to understand the relationship between ε and N in defining the limit of a sequence.     

Path analysis: A model for the development of scientific reasoning abilities in adolescents

A model was formulated and tested for the development of scientific reasoning abilities in adolescents. Piagetian theory provided the framework for choosing potential determinants of the dependent variable, scientific reasoning abilities. A model reflecting hypothesized causal relationships among determinants and with the dependent variable was developed a priori on the basis of theoretical and substantive reasoning. The hypothesized model was tested and revised using path analysis. Data from intact classes of middle-school (n = 101) and high-school (n = 89) students from an upper-middle-class suburb of a midwestern city revealed significant (p < 0.05) path coefficients for these variables and scientific reasoning abilities: age, I.Q., field dependence–independence, and experience. A path from locus of control to scientific reasoning abilities through field dependence-independence was also statistically significant. The revised model explained 61 percent of the variance in scientific reasoning abilities.     

Computer Environments for Proof Construction

Abstract

Does the presentation and use of the search space matter for complex problem solving tasks? We address these questions for the construction of proofs in sentential logic. Using a fully computerized logic course, we isolated crucial features of computer environments and assessed their relative pedagogical effectiveness. After being given a pretest for logical aptitude, students were divided into three matched groups, each of which used a distinct computerized environment to construct proofs. All students were presented with identical course material on sentential logic for approximately five weeks.

Students completed more than one hundred exercises during those five weeks and took a midterm at the end of the period. The group using the most informative and most flexible interface performed substantially better on the midterm— the difference was particularly striking for hard problems. In two follow‐up experiments we added strategic problem solving help; student performance improved again (entirely on the difficult problems). Our interpretation is, first, flexibility in traversing the search space leads students to see the global structure of the search space and to develop effective heuristics; second, strategic help reinforces and extends these heuristics.     

KNOWLEDGE USE IN THE CONSTRUCTION OF GEOMETRY PROOF BY SRI LANKAN STUDENTS

Within the domain of geometry, proof and proof development continues to be a problematic area for students. Battista (2007) suggested that the investigation of knowledge components that students bring to understanding and constructing geometry proofs could provide important insights into the above issue. This issue also features prominently in the deliberations of the 2009 International Commission on Mathematics Instruction Study on the learning and teaching of proofs in mathematics, in general, and geometry, in particular. In the study reported here, we consider knowledge use by a cohort of 166 Sri Lankan students during the construction of geometry proofs. Three knowledge components were hypothesised to influence the students’ attempts at proof development: geometry content knowledge, general problem-solving skills and geometry reasoning skills. Regression analyses supported our conjecture that all 3 knowledge components played important functions in developing proofs. We suggest that whilst students have to acquire a robust body of geometric content knowledge, the activation and the utilisation of this knowledge during the construction of proof need to be guided by general problem-solving and reasoning skills.     

Worldviews in transition: using ecological autobiographies to explore students’ worldviews

College students (n = 292), after completing an American environmental history course, self‐selected, defined and defended their ecological worldview in an ecological autobiography essay that used historic content about different philosophies concerning the environment and natural resource use. The whole sample divided into groups along a spectrum of anthropocentrism to biocentrism with several worldview perspectives that ranged from utilitarian conservationism, which were anthropocentric, to preservationism, which were biocentric. A large group (n = 115), named logical idealists, fell midway in this continuum and expressed conflict with their desires for preserving the environment and their utilitarian lifestyle references. However, another mid‐continuum group, non‐radical environmentalists and ecologists (n = 59), were quite firm in their definition and did not express dissonance with their views, and considered themselves more mainstream environmentalist. The students stated that exposure to different worldviews within contextual content made them more tolerant and understanding of worldviews different from their own. The resulting worldview categories and polarized spread of worldviews have implications for the field of environmental education.     

When Mastery Goals Meet Mastery Learning: Administrator,Teacher, and Student Perceptions

Few studies have examined the impact of mastery learning on mastery goal structures or even on students’ motivation more generally. In this study, we examined one middle school that implemented a schoolwide mastery learning system, conducting interviews with a sample of administrators (n = 3), teachers (n = 4), and students (n = 9) to determine how the system was envisioned by the school leadership, implemented by the teaching staff, and perceived by the students. We used deductive qualitative analysis (DQA) to determine visions, practices, and perceptions aligned with achievement goal theory. Results indicated that evaluation practices have the greatest potential to undermine other positive motivational impacts of mastery learning–based instruction. Implications and transferability for research and practice are discussed.     

Exploring academic and cognitive skills impacting retention and acquisition of word-problem knowledge gained during or after intervention

In the present study, we investigated the impact of a word-problem intervention in retention and acquisition of knowledge after the intervention ended. We based analyses upon Grade 4 students experiencing mathematics difficulty (average age at pretest = 8.77) who received one of two variants of a word-problem intervention (with [n = 111] vs. without [n = 110] embedded pre-algebraic reasoning instruction) and students within a business-as-usual condition (BaU [n = 127]) separately. Findings revealed that students who received the intervention not only tended to retain less, but they also showed more active knowledge acquisition after the intervention ended. Furthermore, word-problem intervention altered the contributions of some prior knowledge and skills on both retention and acquisition.     

Predictors of psychological distress and well-being in a sample of Australian undergraduate students

Previous research has found university students report higher levels of psychological distress compared to the general population. Our aim was to investigate the degree to which personality and contextual factors predict psychological distress and well-being in students over the course of a semester. We also examined whether resilience-building skills, such as positive self-talk, mindfulness meditation and self-management, included in a first-year psychology subject, might reduce distress and improve well-being. Undergraduate first-year students (n?=?150) completed a battery of questionnaires in week three (Time 1; n?=?150) and week 10 (Time 2; n?=?53) of semester. At both times students reported high levels of psychological distress, as measured by the K10, the General Health Questionnaire and the Brief Symptom Inventory, and low levels of psychological well-being, as measured by the Warwick Edinburgh Mental Well-Being Scale. Students exposed to resilience-building skills embedded in a subject (n?=?24) were no less distressed at Time 2 than those not enrolled in that subject (n?=?29). The personality traits of emotional resilience (vs. reactivity) and bounce-back resilience measured at Time 1 were the only significant predictors of psychological distress and well-being measured at Time 2. Students with high emotional and bounce-back resilience had lower psychological distress and higher well-being scores. Future research could consider development and trial of a full semester university subject designed to improve students’ resilience knowledge and skills.     

Unpacking the logic of mathematical statements

This study focuses on undergraduate students' ability to unpack informally written mathematical statements into the language of predicate calculus. Data were collected between 1989 and 1993 from 61 students in six small sections of a bridge course designed to introduce proofs and mathematical reasoning. We discuss this data from a perspective that extends the notion of concept image to that of statement image and introduces the notion ofproof framework to indicate that part of a theorem's image which corresponds to the top-level logical structure of a proof. For simplified informal calculus statements, just 8.5% of unpacking attempts were successful; for actual statements from calculus texts, this dropped to 5%. We infer that these students would be unable to reliably relate informally stated theorems with the top-level logical structure of their proofs and hence could not be expected to construct proofs or validate them, i.e., determine their correctness.     

Degrees of co-creation: an exploratory study of perceptions of international students’ role in community engagement experiences

Increased competition for the international student market has motivated universities to modernize their marketing strategies. Community engagement is an important component of students' international university experience and represents a potential point of competitive advantage. Developing marketing strategies around university–student–community engagement (U–S–CE) requires an understanding of the perspectives of international students, the university and the community. We anchored our study in value co-creation which is a principle of the service dominant logic framework found in the marketing literature. With limited research in the area, a qualitative approach was appropriate. Interviews were undertaken with key university members (n?=?4) and community members (n?=?5) concurrently with focus groups of international students (n?=?22) at a single university. Based on the degree of co-creation by international students in U–S–CE, three groups emerged: consumers, collaborators and co-designers. This study offers theoretical and practical insight, providing a platform for further research into U–S–CE.     

A Pilot Study Examining Religious Organization Affiliation,Sexual Health Information Sources,and Sexual Behaviors Among College Students

We conducted an online survey to examine religiosity, sexual health knowledge, and behavior and sexual health information sources among undergraduate students affiliated with student religious organizations (n?=?45) and unaffiliated students (n?=?82). Analyses included Fisher’s exact tests, t-tests, and exact regression models. Students reporting religious affiliation considered religious sources to be believable (p?=?.004 for sexual health; p?p?=?.0042). Although religiously affiliated students reported fewer sexual partners in the past year (p?=?.020), their reported condom use was not significantly different from that of unaffiliated students. Future research should explore the focus and content of romantic relationship information provided by student religious organizations. Health practitioners and educators should consider strategies for collaborating with religious organizations to meet the information needs of these students.     

On sums of powers of integers

For non-negative integers k, n, let P _k (n) denote the sum {fx27-1}. We show by two different means that if k ≥ 3 and odd, then n ²(n+1)² iss a factor of the polynomial P _k (n); and if k ≥ 2 and even, then n (n+1) (2n+1) is a factor of the polynomial P _k (n). We also derive a relatively unknown result first obtained by Johann Faulhaber in the 17th century. Shailesh Shirali has been at Rishi Valley School, Andhra Pradesh (Krishnamurti Foundation India) since the 1980’s. He has a deep interest in teaching and writing about mathematics at the high school/post school levels, with particular emphasis on problem solving and on historical aspects of the subject. He has been involved in the Mathematics Olympiad movement at the national and international level for the past two decades. He is the author of several expository books and articles aimed at interested high school students.     

An Evaluation of the Linearity of Curriculum‐Based Measurement of Oral Reading (CBM‐R) Progress Monitoring Data: Idiographic Considerations

Educators use curriculum‐based measurement of oral reading (CBM‐R) to measure student response to instruction. Current decision‐making frameworks assume students demonstrate linear growth across a school year. However, growth appears nonlinear for at least a subgroup of students. We assessed the degree to which grade two (n = 800) and grade three (n = 800) students receiving intensive interventions experienced discontinuous growth. We also explored when discontinuous growth tended to occur, and whether students improved or regressed afterward. Results indicate linear patterns were adequate for most students (80 percent). Students who showed discontinuous growth early tended to improve afterward. Conversely, students who showed discontinuous growth later tended to plateau. Findings suggest multilevel models may obscure variability in growth patterns. Practice and research implications are discussed.     

Software that assists learning within a complex abstract domain: the use of constraint and consequentiality as learning mechanisms

This paper describes a research project into undergraduates’ use of a software tool to learn symbolic logic—a complex abstract domain that has been shown to be intimidating for students. The software allows the students to manipulate proofs in certain ways and then calculates the consequences of their actions. A research method has been developed that allowed students’ use of this tool to be modelled, and this model was then used to identify, refine and create visual cues that provide support for students’ reasoning. The focus of this paper is the role of the software as an artefact to aid students’ visualisation of reasoning processes rather than the logic itself. The main mechanisms by which this visualisation is supported are the imposition of constraints on the actions available and the demonstration to students of the consequences of their actions. The study shows that the software encouraged experimentation with different routes to a proof, and constituted a challenge to fixated reasoning.     

The effect of learning style on doctoral course completion in a Web-based learning environment

One hundred and fifty-nine doctoral students, majoring in Computing Technology in Education (CTE), were tracked during the coursework phase in a Web-based learning environment. At the beginning of the coursework, each student completed a demographic data form and Kolb's Learning Style Inventory (LSI). Due to the type of program, it was hypothesized that students would primarily fall into Kolb's Converger and Assimilator categories, and learning style would predict completion of the required courses. Results indicated 84.3% (n=134) of all students finished the required coursework. One hundred and twenty-four of the students (78%) fell into the predicted categories and, of these, 87.1% (n=108) finished the coursework. Students not falling into the predicted categories (n=35) had a 74.3% (n=26) completion rate.An examination of the means scores for both groups indicated that students with a preference for Abstract Conceptualization dropped out of the program at significantly lower rates, t(157)=1.667, p=.045(one-tailed), than students with other preferred learning strategies. The implications are clear. First, students, for the most part, are able to adapt their personal learning styles in order to succeed in a Web-based learning environment. Second, students with a preference for systematic planning and an intellectual understanding of a situation are more likely to succeed than students preferring concrete experience and interaction with other students. Institutions offering programs of this type should be prepared to address learning style issues when developing and offering such programs.     

Questionnaire on Perceived Competency-based Learning for primary school students (#ICOMpri1) / Cuestionario del Aprendizaje Percibido basado en Competencias para el Alumnado de Educación Primaria (#ICOMPri1)

The purpose of this study was to design and validate an assessment tool to find out how primary school students perceive their competency-based learning. By examining the content validity (n = 35 experts), comprehension (n = 173 students) and construct (n = 523 students) of the instrument, the results showed correct psychometric quality, internal consistency, reliability and adequacy of the structural model: χ²/df = 2.08, TLI = 0.88, CFI = 0.90, GFI = 0.90, RMSEA = 0.04, and SRMR = 0.04. The final version of the Questionnaire on Perceived Competency-based Learning of primary school students (#ICOMpri1) includes eight dimensions and 27 items. The results showed a high perceived competency-based learning of primary school students. This is therefore a valid and reliable instrument that provides a more subjective and real vision of primary students’ academic performance. Nevertheless, future studies should analyse the criterion-related validity by comparing perception results with those of international academic achievement.     

The academic writing process in Spanish universities: perceptions of students and faculty / El proceso de escritura académica en la universidad española: percepciones de estudiantes y profesores

Abstract

This paper is intended as an exploration of university faculty and students’ perceptions of a number of dimensions involved in the written composition of academic texts. We analysed the responses to scale 3 in the European Writing Survey (EUWRIT) (in its Spanish version: Encuesta Europea sobre la Escritura Académica, EEEA) by a group of social science and humanities students (n = 1,030) and faculty (n = 230) from nine Spanish universities. We then examined the similarities and differences in their perceptions and established a factorial structure of the different dimensions underlying the writing process. The data indicate that both groups concur in the value assigned to both changing ideas in the course of the composition process (although this process seems to be understood differently by each group) and the revision and feedback processes. The students, however, claim to be involved in more planning and previous reading activities than the teachers perceive them to be. The significance of these results for a process-oriented perspective in academic writing is discussed.