Geometrical representations in the learning of two-variable functions

This study is part of a project concerned with the analysis of how students work with two-variable functions. This is of fundamental importance given the role of multivariable functions in mathematics and its applications. The portion of the project we report here concentrates on investigating the relationship between students’ notion of subsets of Cartesian three-dimensional space and the understanding of graphs of two-variable functions. APOS theory and Duval’s theory of semiotic representations are used as theoretical framework. Nine students, who had taken a multivariable calculus course, were interviewed. Results show that students’ understanding can be related to the structure of their schema for R³ and to their flexibility in the use of different representations.     

Students’ perceptions about peer assessment for writing: their origin and impact on revision work

We investigate students’ negative perceptions about an online peer assessment system for undergraduate writing across the disciplines. Specifically, we consider the nature of students’ resistance to peer assessment; what factors influence that resistance; and how students’ perceptions impact their revision work. We do this work by first examining findings from an end-of-course survey administered to 250 students in ten courses across six universities using an online peer assessment system called SWoRD for their writing assignments. Those findings indicate that students have the most positive perceptions of SWoRD in those courses where an instructor graded their work in addition to peers (as opposed to peer-only grading). We then move to an in-depth examination of perceptions and revision work among 84 students using SWoRD and no instructor grading for assessment of writing in one university class. Findings from that study indicate that students sometimes regard peer assessment as unfair and often believe that peers are unqualified to review and assess students’ work. Furthermore, students’ perceptions about the fairness of peer assessment drop significantly following students’ experience in doing peer assessment. Students’ fairness perceptions—and drops in those perceptions—are most significantly associated with their perceptions about the extent to which peers’ feedback is useful and positive. However, students’ perceptions appear to be unrelated to the extent of their revision work. This research fills a considerable gap in the literature regarding the origin of students’ negative perceptions about peer assessment, as well as how perceptions influence performance.     

Teacher Learning of Technology Enhanced Formative Assessment

This study examined the integration of technology enhanced formative assessment (FA) into teachers’ practice. Participants were high school physics teachers interested in improving their use of a classroom response system (CRS) to promote FA. Data were collected using interviews, direct classroom observations, and collaborative discussions. The physics teachers engaged in collaborative action research (AR) to learn how to use FA and CRS to promote student and teacher learning. Data were analyzed using open coding, cross-case analysis, and content analysis. Results from data analysis allowed researchers to construct a model for knowledge skills necessary for the integration of technology enhanced FA into teachers’ practice. The model is as a set of four technologies: hardware and software; methods for constructing FA items; pedagogical methods; and curriculum integration. The model is grounded in the idea that teachers must develop these respective technologies as they interact with the CRS (i.e., hardware and software, item construction) and their existing practice (i.e., pedagogical methods, curriculum). Implications are that for teachers to make FA an integral part of their practice using CRS, they must: 1) engage in the four technologies; 2) understand the nature of FA; and 3) collaborate with other interested teachers through AR.     

Students’ understanding of the general notion of a function of two variables

In this study we analyze students’ understanding of two-variable function; in particular we consider their understanding of domain, possible arbitrary nature of function assignment, uniqueness of function image, and range. We use APOS theory and semiotic representation theory as a theoretical framework to analyze data obtained from interviews with thirteen students who had taken a multivariable calculus course. Results show that few students were able to construct an object conception of function of two variables. Most students showed difficulties finding domains of functions, in particular, when they were restricted to a specific region in the xy plane. They also showed that they had not fully coordinated their R³, set, and function of one variable schemata. We conclude from the analysis that many of the interviewed students’ notion of function can be considered as pre-Bourbaki.     

Playful and mindful interactions in the recursive adaptations of the zone of proximal development: a critical complexity science approach

We discuss Konstantinos Alexakos, Jayson Jones and Victor Rodriguez’s hermeneutic study of formation and function of kinship-like relationships among inner city male students of color in a college physics classroom. From our Critical Complexity Science framework we first discuss the reading erlebnisse of students laughing at and with each other as something that immediately captured our attention in being transformative of the classroom. We continue by exploring their classroom and research experience as an emergent structure modifying their collective as well as their individual experiences. As we analyze both the classroom and the research space as a complex system, we reflect on the instructor/students interactions characterized by an asymmetrical “power” relationship. From our analysis we propose to consider the zone of proximal development as the constantly emerging and transforming person experience (erlebnisse and erfahrung).     

Framing the framework: discourses in Australia’s national values education policy

In the past, many Australian state schools avoided teaching about values explicitly. However, the Australian government released Australia’s first official values education policy in 2005: the National Framework for Values Education in Australian Schools (NFVEAS). This framework represents a local manifestation of the recent international values education movement. This study contributes to an exploration of what, and who, the government’s construction of Australian values privileges. It uncovered the dominant discourses inherent in the framework through a critical discourse analysis, framing it in relation to the 16 key values education approaches identified in the literature. The data revealed the document’s strong privileging of conservative values education discourses, particularly civics and citizenship education, values inculcation and character education. In practice, some Australian schools have been disrupting this move to conservatism by taking more critical and postmodern approaches. The paper argues for such alternative practices and policy that is more diversified and student-centred.     

Assessing primary school student-teachers’ pedagogic implementations in child sexual abuse protection education

Teacher-educators need ways of assessing the adequacy of university curriculum and the extent to which student-teachers meet learning objectives. One potentially useful tool is Anderson and Krathwohl’s (Addison Wesley Longman, New York, 2001) theoretical framework, which can be applied to assess student-teachers’ knowledge types and their cognitive processes in critical pre-service curriculum areas such as child sexual abuse and personal safety. This study aims to illustrate the use of Anderson and Krathwohl’s framework in assessing student-teachers’ learning of pedagogies in relation to child sexual abuse and personal safety. Participants were a final year cohort of 122 Bachelor of Education (Primary School) students at an Australian university. Student-teachers’ essays regarding the pedagogical practices that they would implement in teaching about child sexual abuse and personal safety were content analysed using Anderson and Krathwohl’s framework. Pedagogies identified by the student-teachers were unevenly distributed across the cells within the theoretical framework. Well-represented pedagogies tended to reflect mid-level cognitive processes (those of understand, apply, and analyse), and low to mid-level knowledge types (those of factual, conceptual, and procedural). Under-represented were pedagogies reflecting higher-level cognition such as creating (in all four knowledge types) and evaluation (of factual and conceptual knowledge). The findings provide a basis for assessing the adequacy of current university teacher-education curriculum structures. Student-teachers’ understandings of under-used theoretical and pedagogical strategies can be identified as a guide to enhance their cognitive processes and knowledge dimensions. This study illustrates a method that has applicability as a diagnostic and assessment tool across a wide range of pre-service teacher education curriculum areas.     

Preservice teachers’ thinking within a research-based framework: what informs decisions?

A research-based framework for teaching science is a heuristic tool used to help preservice teachers conceptualize many complexities of teaching while making explicit the strategy to use a research-based body of professional knowledge to inform instructional decision-making (Clough, 2003, Paper presented at the annual meeting of the Association for the Education of Teachers in Science, St. Louis, MO). Elementary preservice teachers frequently struggle to apply this knowledge to classroom decisions (Madsen, 2002, Paper presented at the annual meeting of the North Central Association for the Education of Teachers of Science, Bettendorf, IA). This study examined the effects of using a video case-analysis within an elementary science methods course focused on the development of a research-based framework. Students in two course sections completed a unit plan, and students in one section completed the video analysis. Video analysis students’ performance on an oral defense with the instructor was compared with oral defense performance from students in the unit plan group. Video analysis students outperformed their peers on questions related to how learning theories influence decisions of selecting content, explaining the use of questioning, and the use of self assessment strategies. Despite these differences, students in both groups still perceive teaching as primarily accomplished through activities and have difficulties understanding the critical role of the teacher in promoting student goals. This study raises issues regarding teachers’ knowledge development during preservice experiences.     

Students’ communicative behavior adaptability in CSCL environments

By the proliferation of online courses, the social dimension of computer supported collaborative learning (CSCL) is becoming more important than before. Research shows that communicative behavior adaptation to the computer medium is a critical issue in CSCL social relationship development. Two dominant theories in the CSCL field, social information processing theory and adaptive structuration theory, argue that individuals do not simply receive the technology passively but they adapt their behavior to increase benefits from the technology. This paper develops an instrument in order to operationalize the notion of individual’s communicative behavior adaptability in CSCL. Through an exploratory factor analysis performed on a small sample of post graduate students of an online degree in an Australian university, three factors have been unveiled: (1) individual perception of self-representation, (2) individual perception of compatibility, and (3) individual perception of the use of computer technology. Identification of these factors is expected to facilitate understanding of individuals’ social behaviors in CSCL environment, which in turn will guide the design of CSCL systems. In addition, the paper examines the relationships between the extracted factors and four environmental factors: learner’s characteristics, course characteristics, instructor characteristics, and technology characteristics. The results show that none of these characteristics strongly affect perception of self-representation or perception of the use of computer technology. On the other hand, a strong relationship was found between perception of compatibility and learner’s and course characteristics. The reliability as well as validity of the study is examined and findings are discussed. These findings will provide further insights into the design process of CSCL systems.     

The Force Concept Inventory as a Measure of Students Conceptual Coherence

The Force Concept Inventory (FCI) is a multiple choice test designed to monitor students’ understanding of the conceptual domain of force and related kinematics (Hestenes et al. Physics Teacher 30:141–158 1992; Halloun et al., 1995, Online at http://modeling.asu.edu/R&E/Research.html). It has gained wide popularity among both researchers and physics instructors in the United States and elsewhere. The FCI has also been criticized, and its validity as a measure of the coherence of a student’s understanding of the force concept has been questioned. In this paper we provide a characterization of students’ conceptual coherence and a way to evaluate it using the FCI. We divide students’ conceptual coherence into three aspects: representational coherence (the ability to use multiple representations and move between them), contextual coherence (the ability to apply a concept across a variety of contexts), and conceptual framework coherence (the ability to fit related concepts together, i.e. to integrate and differentiate between them). Postinstruction FCI results and interview data from two Finnish high school groups (n=49 total) are discussed; the data provide evidence that the FCI can be used to evaluate students’ conceptual coherence—especially contextual coherence—of the force concept.     

PRESERVICE TEACHERS’ INSTRUCTIONAL BELIEFS AND EXAMINATION OF CONSISTENCY BETWEEN BELIEFS AND PRACTICES

The purposes of this study were to determine preservice physics teachers’ instructional beliefs and to investigate the relationship between their beliefs and practices. The theoretical framework was based on the combination Haney & McArthur’s (Science Education, 86(6):783–802, 2002) research and Ford’s (1992) motivation systems theory. A multicase study design was utilized for the research in order to focus on a belief–practice relationship within several examples. Semistructured interviews, observations, and preservice teachers’ written documents were used to collect data. Results showed that most preservice teachers held instructional beliefs aligned with constructivist philosophy. Some of the preservice teachers’ beliefs were consistent with their practices while some of them presented different practices from their beliefs in different placements.     

Conflict in Multicultural Classes: Approaches to Resolving Difficult Dialogues

Survey data are presented from instructors (N = 114) regarding how they would hypothetically use conflict management interventions within multicultural courses. Findings indicate that participants had more difficulty dealing with conflict directed at the instructor than with cognitive conflict, which involved students’ ideas or beliefs. In addition, higher preferences were associated with the use of relationship‐building interventions across all types of conflict.     

Beliefs,Practices, and Reflection: Exploring a Science Teacher’s Classroom Assessment Through the Assessment Triangle Model

This paper describes the Assessment Practices Framework and how I used it to study a high school Chemistry teacher as she designed, implemented, and learned from a chemistry lab report. The framework consists of exploring three teacher-centered components of classroom assessment (assessment beliefs, practices, and reflection) and analyzing components with the assessment triangle model (Pellegrino et al. in, Knowing what students know: The science and design of educational assessment. National Academy Press, Washington DC, 2001). Employing the framework, I report the teacher’s assessment practices, report the alignment in her assessment practices through the three vertices of the assessment triangle (cognition, observation, and interpretation), and suggest relations between her beliefs and practices. I conclude by discussing the contribution and limitations of the Assessment Practices Framework while conducting future research and supporting science teachers in assessing student learning.     

Closing the Gap: Modeling within-school variance heterogeneity in school effect studies

Effective schools should be superior in both enhancing students’ achievement levels and reducing the gap between high- and low-achieving students in the school. However, the focus has been placed mainly on schools’ achievement levels in most school effect studies. In this article, we focused our attention upon the school-specific achievement dispersion as well as achievement level in determining effective schools. The achievement dispersion in a particular school can be captured by within-school variance in achievement (σ²). Assuming heterogeneous within-school variance across schools in hierarchical modeling, it is possible to identify school factors related to high achievement levels and a small gap between high- and low-achieving students. By analyzing data from the TIMMS-R, we illustrated how to detect variance heterogeneity and how to find a systematic relationship between within-school variance and school practice. In terms of our results, we found that schools with a high achievement level tended to be more homogeneous in achievement dispersion, but even among schools with the same achievement level, schools varied in their achievement dispersion, depending on classroom practices.     

A study of learning and motivation in a new media enriched environment for middle school science

This study examines middle school students’ learning and motivation as they engaged in a new media enriched problem-based learning (PBL) environment for middle school science. Using a mixed-method design with both quantitative and qualitative data, we investigated the effect of a new media environment on sixth graders’ science learning, their motivation, and the relationship between students’ motivation and their science learning. The analysis of the results showed that: Students significantly increased their science knowledge from pretest to posttest after using the PBL program, they were motivated and enjoyed the experience, and a significant positive relationship was found between students’ motivation scores and their science knowledge posttest scores. Findings were discussed within the research framework.     

From Gatekeeping to Engagement: A Multicontextual, Mixed Method Study of Student Academic Engagement in Introductory STEM Courses

The lack of academic engagement in introductory science courses is considered by some to be a primary reason why students switch out of science majors. This study employed a sequential, explanatory mixed methods approach to provide a richer understanding of the relationship between student engagement and introductory science instruction. Quantitative survey data were drawn from 2,873 students within 73 introductory science, technology, engineering, and mathematics (STEM) courses across 15 colleges and universities, and qualitative data were collected from 41 student focus groups at eight of these institutions. The findings indicate that students tended to be more engaged in courses where the instructor consistently signaled an openness to student questions and recognizes her/his role in helping students succeed. Likewise, students who reported feeling comfortable asking questions in class, seeking out tutoring, attending supplemental instruction sessions, and collaborating with other students in the course were also more likely to be engaged. Instructional implications for improving students’ levels of academic engagement are discussed.