Elementary Teachers’ Use of Graphical Representations in Science Teaching

The purpose of this study was to obtain data on United States K-5 elementary school teachers’ self-reported instructional practices with graphical representations. Via an electronic survey, 388 elementary teachers, from throughout the US, reported about their teaching of the interpretation and the production of graphics within science. The main findings indicate that: (1) pointing to or referring to graphical representations in books (92% of respondents) was the most frequently used instructional practice across the disciplines and grade levels; (2) five of nine graphical representations (over 90%) were more frequently used in science instruction than in other content areas, and (3) students’ graphical productions involving drawings, labeling, and oral and written explanations were very infrequent. The findings indicate that while teachers may tacitly use graphics within science instruction, they may not be explicitly teaching about this visual form of communication.     

Representational Issues in Students Learning About Evaporation

This study draws on recent research on the central role of representation in learning. While there has been considerable research on students’ understanding of evaporation, the representational issues entailed in this understanding have not been investigated in depth. The study explored students’ engagement with evaporation phenomena through various representational modes. The study indicates how a focus on representation can provide fresh insights into the conceptual task involved in learning science through an investigation of students’ responses to a structured classroom sequence and subsequent interviews over a year. A case study of one child’s learning demonstrates the way conceptual advances are integrally connected with the development of representational modes. The findings suggest that teacher-mediated negotiation of representational issues as students construct different modal accounts can support enriched learning by enabling both (a) richer conceptual understanding by students, and (b) enhanced teacher insights into students’ thinking.     

Facilitating Students’ Problem Solving in a Technological Context: Prospective Teachers’ Learning Trajectory

In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted and developed in their role of facilitating students’ mathematical problem solving with a technology tool. A cycle of planning–experience–reflection was repeated twice during an undergraduate course to allow the prospective teachers to change their strategies when working with two different groups of students. Case study methods were used to identify and analyze critical events that occurred throughout the different phases of the study and how these events may have influenced the prospective teachers’ work with students. Looking across the cases, several themes emerged. The prospective teachers (1) used their problem solving approaches to influence their pedagogical decisions; (2) desired to ask questions that would guide students in their solution strategies; (3) recognized their own struggle in facilitating students’ problem solving and focused on improving their interactions with students; (4) assumed the role of an explainer for some portion of their work with students; (5) used technological representations to promote students’ mathematical thinking or focus their attention; and (6) used the technology tools in ways consistent with the nature of their interactions and perceived role with students. The implications inform the development of an expanded learning trajectory for what we might expect as prospective teachers develop an understanding of how to teach mathematics in technology-rich environments.     

Comparison of Students’ Performance on Algorithmic, Conceptual and Graphical Chemistry Gas Problems

The purpose of this study was to determine whether there were significant differences in students’ performances amongst conceptual, algorithmic and graphical questions tests. Seventy-one eleventh-grade students were involved in this study. In order to assess students’ performance, conceptual, graphical and algorithmic questions tests were utilized. Students’ performances in each test were analyzed statistically. Statistical analysis using one-way ANOVA of student tests scores pointed to statistically significant differences amongst each of three test scores (P < 0.05) in favor of the conceptual test. Further analyses were conducted to compare one type of questions with others. From these comparisons, positive relationships were found between conceptual understanding and algorithmic understanding and between conceptual understanding and graphical understanding. Also, results obtained indicated that most of the students lack of graphical understanding. The results suggest that students need more training about graphical understanding.     

GEOMETRIC AND ALGEBRAIC APPROACHES IN THE CONCEPT OF “LIMIT” AND THE IMPACT OF THE “DIDACTIC CONTRACT”

The present study explores students’ abilities in conversions between geometric and algebraic representations, in problem- solving situations involving the concept of “limit” and the interrelation of these abilities with students’ constructed understanding of this concept. An attempt is also made to examine the impact of the “didactic contract” on students’ performance through the processes they employ in tackling specific tasks on the concept of limit. Data were collected from 222 12th-grade high school students in Greece. The results indicated that students who had constructed a conceptual understanding of limit were the ones most probable to accomplish the conversions of limits from the algebraic to the geometric representations and the reverse. The findings revealed the compartmentalized way of students’ thinking in non-routine problems by means of their performance in simpler conversion tasks. Students who did not perform under the conditions of the didactic contract were found to be more consistent in their responses for various conversion tasks and complex problems on limits, compared to students who, as a consequence of the didactic contract, used only algorithmic processes.     

The Influence of Different Representations on Solving Concentration Problems at Elementary School

This study investigated the students’ learning process of the concept of concentration at the elementary school level in Taiwan. The influence of different representational types on the process of proportional reasoning was also explored. The participants included nineteen third-grade and eighteen fifth-grade students. Eye-tracking technology was used in conducting the experiment. The materials were adapted from Noelting’s (1980a) “orange juice test” experiment. All problems on concentration included three stages (the intuitive, the concrete operational, and the formal operational), and each problem was displayed in iconic and symbolic representations. The data were collected through eye-tracking technology and post-test interviews. The results showed that the representational types influenced students’ solving of concentration problems. Furthermore, the data on eye movement indicated that students used different strategies or rules to solve concentration problems at the different stages of the problems with different representational types. This study is intended to contribute to the understanding of elementary school students’ problem-solving strategies and the usability of eye-tracking technology in related studies.     

Teaching Thinking Skills in Context-Based Learning: Teachers’ Challenges and Assessment Knowledge

For an educational reform to succeed, teachers need to adjust their perceptions to the reform’s new curricula and strategies and cope with new content, as well as new teaching and assessment strategies. Developing students’ scientific literacy through context-based chemistry and higher order thinking skills was the framework for establishing a new chemistry curriculum for Israeli high school students. As part of this endeavor, we developed the Taste of Chemistry module, which focuses on context-based chemistry, chemical understanding, and higher order thinking skills. Our research objectives were (a) to identify the challenges and difficulties chemistry teachers faced, as well as the advantages they found, while teaching and assessing the Taste of Chemistry module; and (b) to investigate how they coped with teaching and assessing thinking skills that include analyzing data from graphs and tables, transferring between multiple representations and, transferring between chemistry understanding levels. Research participants included eight teachers who taught the module. Research tools included interviews, classroom observations, teachers-designed students’ assignments, and developers-designed students’ assignments. We documented different challenges teachers had faced while teaching the module and found that the teachers developed different ways of coping with these challenges. Developing teachers’ assessment knowledge (AK) was found to be the highest stage in teachers’ professional growth, building on teachers’ content knowledge (CK), pedagogy knowledge (PK), and pedagogical-content knowledge (PCK). We propose the use of assignments designed by teachers as an instrument for determining their professional growth.     

Integrating Gender and Group Differences into Bridging Strategy

The main goal of this study was to integrate gender and group effect into bridging strategy in order to assess the effect of bridging analogy-based instruction on sophomore students’ misconceptions in Newton’s Third Law. Specifically, the authors developed and benefited from anchoring analogy diagnostic test to merge the effect of group and gender into the strategy. Newton’s third law misconception test, attitude scale toward Newton’s third law, and classroom observation checklists were the other measuring tools utilized throughout this quasi-experimental study. The researchers also developed or used several teaching/learning materials such as gender and group splitted concept diagrams, lesson plans, gender splitted frequency tables, make sense scales, PowerPoint slides, flash cards, and demonstrations. The convenience sample of the study chosen from the accessible population involved 308 students from two public universities. The results of multivariate analysis of covariance indicated that the bridging strategy had a significant effect on students’ misconceptions in Newton’s third law whereas it had no significant effect on students’ attitudes toward Newton’s third law.     

Using a two-tier test in examining Taiwan graduate students’ perspectives on paraphrasing strategies

This study examines Taiwanese English as a foreign language (EFL) graduate students’ perspectives on paraphrasing strategies. A two-layer scenario survey was developed to identify the reasoning behind students’ judgments that certain paraphrasing is appropriate or inappropriate. The first-layer scenario survey is in a true–false format that consists of nine paraphrasing scenarios and that served to elicit from students their declarative knowledge of appropriate paraphrasing strategies. The second-layer scenario survey is in an open-ended question format that explores students’ explanatory knowledge underlying their first-layer choices. In addition, an attitude survey and a demographic survey were designed and implemented to explore learner variables in relation to the learners’ perspectives on paraphrasing strategies. A total of 141 EFL graduate students participated in the study. The results shed considerable light on students’ diverse perceptions and reasoning regarding paraphrasing strategies. More than half of the students considered surface-level paraphrasing (patchwriting) to be acceptable strategy use. Significant correlation was found between students’ responses to the acceptability of paraphrasing strategies and the following factors: (1) perceived difficulty in paraphrasing, (2) perceived value of appropriate source use, (3) perceived competence in overcoming the temptation to plagiarize, (4) perceived disadvantage as a foreign-language learner with paraphrasing, (5) gender, and (6) paraphrasing-related training. Pedagogical implications of the results are discussed.     

Toward High-Performance Communications Interfaces for Science Problem Solving

From a theoretical viewpoint, educational interfaces that facilitate communicative actions involving representations central to a domain can maximize students’ effort associated with constructing new schemas. In addition, interfaces that minimize working memory demands due to the interface per se, for example by mimicking existing non-digital work practice, can preserve students’ attentional focus on their learning task. In this research, we asked the question: What type of interface input capabilities provide best support for science problem solving in both low- and high-performing students? High school students’ ability to solve a diverse range of biology problems was compared over longitudinal sessions while they used: (1) hardcopy paper and pencil (2) a digital paper and pen interface (3) pen tablet interface, and (4) graphical tablet interface. Post-test evaluations revealed that time to solve problems, meta-cognitive control, solution correctness, and memory all were significantly enhanced when using the digital pen and paper interface, compared with tablet interfaces. The tangible pen and paper interface also was the only alternative that significantly facilitated skill acquisition in low-performing students. Paradoxically, all students nonetheless believed that the tablet interfaces provided best support for their performance, revealing a lack of self-awareness about how to use computational tools to best advantage. Implications are discussed for how pen interfaces can be optimized for future educational purposes, and for establishing technology fluency curricula to improve students’ awareness of the impact of digital tools on their performance.     

Cross-Grade Comparison of Students’ Understanding of Energy Concepts

The aims of this cross-grade study were (1) to determine the level of understanding of energy concepts of students at different academic grades and the differences in understanding between these grades and (2) to analyse the conceptual development of these students. Two hundred and forty-three students at 3 different levels (high school, undergraduate, and postgraduate) participated in this study. The students’ understandings of energy concepts were determined using a questionnaire, which requested them to define the concept verbally, and to represent it graphically. The most important findings of this study may be summarised as follows. Students from the different groups generally succeeded in defining ‘energy’ in a similar way, namely as the ‘ability to do work’. Nevertheless, some students (including those at university) also provided different alternative conceptions related to the energy concept. In addition, some students also found difficulty in visually analysing the relationships between different variables using graphs. This finding could help explain why attainment levels of all groups falls short in questions that involve the graphical representation of data.     

The Effect of Data Acquisition-Probeware and Digital Video Analysis on Accurate Graphical Representation of Kinetics in a High School Physics Class

The effects of two types of two well-established microcomputer-based teaching methods were examined for their effect teaching high school students kinetics. The use of data acquisition probeware and digital video analysis were studied for their impact on students’conceptions and ability to interpret graphical relationships to real world events. The abilities of high school physics students to accurately graph kinetics using distance, velocity and acceleration in one dimensional motion varied between and among the groups. Using a split category random assignment analysis students investigated these motions with both. In a quasi experimental fashion students received similar instruction on each but in a different sequence. Students received the similar teaching in reverse order and both strategies were found to be successful and complementary. There were indications student achievement was higher for velocity–time and acceleration-time graphs using the digital video analysis method. Implications for this study on teaching tools, methodologies, curriculum development, program implementation, and assessment are discussed.     

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.     

Exploring the potential impact of reciprocal peer tutoring on higher education students’ metacognitive knowledge and regulation

It is widely recognized that metacognition is an important mediator for successful and high-level learning, especially in higher education. Nevertheless, a majority of higher education students possess insufficient metacognitive knowledge and regulation skills to self-regulate their learning adequately. This study explores the potential of reciprocal peer tutoring to promote both university students’ metacognitive knowledge and their metacognitive regulation skills. The study was conducted in a naturalistic higher education setting, involving 67 students tutoring each other during a complete semester. A multi-method pretest–posttest design was used combining a self-report questionnaire, assessing students’ metacognitive knowledge and their perceived metacognitive skilfulness, with the analysis of think-aloud protocols, revealing students’ actual use of metacognitive strategies. Results indicate no significant pretest to posttest differences in students’ metacognitive knowledge, nor in their perception of metacognitive skill use. In contrast, significant changes are observed in students’ actual metacognitive regulation. At posttest, students demonstrate significantly more frequent and more varied use of metacognitive regulation, especially during the orientation, monitoring, and evaluation phases. Furthermore, our findings point to an increase in more profound and higher-quality strategy use at posttest.     

Using virtual microscopy to scaffold learning of pathology: a naturalistic experiment on the role of visual and conceptual cues

New representational technologies, such as virtual microscopy, create new affordances for medical education. In the article, a study on the following two issues is reported: (a) How does collaborative use of virtual microscopy shape students’ engagement with and learning from virtual slides of tissue specimen? (b) How do visual and conceptual cues scaffold students’ reasoning? Fifteen pairs of medical students participated in two sessions in which the students used a virtual microscope as a diagnostic tool in the context of learning pathology. The slides provided the students with varying levels of visual and conceptual cueing. The sessions were videotaped, and the students’ reasoning while using the microscope was analysed. The students’ written answers were analysed in terms of the findings they made and the diagnoses suggested. At a general level, the results show that students engage actively in this kind of virtually-mediated environment. The visual and/or conceptual cues improve students’ performance, and guide the students’ perception and reasoning in a manner that is productive from the point of view of learning to make clinically relevant observations. Scaffolding students’ reasoning process through cues furthermore assists the students in avoiding the most obvious pitfalls such as overlooking critical areas of a specimen. Overall, visual and conceptual cues improve students’ reasoning in perceptual and cognitive terms, while still allowing space for the making of “relevant mistakes” that may further the students’ diagnostic skills.     

Changing Primary Students’ Perceptions of Teacher Interpersonal Behaviours in Science

The paper reports on part of a large-scale study aimed at examining students’ perceptions of teacher–student interactions. This paper will report on a study utilising mixed methodology in 12 Queensland primary classrooms. After the students’ perceptions were established, the teachers, through a consultative process, developed strategies to change the students’ perceptions of their classroom over a 3 month period. The paper reports on what strategies these teachers utilised and what changes in students’ perceptions resulted. The classroom teachers were interviewed about the change in students’ perceptions, what changes they had sought to promote in their classrooms, and what they felt had been achieved in their classrooms. The study found that students were able to articulate what changes the teacher had implemented, what their reaction was to these changes and their perception of the classroom environment as a result of these implemented strategies.     

Structures of cognitive and metacognitive reading strategy use for reading comprehension of geometry proof

In this study, we explored the structural relationship between the students’ perceived use of cognitive and metacognitive reading strategies (CMRS) and their reading comprehension of geometry proof (RCGP), and we also examined the differences in students’ perceived use of reading strategies among the poor, moderate and good comprehenders. A sample of ninth graders (N = 533) completed a RCGP test and then the CMRS questionnaire. In the exploratory factor analysis with one subsample (n = 150), principal component analysis was used to extract factors of CMRS use for improving the CMRS instrument. Another subsample of students (n = 370) participated in the study on the confirmatory factor analysis with structural equation modelling method. Results revealed that the use of metacognitive reading strategies exerts an executive function over that of cognitive reading strategies, which directly influenced students’ RCGP. Our interesting findings were that good comprehenders tended to employ more metacognitive reading strategies for planning and monitoring comprehension and more cognitive reading strategies for elaborating proof compared with the moderate comprehenders, who in turn employed these strategies more often compared with the poor comprehenders.     

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.     

Alternative views of the solar system among turkish students

This study examines middle-school students’ alternative frameworks of the earth’s shape, its relative size and its distance from the sun and the moon. The sample was selected in the province of Giresun in Turkey. Sixty-five 14-year-old students participated in the research. A structured interview consisting of open-ended questions was employed to reveal students’ ideas. The students’ verbal responses were scrutinized and categorized according to their level of understanding. The results showed that the students had many alternative frameworks with regard to astronomical concepts. Implications and recommendations were made for teachers, textbook authors, teaching materials developers and researchers for future research to remedy students’ alternative frameworks.     

Secondary school students’ perceptions of teacher–student interaction and students’ attitudes towards project work

Project work (PW) provides one of the pathways for students’ self-inquiry learning and collaboration in Singapore schools. In this context, PW teachers function as facilitators. This study investigated quantitatively how a group of 270 secondary-school students (aged 14 years) perceived their seven PW teacher-facilitators’ face-to-face interactions with students based on the Questionnaire on Teacher Interaction (QTI), and whether their perceptions of teacher–student interaction during PW classrooms were related with their attitudes towards PW learning as a whole. Seven out of eight QTI scales were associated with Enjoyment of Project Work Lessons and two QTI scales were associated with Attitude to Inquiry in Project Work. The findings are discussed in terms of how teachers who function as facilitators can translate their interpersonal behaviours into effective teaching strategies for communicating with students and facilitating students’ learning in PW classrooms.