Students’ Difficulties in Transfer of Problem Solving Across Representations

We introduce the problem of detecting a group of students from classroom videos. The problem requires the detection of students from different angles and the separation of the group from other groups in long videos (one to one and a half hours).We use multiple image representations to solve the problem. We use FM components to separate each group from background groups, AM-FM components for detecting the back-of-the-head, and YOLO for face detection. We use classroom videos from four different groups to validate our approach. Our use of multiple representations is shown to be significantly more accurate than the use of YOLO alone.

The ability of the teacher to represent a concept using various types of representation is a critical competency. Teachers who have limited multiple representation abilities will not be able to provide a holistic and appropriate learning experience because students have different abilities in constructing their knowledge. This study aims to determine the multiple representation ability of Physics teacher by using instruments to test multiple representations on the topic of Newton’s law consisting of text representations, images, pictorial diagrams, tables, graphs, and mathematical equations. The subjects in this study were 30 high school Physics teachers in North Maluku who were determined based on the purposive sampling technique. Data on multiple teacher representation abilities were analyzed using descriptive statistics. The results of the data analysis showed that the multi-representation ability of high school physics teachers in Newton’s law concept was in the medium category (55.7%) with the highest achievement occurring in the type of mathematical representation and the lowest in the pictorial diagram representation types for both female and male teachers. Besides, based on data implemented using SPSS 2.0, it can be concluded that there are no significant differences with the ability of teacher’s multi-representation based on gender and teacher’s teaching experience.

Solving problems presented in multiple representations is an important skill for future physicists and engineers. However, such a task is not easy for most students taking introductory physics courses. We conducted teaching/learning interviews with 20 students in a first‐semester calculus‐based physics course on several topics in introductory mechanics. These interviews helped identify the common difficulties students encountered when solving physics problems posed in multiple representations as well as the hints that help students overcome those difficulties. We found that most representational difficulties arise due to the lack of students’ ability to associate physics knowledge with corresponding mathematical knowledge. Based on those findings, we developed, tested and refined a set of problem‐solving exercises to help students learn to solve problems in graphical and equational representations. We present our findings on students’ common difficulties with graphical and equational representations, the problem‐solving exercises and their impact on students’ problem solving abilities.

Cognitive dissonance represents someone’s cognition discrepancy on a particular concept and then encouraging the person to comprehend that specific concept better. Cognitive dissonance can be constructed through the use of multiple representations in chemistry learning. Chemistry learning’s nature always involves abstract and complex concepts. Therefore, students mostly face difficulty understanding chemical concepts so that they experience misconceptions. This study seeks to describes the syntax of cognitive dissonance combined with multiple representations to illustrate the implementations of multiple representation based cognitive dissonance strategies (MRCD) in reducing the students’ misconception within chemistry learning. It descriptively examined the articles related to cognitive dissonance and multiple representations. The obtained data were secondary in the form of relevant research articles. The data were analyzed using a descriptive qualitative technique. The study results suggest that multiple representation-based cognitive dissonances consist of a number of phases, namely the prerequisite knowledge, creation of cognitive dissonance, implementation of attained knowledge, and reflection. Each of those phases involves multiple representations. In the end, the multiple representations-based cognitive dissonance strategy that refers to syntax has been confirmed to effectively reduce students’ misconception and improve the learning quality. The multiple representation-based cognitive dissonance strategy should be adopted in chemistry learning since it facilitates students to construct abstract chemical knowledge. Further, this strategy can bring the utmost results if combine with the constructivist learning model.

Mathematical problem solving in Basic General Education remains a pedagogical challenge closely related to conceptual understanding, representation, and logical reasoning. This study aimed to analyze the influence of visual thinking and the use of multiple representations on the development of mathematical problem-solving skills at this educational level. A quantitative approach with a quasi-experimental pretest–posttest design was applied to a sample of 120 fifth-, sixth-, and seventh-grade students from public urban schools. The intervention was based on the systematic use of diagrams, schemas, and visual representations within active learning methodologies. The results revealed statistically significant improvements in problem interpretation, procedure selection, and solution justification, as well as an increase in high-performance levels. The study concludes that visual thinking and multiple representations are effective instructional strategies for fostering meaningful and functional mathematical learning in Basic General Education.

Students organize scientific knowledge and reason about issues in the Earth sciences by manipulating internally-constructed mental models and socially-constructed, expressed, conceptual models. The Earth sciences, which focus on the study of complex, dynamic, Earth systems, may present unique cognitive difficulties to students in their development of authentic, accurate expressed conceptual models of these systems. This pilot study came about as we were seeking to construct inquiry modules to assist undergraduate students as they developed an understanding of eutrophication along the coastal margin, a good example of a complex, dynamic, environmental process. The modules we developed coupled the use of physical models and information technology (IT)-based multiple representations with an inquiry-based learning environment that allowed our students to develop and test their conceptual models based on available evidence and to solve authentic, complex, and ill-constrained problems. Our hypothesis was that the quality of students' conceptual models would predict their performance on inquiry modules, and that students' prior knowledge (measured by number of previous courses in geology) would mediate the strength of the relationship between students' model expression and their inquiry performance. Statistical results of this study indicated such a relationship existed only among students in the high prior knowledge group. In the light of our findings, we make recommendations for pedagogical accommodations to improve all undergraduates' abilities to understand complex, dynamic, environmental systems, with a particular emphasis on students who have lower levels of prior knowledge.

In previous chapters, we discussed the use of visualization from the perspective of the different tasks involved, and the different representation formats possible. We now attempt to tie the tasks and representations together. In Section 18.1, we first discuss experimental evidence supporting the use of multiple representations, and then discuss how optimization systems can support multiple representations (Section 18.2). Finally, we discuss how these representations can be built and maintained by multiple users perhaps working in multiple locations at different points in time (Section 18.3).KeywordsMultiple RepresentationGroup Decision Support SystemHomogeneous ApproachMathematical Programming FormulationElectronic Meeting SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This study examines the impact of implementing multiple representation method in responding to the challenge of learning science specifically in relation to enhancing students’ reasoning skill. Pre-experimental method was applied to obtain research data from participants consisted of 8th grader students at a private junior high school in Bandung, Indonesia. The effect on reasoning skill was studied from students’ arguments in answering question related to respiratory system. The arguments were then analyzed by the completeness of argument component, level of argument, and quality of argument referring to Toulmin’s argumentation pattern (TAP). The findings show that students experienced significant improvement in reasoning skill expressed in their arguments. The improvement was evident in the higher argument level and better argument quality achieved by students after the implementation of multiple representation method. In relation to quality of argument, the overall quality of argument shifted from the domination of weak arguments to the domination of strong arguments. Additionally, the use of multiple representation in learning assists students to be able to use various forms of information such as graphics, visual images, tables, scientific formula, and written expression in explaining concepts.

The power of The Geometer's Sketchpad® (GSP) for teaching and learning lies in its potential for enabling students to explore geometric concepts and recognize relationships among these concepts as illustrated through the use of multiple representations. This article explores two problems and examines how the use of tables along with GSP sketches may assist students in understanding these concepts. The first activity investigates the relationship of the length of a trapezoid's median (or midsegment) to that of its bases. The second involves showing how the area of a regular polygon approaches that of a circle when the number of sides increases. In both activities, we will start with the geometric object, look at the measurements, tabulate these, and make a graph to illuminate the situation.

Pedagogical representations to teach linear relations in Chinese and U.S. classrooms: Parallel or hierarchical?

Major difficulties for a novice physics problem solver are how to interpret new problems and how to combine information given in the problem with information already known. A domain expert, by contrast, has the knowledge to take full advantage of problem features at a glance. It takes a long period of practice to acquire such situational knowledge, and it would be desirable for this to be taught more effectively. As a first step, this requires information on how situational knowledge differs across individuals of different competence levels. Related research on mental models and problem representations does not give a direct view on the knowledge subjects have of situations before being confronted with the problem. To assess situational knowledge more directly, we asked participants to respond to physics formulas (from the field of electrodynamics) by describing relevant problem situations. We compared physics problem descriptions by experts (n = 6) and by proficient (n = 6) and less proficient (n = 6) novices. We analyzed the situations that were described at the levels of words, sentences, and complete descriptions. Results indicate that competence is related to the structure of problem situations rather than the use of particular concepts, and that the differences in the use of multiple representations are more prominent than differences in the use of one specific kind of representation. Results also indicate that the differences between experts and novices are along different dimensions than the differences between more and less proficient novices. Implications for teaching are discussed. © 2002 Wiley Periodicals, Inc. J Res Sci Teach 39: 928–951, 2002

Because mathematical formulae and problem solving are such prominent components ofmost introductory physics courses, many students consider these courses to be nothingmore than courses in applied mathematics. As a result, students often do not develop anacceptable understanding of the relationship between mathematics and science and of therole that mathematical modelling plays in science knowledge generation. This paperdescribes an instructional sequence on wave motion based on teaching through modellingthat serves not only to build student understanding of wave characteristics, but also todemonstrate through multiple representations a primary relationship between science andmathematics. This lesson further demonstrates how model building can combinetechnology and pedagogy to strengthen student understanding of the scientificprocess.

Visualization and quantification methods are being developed to analyze our acoustic images of thermal plumes containing metallic mineral particles that discharge from hot springs on the deep seafloor. The acoustic images record intensity of backscattering from the particulate matter suspended in the plumes. The visualization methods extract, classify, visualize, measure and track reconstructions of the plumes, depicted by isointensity surfaces as 3D volume objects and 2D slices. The parameters measured, including plume volume, cross sectional area, centerline location (trajectory), surface area and isosurfaces at percentages of maximum backscatter intensity, are being used to derive elements of plume behavior including expansion with height, dilution, and mechanisms of entrainment of surrounding seawater. Our aim is to compare the observational data with predictions of plume theory to test and advance models of the behavior of hydrothermal plumes through the use of multiple representations.

Images, diagrams, and other forms of visualization are playing increasingly important roles in molecular life science teaching and research, both for conveying information and as conceptual tools, transforming the way we think about the events and processes the subject covers. This study examines how upper secondary and tertiary students interpret visualizations of transport through the cell membrane in the form of a still image and an animation. Twenty upper secondary and five tertiary students were interviewed. In addition, 31 university students participated in a group discussion and answered a questionnaire regarding the animation. A model, based on variation theory, was then tested as a tool for distinguishing between what is expected to be learned, what is present in the visualizations, and what is actually learned by the students. Three critical features of the ability to visualize biomolecular processes were identified from the students’ interpretations of the animation: the complexity of biomolecular processes, the dynamic and random nature of biomolecular interactions, and extrapolation between 2D and 3D. The results of this study support the use of multiple representations to achieve different learning goals.

Concurrent use of somatotopic and external reference frames in a tactile mislocalization task