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Nowadays, there are numerous and wide variety of online learning platforms (OLP) available for students and educators. In order to make the online learning process run smoothly, educators need to be smart in choosing a good medium to use. Many factors should be considered concurrently during decision-making processes. As a result, Multi Criteria Decision-Making (MCDM) method, which seeks to pick the best option from a set of choices, can help decision makers in making suitable and unambiguous judgments in difficult situations. To evaluate such difficulties, this paper combines neutrosophic set with the Best-Worst Method (BWM) approach. The neutrosophic set is important in solving indeterminacy problems and it is more suitable to solve real-world decision-making problems. Besides, in the MCDM problem, similarity measures may be used to describe how different alternatives vary and are similar to one another. However, it appears that the existing similarity measures seem to have a few major weaknesses and inherent problems, such as producing unreasonable results in some cases. Therefore, to cater such problems, this paper introduced a novel single-valued neutrosophic best-worst method, SVN-BWM approach with improved similarity measures of the single-valued neutrosophic set (SVNS) model into a case study of selecting the best online learning platforms based on educators' preferences. The data are collected from six decision makers (DM) among Mathematics lecturers of Universiti Teknologi MARA (UiTM) Shah Alam. From the findings, it is found that Google Meet is the most preferred online learning platform. [ABSTRACT FROM AUTHOR]

Problem solving ability is one of the important abilities that students need to achieve in learning and is part of the Education for Sustainable Development (ESD) goal competence. This paper will describe the implementation of Science Technology Engineering and Mathematics (STEM) - based learning, especially on problems that exist around students related to sustainable development systems. The study use descriptive analysis method. This paper describes the description of the stages of ESD-based STEM learning, and displays the achievements of students at each stage of learning. The implementation of STEM learning is carried out for first-year students of FPMIPA UPI in the 2020-2021 academic year. For 2 semesters, students are given 4 projects related to ESD issues regarding food, transportation, energy, and environment. The stages of the learning process include identifying problems by finding facts about the causes and effects of these problems, carrying out investigations, designing solutions to problems, testing solutions, and redesigning solutions. The learning stages are described and provided with examples of the results of student studies. The results show that the students are able to solve the problems well. This exposure is expected to be an inspiration for researchers, and / or educators in the implementation of STEM-based learning. [ABSTRACT FROM AUTHOR]

This study aims to 1) describe the education transformation and 2) higher-order thinking skills for teachers in the 5.0 society era. This is because 5.0 society provides its own challenges in various fields of life, including learning. The results of research on educational transformation in welcoming the 5.0 society era include: 1) the use of artificial intelligence makes it easier for humans to complete their work better and faster. Information utilization and communication technology (ICT) can help teachers in the learning process in order to achieve results in accordance with expectations. In 5.0 society, humans also remain the center of technology-based activities (artificial intelligence and internet of think). 2) 21st century learning must be directed to support life and career skills, learning and innovation skills, critical thinking and problem solving, communication and collaboration skills, and skills in maximizing information media and technology. Second, the era of 5.0 society requires teachers to transform to be high level thinking skill. For this reason, complex thinking competencies are needed which include skills to apply, analyze, evaluate, and create. Teachers are also required to think critically, logically, systematically, and analytically in order to be able to solve problems and make appropriate decisions. [ABSTRACT FROM AUTHOR]

Data of preliminary analysis showed that students has low level ability of mathematical problem solving. It can be happened because students were less actively participating in learning process and learning tools that had been used not met the needs to increase students' activity. The aims of this research is to develop Problem Based Learning (PBL) based learning tools, consist of Learning Implementation Plans (RPP) and Student Worksheets (LKPD) with criteria: valid, practical and effective. Type of research is development research by using Plomp model with three phases, i.e. preliminary research, development or prototyping and assessment. Preliminary research is done by analyzing the needs, curriculum, student characteristics and concept. Prototype stage is done by designing and determinant the validity and practicality of the product, by using formative evaluation. Assessment stage is to assess the practicality and effectiveness tests on VIII grade students at MTs PPM Al-Kautsar Muhammadiyah Sarilamak. Practical data were obtained from students' questionnaires. The effectiveness data were got from students' final test mathematical problem solving. The results show that PBL-based learning tools are valid, practice (easy to use and understand), efficient, interesting, and contribute in learning. Mathematics problem solving tests show the result that the 83% students pass the passing grades score, viz. score 75. [ABSTRACT FROM AUTHOR]

Education 4.0 is the answer to the demands of the fourth industrial revolution. One of the demands in Education 4.0 is students' unique thinking. That is, students are expected to possess creative thinking skills to solve problems and discover innovations that are helpful to improve modern human life. To fulfill the demand, this study applied a systematic literature review to investigate the implementation of local wisdom-based science learning activities and their effect on creative thinking skills. The findings indicated that local wisdom-based science learning could improve students' creative thinking skills. [ABSTRACT FROM AUTHOR]

21st-century requires citizens in the world to adapt with all changes in the economic system that occurs. Therefore, entrepreneurship skills become an important thing that hopes to be developed in education to grow creative industries that can increase the number of jobs. This paper outlines student's entrepreneurship skills in biology classroom employing visible creative thinking skills as a learning framework that can give an overview to students about the role of the field of Biology to advance the nation's economy. Visible creative thinking skills itself has the meaning of clarifying or showing the stages of student thinking in solving a problem creatively. The visible creative thinking skills is done using creative thinking diagrams to generate entrepreneurial ideas that apply the concept of Biology in solving a problem. Students entrepreneurship skills were measured by technical skills in adaptability, listening skills, work organizing skills, and personal skills in inner-control, self-discipline, risk-taking. To identify those indicators, this paper administrated one group pre-posttest design and mixed-method approach using questionnaires, reflective essays, and interviews. The study was conducted at SMAN 9 Malang and the participants consisted of 33 tenth grade students, specifically 15 men and 18 women. Interestingly, students showed not different results for entrepreneurship skills after visible creative thinking skills framework applied in explaining that ethnography, family background, and individual factors have a big impact. So, the next learning must be analyzed individual culture and habit in the school environment which can influence the learning process. [ABSTRACT FROM AUTHOR]

The use of student's worksheets based on problem based learning was expected to enable students to have problem solving skills and provide opportunities for students to think and work together (collaboration skills) during learning. This study aimed to describe the teacher's need for student's worksheets based on problem-based learning to support the chemistry learning process in the classroom. The type of research is descriptive evaluation, the subjects of evaluation in this study are chemistry teachers, the instruments used in this study were interviews and descriptive data analysis. The results showed that student's worksheet based on problem-based learning were rarely used in the learning process, mostly using textbooks, androids, and PPT/LCD projectors. Making student worksheets based on problem-based learning required a long-time allocation in compiling various concepts according to the syntax of the problem-based learning model so that teachers felt less interested in making student worksheets based on problem-based learning. Meanwhile, at the time of application, the teacher must understand and master the student worksheets based on problem-based learning because it must be explained first to students before being done so that students understand how to work on student worksheets based on problem-based learning. [ABSTRACT FROM AUTHOR]

Students experiences in gaining an understanding of the concept of geometry when learning geometry can be identified through how students solve geometry problems based on spatial abilities. Therefore, this reality is important for further research. This study aims to identify student learning obstacles in learning geometry based on geometric problem solving based on spatial abilities in terms of Van Hiele levels. This research is a qualitative descriptive study involving 60 9th grade students who have studied the material of flat face three dimensional objects. The data collected through a test and depth-interview. The interview was transcribed and then carried out an in-depth analysis to identify possible learning obstacles. The results of this study indicate that in solving geometrical problems based on spatial ability students can be categorized into students at level 0, level 1, and level 2. Based on these three categories, it can be concluded that there are student learning obstacles includes ontogenic, didactic, and epistemological obstacles, in solving geometrical problems based on their spatial abilities. [ABSTRACT FROM AUTHOR]

The Ministry of Education of Malaysia is strongly committed to improving the level of student competency in problem-solving skills, especially for a complex problem. A new policy developed at the governmental level to ensure the change can be made and executed successfully at school level. One of the initiatives is to enhance the complex problem- solving skills for student by introducing the Theory of Inventive Problem Solving (TRIZ) topic in the Curriculum and Assessment Standard Document for Design and Technology subject. The integration of TRIZ is streamlined with other creativity theories and thinking model. The adoption of TRIZ is strategically designed to support and complement the student in developing technological project and design competencies. The teaching and learning process of TRIZ in the subject began in 2018 and the first official textbook is used in all school around Malaysia. A survey was carried out with 1032 respondent involved in the process of teaching and learning of TRIZ in the subject. Results showed positive feedback from respondents, and further issues highlighted to improve the process of teaching and learning in school. [ABSTRACT FROM AUTHOR]

The paper describes a proposal for the creation of an electronic adaptive testing model which can be realized in an electronic environment. Furthermore, it describes the creation of the individual types of test tasks suitable for electronic adaptive testing and the entire adaptive testing process. Adaptive testing is a testing method applicable particularly in the fixing stage which is aimed at retention of acquired knowledge. [ABSTRACT FROM AUTHOR]

The traditional approach of teaching optimization problems in calculus emphasizes more on teaching the students using analytical approach through a series of procedural steps. However, optimization normally involves problem solving in real life problems and most students fail to translate the problems into mathematic models and have difficulties to visualize the concept underlying. As an educator, it is essential to embed technology in suitable content areas to engage students in construction of meaningful learning by creating a technology-based learning environment. This paper presents the applications of technology-based learning tool in designing optimization learning activities with illustrative examples, as well as to address the challenges in the implementation of using technology in teaching and learning optimization. The suggestion activities in this paper allow flexibility for educator to modify their teaching strategy and apply technology to accommodate different level of studies for the topic of optimization. Hence, this provides great potential for a wide range of learners to enhance their understanding of the concept of optimization. [ABSTRACT FROM AUTHOR]

In a companion paper we presented self-diagnosis tasks in which students are explicitly required to self diagnose their problem solutions after being given some feedback. In this paper we suggest a rubric to evaluate diagnosis and exemplify its use in two case studies. We present preliminary results regarding how students' performance on the self-diagnosis tasks relates to their performance in solving problems and to their progress during the course. In preliminary analysis, we find that the correlation between students' self-diagnosis grades and their performance in the mid-semester quiz was very low (0.16), the correlation between the grades in the mid-semester quiz and the final exam grades was also low (0.21) while the correlation between the self-diagnosis grades in the mid-semester quiz and the final exam grades was reasonably high (0.68). We suggest that these results can be explained by the hypothesis that the self-diagnosis grades measure the slope of students' learning curve. [ABSTRACT FROM AUTHOR]

For problem solving to serve as an effective learning opportunity, it should involve deliberate reflection, e.g., planning and evaluating the solver's progress toward a solution, as well as self-diagnosing former steps while elaborating on conceptual understanding. While expert problem solvers employ deliberate reflection, the novices (many introductory physics students) fail to take full advantage of problem solving as a learning opportunity. In this paper we will focus on self-diagnosis as an instructional strategy to engage students in reflective problem solving. In self-diagnosis tasks students are explicitly required to carry out self diagnosis activities after being given some feedback on the solution. In this and a companion paper, we will present research exploring the following questions: How well do students self-diagnose, if at all, their solutions? What are the learning outcomes of these activities? Can one improve the act of self-diagnosis and the resulting learning outcomes by scaffolding the activity? [ABSTRACT FROM AUTHOR]

In a companion paper, we discuss students' ability to take advantage of what they learn from a solved problem and transfer their learning to solve a quiz problem that has different surface features but the same underlying physics principles. Here, we discuss students' ability to perform analogical reasoning between another pair of problems. Both the problems can be solved using the same physics principles. However, the solved problem provided was a two-step problem (which can be solved by decomposing it into two sub-problems) while the quiz problem was a three-step problem. We find that it is challenging for students to extend what they learned from a two-step problem to solve a three-step problem. [ABSTRACT FROM AUTHOR]

Cognitive Science has focused on general principles of problem solving and learning that might be relevant for physics education research. This paper examines three selected issues that have relevance for the difficulty of transfer in problem solving domains: specialized systems of memory and reasoning, the importance of content in thinking, and a characterization of memory retrieval in problem solving. In addition, references to these issues are provided to allow the interested researcher entries to the literatures. [ABSTRACT FROM AUTHOR]

In this paper we focus on some of the recent findings of the physics education research community in the area of multiple representations. The overlying trend with the research is how multiple representations help students learn concepts and skills and assist them in problem solving. Two trends developed from the latter are: how students use multiple representations when solving problems and how different representational formats affect student performance in problem solving. We show how our work relates to these trends and provide the reader with an overall synopsis of the findings related to the advantages and disadvantages of multiple representations for learning physics. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

This paper will cover a small portion of a larger study designed to address the issue of stability of knowledge in an interview and how it is influenced by transfer of learning. An interview over basic mechanics questions will be used to show how one question can influence a student’s answer to another question. Based on this transcript and other data collected during the study, students’ ideas appear to be influenced not only by their experiences and the context presented in the question, but also by the context of the question. This analysis was done based on a new model of transfer called the actor-oriented transfer model developed by Lobato that is based on the “personal construction of similarities” by the student between the learning and transfer contexts. This new model will also be discussed in further detail in the paper. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]

Problem Solving has become an important and necessary competency in the 21st Century Fourth Industrial Revolution (4IR). However, in reality there are still many learning processes that have not maximized the Problem Solving of students. The aim of this research is to determine the problem solving profile students and implementation of the Collaborative Problem Solving (CPS) module in biology. This type of research uses qualitative research with a descriptive approach. The subjects in this study were 36 students of 10th grade in Klaten. The subject taking technique uses simple random sampling technique. The method for collecting data in this study is the method of testing, interviews, and observation sheets. The test method uses a biological problem solving test about the identification of refill drinking water which consists of 8 breakdown questions. Test analysis rubric using Problem Solving ability (PSA) based on PISA assessment: 1) exploring and understanding; 2) representing and formulating; 3) planning and executing; 4) monitoring and reflecting. Data analysis in this study includes data reduction, data presentation and drawing conclusions, while testing the validity of the data in this study using data source triangulation techniques. The results of the study showed that the PSA of students profile were low of 34.80%; comprising planning and executing 30.56% in low category; representing and formulating 33.68% in low category; monitoring and reflecting 36.11% in low category; exploring and understanding amounted to 38.89% in low category. Based on the literature study, Collaborative Problem Solving (CPS) Module is very potential to empower the ability of Problem Solving students in Biology. [ABSTRACT FROM AUTHOR]

Previously we discussed how well students in an introductory physics course diagnosed their mistakes on a quiz problem with different levels of scaffolding support. In that case, the problem they self-diagnosed was unusually difficult. We also discussed issues related to transfer, particularly the fact that the transfer problem in the midterm that corresponded to the self-diagnosed problem was a far transfer problem. Here, we discuss a related intervention in which we repeated the study methodology with the same students in the same intervention groups, using a new quiz problem which was more typical for these students and a near transfer problem. We discuss how these changes affected students’ ability to self-diagnose and transfer from the self-diagnosed quiz problem to a transfer problem on the midterm exam. [ABSTRACT FROM AUTHOR]

Within the context of traditional physics problem solving instruction, major concepts are mentioned but often marginalized by the focus on equation manipulation, resulting in students perceiving concepts as unimportant in problem solving. Additionally, since topics are covered as isolated pieces, students also perceive concepts as unrelated. In response to this disconnect, we discuss the development of a short, animated, web-delivered synthesizing presentation modeled after the 'common learning resource' from the preparation for future learning construct. In the presentation, major concepts of introductory mechanics are structured hierarchically. More specifically, the presentation is an overview of major theorems and conservation laws in mechanics and the conditions under which they are applied. It is linked to previous problems solved by the students and intended to prepare them for future learning by illustrating how concepts guide problem solving processes. [ABSTRACT FROM AUTHOR]

Schwartz, Bransford and Sears [1] propose a two-dimensional framework that describes transfer in terms of efficiency and innovation. Efficiency is the ability to apply prior knowledge to new situations quickly and accurately. Innovation is the ability to question assumptions, let go of prior knowledge and generate new ideas. Schwartz et al. argue that most educational assessments focus on efficiency at the expense of innovation. We suggest that this perspective does not adequately reflect the challenges that our students face while problem solving. For instance, while faculty may find end-of-chapter physics problems to be routine and overly focused on efficiency, our students, who lack prior knowledge and experience may find these problems to be novel and innovative. We propose a framework based on an operational meaning of ‘efficiency’ and ‘innovation’ and development of criteria to measure these constructs in ways that reflect both learners’ challenges as well as educators’ expectations. [ABSTRACT FROM AUTHOR]

The aim of this study was to obtain the perceptions of the teachers regarding communication in teaching and learning Mathematics. This study was conducted in Balik Pulau involving thirty-six mathematics teachers from nine primary schools. This study focused on three aspects of teachers' perceptions on communication in: (1) teaching and learning mathematics; (2) understanding mathematical topics; and (3) planning lesson according to the pupils level of understanding. Result for (1) showed that 86% of the teachers agreed that communication occurs in teaching and learning mathematics when both teacher and pupils were communicating and listening to each other. Findings for (2) showed that 39% of the teachers agreed that pupils were able to understand the lesson carried out by the teacher and were also able to solve moderate levelled questions given to them while 36% of the teachers agreed that pupils were able to understand but they were to be guided by the teacher in solving moderate levelled questions given to them. For (3), the findings showed that 31% of the teachers agreed that teachers can communicate well when they were using suitable teaching aids, employing language that easy to understand and encourage pupils to participate in the group discussion or arguments. Besides that, teacher also need to use simple words in their communication for pupils to understand better. [ABSTRACT FROM AUTHOR]

Developing competency in problem solving and enhancing conceptual understanding are primary objectives in introductory physics, and many techniques and tools are available to help instructors achieve them. Pedagogically, we use an easy-to-implement intervention, the ACCESS protocol, to develop and assess problem-solving skills in our SCALE-UP classroom environment for algebra-based physics. Based on our research and teaching experience, an important question has emerged: while primarily targeting improvements in problem-solving and cognitive development, is it necessary that conceptual understanding be compromised? To address this question, we gathered and analyzed information about student abilities, backgrounds, and instructional preferences. We report on our progress and give insights into matching the instructional tools to student profiles in order to achieve optimal learning in group-based active learning. The ultimate goal of our work is to integrate individual student learning needs into a pedagogy that moves students closer to expert-like status in problem solving. [ABSTRACT FROM AUTHOR]

We report on the Thinking in Physics (TIP) project, which helps students develop basic skills necessary for learning physics. We describe methods used to improve students' thinking and problem-solving skills in TIP introductory mechanics classes, and the effect these methods have had on student learning. [ABSTRACT FROM AUTHOR]

During spring 2010 six students enrolled in an advanced electronics lab worked in pairs on ill-structured capstone projects. They designed electronic circuitry to automate experiments that were completed in a previous advanced physics lab. Some ill-structured features of these capstone projects included open-ended goals, limited guidance from the instructor and the possibility of multiple solution paths. Semi-structured interviews were conducted with both the students and the instructor of the class, before and after the students worked on these ill-structured capstone projects to gauge the participants' expectations of the projects before they began and their views about these projects after they were completed. We report on the pre- and post-project impressions of the students and instructors regarding this ill-structured learning experience. [ABSTRACT FROM AUTHOR]

Identifying the relevant physics principles is a central component of problem solving. A major goal of most introductory physics courses is to help students discern the deep similarities between problems based upon the physics principles so that they can transfer what they learned by solving one problem to solve another problem which involves the same principle. We conducted an investigation in which 251 calculus- and algebra-based introductory physics students were asked explicitly in the recitation quiz to learn from a solved problem and then solve another problem that has different surface features but the same underlying physics principles. We find that many students were able to discern the deep similarities between the problems. When the solved problem was provided, students were likely to invoke the correct principles; however, more scaffolding is needed to help students apply these principles correctly. [ABSTRACT FROM AUTHOR]

We describe a study in which introductory physics students engage in reflection with peers about problem solving. The recitations for an introductory physics course with 200 students were broken into the 'Peer Reflection' (PR) group and the traditional group. Each week in recitation, students in the PR group reflected in small teams on selected problems from the homework. The graduate and undergraduate teaching assistants (TAs) in the PR group recitations provided guidance and coaching to help students learn effective problem solving heuristics. In the recitations for the traditional group, students had the opportunity to ask the graduate TA questions about the homework before they took a weekly quiz. On the final exam with only multiple-choice questions, the PR group drew diagrams on more problems than the traditional group, even when there was no external reward for doing so. Since there was no partial credit for drawing the diagrams on the scratch books, students did not draw diagrams simply to get credit for the effort shown and must value the use of diagrams for solving problems if they drew them. We also find that, regardless of whether the students belonged to the traditional or PR groups, those who drew more diagrams for the multiple-choice questions outperformed those who did not draw them. [ABSTRACT FROM AUTHOR]

Problem solving is a complex process important both in itself and as a tool for learning physics. Currently there is no standard way to measure problem solving that is independent of physics topic, pedagogy, and problem characteristics. At Minnesota we have been developing a rubric to evaluate students’ written solutions to physics problems that is easy to use and reasonably valid and reliable. The rubric identifies five general problem-solving processes and defines the criteria to attain a score in each: useful description, physics approach, specific application of physics, math procedures, and logical progression. An important test of the instrument is to check whether these categories as represented in students’ written solutions correspond to processes students engage in during problem solving. Eight problem-solving interviews were conducted with students enrolled in an introductory university physics course to compare what students write down during problem solving with what they say they were thinking about as determined by their interview statements. [ABSTRACT FROM AUTHOR]

Studies indicate that the use of multiple representations in teaching helps students become better problem solvers. We report on a study to investigate students’ difficulties with multiple representations. We conducted teaching/learning interviews with 20 students in a first semester calculus-based physics course. Each student was interviewed four times during the semester, each time after they had completed an exam in class. During these interviews students were first asked to solve a problem they had seen on the exam, followed by problems that differed in context and type of representation from the exam problem. Students were provided verbal scaffolding to solve the new problems. We discuss the common difficulties that students encountered when attempting to transfer their problem solving skills across problems in different representations. [ABSTRACT FROM AUTHOR]

Helping students learn from their own mistakes can help them develop habits of mind while learning physics content. Based upon cognitive apprenticeship model, we asked students to self-diagnose their mistakes and learn from reflecting on their problem solution. Varying levels of scaffolding support were provided to students in different groups to diagnose their errors on two context-rich problems that students originally solved in recitation quizzes. Here, we discuss students’ cognitive engagement in the two self-diagnosis activities and transfer tasks with different scaffolds. [ABSTRACT FROM AUTHOR]

We describe a modeling approach to help students learn expert problem solving. Models are used to present and hierarchically organize the syllabus content and apply it to problem solving, but students do not develop and validate their own Models through guided discovery. Instead, students classify problems under the appropriate instructor-generated Model by selecting a system to consider and describing the interactions that are relevant to that system. We believe that this explicit System, Interactions and Model (S.I.M.) problem modeling strategy represents a key simplification and clarification of the widely disseminated modeling approach originated by Hestenes and collaborators. Our narrower focus allows modeling physics to be integrated into (as opposed to replacing) a typical introductory college mechanics course, while preserving the emphasis on understanding systems and interactions that is the essence of modeling. We have employed the approach in a three-week review course for MIT freshmen who received a D in the fall mechanics course with very encouraging results. [ABSTRACT FROM AUTHOR]

As part of our efforts to systematically improve our junior-level Electricity & Magnetism I (Electro- and Magneto-Statics) course, we have developed a conceptual instrument, the CUE (Colorado Upper-division Electrostatics) diagnostic. Two central goals of this tool are: to assess impacts of transformed curricula, and to systematically identify and document student learning difficulties. We find persistent issues involving students’ ability to conceptually approach and visualize E&M, to accurately communicate that understanding, and to appropriately identify and apply upper-level problem-solving strategies. Our work underlines the need for further research on the nature of student learning—and appropriate instructional interventions -at the upper division. [ABSTRACT FROM AUTHOR]

Research in cognitive science has shown that students typically have a difficult time acquiring deep conceptual understanding in domains like mathematics and physics and often rely on textbook examples to solve new problems. The use of prior examples facilitates learning, but the advantage is often limited to very similar problems. One reason students rely so heavily on using prior examples is that they lack a deep understanding for how the principles are instantiated in the examples. We review and present research aimed at helping students learn the relations between principles and examples through generating explanations and making analogies. [ABSTRACT FROM AUTHOR]

There exist both explicit and implicit approaches to teaching students how to solve physics problems involving multiple representations. In the former, students are taught explicit problem-solving approaches, such as lists of steps, and these approaches are emphasized throughout the course. In the latter, good problem-solving strategies are modeled for students by the instructor and homework and exams present problems that require multiple representation use, but students are rarely told explicitly to take a given approach. We report on comparative study of these two approaches; students at Rutgers University receive explicit instruction, while students from the University of Colorado receive implicit instruction. Students in each course solve five common electrostatics problems of varying difficulty. We compare student performances and their use of pictures and free-body diagrams. We also compare the instructional environments, looking at teaching approaches and the frequency of multiple-representation use in lectures and exams. We find that students learning via implicit instruction do slightly better and use multiple representations more often on the shorter problems, but that students learning via explicit instruction are more likely to generate correct free-body diagrams on the hardest problem. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]

Student problem-solving ability appears to be tied to the representational format of the problem (math, pictorial, graphical, verbal). In a study of a 367-student algebra-based physics class, we examine student problem solving ability on homework problems given in four different representational formats, with problems as close to isomorphic as possible. In addition, we examine students’ capacity for assessing their own representational competence by giving follow-up quizzes in which the students can choose between various problem formats. We report student performance and consider factors that may influence their ability or choices. As a control, part of the class was assigned a random-format follow-up quiz where students received quiz formats at random. We find that there are statistically significant performance differences between isomorphic problems. We also find that allowing students to choose which representational format they use improves student performance under some circumstances and degrades it in others. © 2005 American Institute of Physics [ABSTRACT FROM AUTHOR]