Explore the vast range of titles available.

Vector problem-solving abilities are fundamental to everyday life and higher education; thus, improving them is important in education and research. However, the role of cognitive and affective factors and learning engagement in vector problem-solving performance is still unclear. This study examines the processes associated with vector problem-solving performance, focusing on the problem-solving strategy as a cognitive factor and math anxiety and task-specific self-efficacy as affective factors. In addition, this study examines the impact of learning engagement as a moderator in this process. A total of 245 Japanese 11th-grade high school students completed questionnaires. A multiple-group structural equation modelling revealed that (1) task-specific self-efficacy, math anxiety, and problem-solving strategies contribute to vector problem-solving performance when learning engagement is above average; (2) task-specific self-efficacy contributes to math anxiety, whereas task-specific self-efficacy and math anxiety contribute to problem-solving strategies when learning engagement is above average and stable; (3) task-specific self-efficacy is a positive predictor of vector problem-solving performance regardless of learning engagement. The results suggest that learning engagement moderates the association between math anxiety, task-specific self-efficacy, problem-solving strategy, and vector problem-solving performance. In addition, task-specific self-efficacy is a strong predictor of vector problem-solving performance.

Background Across many domains, research has shown that students often fail to select and apply appropriate conceptual knowledge when solving problems. Programs designed to support monitoring skills have been successful in several domains. Purpose (Hypothesis) Critical conceptual knowledge in statics appears to be cued by paying attention to the bodies that are present in a problem, as well as to which ones are interacting and how. The research question addresses whether students can be induced to think about the bodies present, and whether focusing on bodies improves problem solving performance. Design/Method Using a pre‐post test design, written and verbal protocols were obtained for students solving problems before and after instruction. During instruction all students saw the same set of examples and corrected answers, but only the experimental group was asked questions designed to promote body centered talk. Solutions and protocols were coded and analyzed for frequency of body centered talk and solution quality. Results The experimental group showed statistically significant increases in relevant body centered talk after instruction. Both groups improved their ability to represent unknown forces in free body diagrams after instruction, with the experimental group showing a greater, but not statistically significant, improvement. However, for both groups, the error rate in representing unknown forces at an interaction was significantly lower when a student referred to the bodies in the particular interaction. Conclusions Problem solving in conceptually rich domains can improve if, in addition to acquiring conceptual knowledge, students develop strategies for recognizing when and how to apply it.

The end-user paradox and the illusion of digital prosperity reveal the contradictory situation in which both non-professional and professional computer scientists and engineers seem satisfied with digital development but unaware of the magnitude of waste generated by end-users and their digital artifacts. To measure this waste and to reveal end-users’ problem-solving strategies, our research group set up an objective measuring system that can calculate the entropy of digital texts (EDT). To calculate EDT, a testing process of 53 participants was launched where erroneous and correct natural language digital texts were modified according to the requirements of the tasks. It was found that erroneous documents require more time and information to be modified, which implies that waste is generated by handling these documents. It was also found that when the problem-solving processes are broken down into atomic steps, EDT can reveal uncertainty and idleness, which further increases waste. The goals of the present paper are to call attention to (1) the hidden waste generated by billions of end-users and its consequences, (2) educational approaches and general ignorance which have led to these low-level results, and (3) the need to set up a standard evaluation system for further analyses.

The overall aim of education is to train proactive, motivated, and independent citizens to face and overcome continuous challenges. Critical thinking—finding solutions to problems—is of primary importance in the 21st century to handle challenging situations and deal with obstacles in careers. A critical literature review approach was used to assess, critique, synthesizes, and expand the theoretical foundation of the topic. Teaching mathematical problem-solving is an efficient way to develop 21st-century skills and to give cross-curricular experiences with real-world meaning to learners. Concrete examples were presented to prove that Pólya’s heuristic could be used in a broader context to help learners acquire the modern skills needed to succeed in their careers. By including in the learning process and practicing specific methods for solving mathematical problems, students could learn a way of thinking to approach and solve problems successfully in a broader context in life. The paper’s outcome provides teachers and educators with methods, learning models, and strategies for developing 21st-century skills in students at all levels during classroom activities.

In this paper we report on the impact of a year-long teacher professional development (PD) workshop on student problem-solving skills. The PD workshop was held in Chile and promoted the use of collaborative problem-solving activities in the classroom, through monthly sessions during the school year. Participant teachers met with a monitor to solve a new problem collaboratively, plan a problem-solving activity for their next lesson, and reflect on their activities from their previous lesson. The study documents the performance of two groups of students when solving non-routine mathematics problems in two similar and non-equal tests consisting of three problems each, before and after the year of application of the workshop. The first group of students was the experimental group with collaborative problem-solving activities, as proposed in the PD workshop. The second group was the control group, composed of students whose teachers followed traditional teaching. In the first part of the paper we present the results of pre- and post-tests in which the students in the experimental group improved their problem-solving performance in a significant way compared with the control group. In the second part, we present a sample of representation strategy used by successful students in both groups and we discuss, in general, student strategies in solving test problems.

In the realm of mathematics education, geometry problems assume a pivotal role by fostering abstract thinking, establishing a connection between theory and practice, and offering a tangible portrayal of reality. This study focuses on comprehending problem-solving methodologies by observing the eye movements of 45 primary and multi-year grammar school pupils, aged 11 to 14, as they tackled pictorial geometry problems without computation. The utilization of eye-tracking technology, specifically the OGAMA tool, was essential in unveiling the nuanced strategies employed by students. Visual attention metrics were determined through fixations on predefined areas of interest, identified using the ScanGraph tool. Through an analysis of eye movements, participants were categorized into three distinct groups based on their problem-solving strategies. This categorization facilitated an exploration of the correlation between the chosen strategy and the success rate in solving geometry problems without computational aids. The findings underscore the imperative for continued investigation into strategies for solving geometry problems without computation. Additionally, the research aims to broaden its scope by delving into the metacognitive strategies applied in solving imaginative geometric tasks.

This study compared the problem-solving abilities of ChatGPT and 58 pre-service teachers (PSTs) in solving a mathematical word problem using various strategies. PSTs were asked to solve a problem individually. Data was collected from PSTs’ submitted assignments, and their problem-solving strategies were analyzed. ChatGPT was also given the same problem to solve with various prompts, and the correctness of its solutions and problem-solving strategies were assessed alongside those of PSTs. The results indicated that PSTs used diverse strategies and achieved accurate solutions, but not always relevant strategies to children’s level of understanding. ChatGPT employed similar strategies to PSTs but mostly produced incorrect solutions, and its performance needed to be contextualized in the primary school context. The study highlights the potential of ChatGPT in mathematics teaching and informs teacher education programs about the possibility of using it in teaching problem-solving strategies.

The purpose of this study is to find the relationship between the levels of intelligence of mathematical logic with the ability to solve problems in terms of the various strategies used at the stage of planning problem solving. This problem is useful for students who solve non-routine problems. The method in this research uses a case study. The results of this study indicate that the average mathematical intelligence of Grade VII students of MTsN 6 Agam is at a complex level. The ability to solve problems in algebra and geometry material in the sample class is at the basic level with an average of 50.6, at the complex level with an average of 62.66 and at a coherent level with an average of 74.75. There is a significant influence between the level of intelligence of mathematical logic with the ability of students to solve problems in Algebra and Geometry material in mathematics in class VII.1 MTsN 6 Agam at 38.2% and for the remaining 61.8% influenced by other factors such as teachers' competence, learning style, learning environment and lack of students in practicing in answering problem solving questions.

The study, which is derived from a larger study, compares grades 10 – 12 mathematics learners’ non-routine problem solving. An exploratory study was conducted on a convenience sample drawn from three high performing high schools located in Tshwane North District, Gauteng province of South Africa.Learners wrote a non-routine problem solving test. Findings revealed that the 11th grade learners obtained the highest mean score while that of the 10th grade learners was the lowest. High school learners’ level of strategy use on solving non-routine problems improved significantly as they progress from grade 10 to higher grades. No significant difference was discovered as learners progress from grade 11 to 12.

In this changing world, peoples are often challenged with problems that require the use of scientific information so that they are able to make informed decisions. However, the study of physics is entangled with many problems including the belief that it is a male domain and the way it is presented to students. The purpose of this study therefore, was to explore the role of Problem Based Learning (PBL) by applying five step problem solving strategy in enhancing conceptual understanding of female students. The study was conducted in Bonga College of teacher education, Ethiopia. To achieve the goal of the study, pedagogical experiment was applied. Data were collected using conceptual understanding inventory test and questionnaire. There was a mean difference between comparison and experimental groups. The difference was statistically significant with large effect size. Students in the experimental group shows good motivation towards the strategy. Based on the findings, it was suggested to apply the five step problem solving strategy at college and tertiary level. Because, this strategy was helpful for students to scrutinize the connection between theory and practice, improves their motivation to learn, and eradicates rote memorization. It also helps to understand concepts and principles central to physics.