Problem-solving Proficiency Research Articles

Mathematical structures in quantum physics education for high school students: Unveiling the power of Dirac notation for conceptual and problem-solving proficiency

[This paper is part of the Focused Collection in Investigating and Improving Quantum Education through Research.] Teaching quantum physics (QP) to high school (HS) students is gaining momentum, necessitating the exploration of various effective methods. Specifically, the research on quantitative teaching methods is still in its early stages. Understanding the power of Dirac notation (DN) in teaching is crucial for grasping the complexities of QP, as it provides a concise and powerful symbolic framework that facilitates both conceptual and computational understanding. This study investigates the proficiency of HS students in interpreting, producing, and manipulating DN within QP. Utilizing qualitative content analysis of student responses to various tasks, quizzes, and final tests, the study aims to uncover the sensemaking opportunities DN provides and the difficulties students encounter. The findings indicate that DN facilitates both conceptual understanding and quantitative problem solving in QP by enabling students to interpret and produce representations of quantum states. The results highlight the importance of extensive practice and well-structured teaching sequences in developing DN proficiency, reinforcing the role of DN as an effective tool for teaching QP at the HS level. The study contributes to the ongoing discourse on integrating mathematical modeling in physics education, emphasizing the potential of DN in enhancing students’ grasp of QP concepts and their application in problem solving. Published by the American Physical Society 2024

Structural-mathematical thinking and its development in teaching Mathematics

Abstract The paper highlights the content and components of structural-mathematical thinking, substantiates its classification basis and establishes typological characteristics. In the conceptual-categorical section of the present study, structural-mathematical thinking is introduced as a form of theoretical thinking that embodies the specifics of mathematical comprehension of reality. The content as well as structural and functional characteristics of the phenomenon under study represent the content and components of the mathematical structure. Hence, the adherence to the deductive nature of Mathematics was ensured in the study, also emphasizing the phenomenological characteristic of structural-mathematical thinking regarded as the ability to reflect reality in accordance with the content components of the mathematical structure. Taking into account the theoretical advances, using the system approach and the modeling method, a model of developmental-conceptual teaching of Mathematics was elaborated. By considering the theoretical advancements and applying both a systemic approach and modeling method, a model for instructing Mathematics in a developmental-conceptual approach was elaborated, which represents a problem-based approach and develops students’ structural-mathematical thinking. The crux of teaching Mathematics through a developmental and conceptual approach lies in creating a framework that addresses the three-fold challenge of problem-solving ↔ competency-building ↔ problem-solving proficiency. Taking into account the addressed issue, the paper elicits the outcomes of a pilot study how structural-mathematical thinking is manifested by the would-be teachers of Mathematics. Furthermore, the efficacy of the authors’ approach to its enhancement is experimentally validated.

Performance of ChatGPT in the In-Training Examination for Anesthesiology and Pain Medicine Residents in South Korea: Observational Study.

ChatGPT has been tested in health care, including the US Medical Licensing Examination and specialty exams, showing near-passing results. Its performance in the field of anesthesiology has been assessed using English board examination questions; however, its effectiveness in Korea remains unexplored. This study investigated the problem-solving performance of ChatGPT in the fields of anesthesiology and pain medicine in the Korean language context, highlighted advancements in artificial intelligence (AI), and explored its potential applications in medical education. We investigated the performance (number of correct answers/number of questions) of GPT-4, GPT-3.5, and CLOVA X in the fields of anesthesiology and pain medicine, using in-training examinations that have been administered to Korean anesthesiology residents over the past 5 years, with an annual composition of 100 questions. Questions containing images, diagrams, or photographs were excluded from the analysis. Furthermore, to assess the performance differences of the GPT across different languages, we conducted a comparative analysis of the GPT-4's problem-solving proficiency using both the original Korean texts and their English translations. A total of 398 questions were analyzed. GPT-4 (67.8%) demonstrated a significantly better overall performance than GPT-3.5 (37.2%) and CLOVA-X (36.7%). However, GPT-3.5 and CLOVA X did not show significant differences in their overall performance. Additionally, the GPT-4 showed superior performance on questions translated into English, indicating a language processing discrepancy (English: 75.4% vs Korean: 67.8%; difference 7.5%; 95% CI 3.1%-11.9%; P=.001). This study underscores the potential of AI tools, such as ChatGPT, in medical education and practice but emphasizes the need for cautious application and further refinement, especially in non-English medical contexts. The findings suggest that although AI advancements are promising, they require careful evaluation and development to ensure acceptable performance across diverse linguistic and professional settings.

Enhancing computational thinking in students with autism spectrum disorder and intellectual disabilities: a robot programming approach

Objectives Research examining computational thinking skills development via programming education using robotic teaching tools for students with Autism Spectrum Disorder and Intellectual Disabilities remains limited. This study aims to analyze the advancements in computational thinking skills among middle school students with Autism Spectrum Disorder and Intellectual Disabilities through participation in robot programming classes. Methods Problem-solving proficiency in computational thinking was assessed utilizing Brennan and Resnick’s three dimensions framework. A tailored teaching and learning approach was implemented for robot programming education, accounting for participants’ cognitive abilities and required levels of support. Four middle school students, comprising one with Autism Spectrum Disorder and three with Intellectual Disabilities, were enrolled. Results Significant enhancements were observed in all participants’ computational thinking skills across conceptual understanding, practical application, and perspective. Notably, all participants successfully resolved the final project problem at their individual proficiency levels. The acquisition of computational concepts was found to correlate positively with improved practical computational skills. Additionally, all participants demonstrated keen interest in and positive attitudes toward both robots and programming. Conclusions This study underscores the efficacy of robotic teaching tools in enhancing computational thinking skills through programming education. Additionally, it highlights considerations for enhancing students’ accessibility in future programming class design.

Analysing The Impact of Erroneous Examples on Third-Grade Students’ Problem-Solving Proficiency

The potential benefits of introducing errors in problem solving has awakened interest in research into this understudied field. Here, we report the results of a quasi-experimental study with 85 third-grade students which examines whether erroneous examples might enhance students' problem-solving proficiency more effectively than worked ones. In the study, two conditions were established: a worked-example condition, where correct examples were presented before the students solved word problems, and an erroneous-example condition, where erroneous examples preceded word-problem solving. Our results demonstrate that post-test scores, after controlling the students’ prior level, are significantly greater for the erroneous-example condition than the worked-example condition. Therefore, the erroneous-example approach seems to be more effective in developing a learner’s problem-solving proficiency compared to a worked-example approach.

Representation Process of Prospective Teachers in Solving Mathematical Problems Based on Cognitive Style

This study investigates the correlation between cognitive styles and the thinking process utilized when solving mathematical problems, emphasizing the significance of aligning problem-solving strategies with problem representations. Employing a qualitative approach, the research examines two cognitive styles—Field Independent (FI) and Field Dependent (FD)—chosen based on participants' mathematical abilities. Conducted at Cenderawasih University's Mathematics Education Study Program, the study reveals that students' mathematical problem-solving proficiency remains relatively low, warranting further exploration of their thinking processes. While FI subjects demonstrate competence in aligning thinking processes with mathematical representations, particularly in structuring problem-solving steps, FD subjects exhibit limitations in articulating meaning and verbal representations. These findings underscore the importance of instructing educators not only in teaching mathematical concepts but also in guiding students to articulate problem-solving steps using verbal representations. This study highlights the need for a holistic approach to mathematical education, integrating conceptual understanding with effective problem-solving strategies tailored to individual cognitive styles.

The Effect of Case-Based Learning on Students’ Problem-Solving Ability

This investigation stems from the observed low problem-solving skills among students as indicated in prior research. The primary objective is to evaluate the impact of employing case-based learning on students’ problem-solving aptitude concerning buffer solutions. Carried out during April-May 2023, the study involved 11th-grade students at a public high school in Jakarta, Indonesia. Employing a quasi-experimental design, two classes were chosen as samples and randomly assigned roles via the flipping coin method: one as the experimental group (11 MIPA-1) and the other as the control group (11 MIPA-4), each comprising 36 students. A problem-solving assessment using an essay test featuring nine questions was administered, with the data analyzed through t-tests. The findings revealed a positive correlation between case-based learning and enhanced problem-solving skills among students in the realm of buffer solutions. In essence, the implementation of case-based learning proved effective in bolstering students’ problem-solving capabilities. Consequently, educators are encouraged to integrate the case-based learning approach to elevate students’ problem-solving proficiency across various subjects.

Mathematics Anxiety and Problem-Solving Proficiency Among High School Students: Unraveling the Complex Interplay in the Knowledge Economy

Mathematics Anxiety and Problem-Solving Proficiency Among High School Students: Unraveling the Complex Interplay in the Knowledge Economy

Use of game-based educational entertainment media to foster mathematical problem-solving proficiency in pre-service mathematics teachers

<span lang="EN-ID">The capacity to solve mathematical problems is an essential component of the professional abilities that pre-service instructors of mathematics are required to possess. When it comes to coping with technological advancements in the sphere of education, this skill serves as the foundation. For the purpose of enhancing one's capacity to solve mathematical problems, this study proposes an innovative method that involves the use of game-based educational entertainment media (GEM). Within the realm of development research, this research technique focuses on the ways in which problem-solving skills can be enhanced by participation in activities that are based on game-based entertainment media. The ADDIE phases—analysis, design, development, implementation, and evaluation—are the steps that are utilised in the process of development. The GEM was utilised by 94 pre-service mathematics teachers who participated in this research. GEM is effective in developing mathematical problem-solving skills, according to the findings of the research. This is accomplished by encouraging pre-service mathematics teachers to identify problems, model them, solve problems mathematically, and assess the results of their efforts.</span>

Empowering Problem-solving in Computer Science: A Need Analysis for a Computational Thinking Mobile Learning Application

The advancement of digital technology has revolutionized education across all levels, giving rise to digital learning as a novel pedagogical environment. Among the subjects at the forefront of this transformation is computer science, introduced in matriculation colleges to supplant traditional information technology courses. However, computer science poses inherent complexity, demanding abstract thinking and diverse problem-solving methodologies. Computational thinking (CT) emerges as a promising approach to address these challenges, recognized as a vital skillset for fostering innovation in digital technology among students. The ubiquity of smartphones and mobile internet facilitates the adoption of mobile learning, offering students the flexibility to access educational content anytime, anywhere. Consequently, this need analysis study aims to assess current teaching practices in computer science and identify the need for mobile learning applications that integrate CT as a problem-solving technique among matriculation college students. Interviews with three computer science lecturers revealed a reliance on conventional pedagogy with limited blended learning approaches through college portals. Notably, specific techniques for imparting programming problem-solving skills were lacking. Nonetheless, it is noteworthy that all instructors recognized the considerable potential of mobile learning applications in effectively engaging students and facilitating the development of problem-solving proficiency.

UNVEILING MATH MASTERY: CRAFTING DYNAMIC LEARNING TOOLS TO ELEVATE PROBLEM-SOLVING PROFICIENCY

In the realm of mathematics education, the quest for effective strategies to enhance problem-solving proficiency is perpetual. This study explores the design and implementation of learning media grounded in discovery learning principles, aiming to unravel its impact on students' problem-solving abilities. The research delves into the intricacies of crafting dynamic learning tools that promote active engagement, critical thinking, and a deeper understanding of mathematical concepts. Through a meticulously structured approach, this study seeks to shed light on the transformative potential of innovative learning media in empowering students to unveil and master the art of problem-solving in mathematics.

치위생과 학생의 문제해결능력에 영향을 미치는 요인

Objectives: This study aimed to explore the impact of self-directed learning ability and critical thinking tendencies among dental hygiene students on their problem-solving skills. Methods: The subject's self-directed learning ability, critical thinking tendency, and problem-solving ability were analyzed by descriptive statistics, t-test, ANOVA, Pearson's correlation, and multiple regression. Results: Self-directed learning ability and critical thinking tendencies were identified as significant factors influencing problem-solving proficiency. Conclusions: The conclusion drawn was a necessity of introducing subjects aimed at enhancing self-directed learning abilities and critical thinking skills, and implementing pedagogical approaches centered around problem-solving.

Problem-Solving Proficiency Profile in Problem-Based Learning Model for Eighth-Grade Students on the Subject of Pressure in Matter

The Problem Based Learning (PBL) model is considered as one of the effective approaches to develop problem-solving skills in students. Hence, the purpose of this study is to assess the problem-solving abilities of eighth-grade students in SMPN 3 Samarinda using the PBL model. The research design employed in this study is descriptive quantitative. The data collection took place at SMPN 3 Samarinda with a total sample of 26 class VIII students. This research yielded the finding that the ability to solve problems for the indicator of understanding the problem reaches 73.50%, then the indicator of making plans obtains the proportion of 49.15%, then the indicator of carrying out the plan 40.17% and finally the indicator of re-examination is obtained 37.18%. So that the average proportion of all indicators capable of solving problems is 50%, this proportion is included in the sufficient category. In accordance with these findings, it can be interpreted that more science material is needed which is taught using the PBL model so that the profile of the problem-solving skills of the students can be better

Error Analysis in Solving Word Problems among Grade-8 Students

Despite the importance of problem-solving skills in preparing students for the workforce and the emphasis on problem-solving in mathematics education, studies have shown that many students struggle with mathematics problem-solving. In the Philippines, low proficiency in mathematics and a high prevalence of errors in problem-solving have been observed, emphasizing the need for further improvement in students’ problem-solving abilities. This research investigated the errors made by eighth-grade students of Talalora National High School in solving word problems and examined their impact on reading comprehension and analytical skills. A quantitative correlational design was employed, and standardized tests were used as data-gathering instruments. The analysis involved statistical measures such as frequency counts, percentages, mean, and standard deviation, as well as inferential statistical methods, including chi-squared for dependence, to establish correlations. The results showed that most respondents were 13 years old, with the instructional level of comprehension being the dominant category. The chi-squared test indicated a significant relationship between reading comprehension levels and problem-solving errors Χ²(6, N = 20) = 26.726, p < 0.001, Cramer’s V = 0.817. The identified errors were primarily related to challenges in comprehending and evaluating the problems. The study emphasized the importance of reading comprehension and analytical skills in solving word problems and suggested that educators should focus on developing these abilities to enhance students’ problem-solving proficiency.

PEMBELAJARAN COOPERATIVE INTEGRATED READING AND COMPOSITION (CIRC) TERHADAP KEMAMPUAN NUMERASI DALAM MENYELESAIKAN SOAL PEMECAHAN MASALAH

Current mathematics education should meet requirements that involve critical thinking skills, real-world relevance, the use of technology, and communication and collaboration abilities. In this regard, students need to have good numeracy skills, which involve the ability to use numbers and mathematical symbols in everyday problem-solving, such as calculations and data interpretation. Numeracy skills are important in shaping responsible and competent individuals. Additionally, problem-solving strategies are also at the core of mathematics teaching. Research has shown that the use of the Cooperative Integrated Reading and Composition (CIRC) instructional model has positive consequences for mathematical problem-solving proficiency. With the CIRC model, students can effectively improve their numeracy skills and mathematical problem-solving strategies. This research was conducted using a quantitative method, t-test, and paired sample test. The research subjects consisted of 50 eighth-grade students at SMP Negeri 7 Tungkal Jaya. Data was collected through documents, observations, and tests. Data analysis was done by conducting a paired sample t-test to assess the significance of the influence of CIRC learning on students' problem-solving competence. It is important to conduct further research involving larger samples and considering factors that may potentially affect learning outcomes.

Pre-service teachers’ flexibility and performance in solving Fermi problems

Fermi problems are real-context estimation tasks that are suitable for introducing open-ended problems in primary school education. To ensure their effective introduction in the classroom, teachers must have adequate proficiency to deal with them. One of the key aspects of problem-solving proficiency is flexibility, but there are few studies on flexibility in solving real-context problems. This study, based on an analysis of the errors made by 224 prospective teachers when solving a Fermi problem sequence, establishes performance levels. In addition, we define levels of flexibility in using multiple solutions across the sequence, which allows us to address the main objective: to study the relationship between performance and flexibility. We found that there are significant relationships between flexibility levels and the number and severity of errors made. Encouraging flexibility in prospective teachers may be an efficient way to improve their performance in solving real-context problems.

Arithmetic Word Problem-Solving and Math Anxiety: The Role of Perceived Difficulty and Gender

ABSTRACT A crucial component of mathematics curriculum in primary education is represented by the ability to solve arithmetic word problems. Previous studies investigated predominantly the cognitive factors underlying this skill, neglecting the role of emotional (e.g. math anxiety – MA) and metacognitive aspects (e.g. perceived difficulty). Some findings suggested that emotional factors could influence perceived task difficulty which would, in turn, impair students’ performance. However, the relation between MA, perceived difficulty, and math problem-solving has not been explored yet. Moreover, although many studies reported gender differences in MA levels, findings involving primary school children are contrasting. Thus, this study aimed to evaluate the role of MA and perceived task difficulty on arithmetic word problem-solving proficiency in a sample of Italian primary school students, and to investigate gender differences in those variables. Results showed that MA had a direct and indirect effect through perceived difficulty on problem-solving performance. Furthermore, findings confirmed that girls exhibited higher MA levels, however no gender difference was observed in problem-solving accuracy nor in perceived difficulty. The study underlines the need to consider emotional factors when investigating children’s difficulties in math problem-solving and highlight the importance of MA interventions, especially for girls, already in primary education.

Instruction in Proportion Word Problems for Secondary Students With Learning Disabilities in Mathematics

Increasing the performance of secondary students with learning disabilities (LD) in mathematics on word problem-solving tasks involving ratios and proportions is challenging for secondary math teachers. Teachers must use evidence-based practices to enhance secondary students’ problem-solving proficiency and math achievement. Schema-based instruction (SBI) is a powerful evidence-based practice to improve students’ understanding and approach to solving word problems involving ratios and proportions. This article describes the protocol for implementing SBI with examples specific to ratios and proportions. Also discussed are the ways teachers can provide additional assistance to students with more intensive instructional needs when implementing SBI.

Factors Affecting Employees’ Problem-Solving Skills in Technology-Rich Environments in Japan and Korea

This study conducts an analysis about the impact of basic background, cultural capital, skill use, and participation in training on employees’ problem-solving proficiency in Japan and Korea based on data from the Programme for the International Assessment of Adult Competencies Survey (PIAAC). This research compared four clusters (basic background, cultural capital, participation in training, skill usage) to determine the factors affecting problem-solving skills in technology-rich environments (PSTRE) in Japan and Korea. In addition, we examined whether aging moderate the relationship between skill usage and participation in training and PSTRE. The finding shows that PSTRE is associated with the basic background, cultural capital, and skill usage. Moreover, the interaction effect between the use of skill at home and age is statistically significant in Japan. Our results provide new insights for vocational psychology and work-life research in the context of employers, employees, as well as policymakers.

Supporting indigenous primary students’ success in problem-solving: learning from Newman interviews

This paper reports on part of a large study investigating how Indigenous students’ mathematical proficiency can be effectively supported in the primary years. Within this study, the problem-solving processes of thirty-six primary aged students in an Indigenous community school were evaluated. This was examined by ascertaining students’ problem-solving proficiency on a written test, conducting error analysis from written test scripts, followed by Newman interviews. The findings indicated that supporting students’ strategic competence and productive dispositions were critical in fostering students’ problem-solving success. When students’ strategic competence was supported through a scaffolded Newman interview, students’ problem-solving proficiency increased. Furthermore, the oral and personal nature of Newman interviews acted to significantly increase students’ productive dispositions towards the tasks. These findings have implications for teaching practice and provide tangible points of action that classroom teachers can implement to support Indigenous students’ success in problem-solving.