Teaching Problem Solving Research Articles

Addressing the Barriers to Design-Thinking Driven Problem Solving in Higher Education

The Higher Education structure was believed to be established to protect itself from either internally or externally motivated change. As time has progressed, ‘change’ has begun to trickle into Higher Education Institutions, with the belief that individuals with characteristics synonymous with ‘innovators’ have spurred change in this space. For Design Thinking to become the primary mode for problem-solving in relation to curriculum and learning design, we must first understand current staff members’ experiences of making changes within Higher Education, and identify the behaviours, attitudes and structural processes involved in making change. This paper will address the following research questions: Through understanding the barriers to making change currently experienced by Higher Educations staff, what can we do to create an environment where the principles of Design and Design Thinking can be fully embraced by members of the Higher Education community? This paper presents the findings from a qualitative research project conducted by the authors, where 32 members of staff in a selected Higher Education Institution were interviewed to understand their experiences of making changes to their teaching and working practices. Emphasis is placed on understanding the barriers to making change, namely: the embedded conservatism in Higher Education and associated fear of change; committee structures; energy; the current institutional understanding of ‘collaboration,’ and; the Institution’s commitment to making change. Drawing on the findings of this research, three actionable insights will be presented which will help Design and Design Thinking methods become embraced in terms of further developing teaching, learning, and working practices in Higher Education.

A Systematic Review of Complex Problem-Solving in Education and Mathematics Education

A Systematic Review of Complex Problem-Solving in Education and Mathematics Education

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.

Experiences of Pre-Service Teachers’ on Skill-Based Problem Solving Oriented Lesson Study

This study aims to present the experiences of pre-service mathematics teachers’ on skill-based problem solving-oriented lesson study. In the study, the activities related to the learning environments designed by the lesson study groups before and after the research lesson with a focus on problem solving are investigated. In this way, the study aims to reveal how lesson study affects pre-service mathematics teachers’ awareness of teaching problem solving. In the study, 31 pre-service mathematics teachers first received a comprehensive training on teaching problem solving in mathematics for six weeks. Then, the pre-service teachers received a one-week training on the lesson study professional development model. In the last stage, they carried out problemsolving-focused lesson study processes under the guidance of the researcher with ten lesson study groups that they formed on the basis of volunteerism. Finally, the lesson study groups shared their experiences with the other pre-service teachers participating in the study by presenting the bulletins they prepared. The data were obtained through planning and evaluation meeting minutes, observation notes of research lesson practitioners and observers, initial and final lesson plans and documents. The data obtained in the study, in which the case study design of the qualitative research approach was preferred, were subjected to descriptive analysis using Polya’s (1957) problem solving process steps framework. During the lesson study process that they experienced within the scope of the research, pre-service teachers shared their knowledge and experiences about the problem solving process and teaching with each other, as well as activities such as collaborative work in groups, designing and implementing teaching materials such as lesson plans and worksheets. According to the results obtained in the study, it was seen that the activities in the problem solving-oriented learning environments of the pre-service teachers varied thanks to the collaborative structure of the lesson study. In addition, it was seen that the pre-service teachers had the opportunity to experience the steps of the problem solving process and the instructions they could use in these steps on the students through the research lesson and then make the necessary rearrangements through evaluation meetings. Considering the opportunities offered by the collaborative and school-based structure of lesson study, it is thought that lesson study can be a functional model for pre-service teachers to use theory and practice together in courses on problem solving instruction.

The Effect of Using Blended Jigsaw-4 Problem-Solving Instruction on Preservice Physics Teachers’ Problem Solving Skill

The Effect of Using Blended Jigsaw-4 Problem-Solving Instruction on Preservice Physics Teachers’ Problem Solving Skill

What is the area of a pig? Problem posing and problem solving in early childhood education

Problem posing and problem solving serve as a crucial element of classroom instruction in early mathematics education, and have long been a topic of study of many practitioners and researchers. Used as a powerful tool for differentiation, they affect the ways in which the practice of mathematics is perceived by students and also help teachers gauge children’s understanding of concepts. In the student-centered approach, problem posing and problem solving can successfully engage students in creative educational situations. This research has been part of a broader design research project, the aim of which was to investigate the relationship between a classroom environment that allows for dialogue and young children’s propensity to design and solve their own tasks. Methodology included taking field notes and photographs, followed by reflection sessions. Turning young mathematicians into independent inquirers helped them gain authentic ownership of their knowledge. Additionally, it aided in the development of the young children’s competencies in effective engagement in problem posing activities. The toolbox of instructional techniques for problem posing in the classroom evolved, transforming mathematical classrooms into inquiry polygons for all learners.

Enhancing university students' creative confidence, learning motivation, and team creative performance in design thinking using a digital visual collaborative environment

The pedagogy of design thinking (DT) is increasingly being used to promote creative problem-solving in higher education. The DT approach traditionally relies heavily on face-to-face collaboration to address ‘wicked’ challenges. However, technological advances have enabled the digitization of design collaboration to support DT co-creation. This study compares students' creative confidence, learning motivation, and team creative performance in digital visual collaboration (DVC) with traditional face-to-face collaboration in DT activities. Mixed quasi-experimental pre-post surveys were used as the quantitative method, and an open-ended questionnaire was used as the qualitative method. The results indicate that (1). DT pedagogy positively affected students' creative confidence in both groups. Nevertheless, the experimental group significantly improved more than the comparison group. (2). The experimental group also showed better learning motivation and perceived competence than students in the comparison group. (3). Finally, students performed significantly better on design projects during DVC than those who collaborated face-to-face. Most importantly, students' qualitative responses suggest that digital visual collaboration platforms can be a productive environment to support DT projects.

A Cross-Sectional Study Investigating the Effects of Learning-Based Activities, Algebra Tiles and Problem-Solving Teaching Techniques on Students’ Conceptual Understanding and Problem-Solving Skills in the Jamaican Mathematics Classroom

A Cross-Sectional Study Investigating the Effects of Learning-Based Activities, Algebra Tiles and Problem-Solving Teaching Techniques on Students’ Conceptual Understanding and Problem-Solving Skills in the Jamaican Mathematics Classroom

A model for scaffolding mathematical problem-solving: From theory to practice

Devising a plan is an important phase in the teaching and learning of mathematical problem-solving in a mathematics classroom. In this paper, we propose devise a plan (DP) model for scaffolding students in devising a plan to engage them in mathematical problem-solving for classroom instruction and beyond. Although mathematics educators have proposed problem-solving scaffold, mainly building on Polya’s (1945) and Schoenfeld’s (1985) problem-solving models, for authentic problem-solving in the classroom, the phase on devising a plan was generally brief. We expand on the scaffolding of the intermediate stages of devising the plan for teachers to teach problem-solving, with a more ambitious goal of enabling students to engage in independent problem-solving beyond the classrooms. Features that are used in the planning stage of problem-solving are identified through a systematic literature review. Our proposed DP model includes the use of both metacognitive strategies and problem-solving heuristics. The application of our proposed model was exemplified by the solution of three non-routine problem on proportionality.

간호대학생의 윤리적 성향, 전문직 자아개념, 심폐소생술 태도가 생명의료윤리의식에 미치는 영향

Purpose : The purpose of this study is a descriptive study to identify the factors that influence nursing students’ ethical disposition, professional self-concept, and cardiopulmonary resuscitation attitude on bio-medical ethics.
 Method : This study identifies the factors that affect bio-medical ethics by convenience sampling. Data were collected using a questionnaire from 257 students participating in bio-medical ethics education from December 15, 2019 to January 15, 2020.
 Results : The subjects’ ethical disposition were 42.21±5.18 for idealism and 38.91±5.96 for relativism. The average professional self-concept was 3.72±0.43, and the CPR attitude was 3.83±0.47. The overall average of bio-medical ethics was 3.17±0.44. The relationship between idealism (r＝.54), relativism (r＝.28), professional self-concept (r＝.39), CPR attitude (r＝.26), and bio-medical ethics of nursing students showed a statistically significant positive correlation. The significant predictors of bio-medical ethics were idealism (β＝.04) and professional self-concept (β＝.18).
 Conclusion : Based on the research results, the development of various types of educational programs that can improve bio-medical ethics capabilities should be developed. First, comprehensive education on ethical principles and concepts should be provided in ethical decision-making situations. Second, educational content that can foster professional self-concept and idealistic ethical disposition should be included to understand ethical beliefs. It is necessary to apply educational programs, such as simulation, discussion, and problem-solving teaching and learning methods, so nursing students can actively participate in and judge bio-medical ethics situations.

A literature review on dyscalculia: What dyscalculia is, its characteristics, and difficulties students face in mathematics class

Dyscalculia is a specific learning condition that affects the comprehension and manipulation of numerical concepts, which can impact students' academic performance and well-being in mathematics education. The research methodology used was a systematic literature review that aimed to identify and synthesize the existing evidence regarding the differences in understanding of dyscalculia, its characteristics and the difficulties that students with dyscalculia may face in class. The search string used in electronic databases, such as Crossref and Google Scholar, to generate articles for the review were “dyscalculia” and “dyscalculia characteristics.” After the study selection process and appraising its quality, 23 articles met the selection criteria and were reviewed to synthesize answers to the research questions. The findings suggest despite many differences in understanding what dyscalculia was and it was clear that dyscalculia is a specific learning condition that affected students’ comprehension and manipulation of numerical concepts. Students with dyscalculia exhibit various characteristics, the most noticeable of which was low mathematics achievement scores. The difficulties faced by students with dyscalculia in the classroom were numerous. However, the primary obstacles they faced involved comprehending and applying mathematical concepts, as these difficulties could lead to others, such as executing mathematical problem-solving instructions. Educators might comprehend the diverse characteristics of dyscalculia to provide appropriate support and accommodations for students with difficulties.

Self-Regulated Strategy Development for Algebra Problem Solving

In the era of 21st century learning, many secondary students with learning disabilities continue to struggle with mathematics problem solving. Emerging evidence suggests self-regulated strategy development can be combined with existing evidence-based and promising practices during mathematics instruction. These practices include explicit instruction, metacognition, use of visual representations, ongoing formative assessment and feedback, multiple examples, and self-regulation. We describe the promising and practical potential of SRSD and STAR, a research-based, metacognitive problem-solving strategy, for instruction in algebraic problem-solving. A practical example is provided to illustrate the combination of practices.

Supporting creative problem solving in primary geometry education

This intervention study aimed to identify how creative thinking can be supported in geometry education. Fifth-graders received five geometry lessons that incorporated divergent and convergent thinking. Children were assigned to a condition with either no creative thinking support (n = 60), support for divergent thinking (partial support; n = 55) or support for divergent and convergent thinking (full support; n = 59). Divergent thinking was assessed by a multiple-solution task and scored in terms of fluency, flexibility and originality. Convergent thinking was assessed by an idea evaluation task. Repeated measures MANOVA showed that different aspects of divergent thinking (i.e., fluency, flexibility and originality) benefited from different types of support. Students’ fluency scores improved in the full support condition, but decreased in the other two conditions. A reverse pattern was found for flexibility and originality, which decreased in the full support condition but increased in the other conditions. No time and condition effects were found for convergent thinking. In all conditions, there was a non-significant increase in geometry scores. However, geometry performance differed between conditions, and was lower (across pretest and posttest) in the full support condition than in the no support and partial support conditions. These results provide some initial evidence that divergent thinking can be promoted in geometry education. Convergent thinking, on the other hand, might be more difficult to support effectively. As different types of support seem to affect different aspects of divergent thinking, teachers might consider adapting support to the specific task or individual needs of children.

Introducing Assistive Technology (AT) to Pre-Service Teachers: Observations and Experiences

Assistive technology (AT) can help students with special needs with their learning, and the importance of AT is on the rise with the development of new technologies and the diversification of student body. However, it is observed that pre-service teachers need to be better prepared for the use of AT in their teaching, including awareness, creative and innovative ways of problem solving, and pedagogical use of “low-tech” “mid-tech” and “high-tech” AT. Based on the observation and experience of the author in his teaching of an ICT (Information and Communication Technologies) course in a teacher education program at a middle-sized university in Ontario, Canada, this paper intends to broaden educators’ understanding of AT including hardware and software, emphasize the necessity of the introduction of AT in teacher education programs, and discuss the pedagogical uses of various types of AT tools. By sharing our observations and experiences, it is hoped that educators can be inspired to use various methods to expand the understanding of AT in pre-service teacher education and in-service teacher professional development programs.

Life Tasks as a Means of Studying New Material When Teaching Geometry in Secondary School

The article reveals the role of life tasks in teaching geometry in high school. The teaching of mathematics in a general education school, in addition to equipping students with certain knowledge, skills and abilities necessary to prepare them for life activities in the conditions of modern production, also pursues the goal of achieving such a level of their mathematical development that they need to study other school subjects at a high level, to continue their education in higher education. And also, for the formation of key and subject competencies in mathematics. The article deals with life tasks as a means of learning new material when teaching geometry in high school. Examples from the production industry are given. And also, the article presents the requirements and goals of studying mathematics, geometry in high school. The content of the textbooks proposed by the Ministry of Education, respectively, for general education and subject state standards in mathematics, contains many examples related to life tasks. The above conclusions define the main problem of the study: to study the role and place of tasks with vital content in revealing the content-applied significance of the school geometry course and in solving general educational problems facing the school. Develop a methodology for teaching problem solving. In the school teaching of geometry, the connection of the studied material with life, with practice, is often not yet rationally realized. Students have poorly developed skills and abilities to apply the acquired knowledge in practice. The goals and requirements of education standards for student-centered learning, i. e. to connect the teaching of mathematics, geometry with life, the passion for studying the basics of production, to form the key and subject competencies of students.

Effect of Problem-Solving Teaching Method on Improvement of Higher Order Thinking Skills of Early C

Mathematics subject is known as the queen of all subjects. InPakistan it is taught as a compulsory subject from class one to secondarylevel but it is also considered the uninterested subject for the students.There are many reasons but the major one is the teaching method of theteacher. This study was intended to find Problem Solving TeachingMethod having effect on the improvement of HOTs among Prospectiveteachers at early childhood level who learn Mathematics at the Universitylevel. The major objectives of the present study were; to find out the effectof the Problem Solving Teaching Method on element of conceptualknowledge sub level analysis, evaluating and creating. This study was trueexperimental double control group. The sample of this study consisted of75 Prospective teachers from department of Education, InternationalIslamic University Islamabad. The students were from BS Educationgroup of fifth semester, for the collection of data course contents ofmathematics including theoretical geometry, practical geometry and wordproblem of BS Education of the 5th semester were selected. Data wereanalyzed by using Pre-test, post-test, Levene test, ANOVA, Post Hockanalysis, mean and standard deviation. The major finding showed that theachievement scores of per-test and post-test of experimental group weresignificant. The achievement scores of both control groups-I and II showednon-significant difference. The difference between the achievement scoresof control group-I and II were same to some extent. The major conclusionof the study was that problem solving method of teaching developed thehigher order thinking skills among the prospective teachers as compete toconventional method, so this method may be added in professional trainingof mathematics science teachers.

Enhancing College Students’ Procedural Knowledge of Physics Using Blended Jigsaw-IV Problem-Solving Instruction

Jigsaw-IV Problem-solving method is innovative active learning instruction used to improve college student’s learning. The main purpose of the study was to investigate the effect of Jigsaw-IV problem-solving instruction on preservice physics teachers' (PSPT) procedural knowledge in college of teacher education in the Southern nation nationality region of Ethiopia. The study involves 136 first year PSPTs who are attending their preservice teacher education program in four colleges of teacher education. To achieve the goal of the study, a quasi-experimental research method with the pretest-posttest design was used. Procedural knowledge test was used for Data collection. The reliability of the test was checked using KR-20 and found to be 0.83. In treatment groups one, two, and three, the TECDRER (Thinking, Exploring, Choosing, and Manipulating), Discussing, Reflecting, Evaluating, and Re-teaching) model used in Jigsaw-IV problem-solving strategies (J-IVPSS), Jigsaw-IV (J-IV), and Problem Solving Strategies (PSS) were employed, while the customary method was employed for the comparison group. After checking all necessary assumption the data was analyzed using descriptive statistics and inferential statistics such as ANOVA and ANCOVA. The results showed that treatment groups performed significantly better than the comparison group. It was suggested that the J-IVPSS is a good approach to enhance PSPT's Procedural knowledge.

Multimodal learning analytics of collaborative patterns during pair programming in higher education

Pair programming (PP), as a mode of collaborative problem solving (CPS) in computer programming education, asks two students work in a pair to co-construct knowledge and solve problems. Considering the complex multimodality of pair programming caused by students’ discourses, behaviors, and socio-emotions, it is of critical importance to examine their collaborative patterns from a holistic, multimodal, dynamic perspective. But there is a lack of research investigating the collaborative patterns generated by the multimodality. This research applied multimodal learning analytics (MMLA) to collect 19 undergraduate student pairs’ multimodal process and products data to examine different collaborative patterns based on the quantitative, structural, and transitional characteristics. The results revealed four collaborative patterns (i.e., a consensus-achieved pattern, an argumentation-driven pattern, an individual-oriented pattern, and a trial-and-error pattern), associated with different levels of process and summative performances. Theoretical, pedagogical, and analytical implications were provided to guide the future research and practice.

Technological-pedagogical knowledge in problem-solving teaching: an exploratory study of mathematics teachers

Technological-pedagogical knowledge in problem-solving teaching: an exploratory study of mathematics teachers

Activity-Based Approach to the Teaching and Psychology of Insightful Problem Solving: Scientific Concepts as a Form of Constructive Criticism.

This article is dedicated to the 100-year anniversary of the birth of N.F. Talyzina and contains an assessment of the prospects for developing ways to master a scientific concept, in theories of learning according to the activity approach. The assessment takes into account achievements following the approach of L.S. Vygotsky, the "conceptual changes" approach, and theories of the psychology of insightful problem solving. To demonstrate the necessity and productivity of the activity approach to scientific concepts that students learn as forms of constructive criticism. A comparative analysis of the theories of the activity approach to learning, the approach of L.S. Vygotsky, the "conceptual changes" approach, and theories of the psychology of insightful problem solving, from the standpoint of identifying the most effective way of mastering scientific concepts. The main substantiated thesis of the article is that mastery of a scientific concept is most effective when it is presented as a form of constructive criticism of another concept. Taking into account the conceptual forms of constructive criticism allows us to outline the actual paths of development of the activity approach to learning. These forms were developed, on the one hand, through the methodology of science, and on the other, in a less developed way, through the psychology of insightful problem solving, with reliance on certain forms of "critical" action. In particular, when using a special kind of obstacle to teach a task, it is proposed to use the analysis of "full insight" to reveal a special type of reason for an erroneous action.