Understanding Problem Solving Research Articles

Enhancing Problem-Solving Skills in Mathematics: Applying LDMAT and SRL for Students with Learning Difficulties

This study examines the effectiveness of the LDMAT and SRL models in improving problem-solving skills in students with learning difficulties in mathematics. The research involved 18 junior high school students and employed a mixed research design. The assessment of problem-solving skills was conducted through pre-test and post-test measurements, consisting of 10 essay-based tests and weekly assignments. Furthermore, problem-solving understanding was assessed based on the strategies utilized by students in the post-test. Data analysis involved using paired t-tests to compare pre-test and post-test results. The findings indicate that applying the LDMAT and SRL models significantly enhanced problem-solving skills in students with learning difficulties in mathematics, particularly among female students. Moreover, the students exhibited an improved understanding of problem-solving procedures. This study underscores the efficacy of the LDMAT and SRL models in enhancing problem-solving abilities and promoting deeper comprehension of problem-solving strategies among students with learning difficulties in mathematics.

Effect of Model-Based Problem Solving on Error Patterns of At-Risk Students in Solving Additive Word Problems

Students with learning disabilities/difficulties in mathematics often apply ineffective procedures to solve word problems due to a lack of conceptual understanding of word problem solving, which results in poor mathematics performance and falling further behind the normal achievements of their peers. Current mathematics curriculum standards emphasize conceptual understanding in problem solving as well as higher-order thinking and reasoning, including all students. The purpose of this study was to evaluate the impact of a computer-assisted model-based problem-solving intervention program (MBPS) on elementary students’ word problem-solving performance by analyzing the error patterns. Results indicate that after the MBPS intervention, participants significantly improved their problem-solving performance and made fewer errors in solving problems across a range of additive word problem situations. Specifically, the participating students made their attempt to represent the mathematical relation, decontextualized from the word problem story, in the model equation before solving the problem, rather than blindly applying an operation or relying on the “keyword” strategy as they did during the preassessment. Implications of the study are discussed in the context of the National Council of Teachers of Mathematics’ calling for teaching big ideas to help students develop a deep understanding of mathematics knowledge.

The influence of students’ problem-solving understanding and results of students’ mathematics learning

Problem-solving is the ability to understand issues and steps that will affect students’ mathematics learning results. The research goals are: describing students’ problem-solving understanding and mathematics learning results; testing the influence of gender and grade level on students’ problem-solving understanding and mathematics learning results; and testing the influence of students’ problem-solving understanding on mathematics learning results. The population is all students in the fourth through sixth grades at two primary schools (263 respondents). The sample consists of 244 respondents, with female and male respondents of 123 and 121, and low- and high-grade students of 74 and 170, respectively. The researchers calculated and converted scores into values. Statistical tests were carried out by means of analysis of linear regression and the t-test. The Me of students’ mathematics learning results and problem-solving understanding are 69.679 and 66.889. The female students’ problem-solving understanding Me is greater than male ones’, but male students’ mathematics learning results Me is greater than female ones. The low-grade students’ problem-solving understanding Me is greater than high-grade students, but high-grade students’ mathematics learning results Me is greater than low-grade students. Gender has no influence on students’ mathematics problem-solving understanding or learning results. The grade level has a significant influence on students’ problem-solving understanding but no significant influence on mathematics learning results. The students’ problem-solving understanding has a significant influence on mathematics learning results, with a p value of 0.000. The research findings and results have implications for and contribute to assisting students in processing information and building mathematical knowledge.

Preservice mathematics teachers' perceptions of mathematical problem solving and its teaching: A case from China.

Preservice mathematics teachers' accurate understanding of mathematical problem solving and its teaching is key to the performance of their professional quality. This study aims to investigate preservice mathematics teachers' understanding of problem solving and its teaching and compares it with the understanding of in-service mathematics teachers. After surveying 326 in-service mathematics teachers, this study constructs a reliable and valid tool for the cognition of mathematical problem solving and its teaching and conducts a questionnaire survey on 26 preservice mathematics teachers. Survey results reveal that preservice mathematics teachers have a good understanding of mathematical problem solving and its teaching and are more confident in the transfer value of problem solving ability. By contrast, in-service teachers are more optimistic that problem solving requires exploration, continuous thinking, and the participation of metacognition. This article concludes that preservice mathematics teachers should focus more on the initiative and creativity of students and put students at the center of education. In addition, teacher educators should provide more teaching practice opportunities for preservice teachers. The findings also show that in-service teachers' understanding of problem solving and its teaching is inferior to that of preservice teachers on some indicators, implying the importance of post-service training for in-service teachers.

Mindset and Levels of Conceptual Understanding in the Problem-Solving of Preservice Mathematics Teachers in an Online Learning Environment

Mindset plays a vital role in tackling the barriers to improving the preservice mathematics teachers’ (PMTs) conceptual understanding of problem-solving. As the COVID-19 pandemic has continued to pose a challenge, online learning has been adopted. This led this study to determining the PMTs’ mindset and level of conceptual understanding in problem-solving in an online learning environment utilising Google Classroom and the Khan Academy. A quantitative research design was employed specifically utilising a descriptive, comparative, and correlational design. Forty-five PMTs were chosen through simple random sampling and willingly took part in this study. The data was gathered using validated and reliable questionnaires and problem-solving tests. The data gathered was analysed using descriptive statistics, analysis of variance, and simple linear regression. The results revealed that the college admission test, specifically numerical proficiency, influences a strong mindset and a higher level of conceptual understanding in problem-solving. Additionally, this study shows that mindset predicts the levels of conceptual understanding in problem-solving in an online environment where PMTs with a growth mindset have the potential to solve math problems. The use of Google Classroom and the Khan Academy to aid online instruction is useful in the preparation of PMTs as future mathematics teachers and problem-solvers. Further studies may be conducted to validate these reports and to address the limitations of this study.

The Development of Simulation Video for Problem Solving

This paper examines the development of simulation video using virtual reality technology to enhance students' understanding in Problem Solving & Program Design (DFC10042) course. This simulation video is captured by using 360 camera and edited using VR technology applications (Wonda VR) which is it provides a variety of interesting and easy features in exploring the simulation process. In the process of developing this application, the ADDIE model is used as a development methodology. This video shows a simulation of 3 scenarios in daily life. For each scenario, the Input, Process and Output (IPO) are clearly stated and detailed with descriptions and evaluation questions provided at the end of the video. The findings found that this simulation video gave a positive impact to students where more than 75% gave a score of 4 and 5 for a questionnaire, involved 114 respondents. Assessment scores involved the topic of problem solving techniques also increased by 65% compared to data for students who did not use simulation video. The intention for the development of simulation video are focusing to teaching aids that can help to improve students' understanding of problem solving and logical thinking in order to increased student’s ability to learn better. Extend from that, this method can be applied more widely by the students and lecturers whose involves in the teaching and learning of DFC10042 in Malaysia’s Polytechnic in general, which make the learning process more dynamic and interesting.

The 9th grade students’ mathematical understanding in problem solving based on Pirie-Kieren theory

The purpose of this study is to analyse the mathematical understanding in 9th grade students’ problem solving based on Pirie-Kieren theory. The Pirie-Kieren theory provides a framework to evaluate the students’ mathematical understanding in solving mathematical problem. The layers of mathematical understanding in Pirie-Kieren theory consist at primitive knowing, image making, image having, property noticing, formalising, observing, structuring, and inventizing. This study designed according to case study toward two students who are studying at one of primary school in Bandung district. The participants in this study were selected among voluntary students by considering their mathematics interesting and recommendation from the mathematics teacher. The data was collected by testing and interviewing. One problem solving item was posed for the mathematics test. The interview of this study was collected by through a semi-structured interview. The obtain data was descriptive analysis with qualitative approach based on Pirie-Kieren theory. The result show that two of participant was started working at image having layer and they have placed at formalising layer. The participants have lacked at primitive knowing and image making according to Pirie-Kieren theory.

Exploring Teachers’ Meta-Cognitive Skills in Mathematics Classes in Selected Rural Primary Schools in Eastern Cape, South Africa

Undoubtedly the acquisition of mathematical skills for problem solving is critically important in today’s sophisticated technological world. There is growing evidence that meta-cognition application is an important component of academic success in general and impacts on mathematical achievement in particular. Teachers’ application of meta-cognition therefore directs and reflects their teaching-practice behaviour which influences their learners’ learning with understanding in problem-solving. The purpose of the study reported on in this article was to explore teachers’ available meta-cognitive skills in class with the intention of supporting learners’ development of mathematics in problem-solving in some selected rural primary schools in the Eastern Cape, South Africa. The participants were three teachers purposefully selected from three primary schools. Interviews were conducted with the three teachers and three lessons were observed. The interviews, as an extension of observation, focused on the teachers’ knowledge or understanding of available meta-cognitive skills and how they used these skills in helping their learners’ development of mathematics problem-solving. The findings included a detailed exploration of the teachers’ acquisition and use of specific metacognitive skills, either consciously or unconsciously, during teaching and learning processes in order to develop their mathematics learners’ meta-cognitive skills as well as in solving mathematical problems. The results of the observation showed that there was evidence of teachers applying meta-cognitive skills unconsciously in assisting their learners in problemsolving in class. The interviews confirmed this evidence of available meta-cognitive skills which the teachers usually applied in assisting their learners in problem-solving in class. Recommendations have been made regarding teachers’ methods of teaching to improve the development of such skills in the lives of their mathematics learners through problemsolving.

Influence of a Mathematics Teachers' Circle on Elementary Teachers' Use of Problem Solving

Math teachers' circles are a form of professional development that is recommended by the Conference Board of the Mathematical Sciences in their publication Mathematical Education of Teachers II (2012). However, little research has been published on how effective math teachers' circles are in advancing the mathematical knowledge of teachers and influencing their actual teaching practice. This study reports how 25 elementary teachers from schools with minority and economically disadvantaged populations responded to a math circle experience. A pretest and posttest showed a significant increase in problem‐solving ability. Through analysis of journals, all but 4 of the 25 teachers indicated that participation in the math circle increased their understanding of problem solving and advanced their use of problem solving in the classroom.

DISTANCE LEARNING IN THE MODERN TEACHER PROFESSIONAL DEVELOPMENT

The article deals with the peculiarities of distance education, its advantages and disadvantages describing programs of professional development MOOC (Massive Open Online Course), E-Teacher and Cambridge English Teacher. MOOC distance learning programs are free and open, they cover different areas - from science to teaching writing. In addition to participation in distance learning, teachers can become moderators and gain valuable experience. To obtain a certificate a participant should complete half of tasks and write an essay. In order to promote the programs, seminars supported by US embassies are held around the world. Unlike MOOC, program E-Teacher Scholarship is highly specialized, participants (winners of scholarships) can choose one of seven courses lasting 10 weeks. Participants are encouraged to find study buddies and work in groups, which makes it possible to establish professional contacts with colleagues from different countries. One must perform 70% of tasks and compete two projects for successful completion of the program. Distance Learning Program Cambridge English Teachers, which is designed for English teachers and is not free, offers 23 courses to complete during one year. Participants are expected to study theory, watch videos, complete checking compehension activities, tests and assignments that need to be done with students, conduct surveys and write reflective notes. Despite the fact that the above programs are designed primarily for teachers of English, they embody the features characteristic of distance learning programs in other areas of specialization. Participation in distance learning enables teachers to enrich their subject knowledge, overcome cross-cultural differences and gain an understanding of problem solving in education.

Collaboration and the importance for novices in learning java computer programming

The authors propose that a correlation exists between collaboration and success by novices when learning computer programming. Research in an introductory course was conducted that focused on answering several questions: At what time in their learning java programming and algorithmic problem solving, would a student benefit best by collaboration? At what time during the problem solving process would the learner benefit greatest by collaboration? Would the student benefit greater by collaborating with 1 student in the class, a group, or an expert mentor/coach? What cognitive and affective strategies are used during various types of collaboration? Does collaboration increase problem solving performance by females. This research will advance fundamental knowledge of teaching and learning of computer science. It will further the understanding of problem solving and strategies used in learning computer programming and whether collaboration is important.

Mathematical problem solving: What we know and where we are going

In the last three decades, there has been a great deal of educational research on mathematical problem solving, and this research has deepened our understanding of problem solving and related pedagogical issues immensely. As we reflect on the research trends in mathematical problem solving, we realize just how dynamic research on mathematical problem solving is. This is hardly surprising when one considers some of the fundamental questions that the field has to address: What is mathematical problem solving? What are the cognitive processes used in solving mathematical problems? What are the purposes of problem solving? What are the actual mechanisms that students use to learn and make sense of mathematics through problem solving? What is the teacher’s role in implementing problem solving in the mathematics classroom? The views of the mathematics education community on each of these questions have evolved over time and are still in flux. It is appropriate to periodically take stock of the field by examining how mathematics educators are currently looking at problem solving and seeing what issues currently have need of further research. One of the purposes of this special issue of the Journal of Mathematical Behavior is to conduct such an examination. It should be noted that while we will refer to a single special issue, it is really two issues combined into one. This special issue originated from the 10th International Congress of Mathematics Education’s Topic Study Group 18: Problem Solving in Mathematics Education. The general aims of the Topic Study Group were to provide a forum for those who are interested in any aspect of problem-solving research at any educational level, to present recent findings, and to exchange ideas. We set up three specific goals for the Problem Solving Topic Study Group: (1) to examine the understanding of the complex cognitive processes involved in problem solving; (2) to explore the actual mechanisms by which students learn and make sense of mathematics through problem solving, and how this can be supported by teachers; and (3) to identify future directions of problem-solving research, including the use of information technology. The Topic Study Group received a good response. There were 22 papers presented, authored by nearly 30 researchers from 13 different countries. A total of roughly 350 mathematics education researchers from around the world attended at least one of the sessions for the Topic Study Group. Most of the papers in this special issue are from those who presented at the Topic Study Group. In addition, we invited a few other researchers to submit papers in order to cover various aspects of problem-solving research that we wished to be represented in this issue. This special issue includes 12 papers, each addressing at least one of the three goals listed above. The first six papers that appear are empirically based; in these papers, the authors present the results of the fieldwork that they have conducted and also raise research questions for future studies. The remaining six

Mathematical problem solving in support of the curriculum?

The paper describes the results of part of a study into mathematical problem solving in secondary schools. The research project was an attempt to work with teachers, using almost an action research model, to try to develop good practice with the teaching of problem solving. At the same time we were interested in the students' reactions and how their learning and understanding of problem solving could be enhanced. The results described here show how two classes performed over the best part of a school year. The most spectacular result was the performance of a class of lower ability students on the end of year examination. They improved considerably over their results of the previous year and in this sense their results were better than the other classes at that level. We conjecture that the results were achieved in part, as a consequence of the time that was spent in the problem-solving lessons which allowed them to practise reading and working with wordy problems and working on basic material, especially arithmetic and algebra, at their own pace.

Teachers' salient beliefs about a problem-solving demonstration classroom in-service program

Each year science teachers have the opportunity to participate in a variety of in-service pro- grams, with the most traditional yearlong in-service agendas consisting of a preprogram, program, and follow-up program. One alternative to the traditional program is the inclusion of demonstration classrooms within the follow-up segment. This study specifically explored the beliefs of in-service teachers about one such program; the Problem-Solving Demonstration Classroom in-service program. To capture participants' beliefs, open-ended interviews, focus groups, and observations were conducted throughout a yearlong Problem-Solving Demonstration Classroom in-service program. The collected data were inductively ana- lyzed to identify the salient beliefs of participants. The results of this study suggest that the Problem- Solving Demonstration Classroom in-service program provided participating teachers an opportunity to address their instructional needs pertaining to problem solving, develop a view of the student in the con- text of problem solving, redefine their understanding of problem solving, reflect upon their own instruc- tional practice, and engage in a collegial and mentoring dialogue with peers. This preliminary investiga- tion suggests that the demonstration classroom program may be one variation to the traditional yearlong in-service program that is worthy of further exploration. © 1999 John Wiley & Sons, Inc. J Res Sci Teach 36: 141 - 158, 1999 The current menu of professional development strategies for science educators includes conventions, workshops, institutes, in-service programs, and academic coursework. In the Unit- ed States, these programs are often supported by the Department of Education's Dwight D. Eisenhower mathematics and science funds; Regional Educational Laboratories; National Sci- ence Foundation's initiatives in science, mathematics, engineering, and technology; the Nation- al Diffusion Network; and major organizations (e.g., National Science Teachers Association, Na- tional Association of Biology Teachers). The funding provided by these organizations is often substantial. In 1992, the National Science Foundation allocated approximately $50 million to stimulate curricular content and pedagogical change in science and mathematics (Suter, 1993), while the Eisenhower program spent $246 million to improve the skills of teachers and quality of instruction in science and mathematics (Crudup, 1993). In addition to large-scale organiza- tions, regional agencies, state agencies, and local districts expend funds for the professional de- velopment of in-service teachers. The financial support provided for a variety of professional development activities is one indicator of organizational and agency commitment to the im- provement of mathematics and science education.

Integrating math and science through problem centered learning in methods courses: Effects on prospective teachers’ understanding of problem solving

This study reports our understanding of the views on problem-solving developed by prospective elementary teachers as a result of experiencing problem centered learning in an integrated math-science methods course. The course was designed to assist the prospective teachers to develop their problem solving skills in mathematics and science contexts and to develop problem-solving activities that integrate mathematics and science to use in their classrooms. Small group activities, where students had multiple opportunities to interact with concrete materials and to discuss their ideas, were emphasized. Data sources included audio taped interviews, field notes, and documents such as portfolios and lesson plans students produced during problem solving activities. Four assertions related to students’ attitudes toward problem solving, their knowledge of problem solving and problem solving processes, and the role of problem solving in elementary classrooms are discussed. Implications for planning and implementing integrated mathematics and science problem solving activities in methods courses and for continued research are presented.

Children's application of simultaneous and successive processing in inductive and deductive reasoning problems: Implications for developing scientific reasoning skills

AbstractThe research reported in this article was undertaken to obtain a better understanding of problem solving and scientific reasoning in 10‐year‐old children. The study involved measuring children's competence at syllogistic reasoning and in solving a series of problems requiring inductive reasoning. Children were also categorized on the basis of levels of simultaneous and successive synthesis. Simultaneous and successive synthesis represent two dimensions of information processing identified by Luria in a program of neuropsychological research. Simultaneous synthesis involves integration of information in a holistic or spatial fashion, whereas successive synthesis involves processing information sequentially with temporal links between stimuli. Analysis of the data generated in the study indicated that syllogistic reasoning and inductive reasoning were significantly correlated with both simultaneous and successive synthesis. However, the strongest correlation was found between simultaneous synthesis and inductive reasoning. These findings provide a basis for understanding the roles of spatial and verbal‐logical ability as defined by Luria's neuropsychological theory in scientific problem solving. The results also highlight the need for teachers to provide experiences which are compatible with individual students' information processing styles.

Situating natural language understanding within experience-based design

Building useful systems with an ability to understand "real" natural language input has long been an elusive goal for Artificial Intelligence. Well-known problems such as ambiguity, indirectness, and incompleteness of natural language inputs have thwarted efforts to build natural language interfaces to intelligent systems. In this article, we report on our work on a model of understanding natural language design specifications of physical devices such as simple electrical circuits. Our system, called KA, solves the classical problems of ambiguity, incompleteness and indirectness by exploiting the knowledge and problem-solving processes in the situation of designing simple physical devices. In addition, KA acquires its knowledge structures (apart from a basic ontology of devices) from the results of its problem-solving processes. Thus, KA can be bootstrapped to understand design specifications and user feedback about new devices using the knowledge structures it acquired from similar devices designed previously.In this paper, we report on three investigations in the KA project. Our first investigation demonstrates that KA can resolve ambiguities in design specifications as well as infer unarticulated requirements using the ontology, the knowledge structures, and the problem-solving processes provided by its design situation. The second investigation shows that KA's problem-solving capabilities help ascertain the relevance of indirect design specifications, and identify unspecified relations between detailed requirements. The third investigation demonstrates the extensibility of KA's theory of natural language understanding by showing that KA can interpret user feedback as well as design requirements. Our results demonstrate that situating language understanding in problem solving, such as device design in KA, provides effective solutions to unresolved problems in natural language processing.

Metacognition and insight during problem solving: Comment on Metcalfe.

Metcalfe (1986a, 1986b; Metcalfe & Weibe, 1987) used two types of metacognitive judgments, prediction of solution and rating of warmth, to support the claim that there is a nonincremental process corresponding to the Gestalt notion of insight that occurs in the solution of certain sorts of problems. However, there are logical and empirical issues that can be raised about Metcalfe's analysis and conclusions : a) Metcalfe's finding that Ss cannot predict their performance on «insight» problems does not not logically necessitate that solutions to such problems occur in sudden bursts of insight, b) Metcalfe's feeling-of-warmth data for insight problems are problematic as support for her hypothesis, and c) Metcalfe's definition of insight is circular and does not further our understanding of problem solving

The recognition and non‐recognition of problem‐solving stages in nursing practice

A requirement for high-quality individualized nursing care is that nurses must recognize and attempt to solve patients' health problems. In this study, it was decided to investigate problem solving using a model similar to the nursing process derived from the general literature. Insight into nurses' perceptions and understanding of problem solving was gained by interviewing 116 nurses using vignettes of clinical problem solving. Data analysis revealed that many informants failed to discuss some problem-solving stages, in particular planning and evaluation. Conversely, problem assessment and implementation attracted more comment. The implications for these variations in nurses' problem-solving behaviour are examined in relation to contemporary nursing issues.

Successful and unsuccessful problem solving in classical genetic pedigrees

AbstractUsing the think‐aloud interview technique, 16 undergraduates and 11 genetics graduate students and biology faculty members were asked to solve from 1 to 3 classical genetics problems which require pedigree analysis. Subjects were classified as either successful or unsuccessful and the performances of these groups were analyzed from videotaped recordings of the interviews. A number of previously reported findings were corroborated. Additional observations are discussed in terms of genetic knowledge, use of production rules, strategy selection, use of critical cues, hypothesis testing, use of logic, understanding of issues of probability, and the thinking process itself. Taken collectively, these findings evidence a remarkable similarity between the successful solution of pedigree problems and the processes of medical diagnosis and scientific investigation. This convergence of research findings suggests a qualitative advance in the understanding of problem solving. Based on this understanding, recommendations for classroom instruction are presented.