Teaching Problem Solving Research Articles

Practical Research on Primary Mathematics Teaching Based on Deep Learning

With the rapid development of the knowledge economy, learning that stays at a shallow level is no longer able to meet the challenges of the times and deep learning has come into being. The key to deep learning is to develop students’ critical thinking, information integration, communication and collaboration, and constructive reflection skills, which can be cultivated in the process of problem solving. By exploring the theories of deep learning and problem solving, the basic elements of deep learning theory are incorporated into the design system of problem-solving teaching, and the problem-solving teaching model based on deep learning is proposed in conjunction with the content of elementary school mathematics, so that students can further develop their core literacy based on acquiring deep learning skills.

Designing a Framework to Facilitate Metacognitive Strategy Development in Computer-Mediated Problem-Solving Instruction.

Metacognition is a key component of ill-structured problem solving. As such, there is a need for instructional design guidance for metacognitive skill development. This study addressed this need through the creation of a computer-based interactive content design framework to guide the design of metacognitive scaffolds for ill-structured problem-solving instruction. It utilized a type II design and development research approach and formative design principles to create a comprehensive and generalizable instructional design framework. The framework was composed by synthesizing research and practical literature and evaluated by experts in related fields. Key components of the framework include metacognitive strategies, instructional design strategies, interactive media types, question prompts, and feedback. Instructors, course developers, and other key stakeholders could follow the guidelines proposed in this framework to create metacognitive-based ill-structured problem-solving instruction using e-Learning authoring tools. This study bridges the gap between theory and practice, as well as adds to literature in media research with focusing on utilizing various media types to create effective learning materials.

Intelligent tutoring systems for word problem solving in COVID-19 days: could they have been (part of) the solution?

The COVID-19 pandemic led to the lockdown of schools in many countries, forcing teachers and students to carry out educational activities remotely. In the case of mathematics, developing remote instruction based on both synchronous and asynchronous technological solutions has proven to be an extremely complex challenge. Specifically, this was the case in topics such as word problem solving, as this domain requires intensive supervision and feedback from the teacher. In this piece of research, we present an evaluation of how technology is employed in the teaching of mathematics, with particular relevance to learning during the pandemic. For that purpose, we conducted a systematic review, revealing the almost complete absence of experiments in which the use of technology is not mediated by the teacher. These results reflect a pessimistic vision within the field of mathematics education about the possibilities of learning when the student uses technology autonomously. Bringing good outcomes out of a bad situation, the pandemic crisis may represent a turning point from which to start directing the research gaze towards technological environments such as those mediated by artificial intelligence. As an example, we provide a study illustrating to what extent intelligent tutoring systems can be cost-effective compared to one-to-one human tutoring and mathematic learning-oriented solutions for intensive supervision in the teaching of word problem solving, especially appropriate for remote settings. Despite the potential of these technologies, the experience also showed that student socioeconomic level was a determining factor in the participation rate with an intelligent tutoring system, regardless of whether or not the administration guaranteed students' access to technological resources during the COVID-19 situation.

학습자 참여중심 토의를 활용한 과학수업이 예비유아교사들의 과학교수효능감, 의사소통능력, 문제해결능력에 미치는 효과

Objectives The purpose of this study was to explore the effect of the learner participation-centered discussion class on the science teaching efficacy, communication capability, and problem solving ability of pre-service early childhood teachers. Methods The subjects of this study were 32 students enrolled in a four-year early childhood education program. The learner participation-centered discussion class were carried out through the science education class (45 hours) during the first semester in 2021. Data were collected from science teaching efficacy, communication capability, and problem solving ability rating scales. Results The results of quantitative analysis were as follows. First, the learner participation-centered discussion class brought statistically significant difference to pre-service early childhood teachers’ science teaching efficacy(both science teaching outcome expectancy and science teaching self-efficacy). Second, the learner participation-centered discussion class brought statistically significant difference to pre-service early childhood teachers’ communication capability(especially in message converting capability out of all sub-domains). Third, the learner participation-centered discussion class brought statistically significant difference to pre-service early childhood teachers’ problem solving ability(especially in the production of alternative resolution method, and the implement and confirmation of resolution method out of all sub-domains). Conclusions Therefore, the learner participation-centered discussion class is the meaningful teaching method to improve the science teaching professionality and problem solving ability of pre-service early childhood teachers.

Virtual robotics in education: The experience of eighth grade students in STEM

Classroom teaching with robotics points to a more engaging learning environment in many respects, particularly in terms of tasks related to problem solving and critical thinking in education. Nevertheless, previous studies have cited many obstacles to using robotics in the classroom. These obstacles include the costs of supplying students with robots, fixing and modifying the robots, and school facilities and infrastructure that negatively influence a teacher’s ability to teach a particular STEM subject or to apply new teaching approaches with robotics; these issues seem to have discouraged some teachers from utilizing robotics in their teaching approaches. Accordingly, this study aims to facilitate teaching with robotics through the use of virtual robotics. The study explores the experience of eighth grade students and their teachers engaging with a virtual platform in five different K–12 schools that have formally incorporated physical robotics into STEM classroom teaching. A qualitative phenomenological approach is utilized to explore the experience, using focus groups with students and interviews with teachers. The focus of this study is on the processes of teaching and learning STEM with robotics via virtual platforms, and the perceived effectiveness and practicability of the virtual platform. The study revealed that the use of virtual classrooms and applications has become acceptable by many educational institutions, influenced to move to online platforms during the COVID-19 pandemic. This has laid the foundation for teachers and students, as the end users and main actors in education, to invest the time and effort in improving STEM and other related skills using virtual robotics. They were motivated by the perceived and acquired benefits that are associated with using virtual robotics in a web-mediated educational process. The main barriers were associated with web-mediated cultural norms and educational regulations/policies related to virtual learning. The main recommendations of the study are for teachers to be innovative, to observe, and to listen carefully to their students, relying on their pedagogical knowledge to use available technology to serve student-teacher objectives.

Educational Social Enterprise and the Wicked Problem of Creativity and Literacy

This article examines the potential contribution of social enterprise to the “wicked” problem of creativity and literacy in a performative schooling environment, drawing on an ethnographic study of Ciento, a social enterprise organization that works with under-resourced young people, families, and communities in Melbourne, Australia. In light of the growing body of research on the ways in which schools navigate creativity and performativity, this article contributes new knowledge on non-school organizations that is largely missing from this conversation, as well as new insights on the operations of education-focused social enterprises in Australia. It considers the social, political, and historical factors that have shaped this unique space of educational “wickedity” and the ways in which organizational rationales and practices, as well as the experiences and views of staff and participants, indicate a complex, promising, and innovative approach to educational problem-solving.

Effect of Problem Solving Teaching Method in Mathematics on the Performance of 7th Grade Students

The study aimed to analyze the effect of problem-solving teaching methods in mathematics on the achievements of elementary level students. The major objective of the study was to; i. To compare the mathematics academic achievements and ability of problem-solving among 7th class students taught through traditional and problem-solving teaching methods. 7th class students of Govt.Secondary School 47 NB Sargodha were divided into two groups and randomly assigned as contro land experimental groups. Two tests were validated through peer review, expert opinion and pilot testing; one “Problem Solving Ability Test in mathematics” (PSATM) and “Achievement Test in mathematics” (ATM) for 7th grade were used as pre-test and post-test. The experiment was conducted for a period of six weeks. The t-test and ANOVA were applied for data analysis. The major conclusion was that the participants treated with a new method of problem-solving teaching showed better results than the participants taught by traditional teaching methods in the achievement test and problem-solving ability test. It is recommended that elementary level mathematics teachers teach the students by using problem-solving teaching methods in their lesson plans for the development of problem-solving ability among learners.

A didactic model to support the use of senses and sensors in environmental education problem solving

AbstractProblem solving, and specifically the goal of developing problem-solving competences, is a significant dimension of environmental education. Moreover, human senses and electronic sensors have been recognized as important tools in authentic problem-based learning. The purpose of this paper is to present a model to support teachers in creating didactic activities that use human senses and electronic sensors as epistemic mediators in participatory environmental education problem-based learning. The EcoSolvingS model is based on a set theoretical and practical perspectives, and on a cross analysis of a selection of environmental education problem-solving case studies. In a first part, this paper presents the dimensions of the theoretical foundations of the EcoSolvingS model. Subsequently, the results of the cross analysis of the environmental education problem-solving case studies are presented and related to the components of the EcoSolvingS model. Finally, the model is described, and its utility and future developments are discussed.

Identifying Key Component of Collaborative Problem Solving in Teaching and Learning Process: The Challenges Ahead in Preparing for 21st Century Skills

In recent years many researchers have paid close attention to and conducted extensive research on Collaborative Problem Solving (CPS). This is because many complex projects in the modern world can only be completed through teamwork. However, education and training that emphasize the systematic strengthening of the CPS aspect are still insufficient in preparing graduates to enter the workforce. In fact, CPS as one of the most important skills in the 21st century besides critical thinking, communication, creativity, and innovation. This paper deals with the CPS as an important skill in 21st Century. The first part of the paper attempt to explicate the basic concept of CPS. Subsequently, Collaboration and Problem￾Solving Process in the context of teaching and learning processes will be presented in the next section. Besides, a conceive illustrated of Assessment Framework of 2015 PISA CPS will also described. The article is devoted to explain the Dimensions and Elements of CPS Assessment; in particular, the social domain of collaborative problem-solving as well as Cognitive domain of CPS are discussed.

Mitigating Bias in Recruitment: Attracting a Diverse, Dynamic Workforce to Sustain the Future of Radiation Oncology

Why do we need a diverse workforce? Diversity allows for improved collective intelligence,1 and can include diversity of professional knowledge, interests, and perspectives. Benefits of workforce diversity include providing different perspectives, better serving patients,2,3 and improving outcomes.4-6 Diversity is not only about social justice, but an essential strategy for complex problem solving in clinical care, research, and teaching. However, racial, ethnic, and gender disparities in outcomes remain pervasive in the U.S.

Effects of Professional Development on English Learners’ Problem Solving

Teacher preparation for problem-solving instruction is essential to meeting the math needs of English learners (ELs) with math learning disabilities (MLD) in U.S. public schools. In investigating this instruction with Hispanic ELs with MLD, this study focused on how professional development supported one special educator’s implementation of effective practices for both academic language and problem-solving instruction. The professional development prepared the teacher for instructional and cooperative learning phases that faded prompting as students achieved independence in applying the problem-solving strategy. A multiple-baseline design was used to assess nine third-grade Hispanic ELs with MLD. As compared with the baseline phase, instructional scaffolding increased word problem solving for all the participants. All students’ level of probe performance was maintained during follow-up sessions. The results suggest the intervention facilitated improved math problem-solving performance.

Teaching Discipline-Based Problem Solving.

Problem solving plays an essential role in all scientific disciplines, and solving problems can reveal essential concepts that underlie those disciplines. Thus, problem solving serves both as a common tool and desired outcome in many science classes. Research on teaching problem solving offers principles for instruction that are guided by learning theories. This essay describes an online, evidence-based teaching guide (https://lse.ascb.org/ evidence-based-teaching-guides/problem-solving) intended to guide instructors in the use of these principles. The guide describes the theoretical underpinnings of problem-solving research and instructional choices that can place instruction before problem solving (e.g., peer-led team learning and worked examples) or problem solving before instruction (e.g., process-oriented guided inquiry learning, contrasting cases, and productive failure). Finally, the guide describes assessment choices that help instructors consider alternative outcomes for problem-solving instruction. Each of these sections consists of key points that can be gleaned from the literature as well as summaries and links to articles that inform these points. The guide also includes an instructor checklist that offers a concise summary of key points with actionable steps to direct instructors as they develop and refine their problem-solving instruction.

Efficacy of Peer-Delivered Mathematical Problem-Solving Instruction to Students With Extensive Support Needs

Mathematical problem solving has been identified as one foundational area of mathematics for all students but is an area of weakness for students with disabilities. This investigation sought to determine the effects of peer-delivered schema-based instruction on the mathematical problem solving of the change problem type with four middle school students with extensive support needs using a single-case multiple-probe-across-participants design. We also wanted to determine if same-age peer tutors who received behavior skills training could deliver the academic instruction with fidelity. Students and peer tutors were representative of diverse backgrounds. Results showed a functional relation between peer-delivered modified schema-based instruction and students’ acquisition and maintenance of mathematical word problem–solving skills, and strong effect sizes were found. Peer tutors were able to provide instruction with high levels of fidelity across the study. Social validity data showed that all participants benefited from the peer-delivered instruction.

기업체에서 코칭 기법을 활용한 창의적 문제해결 수업모형 개발

The purpose of this study is to develop a class model for creative problem-solving using coaching techniques. Regarding the research method, a draft of the class model was devised, and the final form was derived through expert verification. Concerning the final draft, the validity of the teaching model was verified by professors who were employed by companies that specialized in the teaching of creative problem solving and by experts with a doctorate in education. Unlike the draft instructional model, the final instructional model included the application of coaching techniques to each stage of the creative problem-solving model. Consequently, a model focusing on the creative problem-solving technique was developed. The class model for creative problem-solving developed in this study provides a class model to educate businesses to solve problems creatively. Therefore, I expect that the model can help teachers to introduce creative problem-solving education and to provide education that is more systematic.

Improving the Trigonometric Functions Learning Concept with Dynamic Mathematics Software

Since the 21st century, the new model of Internet+Education has gradually penetrated into the field of mathematics education and has become a hot topic in the current research on mathematics education, and education informatization has become the main development trend. Therefore, the purpose of this research is to help students and teachers how to use Hawgent dynamic mathematics software to help students learn trigonometric functions and help teachers practice trigonometric functions. The research method used is the research and development (R&D) method and this research was done at Chongqing Zhongxian Senior Middle School for the period month of July to August 2021. The model has adaptive guiding principles that can help researchers develop ICT based learning media in the five stages of analysis, design, development, implementation, and evaluation. This research is based on the Hawgent dynamic mathematics software to design a trigonometric function integrable ware design model, dynamically presenting the concept of trigonometric function and its image and properties, and then use integrable ware to assist the teaching of trigonometric functions, and verify it through experimental teaching. The results show that the learning of trigonometric functions assisted by Hawgent dynamic integrable ware design can help improve students' understanding and interest in trigonometric functions. In the future, other researchers can study the influence of information technology on the teaching of mathematical formulas, theorems, and mathematical problem solving, and explore SEM models of influencing factors.

Effect of Polya Problem Solving Teaching Method on the Achievement of Students in Algebra

The study investigated the effect of Polya problem solving teaching method on the achievement of students in algebra. The study employed quasi-treatment design. Three (3) research questions were asked and three (3) null hypotheses were formulated for the study. The population of the study was made up of 3600 SSII students in all the thirty one (31) secondary schools in Nsukka education zone of Enugu State. The sample for the study comprised of 300 SSII students drawn from four (4) co-educational schools out of 31 co-educational schools in Nsukka Education Zone of Enugu State drawn through simple random technique. In each of the 4 co-educational schools drawn 8 intact classes of SSII were randomly drawn. 4 intact classes out of the 8 intact classes were assigned to treatment group, while the 4 intact classes were assigned to control group. The treatment group consisted of 160 students who were taught algebra using Polya problem solving teaching method and the control group comprising 140 students who were taught algebra using the conventional method. Data were collected using algebra achievement test (AAT) for both pretest and post-test. Data were analyzed quantitatively using mean and standard deviation, while null hypotheses were tested at 0.05 level of significance using ANOVA. It was revealed from the study that polya problem solving teaching method increased the achievement of students in algebra and is superior to the conventional method of teaching algebra. Also, the study revealed that there was no significance difference in mean achievement scores of males an females in algebra. Based on the findings of the study, the researcher recommended among other things that polya problem solving teaching method should be used in teaching algebra and that mathematics teacher should be trained through workshops, in-service training, seminars etc on the uses of Polya problem solving teaching method approach in teaching algebra in all senior secondary schools for higher academic excellence mathematics generally and algebra in particular. In conclusion, students taught algebra with polya problem solving teaching method had higher mean achievement score than those taught with conventional teaching method. It was therefore concluded that Polya problem solving teaching method enhances students’ achievement in algebra. Keywords: Polya, problem solving, teaching method DOI: 10.7176/RHSS/12-6-04 Publication date: March 31 st 2022

Elementary Computational Thinking Instruction and Assessment: A Learning Trajectory Perspective

There is little empirical research related to how elementary students develop computational thinking (CT) and how they apply CT in problem-solving. To address this gap in knowledge, this study made use of learning trajectories (LTs; hypothesized learning goals, progressions, and activities) in CT concept areas such as sequence, repetition, conditionals, and decomposition to better understand students’ CT. This study implemented eight math-CT integrated lessons aligned to U.S. national mathematics education standards and the LTs with third- and fourth-grade students. This basic interpretive qualitative study aimed at gaining a deeper understanding of elementary students’ CT by having students express and articulate their CT in cognitive interviews. Participants’ (n= 22) CT articulation was examined usinga prioricodes translated verbatim from the learning goals in the LTs and was mapped to the learning goals in the LTs. Results revealed a range of students’ CT in problem-solving, such as using precise and complete problem-solving instructions, recognizing repeating patterns, and decomposing arithmetic problems. By collecting empirical data on how students expressed and articulated their CT, this study makes theoretical contributions by generating initial empirical evidence to support the hypothesized learning goals and progressions in the LTs. This article also discusses the implications for integrated CT instruction and assessments at the elementary level.

Assessment of Collaborative Problem Solving in Engineering Students Through Hands-On Simulations

Contribution: This article discusses the use of manufacturing simulation games to study collaborative problem-solving skills in engineering students. The simulation represents the mass production paradigm in which large quantities of identical products are produced. Empirical data is collected from the simulation to evaluate the skills engineering students used in solving the problem and their group effectiveness. Background: The use of simulation games to teach problem solving in design and manufacturing is an effective approach to convey concepts to students. Simulation games engage students in experiential and collaborative learning with fun elements. Research Questions: How does hands-on simulation engage students in collaborative problem solving? How does participation in collaborative problem solving affect group effectiveness? Methodology: This work presents a study of 37 university-level engineering students in the United States. Participants worked in groups completing the simulation game and responded to surveys on their various skills used. Findings: Participants utilized analytical, metacognitive, and thinking skills in their engagement, reported that the simulation games enhanced their understanding of manufacturing concepts and active collaboration improved problem-solving effectiveness.

Investigating unprompted and prompted diagrams generated by physics majors during problem solving

Diagrams are ubiquitous in physics, especially in physics education and physics problem solving. Physics problem solvers may generate diagrams to orient to a scenario, to organize information, to directly obtain an answer, or as a tool of communication. In this study, we asked 19 undergraduate and graduate physics majors to answer 18 multiple-choice (MC) physics questions and then complete six diagramming tasks of situations similar to six of the MC problems: the MC problems contained no prompting regarding diagrams, while the diagramming tasks explicitly asked participants to carefully generate diagrams. This prompting placed participants in one of two epistemic frames, problem solving or communicating, which allowed us to explore which elements and features the students include (or not) in diagrams generated when students are working within these two frames. By comparing students’ spontaneously generated diagrams to their prompted diagrams, we found differences in size, accuracy, and amount of detail in unprompted problem-solving diagrams and prompted communicating diagrams. We also looked at correlations between the presence and features of unprompted diagrams with participants’ answer choice. Looking at the different cohorts (e.g., lower-division undergraduate and graduate students), we found that the differences in diagramming between cohorts were generally smaller than the differences within a cohort. We also explore implications for teaching and research.4 MoreReceived 16 June 2021Accepted 20 December 2021DOI:https://doi.org/10.1103/PhysRevPhysEducRes.18.010104Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasResearch methodologyScientific reasoning & problem solvingPhysics Education Research

“Teaching Problem Solving in Mathematics”

From the Archives highlights articles from NCTM’s legacy journals, as chosen by leaders in mathematics education.