Design‐based science and real‐world problem‐solving

Design‐based science (DBS) is a science pedagogy in which new scientific knowledge and problem‐solving skills are constructed in the context of designing artifacts. This paper examines whether the enactment of a DBS unit supported students’ efforts to construct and transfer new science knowledge and ‘designerly’ problem‐solving skills to the solution of a new real‐world design problem in a real‐world setting. One hundred and forty‐nine students participated in the enactment of a DBS unit. Their understanding of the curricular content was assessed by identical pre‐instructional and post‐instructional written tests. They were then given a new design problem as a transfer task. There was a statistically significant increase on scores from pre‐test to post‐test with an effect size of 1.8. There was a stronger correlation between the scores of the transfer task and those of the post‐test than with those of the pre‐test; we use this finding to suggest that the knowledge that was constructed during the unit enactment supported the solution of the transfer task. This has implications for the development of science curricula that aim to lead to the construction of knowledge and skills that may be useful in extra‐classroom settings. Whether participation in consecutive enactments of different DBS units increases transfer remains to be investigated in more depth.     

Developing an instrument to characterise peer‐led groups in collaborative learning environments: assessing problem‐solving approach and group interaction

Collaborative learning is being used extensively by educators at all levels. Peer‐led team learning in a version of collaborative learning that has shown consistent success in science, technology, engineering and mathematics disciplines. Using a multi‐phase research study we describe the development of an observation instrument that can be used to assess peer‐led group learning. This paper illustrates the development of a classification system for peer‐led learning groups and an instrument based on this classification system. The instrument evaluates small learning groups on two important aspects of group learning: problem solving approach and group interaction style. We provide evidence of the factor structure of the two dimensions using both exploratory and confirmatory factor analysis. We also provide information about the reliability of the two scales as measured by the Cronbach's alpha coefficient. Data from a large peer‐led learning programme was used to conduct the factor analysis. Results from the factor analysis confirmed that the instrument is actually measuring two key characteristics of small learning groups: problem solving approach and group interaction style, characteristics that have been linked to effective functioning of the group and to the student learning outcomes. This instrument may be particularly appealing to practitioners (faculty members, those running small‐group learning programmes, etc.) because it is easy to use and it does not require extensive time for analysis.     

Issues in science education: problem‐solving,creativity and originality

In this paper the author explores the concept of problem‐solving as generally employed in the science education literature and suggests that a useful distinction can be drawn between puzzles, for which solutions are known or assumed to exist, and problems, for which no solution may be possible. The ability to recognize a problem, it is suggested, is possibly more important than its solution and this is dependent upon the experience, knowledge and interests of the individual. Successful encountering of problems and puzzles and the relationship of this activity to originality and creativity is also discussed. It is proposed that both puzzle and problem‐solving activities are important to provide in school science but that too little attention is paid to real problem‐solving with the result that the specific skills required are not practised.     

Case-based learning in virtual groups – collaborative problem solving activities and learning outcomes in a virtual professional training course

This article analyzes the collaborative problem solving activities and learning outcomes of five groups that worked on two different complex cases in a virtual professional training course. In this asynchronous virtual learning environment, all knowledge management content was delivered virtually and collaboration took place through forums. To measure the effects of the problem solving activities, learners' contributions were analyzed with respect to four different problem solving activities: Two content-specific problem solving activities, namely gathering information and developing a solution, and two coordination-specific problem solving activities, namely planning the common approach and steering the interaction process. Results indicated that the learning process was dominated by two central activities: developing a solution and steering the interaction process. Furthermore, the results indicated that the groups with the more complex case used more overall problem solving activities than the groups with the less complex case. There was also a greater range of learning outcomes for learners with the more complex case than for learners with the less complex case. Finally, the number of overall problem solving activities for most of the successful groups was higher than for the less successful groups. Additionally, the more successful groups used more coordination-specific activities than content-specific activities during the problem solving process.     

The problem‐solving methods of mathematically gifted and older average‐attaining students

This paper examines some of the ways gifted students are said to be different from non‐gifted students by comparing the responses of 475, 9‐year‐old “gifted” students with those of 230 average‐attaining 13‐year‐old students on the same mathematical problem‐solving questions. The questions were specifically written for mathematically gifted 9 year olds as part of the World Class Tests project. The performance and approaches used by students in the two samples were found to be very similar, as was the frequency of different responses to the questions, suggesting that many of the mathematically “gifted” are not qualitatively different in their problem‐solving approaches from students of average ability, but are merely precocious.     

Computer: The use of computer‐mediated communication in training students in group problem‐solving and decision‐making techniques

Abstract

A cost‐effectiveness analysis of training Army National Guard soldiers by audio teletraining technology was conducted. The trainees were n = 225 soldiers nationwide. About half of the trainees received training in a three‐week Unit Clerk Course through traditional residence training, and the remainder received the same instruction through audio teletraining. Objective performance data were collected from written tests on sixteen of the forty‐seven tasks taught. The percentage of trainees in the audio teletraining group that reached criterion (93%) on the first test was significantly higher (by statistical test) than the residence group (85%). In comparing costs, the audio teletraining group had lower training costs per trainee. Projected on an annual basis, the Army National Guard can save $292,404 per year through the use of audio teletraining for the Unit Clerk Course.     

The effect of technology-supported collaborative problem solving method on students’ achievement and engagement

Education and Information Technologies - This study aimed to determine the effect of web 2.0 technologies supported collaborative problem solving method on students’ achievement and...     

Approach to mathematical problem solving and students’ belief systems: two case studies

The goal of the study reported here is to gain a better understanding of the role of belief systems in the approach phase to mathematical problem solving. Two students of high academic performance were selected based on a previous exploratory study of 61 students 12–13 years old. In this study we identified different types of approaches to problems that determine the behavior of students in the problem-solving process. The research found two aspects that explain the students’ approaches to problem solving: (1) the presence of a dualistic belief system originating in the student’s school experience; and (2) motivation linked to beliefs regarding the difficulty of the task. Our results indicate that there is a complex relationship between students’ belief systems and approaches to problem solving, if we consider a wide variety of beliefs about the nature of mathematics and problem solving and motivational beliefs, but that it is not possible to establish relationships of causality between specific beliefs and problem-solving activity (or vice versa).     

The role of number words in preschoolers’ addition concepts and problem‐solving procedures

Preschoolers’ conceptual understanding and procedural skills were examined so as to explore the role of number‐words and concept–procedure interactions in their additional knowledge. Eighteen three‐ to four‐year‐olds and 24 four‐ to five‐year‐olds judged commutativity and associativity principles and solved two‐term problems involving number words and unknown numbers. The older preschoolers outperformed younger preschoolers in judging concepts involving unknown numbers and children made more accurate commutativity than associativity judgements. Children with conceptual profiles indicating a strong understanding of concepts applied to unknown numbers were more accurate at solving number‐word problems than those with a poor conceptual understanding. The findings suggest that an important mathematical development during the preschool years may be learning to appreciate addition concepts as general principles that apply when exact numbers are unknown.     

Play and Problem‐solving in a New Light

This article presents a model of children's play, explored from an evolutionary perspective. Surprisingly, an evolutionary approach has only recently been introduced into this field, especially as far as learning is concerned, and is virtually unknown in educational studies. However, such an approach seems entirely reasonable if one accepts that cognitive activities are a product of evolution and selection. Moreover, there is some urgency in stressing the contribution biological sciences can make to the study of children's early development, since there exists an enormous amount of research of immediate relevance to educators that has apparently been ignored.     

The effects of computer programming on high school students’ reasoning skills and mathematical self-efficacy and problem solving

In this paper we investigate whether computer programming has an impact on high school student’s reasoning skills, problem solving and self-efficacy in Mathematics. The quasi-experimental design was adopted to implement the study. The sample of the research comprised 66 high school students separated into two groups, the experimental and the control group according to their educational orientation. The research findings indicate that there is a significant difference in the reasoning skills of students that participated in the “programming course” compared to students that did not. Moreover, the self-efficacy indicator of students that participated in the experimental group showed a significant difference from students in the control group. The results however, failed to support the hypothesis that computer programming significantly enhances student’s problem solving skills.     

The effects of students' cognitive styles on conceptual understandings and problem‐solving skills in introductory mechanics

The purpose of this study was to determine if there are relationship among freshmen students' Field depended or field independent (FD/FI) cognitive style, conceptual understandings, and problem solving skills in mechanics. The sample consisted of 213 freshmen (female = 111, male = 102; age range 17–21) who were enrolled in an introductory physics course required for science education prospective teachers. Data collection was done during the fall semesters in three successive years. At the beginning of each semester the Force Concept Inventory (FCI) and the Group Embedded Figure Test (GEFT) were administered to assess students' initial understanding of basic concepts in mechanics and FD/FI tendency of students, respectively. After completion of the course, the FCI and the Mechanics Base Line Test (MBT) were administered. The results indicated that students conceptual understanding were not statistically related to their FD/FI cognitive styles for both pre and post results. However, their problem‐solving skills were statistically related to their FD/FI cognitive style. The findings of the present and previous studies are compared, and the possible effects of the present studies on previous studies on teaching, learning and assessment for introductory mechanics are discussed.     

Sociomathematical and mathematical norms related to definition in pre-service primary teachers’ discourse

This study is part of a wider research program, which seeks to investigate the existence (or not) of relationships between sociomathematical and mathematical norms at different academic levels. Here, we consider the norms that arise in the interaction between primary student teachers when they solve a mathematical task related to the mathematical definition. We hypothesize that in the colloquial mathematical discourse between these students coexist two types of discourse as follows: sociomathematical and mathematical, each one with its specific norms. This coexistence can originate commognitive conflicts. We have been able to identify different commognitive conflicts that arose from the simultaneous existence of sociomathematical norms and mathematical norms linked to defining, approaching their generation.     

Procedural and conceptual changes in young children’s problem solving

This study analysed the different types of arithmetic knowledge that young children utilise when solving a multiple-step addition task. The focus of the research was on the procedural and conceptual changes that occur as children develop their overall problem solving approach. Combining qualitative case study with a micro-genetic approach, clinical interviews were conducted with ten 5–6-year-old children. The aim was to document how children combine knowledge of addition facts, calculation procedures and arithmetic concepts when solving a multiple-step task and how children’s application of different types of knowledge and overall solving approach changes and develops when children engage with solving the task in a series of problem solving sessions. The study documents children’s pathways towards developing a more effective and systematic approach to multiple-step tasks through different phases of their problem solving behaviour. The analysis of changes in children’s overt behaviour reveals a dynamic interplay between children’s developing representation of the task, their improved procedures and gradually their more explicit grasp of the conceptual aspects of their strategy. The findings provide new evidence that supports aspects of the “iterative model” hypothesis of the interaction between procedural and conceptual knowledge and highlight the need for educational approaches and tasks that encourage and trigger the interplay of different types of knowledge in young children’s arithmetic problem solving.     

Analysing cognitive or non‐cognitive factors involved in the process of physics problem‐solving in an everyday context

Recently, the importance of an everyday context in physics learning, teaching, and problem‐solving has been emphasized. However, do students or physics educators really want to learn or teach physics problem‐solving in an everyday context? Are there not any obstructive factors to be considered in solving the everyday context physics problems? To obtain the answer to these questions, 93 high school students, 36 physics teachers, and nine university physics educators participated in this study. Using two types of physics problems—everyday contextual problems (E‐problems) and decontextualized problems (D‐problems)—it was found that even though there was no difference in the actual performance between E‐problems and D‐problems, subjects predicted that E‐problems were more difficult to solve. Subjects preferred E‐problems on a school physics test because they thought E‐problems were better problems. Based on the observations of students' problem‐solving processes and interviews with them, six factors were identified that could impede the successful solution of E‐problems. We also found that many physics teachers agreed that students should be able to cope with those factors; however, teachers' perceptions regarding the need for teaching those factors were low. Therefore, we suggested teacher reform through in‐service training courses to enhance skills for teaching problem‐solving in an everyday context.     

Assessing and tracking students’ problem solving performances in anchored learning environments

The purpose of this randomized experiment was to compare the performance of high-, average-, and low-achieving middle school students who were assessed with parallel versions of a computer-based test (CBT) or a paper-pencil test (PPT). Tests delivered in interactive, immersive environments like the CBT may have the advantage of providing teachers with diagnostic tools that can lead to instruction tailored to the needs of students at different achievement levels. To test the feasibility of CBT, students were randomly assigned to the CBT or PPT test conditions to measure what they had learned from an instructional method called enhanced anchored math instruction. Both assessment methods showed that students benefited from instruction and differentiated students by achievement status. The navigation maps generated from the CBT revealed that the low-achieving students were able to navigate the test, spent about the same amount of time solving the subproblems as the more advanced students, and made use of the learning scaffolds.