The refinement and validation of the critical decision making and problem solving scale moral dilema (CDP-MD)

This thesis extended previous research on critical decision making and problem solving by refining and validating a measure designed to assess the use of critical thinking and critical discussion in sociomoral dilemmas. The purpose of this thesis was twofold: 1) to refine the administration of the Critical Thinking Subscale of the CDP to elicit more adequate responses and for purposes of refining the coding and scoring procedures for the total measure, and 2) to collect preliminary data on the initial reliabilities of the measure. Subjects consisted of 40 undergraduate students at Florida International University. Results indicate that the use of longer probes on the Critical Thinking Subscale was more effective in eliciting adequate responses necessary for coding and evaluating the subjects performance. Analyses on the psychometric properties of the measure consisted of test-retest reliability and inter-rater reliability.

Parallel Problem Solving from Nature – PPSN XIV:14th International Conference, Edinburgh, UK, September 17-21, 2016, Proceedings

This book constitutes the refereed proceedings of the 14th International Conference on Parallel Problem Solving from Nature, PPSN 2016, held in Edinburgh, UK, in September 2016. The total of 93 revised full papers were carefully reviewed and selected from 224 submissions. The meeting began with four workshops which offered an ideal opportunity to explore specific topics in intelligent transportation Workshop, landscape-aware heuristic search, natural computing in scheduling and timetabling, and advances in multi-modal optimization. PPSN XIV also included sixteen free tutorials to give us all the opportunity to learn about new aspects: gray box optimization in theory; theory of evolutionary computation; graph-based and cartesian genetic programming; theory of parallel evolutionary algorithms; promoting diversity in evolutionary optimization: why and how; evolutionary multi-objective optimization; intelligent systems for smart cities; advances on multi-modal optimization; evolutionary computation in cryptography; evolutionary robotics - a practical guide to experiment with real hardware; evolutionary algorithms and hyper-heuristics; a bridge between optimization over manifolds and evolutionary computation; implementing evolutionary algorithms in the cloud; the attainment function approach to performance evaluation in EMO; runtime analysis of evolutionary algorithms: basic introduction; meta-model assisted (evolutionary) optimization. The papers are organized in topical sections on adaption, self-adaption and parameter tuning; differential evolution and swarm intelligence; dynamic, uncertain and constrained environments; genetic programming; multi-objective, many-objective and multi-level optimization; parallel algorithms and hardware issues; real-word applications and modeling; theory; diversity and landscape analysis.

Students’ Self-Report of Motivational Orientation and Teacher Evaluation on Coping and Motivational Orientation Related to Elementary Students’ Mathematical Problem Solving and Reading Comprehension

The present study examined the correlations between motivational orientation and students’ academic performance in mathematical problem solving and reading comprehension. The main purpose is to see if students’ intrinsic motivation is related to their actual performance in different subject areas, math and reading. In addition, two different informants, students and teachers, were adopted to check whether the correlation is different by different informants. Pearson’s correlational analysis was a major method, coupled with regression analysis. The result confirmed the significant positive correlation between students’ academic performance and students’ self-report and teacher evaluation on their motivational orientation respectively. Teacher evaluation turned out with more predictive value for the academic achievement in math and reading. Between the subjects, mathematical problem solving showed higher correlation with most of the motivational subscales than reading comprehension did. The highest correlation was found between teacher evaluation on task orientation and students’ mathematical problem solving. The positive relationship between intrinsic motivation and academic achievement was proved. The disparity between students ’ self-report and teacher evaluation on motivational orientation was also addressed with the need of further examination.

Losing their marbles : syntax-free programming for assessing problem-solving skills

Novice programmers have difficulty developing an algorithmic solution while simultaneously obeying the syntactic constraints of the target programming language. To see how students fare in algorithmic problem solving when not burdened by syntax, we conducted an experiment in which a large class of beginning programmers were required to write a solution to a computational problem in structured English, as if instructing a child, without reference to program code at all. The students produced an unexpectedly wide range of correct, and attempted, solutions, some of which had not occurred to their teachers. We also found that many common programming errors were evident in the natural language algorithms, including failure to ensure loop termination, hardwiring of solutions, failure to properly initialise the computation, and use of unnecessary temporary variables, suggesting that these mistakes are caused by inexperience at thinking algorithmically, rather than difficulties in expressing solutions as program code.

Group metacognition during mathematical problem solving

Although various studies have shown that groups are more productive than individuals in complex mathematical problem solving, not all groups work together cooperatively. This review highlights that addressing organisational and cognitive factors to help scaffold group mathematical problem solving is necessary but not sufficient. Successful group problem solving also needs to incorporate metacognitive factors in order for groups to reflect on the organisational and cognitive factors influencing their group mathematical problem solving.

Future directions and perspectives for problem solving research and curriculum development

Since the 1960s, numerous studies on problem solving have revealed the complexity of the domain and the difficulty in translating research findings into practice. The literature suggests that the impact of problem solving research on the mathematics curriculum has been limited. Furthermore, our accumulation of knowledge on the teaching of problem solving is lagging. In this first discussion paper we initially present a sketch of 50 years of research on mathematical problem solving. We then consider some factors that have held back problem solving research over the past decades and offer some directions for how we might advance the field. We stress the urgent need to take into account the nature of problem solving in various arenas of today’s world and to accordingly modernize our perspectives on the teaching and learning of problem solving and of mathematical content through problem solving. Substantive theory development is also long overdue—we show how new perspectives on the development of problem solving expertise can contribute to theory development in guiding the design of worthwhile learning activities. In particular, we explore a models and modeling perspective as an alternative to existing views on problem solving.

Methodologies for investigating relationships between concept development and the development of problem solving abilities

This paper is the second in a pair that Lesh, English, and Fennewald will be presenting at ICME TSG 19 on Problem Solving in Mathematics Education. The first paper describes three shortcomings of past research on mathematical problem solving. The first shortcoming can be seen in the fact that knowledge has not accumulated – in fact it has atrophied significantly during the past decade. Unsuccessful theories continue to be recycled and embellished. One reason for this is that researchers generally have failed to develop research tools needed to reliably observe, document, and assess the development of concepts and abilities that they claim to be important. The second shortcoming is that existing theories and research have failed to make it clear how concept development (or the development of basic skills) is related to the development of problem solving abilities – especially when attention is shifted beyond word problems found in school to the kind of problems found outside of school, where the requisite skills and even the questions to be asked might not be known in advance. The third shortcoming has to do with inherent weaknesses in observational studies and teaching experiments – and the assumption that a single grand theory should be able to describe all of the conceptual systems, instructional systems, and assessment systems that strongly molded and shaped by the same theoretical perspectives that are being used to develop them. Therefore, this paper will describe theoretical perspectives and methodological tools that are proving to be effective to combat the preceding kinds or shortcomings. We refer to our theoretical framework as models & modeling perspectives (MMP) on problem solving (Lesh & Doerr, 2003), learning, and teaching. One of the main methodologies of MMP is called multi-tier design studies (MTD).

Problem solving in a middle school robotics design classroom

Little research has been conducted on how students work when they are required to plan, build and evaluate artefacts in technology rich learning environments such as those supported by tools including flow charts, Labview programming and Lego construction. In this study, activity theory was used as an analytic tool to examine the social construction of meaning. There was a focus on the effect of teachers’ goals and the rules they enacted upon student use of the flow chart planning tool, and the tools of the programming language Labview and Lego construction. It was found that the articulation of a teacher’s goals via rules and divisions of labour helped to form distinct communities of learning and influenced the development of different problem solving strategies. The use of the planning tool flow charting was associated with continuity of approach, integration of problem solutions including appreciation of the nexus between construction and programming, and greater educational transformation. Students who flow charted defined problems in a more holistic way and demonstrated more methodical, insightful and integrated approaches to their use of tools. The findings have implications for teaching in design dominated learning environments.

Problem solving for the 21st century

Mathematical problem solving has been the subject of substantial and often controversial research for several decades. We use the term, problem solving, here in a broad sense to cover a range of activities that challenge and extend one’s thinking. In this chapter, we initially present a sketch of past decades of research on mathematical problem solving and its impact on the mathematics curriculum. We then consider some of the factors that have limited previous research on problem solving. In the remainder of the chapter we address some ways in which we might advance the fields of problem-solving research and curriculum development.

A problem-posing intervention in the development of problem-solving competence of underachieving, middle-year students

This study reported on the issues surrounding the acquisition of problem-solving competence of middle-year students who had been ascertained as above average in intelligence, but underachieving in problem-solving competence. In particular, it looked at the possible links between problem-posing skills development and improvements in problem-solving competence. A cohort of Year 7 students at a private, non-denominational, co-educational school was chosen as participants for the study, as they undertook a series of problem-posing sessions each week throughout a school term. The lessons were facilitated by the researcher in the students’ school setting. Two criteria were chosen to identify participants for this study. Firstly, each participant scored above the 60th percentile in the standardized Middle Years Ability Test (MYAT) (Australian Council for Educational Research, 2005) and secondly, the participants all scored below the cohort average for Criterion B (Problem-solving Criterion) in their school mathematics tests during the first semester of Year 7. Two mutually exclusive groups of participants were investigated with one constituting the Comparison Group and the other constituting the Intervention Group. The Comparison Group was chosen from a Year 7 cohort for whom no problem-posing intervention had occurred, while the Intervention Group was chosen from the Year 7 cohort of the following year. This second group received the problem-posing intervention in the form of a teaching experiment. That is, the Comparison Group were only pre-tested and post-tested, while the Intervention Group was involved in the teaching experiment and received the pre-testing and post-testing at the same time of the year, but in the following year, when the Comparison Group have moved on to the secondary part of the school. The groups were chosen from consecutive Year 7 cohorts to avoid cross-contamination of the data. A constructionist framework was adopted for this study that allowed the researcher to gain an “authentic understanding” of the changes that occurred in the development of problem-solving competence of the participants in the context of a classroom setting (Richardson, 1999). Qualitative and quantitative data were collected through a combination of methods including researcher observation and journal writing, video taping, student workbooks, informal student interviews, student surveys, and pre-testing and post-testing. This combination of methods was required to increase the validity of the study’s findings through triangulation of the data. The study findings showed that participation in problem-posing activities can facilitate the re-engagement of disengaged, middle-year mathematics students. In addition, participation in these activities can result in improved problem-solving competence and associated developmental learning changes. Some of the changes that were evident as a result of this study included improvements in self-regulation, increased integration of prior knowledge with new knowledge and increased and contextualised socialisation.

Interdisciplinarity vs disciplinarity : developing knowledge for problem solving in middle years of schooling

Interdisciplinary studies are fundamental to the signature practices for the middle years of schooling. Middle years researchers claim that interdisciplinarity in teaching appropriately meets the needs of early adolescents by tying concepts together, providing frameworks for the relevance of knowledge, and demonstrating the linking of disparate information for solution of novel problems. Cognitive research is not wholeheartedly supportive of this position. Learning theorists assert that application of knowledge in novel situations for the solution of problems is actually dependent on deep discipline based understandings. The present research contrasts the capabilities of early adolescent students from discipline based and interdisciplinary based curriculum schooling contexts to successfully solve multifaceted real world problems. This will inform the development of effective management of middle years of schooling curriculum.