Exploring problem conceptualization and performance in STEM problem solving contexts

Problem solving abilities are critical components of contemporary Science, Technology, Engineering and Mathematics (STEM) education. Research in the area of problem solving has uncovered much about the representation, processes and heuristic approaches to problem solving. However, critics claim this overemphasis on the process of solving problems has led to a dearth in understanding of the earlier stages such as problem conceptualization. This paper aims to address some of these concerns by exploring the area of problem conceptualization and the underlying cognitive mechanisms that may play a supporting role in reasoning success. Participants (N?=?12) were prescribed a series of convergent problem-solving tasks representative of those used for developmental purposes in STEM education. During the problem-solving episodes, cognitive data were gathered by means of an electroencephalographic headset and used to investigate students’ cognitive approaches to conceptualizing the tasks. In addition, interpretive qualitative data in the form of post-task interviews and problem solutions were collected and analyzed. Overall findings indicated a significant reliance on memory during the conceptualization of the convergent problem-solving tasks. In addition, visuospatial cognitive processes were found to support the conceptualization of convergent problem-solving tasks. Visuospatial cognitive processes facilitated students during the conceptualization of convergent problems by allowing access to differential semantic content in long-term memory.

     

Integrating eye trackers with handwriting tablets to discover difficulties of solving geometry problems

To deepen our understanding of those aspects of problems that cause the most difficulty for solvers, this study integrated eye‐tracking with handwriting devices to investigate problem solvers' online processes while solving geometry problems. We are interested in whether the difference between successful and unsuccessful solvers can be identified by employing eye‐tracking and handwriting. Sixty‐two high school students were required to complete a series of geometry problems using pen tablets. Responses, including eye movement measures, wrote/drew trace, perceived cognitive load and questionnaires concerning the source of difficulties, were collected. The results suggested that the technique could enhance methods to diagnose difficulties by differentiating between successful and unsuccessful solvers. We considered mental rotation could be a primary obstacle in the integrating stage of diagram comprehension. The technique can be extensively applied in various instructional scenarios. Educational implications for problem solving are discussed.     

案例知识与复杂问题解决

人们在日常生活中需要不断地解决各种问题,正如波普尔所说"全部的生活就是问题解决"。问题解决,尤其是复杂问题的解决,已成为认知科学和学习研究中关注的焦点。复杂问题的解决是一个动态的复杂过程,需要综合运用多种认知和非认知成分。先前的研究已经提出了解决复杂问题的多种模型,给人们解决复杂问题提供了可依靠的支架。而案例知识作为一种典型性、叙事性、情境性、实践性、个人性、整体性的经验知识在问题解决中得到了广泛应用,已成为支持复杂问题解决的有效形式,具体表现为:支持问题境脉的阐释、支持问题的多视角认识、支持解决方案的生成、支持解决方案的确定以及支持对问题解决结果的评价。它正作为一种支持人们解决问题的资源,在现实中发挥越来越大的作用。     

Team-based complex problem solving: a collective cognition perspective

Today, much problem solving is performed by teams, rather than individuals. The complexity of these problems has exceeded the cognitive capacity of any individual and requires a team of members to solve them. The success of solving these complex problems not only relies on individual team members who possess different but complementary expertise, but more importantly, their collective problem solving ability. To better conceptualize large scale complex problem solving, an understanding of collective cognitive components and processes during team-based complex problem solving is necessary. This paper offers a conceptual discussion about complex problem solving from a collective cognition perspective. The types of cognitive processing and cognitive components of team-based problem solving (TBPS) as well as the cognitive states of collective emergent cognitive states and the interactive mechanisms will be discussed. Also, implications from the model for assessing TBPS performance and suggestions for future research will be offered.     

Teaching Creativity and Inventive Problem Solving in Science

Engaging learners in the excitement of science, helping them discover the value of evidence-based reasoning and higher-order cognitive skills, and teaching them to become creative problem solvers have long been goals of science education reformers. But the means to achieve these goals, especially methods to promote creative thinking in scientific problem solving, have not become widely known or used. In this essay, I review the evidence that creativity is not a single hard-to-measure property. The creative process can be explained by reference to increasingly well-understood cognitive skills such as cognitive flexibility and inhibitory control that are widely distributed in the population. I explore the relationship between creativity and the higher-order cognitive skills, review assessment methods, and describe several instructional strategies for enhancing creative problem solving in the college classroom. Evidence suggests that instruction to support the development of creativity requires inquiry-based teaching that includes explicit strategies to promote cognitive flexibility. Students need to be repeatedly reminded and shown how to be creative, to integrate material across subject areas, to question their own assumptions, and to imagine other viewpoints and possibilities. Further research is required to determine whether college students'' learning will be enhanced by these measures.     

Exploring the Use of Electroencephalography to Gather Objective Evidence of Cognitive Processing During Problem Solving

Currently, there is significant interest being directed towards the development of STEM education to meet economic and societal demands. While economic concerns can be a powerful driving force in advancing the STEM agenda, care must be taken that such economic imperative does not promote research approaches that overemphasize pragmatic application at the expense of augmenting the fundamental knowledge base of the discipline. This can be seen in the predominance of studies investigating problem solving approaches and procedures, while neglecting representational and conceptual processes, within the literature. Complementing concerns about STEM graduates’ problem solving capabilities, raised within the pertinent literature, this paper discusses a novel methodological approach aimed at investigating the cognitive elements of problem conceptualization. The intention is to demonstrate a novel method of data collection that overcomes some of the limitations cited in classic problem solving research while balancing a search for fundamental understanding with the possibility of application. The methodology described in this study employs an electroencephalographic (EEG) headset, as part of a mixed methods approach, to gather objective evidence of students’ cognitive processing during problem solving epochs. The method described provides rich evidence of students’ cognitive representations of problems during episodes of applied reasoning. The reliability and validity of the EEG method is supported by the stability of the findings across the triangulated data sources. The paper presents a novel method in the context of research within STEM education and demonstrates an effective procedure for gathering rich evidence of cognitive processing during the early stages of problem conceptualization.     

An investigation of undergraduates' transformational problem solving strategies: cognitive/metacognitive processes as predictors of holistic/analytic strategies

Recent years have seen increasing interest in the role of metacognition in mathematical problem solving. The study described in this paper explored problem solving strategies used by undergraduates. Furthermore, cognitive/metacognitive processes are predicted each of holistic and analytic strategies. Educational sciences students (n=178) were asked to talk/think aloud while solving two constructed response transformational problems. The protocols were transcribed and analysed, revealing that the cohort used nine strategies. The results showed that a holistic strategy was predicted by five cognitive/metacognitive processes, two of which were suppressors; whilst an analytic strategy was predicted by four cognitive/metacognitive processes, three of which were suppressors.     

PROBING THE RELATIONSHIP BETWEEN PROCESS OF SPATIAL PROBLEMS SOLVING AND SCIENCE LEARNING: AN EYE TRACKING APPROACH

There were two purposes in the study. One was to explore the cognitive activities during spatial problem solving and the other to probe the relationship between spatial ability and science concept learning. Twenty university students participated in the study. The Purdue Visualization of Rotations Test (PVRT) was used to assess the spatial ability, whose items were divided into different types of problems with respect to the rotation angles and levels of plane invisibility. The eye tracking technology and the interview technique were employed to analyze subjects’ the online cognitive processes and problem solving strategies. Students’ concept gains were examined by content analysis after reading a science report. The result shows that, first, the interview analysis shows that students of different PVRT performances employed different problem solving strategies. Second, rotation angles as well as levels of plane invisibility inserted significant effects on the online processes and performances of the spatial problem solving. Third, the accuracy performance of PVRT was correlated with eye movement patterns. At last, it was found that concept performance was not correlated with PVRT performance but associated with spatial memory and problem solving strategies.     

Instruction and Cognitive Change in Mathematics

A methodology for studying change during instruction in content-specific cognitive processes is presented. The methodology borrows both from the cognitive mediational approach in instructional effectiveness research and the instructional approach in cognitive psychology research. It is argued that learning from instruction must be understood in terms of the way in which instruction changes the cognitive processes used to solve tasks. The methodology is illustrated by summarizing a project on instructing middle-school students in semantic processes for solving decimal-fraction problems. The benefits of the methodology, such as tracing the effects of instruction on performance change, are discussed.     

Problem solving and classical genetics: Successful versus unsuccessful performance

Expert-novice problem-solving research is extended in this study to include classical genetics. Eleven undergraduates (novices) and nine graduate students and instructors (experts) were videotaped as they solved moderately complex genetics problems. Detailed analysis of these “think aloud” protocols resulted in 32 common tendencies that could be used to differentiate between successful and unsuccessful problem solvers. Experts perceive a problem as a task requiring analysis and reasoning and they tend to use a knowledge-development (forward-working) approach. They make frequent checks on the correctness of their work, use accurate and detailed bookkeeping procedures, and have a broader range of heuristics to apply to the problem. It is clear that studying problem solving using the expert/novice design requires that the problems be difficult enough to require more than more recall and yet simple enough to allow novices a chance for solution. Applying elementary probability concepts seemed to be the most difficult aspect of many of the genetics problems, even for the experts.     

Error Analysis of Mathematical Word Problem Solving Across Students with and without Learning Disabilities

Solving word problems is a common area of struggle for students with learning disabilities (LD). In order for instruction to be effective, we first need to have a clear understanding of the specific errors exhibited by students with LD during problem solving. Error analysis has proven to be an effective tool in other areas of math but has had little application to errors in word problems. Using an error analysis approach, this study aimed to investigate in depth the various types and frequency of errors made by students with LD and their AA peers during math problem solving. The resulting similarities and differences between the two groups of students are discussed with insight into underlying cognitive processes, and implications for future research.     

Improving problem solving with subgoal labels in expository text and worked examples

In highly procedural problem solving, procedures are typically taught with context-independent expository text that conceptually describes a procedure and context-dependent worked examples that concretely demonstrate a procedure. Subgoal labels have been used in worked examples to improve problem solving performance. The effect of subgoal labels in expository text, however, has not been explored. The present study examined the efficacy of subgoal labeled expository text and worked examples for programming education. The results show that learners who received subgoal labels in both the text and example are able to solve novel problems better than those who did not. In addition, subgoal labels in the text appear to have a different, rather than an additive, effect on learners compared to subgoal labels in the example. Specifically, subgoal labels in the text appear to help the learner articulate the procedure, and subgoal labels in the example appear to help the learner apply the procedure.     

How Can We Improve Problem Solving in Undergraduate Biology? Applying Lessons from 30 Years of Physics Education Research

If students are to successfully grapple with authentic, complex biological problems as scientists and citizens, they need practice solving such problems during their undergraduate years. Physics education researchers have investigated student problem solving for the past three decades. Although physics and biology problems differ in structure and content, the instructional purposes align closely: explaining patterns and processes in the natural world and making predictions about physical and biological systems. In this paper, we discuss how research-supported approaches developed by physics education researchers can be adopted by biologists to enhance student problem-solving skills. First, we compare the problems that biology students are typically asked to solve with authentic, complex problems. We then describe the development of research-validated physics curricula emphasizing process skills in problem solving. We show that solving authentic, complex biology problems requires many of the same skills that practicing physicists and biologists use in representing problems, seeking relationships, making predictions, and verifying or checking solutions. We assert that acquiring these skills can help biology students become competent problem solvers. Finally, we propose how biology scholars can apply lessons from physics education in their classrooms and inspire new studies in biology education research.     

Effects of worked examples, example-problem, and problem-example pairs on novices’ learning

Research has demonstrated that instruction that relies more heavily on example study is more effective for novices’ learning than instruction consisting of problem solving. However, ‘a heavier reliance on example study’ has been implemented in different ways. For example, worked examples only (WE), example-problem pairs (WE-PS), or problem-example pairs (PS-WE) have been used. This study investigated the effectiveness of all three strategies compared to problem solving only (PS), using electrical circuits troubleshooting tasks; participants were secondary education students who were novices concerning those tasks. Based on prior research, it was hypothesized and confirmed that WE and WE-PS would lead to lower cognitive load during learning and higher learning outcomes than PS. In addition, the open questions of whether there would be any differences between WE and WE-PS, and whether there would be any differences between PS-WE and PS were explored. Results showed no differences between WE and WE-PS or between PS-WE and PS. This study can inform instructional designers on which example-based learning strategies to implement: it does not seem necessary to alternate example study and problem solving, but when doing so, example-problem pairs should be used rather than problem-example pairs.     

“Accepting Emotional Complexity”: A Socio-Constructivist Perspective on the Role of Emotions in the Mathematics Classroom

A socio-constructivist account of learning and emotions stresses the situatedness of every learning activity and points to the close interactions between cognitive, conative and affective factors in students’ learning and problem solving. Emotions are perceived as being constituted by the dynamic interplay of cognitive, physiological, and motivational processes in a specific context. Understanding the role of emotions in the mathematics classroom then implies understanding the nature of these situated processes and the way they relate to students’ problem-solving behaviour. We will present data from a multiple-case study of 16 students out of 4 different junior high classes that aimed to investigate students’ emotional processes when solving a mathematical problem in their classrooms. After identifying the different emotions and analyzing their relations to motivational and cognitive processes, the relation with students’ mathematics-related beliefs will be examined. We will specifically use Frank’s case to illustrate how the use of a thoughtful combination of a variety of different research instruments enabled us to gather insightful data on the role of emotions in mathematical problem solving.     

The consistency effect depends on markedness in less successful but not successful problem solvers: An eye movement study in primary school children

This study examined the effects of consistency (relational term consistent vs. inconsistent with required arithmetic operation) and markedness (relational term unmarked [‘more than’] vs. marked [‘less than’]) on word problem solving in 10–12 years old children differing in problem-solving skill. The results showed that for unmarked word problems, less successful problem solvers showed an effect of consistency on regressive eye movements (longer and more regressions to solution-relevant problem information for inconsistent than consistent word problems) but not on error rate. For marked word problems, they showed the opposite pattern (effects of consistency on error rate, not on regressive eye movements). The conclusion was drawn that, like more successful problem solvers, less successful problem solvers can appeal to a problem-model strategy, but that they do so only when the relational term is unmarked. The results were discussed mainly with respect to the linguistic–semantic aspects of word problem solving.