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.

     

The acquisition of problem-solving skills in mathematics: How animations can aid understanding of structural problem features and solution procedures

In this paper the augmentation of worked examples with animations for teaching problem-solving skills in mathematics is advocated as an effective instructional method. First, in a cognitive task analysis different knowledge prerequisites are identified for solving mathematical word problems. Second, it is argued that so called hybrid animations would be most effective for acquiring these prerequisites, because they show the continuous transition from a concrete, but superficial problem representation to a more abstract, mathematical problem model that forms a basis for solving a problem. An experiment was conducted, where N = 32 pupils from a German high school studied either only text-based worked examples explaining different problem categories from the domain of algebra or worked examples augmented with hybrid animations. Learners with hybrid animations showed superior problem-solving performance for problems of different transfer distance relative to those in the text-only condition.     

Metacognitive Instruction: Trainers Teaching Thinking Skills

Humans have the ability to monitor and control their conscious cognitive processes. This ability, called metacognition, implies that people can learn to optimize their cognitive processes. Recent research in metacognition provides new ways of accelerating learning and skill transfer through an improvement in the decision-making, problem solving, and attentional skills of trainees. This paper provides a critical review of recent research in metacognition and presents recommendations for assessing and facilitating metacognitive skills in trainees, using cognitive-based techniques for task analysis and instructional design.     

Evaluating text-based information on the World Wide Web

This special section contributes to an inclusive cognitive model of information problem solving (IPS) activity, touches briefly IPS learning, and brings to the notice methodological pitfalls related to uncovering IPS processes. Instead of focusing on the IPS process as a whole, the contributing articles turn their attention to what is regarded the heart of IPS, namely the evaluation of information. In this commentary we reflect on theoretical, methodological, and instructional design issues. Results are commented upon and future research is addressed. A vignette is presented to illustrate the aforementioned issues.     

Rapid Prototyping in the Instructional Design Process

Instructional models guide designer activity as they attempt to solve instructional problems. Models provide structure to the project, problem solving strategies, evaluation, and feedback. This paper is designed to examine Rapid Prototyping, a model born in the computer age. Rapid Prototyping embraces computer design strategies, constructivist learning theory, and cognitive psychology. This paper will first look at the “classic” forms of instructional design models, which form the foundation of instructional design. A review of the critical elements of these models will provide the framework to understand the concepts behind the Rapid Prototyping model. Next, this paper will examine how researchers define Rapid Prototyping, how the model is used, whether it is successful, and why some consider it a major shift in the way instruction is designed. By clarifying how RP is structured to solve instructional problems and the processes it uses to produce instructional materials, this paper will strive to determine whether it is a viable alternative to traditional design models.     

面向高阶认知发展的成长式问题化学习(GPBL)研究--概念、设计与案例

促进学习者高阶认知和问题解决能力的发展,是当代教学设计的核心诉求之一。问题化学习(PBL)虽致力于此,但实践效果却不够理想。面向高阶认知发展的成长式问题化学习(GPBL),是在分析PBL的价值与困境的基础上所提出的一种扬长避短的教学设计方法。它将学习置于复杂而真实的问题空间中,使其难度可随学习者能力发展而循序渐进动态变化,进而促进其高阶认知发展。以此方法开展的“教育游戏设计”教学案例表明,学习者在复杂问题解决、远迁移、合作及编程等能力上,都有较为明显的发展,这在一定程度上验证了设计目的。     

Designer Thinking: How Novices and Experts Think About Instructional Design

Instructional design can be characterized as a complex problem-solving task, yet little is known about what cognitive processes it requires. This research sought to identify differences in the thinking of expert and novice instructional designers given the same design task. A talk-aloud procedure was used to capture their problem-solving procedures and representations while designing instruction for a computer simulation. A coding scheme based on design principles, strategies, and subtasks was applied to the verbal protocols. Quantitative and qualitative analyses indicated that expert and novice instructional designers do appear to use divergent design paths. These design paths were further analyzed using design trees.     

How instructional design experts use knowledge and experience to solve ill‐structured problems

This study examined how instructional design (ID) experts used their prior knowledge and previous experiences to solve an ill‐structured instructional design problem. Seven experienced designers used a think‐aloud procedure to articulate their problem‐solving processes while reading a case narrative. Results, presented in the form of four assertions, showed that experts (1) narrowed the problem space by identifying key design challenges, (2) used an amalgam of knowledge and experience to interpret the problem situation, (3) incorporated a mental model of the ID process in their problem analyses, and (4) came to similar conclusions about how to respond to the situation, despite differences in their initial conceptualizations. Implications for educating novice instructional designers are discussed.     

Dealing with graphic output from diagram processing tasks: Approaches to characterisation and analysis

The current relative lack of detailed knowledge about how learners interact with the types of diagrams used in instructional materials is partly due to the research difficulties in characterising the cognitive structures and processes involved in these interactions. One of these difficulties arises from the lack of research tools specifically designed for the collection and meaningful analysis of relevant data. This paper describes computer-based approaches developed to analyse and characterise graphic output produced during diagram processing tasks. Specializations: Mental representation and processing of scientific diagrams, characteristics of explanatory diagrams, visual aspects of problem solving, instructional design.     

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.     

Teaching Instructional Design: An Apprenticeship Model

Several cognitive psychologists have written about the importance of placing instruction within “authentic” contexts that mirror real-life situations. They argue that knowledge learned in academic settings does not necessarily transfer to non-academic settings. Whether preparing performance technologists or instructional designers, educators must strive to create meaningful problem-solving contexts that enable students to define, and subsequently solve, real-world problems. In an attempt to address this issue we have modified the way we teach instructional design. This paper discusses a cognitive apprenticeship approach to teaching design, which incorporates elements of modeling, coaching, reflection, articulation, and exploration. We describe how these features are embedded within three phases (orientation, situated training/learning, and exploration) of an introductory instructional design course designed to move our novice designers along a continuum of expertise as they develop and refine their own professional design skills. Although the apprenticeship model described here specifically addresses concerns within the context of preparing instructional designers, we believe that this model can be adapted to address similar issues in the education of performance technologists.     

A further study of productive failure in mathematical problem solving: unpacking the design components

This paper replicates and extends my earlier work on productive failure in mathematical problem solving (Kapur, doi:, 2009). One hundred and nine, seventh-grade mathematics students taught by the same teacher from a Singapore school experienced one of three learning designs: (a) traditional lecture and practice (LP), (b) productive failure (PF), where they solved complex problems in small groups without any instructional facilitation up until a teacher-led consolidation, or (c) facilitated complex problem solving (FCPS), which was the same as the PF condition except that students received instructional facilitation throughout their lessons. Despite seemingly failing in their collective and individual problem-solving efforts, PF students significantly outperformed their counterparts in the other two conditions on both the well-structured and higher-order application problems on the post-test, and demonstrated greater representation flexibility in working with graphical representations. The differences between the FCPS and LP conditions did not reach significance. Findings and implications of productive failure for theory, design of learning, and future research are discussed.     

基于问题解决的处方教学设计

问题是知识结构的心脏,是教师教学的心脏,是学生学习的心脏。教学过程实质上是师生基于问题解决的互动过程,教学设计则指向于问题与问题解决过程的有效设计。前者在于教学过程中的“临床诊断”,后者在于“开处方”。教学设计可归结为基于问题解决的处方教学设计。     

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.     

Problem Solving and Teaching How to Solve Problems in Technology-Rich Contexts

ABSTRACT

Problem solving is perhaps the key characteristic that makes us human. Given the kinds of problems that we face in a competitive economy and society, the new generation of learners is ever more required to have problem-solving abilities. By drawing from the literature on technological pedagogical content knowledge, design thinking, general and specific methods of problem solving, and role of technologies for solving problems, this article highlights the importance of problem solving for future teachers and discusses strategies that can help them become good problem solvers and understand the requirements of teaching their students problem solving in technology-rich contexts. This article consists of two main parts. Part 1 focuses on strategies required to help preservice teachers to be better problem solvers, and Part 2 summarizes approaches to introduce preservice teachers to the methods of teaching problem solving. The strategies reviewed provide a tangible guidance for teacher education programs regarding how to promote future teachers’ problem-solving skills.     

The design and evaluation of hypertext structures for supporting design problem solving

Computer-based complex information systems are used increasingly more often, for a growing variety of purposes, in both educational and professional contexts. Since the effectiveness of information systems will largely depend on the particular purpose and the particular task context at hand, at least part of our research efforts should be directed at studying specific application areas. This paper reports a study on the use of hypertext information systems during architectural-design problem solving. Theoretical notions on design problem solving, such as distinguishing between a problem-structuring and a problem-solving phase, provide us with expectations about the changing informational needs during the design process. Specific information structures are proposed, incorporating design principles from learning research, to accommodate these informational needs. Results of an empirical study indeed showed interactions between design phase and information structure when separately inspecting the outcomes for problem structuring and problem solving. Educational implications include the use of a combination of hierarchical decomposition and cross-referencing for certain instructional goals, such as teaching complexity and abstraction.     

Applying Lakatos' theory to the theory of mathematical problem solving

In this paper, the relation between Lakatos' theory and issues about mathematics education — especially issues about mathematical problem solving — is reinvestigated by paying attention to Lakatos' methodology of a scientific research programme. By comparing the same findings about mathematical problem solving with the discussion in Lakatos' theory — e.g. research programmes' hard cores, their negative and positive heuristics, and their goals — we establish the correspondence between research programmes and solver's structures of a problem situation, i.e. structures given by a solver to a problem situation. After establishing this, the implications of Lakatos' theory, i.e. the nature of selection from competing programmes and the social origins of the cores of programmes, are applied to the discussion about mathematical problem-solving, with indications of the related evidence in the theory of mathematical problem solving which seems to support the application of those implications. Such an application leads to one view of mathematical problem solving, which reflects the irrational nature and social aspects of problem-solving activities, both in solving problems and in selecting better solutions.