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Teaching and Learning of Divergent and Convergent Thinking Through Open-Problem Solving in a Data Structures Course

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Teaching and Learning of Divergent and Convergent Thinking Through Open-Problem Solving in a Data Structures Course 2016 International Conference on Learning and Teaching in Computing and Engineering Teaching and Learning of Divergent and Convergent Thinking through Open-Problem Solving in a Data Structures Course Patil Deepti Reddy Sridhar Iyer Sasikumar M. IDP - Educational Technology, IDP- Educational Technology, CDAC, Indian Institute of Technology Bombay Indian Institute of Technology Mumbai, India. Mumbai, India. Bombay, Mumbai, India. [email protected] [email protected] [email protected] Abstract— Divergent thinking is the process of generating problem may not help student in applying them to solve multiple solutions for a given problem, while convergent thinking unfamiliar open problem. Today’s workplaces demand people is evaluating and selecting accurate solution based on constraints, who can solve non-routine complex problems [2, 3]. This gap assumptions, and pros and cons analysis. Divergent and between academia and industry can be bridged by training and convergent thinking is an important thinking skill needed to nurturing students to develop the cognitive thinking skills generate novel or innovative solutions to a given problem. needed to solve an unfamiliar problem effectively [5]. According to ABET guidelines, it is also one of the important skill to design an engineering solution to a given open problem. In engineering design subjects like software engineering, The training in developing both divergent and convergent students are taught to follow engineering design process thinking during multiple phases of problem solving can allow having phases: requirement gathering, analysis, design and students to design a better solution. In this paper, we propose an implementation. The engineering design process support intervention to develop divergent and convergent thinking skill convergent thinking as the focus is on evaluating and selecting through open problem solving in data structures course. The the single correct solution. This process does not encourage research methodology followed is Design Based Research (DBR) student to do lateral thinking or brainstorming to generate and the intervention proposed in this paper is operationalized and evaluated by following first cycle of DBR. A preliminary divergent ideas and then converge to evaluate and select idea study was conducted on second year Computer Engineering based on judgment, evidence, assumptions and principles. The students to study the effects of intervention. The results show integration of divergent and convergent thinking in each phase significant improvement in learners’ thinking in both divergent of engineering design process can enhance the creativity and and convergent thinking during open-problem solving. quality of the product designed [9]. Thus training in synchronizing both divergent and convergent thinking can Keywords—Divergent thinking, Convergent thinking, Open allow students to generate varied solutions and then select to problem solving, Data Structures, Multiple solution generation. get an innovative or creative solution [5]. In this paper, we propose an intervention to develop 1. INTRODUCTION divergent and convergent thinking skill through open problem Divergent thinking is the process of generating different solving. The open problems posed are ill-structured, real-life possible solutions for a given problem, while convergent problems and students are asked to apply data structures thinking is evaluating and selecting accurate solution based on concepts to solve them. The intervention is based on constraints, assumptions, and pros and cons analysis systematic problem solving models used to solve engineering [12,7,5,13,14,8]. Both divergent and convergent thinking are design and creative problems [5, 21]. The intervention aims to important thinking skills to generate novel or innovative develop divergent thinking skills- looking at the problem from solutions to a given open problem. According to ABET multiple perspectives and generating multiple solutions, and guidelines, it is also one of the important thinking skill for convergent thinking skills- identifying constraints, developing engineering design competency. The students need requirements, pros and cons analysis and justification of the to design an engineering solution or product by generating selected solution. The intervention consists of question potential solutions by thinking from multiple perspectives and prompts to start with divergent thinking and gradually shifts to evaluate them based on pros and cons analysis and constraints convergent thinking. For a given open problem, students are [7, 13]. In Computer Science & Engineering(CSE) education, prompted to elicit multiple solutions, and then to converge by the divergent and convergent thinking skills are important in filtering the solutions based on constraints and requirements. subjects such as software engineering, computer network, and data structures, in which a system or solution is to be designed The research methodology used to design the intervention for an open problem. is Design Based Research (DBR). In this paper the design and The content and procedures to taught to solve a simple evaluation of the intervention in first cycle of DBR is reported. 978-1-5090-2504-6/16 $31.00 © 2016 IEEE 178 DOI 10.1109/LaTiCE.2016.13 The broad research question investigated is: Does training on students to design better solutions it is important to integrate divergent and convergent thinking improve student open- creative thinking and engineering design models. problem solving ability? A preliminary study was conducted on second year Computer Engineering students to study the Basadur[4 ,5] proposed an integrated model in which effects of intervention in improving student’s open-problem divergent and convergent thinking is incorporated in all three solving ability by developing divergent and convergent phases of problem solving- problem finding, solving and thinking skill. implementation. The study was done to investigate the effects of training in integrated problem solving model. The In next section, the research in divergent and convergent participants of the training were professionals at various levels thinking is synthesized. Then the first cycle of DBR is from senior manager to junior engineers from various reported to explain the design process of the intervention organizations. They were made to practice the cognitive followed by evaluation of the intervention using experiment. process and techniques of divergent thinking to solve real- Later the results are discussed and analyzed to refine the world, open creative problems. The attitude towards divergent intervention in next cycle of DBR. and convergent thinking of the participants was measured before and after the training using survey. The increase in 2. RELATED WORK preference for divergence was significant for managers than non managers. Divergent thinking is process of generating large number of ideas with focus on quantity and not on quality [12, 7, 5]. We have adopted the Basadur’s integrated model to solve The sub-skills associated with divergent thinking are -fluency: real-world, open design problems to train engineering students the ability to generate many responses or ideas, flexibility: the in developing both divergent and convergent thinking as ability to generate varied ideas from different perspectives, or shown below: the ability to change the form, modify information, or shift perspectives, originality: the ability to generate unusual or • Establishing a need and analysis of task (outcome is novel responses and elaboration: the ability to embellish an problem statement) idea with details [19]. o Divergence to convergence • Design (outcome is design of the solution) In contrast to divergent thinking, convergent thinking is o Divergence to convergence associated with critical thinking where importance is given to • Implementation (outcome is the final product) systematically making decisions based on judgment, evidence, o Divergence to convergence assumptions and principles or concepts [14, 8]. The focus is In the first phase of problem solving- Establishing a need on systematically evaluating and selecting a single correct and analysis, student has to understand the problem and restate solution based on assumptions, constraints and principles. The the problem statement. In this phase, divergence is encouraged sub-skills needed in convergent thinking are- pros & cons using the design thinking principles stated as looking at the analysis of various solutions, making suitable assumptions for problem from different stakeholders viewpoints [6] and then a given problem, selection of accurate solution based on converge to restate the problem based on the requirements and constraints identified in a given problem and justifying constraints of the problem. selected solution [13]. In the second stage of problem solving- Design, the Both divergent and convergent thinking skills are student start with divergent thinking by providing prompts to important in generating innovative or creative solutions for an generate multiple solutions and then converge to evaluate and open problem. These skills can be encouraged in engineering select the best solution among the solutions generated. During curriculum by incorporating following pedagogical changes: divergent thinking, students should be encouraged to use 1. Projects in design classes must have open-ended various divergent thinking techniques- analogical thinking: transfer an idea from one context to a new one, brainstorming: solutions
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