Creativity in problem solving: integrating two different views of insight

Abstract

Even after many decades of productive research, problem solving instruction is still considered ineffective. In this study we address some limitations of extant problem solving models related to the phenomenon of insight during problem solving. Currently, there are two main views on the source of insight during problem solving. Proponents of the first view argue that insight is the consequence of analytic thinking and a sequence of conscious and stepwise steps. The second view suggests that insight is the result of unconscious processes that come about only after an impasse has occurred. Extant models of problem solving within mathematics education tend to highlight the first view of insight, while Gestalt inspired creativity research tends to emphasize the second view of insight. In this study, we explore how the two views of insight—and the corresponding set of models—can describe and explain different aspects of the problem solving process. Our aim is to integrate the two different views on insight, and demonstrate how they complement each other, each highlighting different, but important, aspects of the problem solving process. We pursue this aim by studying how expert and novice mathematics students worked on two ill-defined mathematical problems. We apply both a problem solving model and a creativity model in analyzing students’ work on the two problems, in order to compare and contrast aspects of insight during the students’ work. The results of this study indicate that sudden and unconscious insight seems to be crucial to the problem solving process, and the occurrence of such insight cannot be fully explained by problem solving models and analytic views of insight. We therefore propose that extant problem solving models should adopt aspects of the Gestalt inspired views of insight.

Farewell to Virtual Environments and Welcome to Post-pandemic Mathematical Problem Posing and Solving

“…Creativity in the approach and resolution of mathematical problems has significant and cognitive effects to face the solution and improve the academic performance of students [5], while this situation worries the teacher of the educational institution because it does not have materials available for its development during the academic work and has to intercalate this methodology with students to generate satisfaction and student learning. The existence of two groups (because of the methodology) with different perspectives still leads to many results in both directions without concluding and arriving at a single result, even though better results are obtained with the second point of view (method imposed by Gestalt) [9], i.e. they cannot be explained with only a few good results or points of view in an analytical way of what generates intuition.…”

“…Mathematical imagination is gaining strength in its application at different educational levels to face and solve mathematical problems, but with not very encouraging results due to the existence of two groups with different points of view (1st: "intuition is the consequence of analytical thinking and a sequence of conscious and gradual steps" and 2nd: "intuition is the result of unconscious processes that occur only after a deadlock has occurred") [9].…”

Gifted students' skill in solving mathematics problems: A study used gender and ethnicity as differentiating factors in senior high school

“…The data collection of mathematical problem-solving skills is carried out utilizing two instruments, namely the equivalent of a math olympiad level consist of three fields: number theory (Figure 1), algebra(Figure 2), and geometry(Figure 3), that has been tested for validity and reliability and a questionnaire that refers to the stages of Lester's problemsolving (Haavold & Sriraman, 2021) : Orientation (5 questions), Organization (3 questions), Execution (5 questions) and Verification (4 ques-tions) (Table 1). The score of every response to every question uses a scale of 0-1.…”

Gender Differences in High School Students’ Beliefs about Mathematical Problem Solving

“…As a teaching approach, problem solving has been found to be effective at boosting students' motivation to engage with mathematical problems (Habtamu et al, 2022) and to develop their mathematical abilities (Soebagyo et al, 2022). However, some researchers of this instructional strategy consider it ineffective, partly due to the complex nature of the problem-solving process (Haavold & Sriraman, 2022). In their study about creativity in problem solving, which focused on the role and importance of insight, Haavold and Sriraman (2022) found that unconscious insight emerges as students go through the process of problem solving.…”

“…However, some researchers of this instructional strategy consider it ineffective, partly due to the complex nature of the problem-solving process (Haavold & Sriraman, 2022). In their study about creativity in problem solving, which focused on the role and importance of insight, Haavold and Sriraman (2022) found that unconscious insight emerges as students go through the process of problem solving. They encourage teachers to use problem-solving models that speak to insight as the unconscious processes that occur during problem solving.…”