Mathematical pathologies as pathways into creativity

Sriraman, Bharath; Dickman, Benjamin

doi:10.1007/s11858-016-0822-8

Cited by 21 publications

(6 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In line with researchers' suggestions of using theory in teacher education (for example, Beghetto and Sriraman 2017;Schoenfeld and Kilpatrick 2008;Tsamir 2008), research studies in three categories were given to PTs: (1) general perspectives on creativity education focusing on studies about creative people, creative processes, creative products, and confluence perspectives (e.g., Csikszentmihalyi 1999Csikszentmihalyi , 2014Kaufman and Sternberg 2006;Sternberg 2003); (2) studies on enhancing creativity by increasing or maintaining levels of cognitive demands in tasks (e.g., Hughes et al 2009); and (3) studies about encouraging creative thinking by facing and dealing with ambiguity or pathologies and misconceptions (e.g., Amit and Gilat 2012;Sriraman 2005Sriraman , 2006Sriraman , 2009Sriraman and Dickman 2017). All the literature reviewed was actively quoted by PTs when justifying their TTM and micro-teaching in the two reports.…”

Section: Pts' Justification Of Their Own Ttms For Creativity Educationmentioning

confidence: 99%

Convergent and divergent thinking in task modification: a case of Korean prospective mathematics teachers’ exploration

Lee

2017

ZDM Mathematics Education

View full text Add to dashboard Cite

Section: Pts' Justification Of Their Own Ttms For Creativity Educationmentioning

confidence: 99%

Convergent and divergent thinking in task modification: a case of Korean prospective mathematics teachers’ exploration

Lee

2017

ZDM Mathematics Education

View full text Add to dashboard Cite

“…Problem 2: wrong arithmetic, but correct result The second problem was based on the idea of mathematical pathologies, which refer to examples that are specifically designed to violate properties that are perceived as valid (Sriraman & Dickman, 2017):…”

Section: Data Collection and Materialsmentioning

confidence: 99%

Creativity in problem solving: integrating two different views of insight

Haavold

Sriraman

2021

ZDM Mathematics Education

Self Cite

View full text Add to dashboard Cite

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.

show abstract

“…Encouraging learners to pursue multiple solutions to mathematical problems can improve their effectiveness and flexibility in solving such problems (Daher, Tabaja-Kidan, & Gierdien, 2017;Levav-Waynberg & Leikin, 2012a, 2012bStanislaw & Krug, 2014) even though it does not always affect their performance in mathematics (Schindler et al, 2018;Schukajlow, Krug, & Rakoczy, 2015). Furthermore, utilising MSTs allows more potentially creative learners to present their creative solutions to problems (Levav-Waynberg & Leikin, 2012a;Sriraman & Dickman, 2017). Deductive reasoning and critical thinking skills are important in geometry problem-solving and in the 21st century, and the use of MSTs can improve these skills (Segal, Stupel, & Flores, 2017;Sriraman & Dickman, 2017).…”

Section: Developing Mathematical Thinking and Problemsolvingmentioning

confidence: 99%

“…Furthermore, utilising MSTs allows more potentially creative learners to present their creative solutions to problems (Levav-Waynberg & Leikin, 2012a;Sriraman & Dickman, 2017). Deductive reasoning and critical thinking skills are important in geometry problem-solving and in the 21st century, and the use of MSTs can improve these skills (Segal, Stupel, & Flores, 2017;Sriraman & Dickman, 2017). MSTs can also be used as a strategy to develop young mathematicians who can thrive in the fourth industrial revolution (4IR), relying on their ability to use different solution strategies to solve problems.…”

Section: Developing Mathematical Thinking and Problemsolvingmentioning

confidence: 99%

The State of South African Mathematics Education: Situating the Hidden Promise of Multiple-solution Tasks

Mahlaba

2020

EURASIA J Math Sci Tech Ed

View full text Add to dashboard Cite

We live in the challenging times of the 21st-century with the increased need for humans to possess specific skills that will help them to be successful in this era. This means that education should in learners, develop these skills effectively. Different global countries have begun to recognize the significance of multiple solutions tasks in the teaching and learning of mathematics in the 21st-century. However, this practice is not visible in South Africa. Hence, the current study explores and synthetize the sparsely available literature on MSTs to answer the question: What is the significance of multiple-solution tasks (MSTs) in mathematics education and why is it relevant for South African mathematics education to make the exercise of producing multiple solutions accessible to learners? The literature that is being synthetized here is viewed through the optic lens of the social constructivism theory as proposed by Vygotsky and explicated in Jean Lave and Etienne Wenger`s Situated learning: Legitimate peripheral participation. In the conclusion I engage in an argumentation that illuminates the significance of MSTs in mathematics education and provide reasons why it would be beneficial for the South African mathematics curriculum to incorporate MSTs.

show abstract

Mathematical pathologies as pathways into creativity

Cited by 21 publications

References 27 publications

Convergent and divergent thinking in task modification: a case of Korean prospective mathematics teachers’ exploration

Convergent and divergent thinking in task modification: a case of Korean prospective mathematics teachers’ exploration

Creativity in problem solving: integrating two different views of insight

The State of South African Mathematics Education: Situating the Hidden Promise of Multiple-solution Tasks

Contact Info

Product

Resources

About