Mathematical Creativity: A Systematic Review of Definitions, Frameworks, and Assessment Practices

Level of student's creative thinking in classroom mathematics

Problem-solving has the potential to elicit creative mathematical thinking, especially when requesting to solve the problem in different ways. The current study focuses on the mathematical creativity elicited by such a problem, where there were infinitely many possible outcomes. Participants were adults with a range of mathematical backgrounds and resources. Their solutions were evaluated to identify both divergent and convergent thinking, taking into consideration fluency and flexibility. Findings show that the task was a suitable vehicle for eliciting mathematical creativity. For some participants, divergent thinking was coupled with convergent thinking, resulting in the identification of sets of infinitely many solutions to the task. Methodological issues relating to the analysis of mathematical creativity are discussed.

This study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity in elementary school classrooms. Collective learning takes place when mathematical ideas and actions, initially stemming from an individual, are built upon and reworked, producing a solution which is the product of the collective. Referring to characteristics of individual mathematical creativity, such as fluency, flexibility, and originality, this paper examines the possibility that collective mathematical creativity may be similarly characterized. The paper also explores the role of the teacher in fostering collective mathematical creativity and the possible relationship between individual and collective mathematical creativity.Many studies have investigated ways of characterizing, identifying, and promoting mathematical creativity. Haylock (1997), for example, and more recently, Kwon, Park, and Park (2006) assessed students' mathematical creativity by employing open‐ended problems and measuring divergent thinking skills. Leikin (2009) explored the use of multiple solution tasks in evaluating a student's mathematical creativity. These studies focused on an individual's mathematical creativity as it manifests itself in the solving of various problems. Yet students, acting in a classroom community, do not necessarily act on their own. Ideas are interchanged, evaluated, and built‐upon, often with the guidance of the teacher. The resultant mathematical creativity of an individual may be a product of collective community practice. The question which then arises is: Who is being mathematically creative, the individual or the community? This study focuses on the collective, not as the aggregation of a few individuals, but as a unit of study. Although some of the studies mentioned above acknowledged the effect of classroom culture on the development of mathematical creativity, and others considered the creative range of a group of students, those studies did not necessarily investigate mathematical creativity as a collective process or as the product of participating in a collective endeavour.This study combines theories related to collective learning and theories related to mathematical creativity to investigate the notion of collective mathematical creativity. The notion of collective creativity has been used to investigate creativity in several contexts including the work place (Hargadon & Bechky, 2006) and the global community (Family, 2003). In those cases, collective creativity was considered to occur when the social interactions between individuals yielded new interpretations that the individuals involved, thinking alone, could not have generated. Can the notion of collective creativity also be applied to the classroom community?

Divergent thinking and convergent thinking play a very important role in a person's creative thinking process to solve problems and these two types of thinking are related to hemispheric functions that will affect the way a person perceives information processing. This makes research important. The purpose of this study was to obtain a picture of divergent thinking and convergent thinking in the mathematical creative thinking process in terms of brain dominance. The research method used is qualitative with a descriptive exploratory approach. The instruments used were mathematical creative thinking questions, brain dominance tests, and unstructured interviews. The result of this research is that students who dominate the left brain in the creative thinking process are more dominant in convergent thinking, students who dominate the balanced brain in the creative thinking process are balanced in divergent thinking and convergent thinking, while student who dominate the right brain in the creative thinking process are more dominant in divergent thinking.

The purpose of this article is to explain how students' varied cognitive styles and the outcomes of their mathematical creative thinking interact. The Systematic Literature Review (SLR) method. To find, examine, assess, and interpret all of the research that is currently available on the topic of interest, the SLR technique is employed. All publications pertaining to mathematical creative thinking and cognitive style in student learning achievement are compiled and reviewed in order to gather data. The international journals used were 5 which only focused on Scopus. The results showed that creative thinking can be strengthened in the science curriculum, but empirical evidence supporting the relationship between the two is still limited, but examining the predictive value of creative thinking (divergent and convergent thinking) for scientific reasoning, while considering task specificity and academic achievement, various aspects of divergent thinking (i.e. fluency, flexibility, and originality) benefit from different types of support. Students' fluency scores increased under the full support condition, but decreased in the other two conditions, the FI group had lower and more efficient cognitive load than the FD group. The effect of information load on cognitive load follows a piecewise linear correlation with two prominent nodes, field dependence-independence (FDI) can affect academic performance, selective attention, and working memory. However, the underlying mechanisms of how FDI modulates selective attention and working memory remain unclear, field independence (FDI) may affect academic performance, selective attention, and working memory. However, the underlying mechanism of how FDI modulates selective attention and working memory remains unclear and field-independent students produced better learning achievement but field-dependent students showed higher frustration tolerance, low-ability students experienced more significant improvement than high-ability students. Low ability students also showed higher frustration tolerance.

To find out students' mathematical creative thinking abilities, this can be done by giving students open-ended problems. The aim of this research is to describe students' mathematical creative thinking abilities in solving open-ended problems when viewed from their self-concept. This type of research is qualitative descriptive research. The subject selection technique used in this research was purposive sampling. The subjects of this research consisted of one student with a high self-concept category, one student with a medium self-concept category, and one student with a low self-concept. Data collection methods in this research include questionnaire methods and tests. And the data analysis techniques used include: analysis of mathematical self-concept questionnaires, analysis of open-ended mathematics questions. The research results show that students with a high self-concept category can fulfill all aspects of creative thinking abilities, including fluency, flexibility and originality, so that their mathematical creative thinking abilities are also high. In contrast to students with moderate self-concept, it was found that their creative thinking abilities were low and students with low self-concept actually had moderate mathematical creative thinking abilities. So it can be concluded that based on this research, it shows that students' self-concept does not always describe students' mathematical creative thinking abilities in solving open-ended problems.

The relative influences of domain knowledge and domain-general divergent thinking on scientific creativity and mathematical creativity

When creativity is considered as field-specific, creativity that is specific to one field may differ from creativity in another field in terms of necessary knowledge, creative thinking skills, or tendencies. In this context, mathematical creativity is distinguished from general creativity and other field-specific creativity. This chapter discusses how mathematical creativity can be defined. In addition, the concepts of fluency, flexibility, originality, and elaboration, which are important divergent thinking components in the definitions and measurement of mathematical creativity, are explained in a mathematical context. The tools used to measure mathematical creativity are discussed. Among the methods that are effective in the development of general creativity, those that are thought to be effective in the development of mathematical creativity are explained. Open-ended questions and tasks in mathematics are introduced, and their role in developing mathematical creativity is discussed. Finally, suggestions and activity examples for the development of mathematical creativity are presented.

Mathematical creativity is one of the most fascinating research topics in mathematics education. Following preferred reporting items for systematic reviews and meta-analysis (PRISMA) data retrieval protocol, a total of 235 related publications published from 1994 to 2004 were retrieved from Scopus database. By using Microsoft Excel and VOSviewer, bibliometric analysis was performed to comprehensively capture the research trends in the field of mathematical creativity. The results revealed that the publication and citation trends have been rising over time. The publications were dispersed throughout the five continents. The United States is the most prolific and influential nation, with the greatest number of publications, g-index and h-index. Eight research foci have been identified, namely: i) student mathematical creativity and their achievement; ii) assessment of students’ mathematical creativity in geometry problem solving; iii) eliciting mathematical creativity; iv) mathematical creativity process; v) assessing of convergent and divergent thinking of gifted students; vi) pre-service teacher mathematical creativity in problem posing and with the aid of technology; vii) mathematical creativity tasks; and viii) mathematical creativity in early childhood. Overall, the findings of this bibliometric analysis are expected to guide researchers in understanding the research pattern over time. This study also provides direction for future research on mathematical creativity.

Mathematics improves higher order thinking skills, especially creative thinking. Creative thinking involves logical and divergent thinking based on intuition. This allows students to solve problems through a variety of methods. However, traditional learning methods limit this ability. The Discovery Learning model that involves active student participation can improve these skills. This research aims to improve students' mathematical creative thinking abilities through the Discovery Learning model. The research method used is quantitative with Non-equivalent Control Group Design. The sample for this research was Class The experimental group received the Discovery Learning model, while the control group used conventional methods. Pretest and posttest data were analyzed using statistical tests including normality, homogeneity and T test. The experimental class used the Discovery Learning method, while the control class used conventional methods. The pretest and posttest results showed a significant improvement in the experimental group. The findings show that Discovery Learning increases creative thinking in mathematics.

This study aimed to 1) create students' worksheets (LKPD) for mathematics learning based on Open-Ended Problems on students' mathematical creative thinking skills that meet the validity aspect. 2) create students' worksheets (LKPD) for mathematics learning based on Open-Ended Problems on students' mathematical creative thinking skills that meet practical Aspects. 3) create students' worksheets (LKPD) for mathematics learning based on Open-Ended Problems on students' mathematical creative thinking skills that meet the aspect of effectiveness. This research used 4D development, modified into three stages, namely Define, Design, and Develop. The trial was carried out in MTs. Wathoniyah Islamiyah Kebarongan with research subjects of 9 students in Grade IXA. The research found that the mathematics learning worksheets that had been developed met the validity aspects as measured by the assessment of the validation results of experts with an average score of 4.1. The practicality of the LKPD was measured based on the observation of the implementation of the LKPD which was shown to be fulfilled in the fully implemented category. The teacher's response indicated an average score of 4.0 meaning that the mathematics worksheets are practical for learning activities. The effectiveness of the LKPD was shown by the fulfilment of the established effectiveness indicators, namely the average N-Gain normality test, the results of which were carried out through the results of the pretest and posttest. The N-Gain normality test got an average score of 0.5130 which was interpreted as moderate. Thus, the development of mathematics worksheets effectively affects students' creative thinking abilities. It can be concluded that the LKPD developed is valid, practical, and effective

The Frontage of Creativity and Mathematical Creativity

This research is used to study engineering undergraduates fostering their mathematical creativity during creative problem solving. This was an exploratory research carried out in a public university as to find out the impact of CPS towards mathematical creativity among the engineering undergraduates. A case study was used to provide deep exploration of how the engineering undergraduates using their creative methods to solve open-ended mathematical problems creatively. Qualitative research design was applied in order to understand in depth the engineering undergraduates working collaboratively to generate their creative ideas during mathematical problem solving. Three final years engineering undergraduates took part in the study. They had to use their divergent and convergent thinking to generate creative methods to solve twelve open-ended mathematical problems. Qualitative research design of case study was used in this study to explore the engineering undergraduates using creative methods to solve open-ended mathematical problems during creative problem solving processes. By analyzing the data collected from the case study can provide in-depth and detail understanding of the creative processess and products of the research. Observation and recording sheets were used to collect all the data. SCAMPER was also used as a guideline for them to spark their creaivity. All the qualitative data of drawing from documents, videotape from observation and snapshot texts from recording sheets were collected and then analyzed. They were coded and categorized into different themes in order to find out the mathematical creativity among the engineering undergraduates. The results in this study shows that the engineering undergraduates were able to generate different creative methods with the help of the SCAMPER.

Creative thinking abilities are developed through divergent thinking in mathematics learning. This research aims to explore junior high school students' mathematical creative thinking abilities in solving geometric problems, specifically in terms of their overall mathematical abilities. This study is a qualitative descriptive research project. The subjects were 27 eighth-grade students from a state middle school in Loghia District. Data were collected using tests and interviews. The findings indicate that junior high school students with high mathematical abilities demonstrated creative thinking in solving geometric problems. In contrast, students with moderate and low mathematical abilities showed less creative thinking, particularly when answering questions about surface area and volume. Specifically, there were 3 students identified as creative, 4 students as less creative, and 20 students as not creative. Overall, most junior high school students were not creative in their approach to solving geometric problems. They struggled to demonstrate indicators of creative mathematical thinking, such as fluency, flexibility, and novelty.

Metacognition is vital for creativity; however, the specific contributions of its components (i.e., metacognition knowledge, metacognition experience, and metacognition monitoring and control) have received varying levels of attention, particularly due to the limited research on metacognitive experience. Additionally, the interactions among these components in influencing creative cognition remain unclear. We conducted two experiments to explore the influence of metacognitive experience on divergent thinking (e.g., alternative uses tasks, AUT) and the moderating role of creative mindsets-a core element of metacognitive knowledge-in this process. In Experiment 1, retrieval fluency, measured by the quantity of the ideas generated, was used to activate varying levels of metacognitive experience (fluency vs. disfluency) during the AUT. The findings showed that the originality of ideas generated under the disfluency condition was significantly higher than under the fluency condition, suggesting a positive effect of metacognitive disfluency experience on AUT. In Experiment 2, a multiple-choice task was used to prime individuals' creative mindsets (entity vs. incremental). The results indicated that individuals with a creative growth mindset exhibited greater cognitive persistence under the disfluency condition, subsequently enhancing the originality of their ideas, indicating that creative mindsets moderate the effect of metacognitive disfluency experience on AUT performance via cognitive persistence. We integrated previous findings to describe the interactive impacts of creative mindsets, metacognitive experience, and metacognitive monitoring and control on divergent and convergent creative thinking processes within a metacognitive framework, providing a model to reveal the dynamic interplay of metacognitive processes in creative cognition. Practically, fostering individuals' growth-oriented creative mindsets may represent a promising avenue for creativity development.