Mathematical Giftedness and Creativity in Primary Grades

Aßmus, Daniela; Fritzlar, Torsten

doi:10.1007/978-3-319-73156-8_3

Cited by 16 publications

(21 citation statements)

References 22 publications

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“…In psychological discourse, it is emphasized that the learning of mathematics can contribute to the promotion of creative thinking, not only merely in mathematics but also in general (Sternberg, 2017). Mathematical creativity is usually considered one sub-component of mathematical ability (Kattou et al, 2013) and is researched through studies on problem-solving and problem-posing, often embedded in comprehensive theory building processes (Assmus & Fritzlar, 2018). Torrance (1966), in his seminal work, defined creativity in the following manner:…”

Section: Creativity and Its Relationship With Mathematical Modellingmentioning

confidence: 99%

“…This aspect should be considered in the evaluation of modelling competencies but not be limited to the originality of the mathematical means used and also include the interpretation of real-world situations. Originality is usually evaluated within a reference group to consider the reference norm, which is particularly appropriate for younger students; however, this relative originality leads to the evaluation of relative creativity (Assmus & Fritzlar, 2018). Therefore, Leikin (2013) proposed a combination of relative and absolute originality by involving more reference groups, like a group of expert solvers in addition to beginners.…”

Section: Measuring Mathematical Modelling From the Perspective Of Creativitymentioning

confidence: 99%

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Creativity in students’ modelling competencies: conceptualisation and measurement

Kaiser

2021

Educ Stud Math

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Modelling competencies are currently included in numerous curricula worldwide and are generally accepted as a complex, process-oriented construct. Therefore, effective measurement should include multiple dimensions, like the sub-competencies required throughout the modelling process. Departing from the characteristics of modelling problems as open and often underdetermined real-world problems, we propose to enrich the current conceptualisation of mathematical modelling competencies by including creativity, which plays an important role in numerous phases of the mathematical modelling process but has scarcely been considered in modelling discourse. In the study described in this paper, a new instrument for the evaluation of this enriched construct has been developed and implemented. The modelling competencies incorporating creativity of the students were evaluated based on the adequacy of the models and the modelling processes proposed, and the appropriateness and completeness of the approaches were evaluated in detail. Adapting measurement approaches for creativity that have been developed in the problem-solving discourse, certain criteria of creativity were selected to evaluate the creativity of the students’ approaches in tackling modelling problems—namely, usefulness, fluency, and originality. The empirical study was conducted among 107 Chinese students at the upper secondary school level, who attended a modelling camp and independently solved three complex modelling problems. The results reveal significant correlations between fluency and originality in students’ performances across all tasks; however, the relationships between usefulness and the other two creativity aspects were not consistent. Overall, the results of the study support the importance of the inclusion of creativity in the construct of modelling competencies.

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Section: Creativity and Its Relationship With Mathematical Modellingmentioning

confidence: 99%

Section: Measuring Mathematical Modelling From the Perspective Of Creativitymentioning

confidence: 99%

Creativity in students’ modelling competencies: conceptualisation and measurement

Kaiser

2021

Educ Stud Math

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“…Creativity does not only help us to adapt to changes, but is also a prerequisite for technical and scientific advances ( Leikin 2013 ). Research on creativity in the domain of mathematics has recently moved in the focus of attention ( Assmus and Fritzlar 2018 ; Sak et al 2017 ). On the one hand, mathematics, as a science, serves as the foundation for various other scientific and technological discoveries.…”

Section: Introductionmentioning

confidence: 99%

Mathematical Creativity in Adults: Its Measurement and Its Relation to Intelligence, Mathematical Competence and General Creativity

et al. 2021

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Mathematical creativity is perceived as an increasingly important aspect of everyday life and, consequently, research has increased over the past decade. However, mathematical creativity has mainly been investigated in children and adolescents so far. Therefore, the first goal of the current study was to develop a mathematical creativity measure for adults (MathCrea) and to evaluate its reliability and construct validity in a sample of 100 adults. The second goal was to investigate how mathematical creativity is related to intelligence, mathematical competence, and general creativity. The MathCrea showed good reliability, and confirmatory factor analysis confirmed that the data fitted the assumed theoretical model, in which fluency, flexibility, and originality constitute first order factors and mathematical creativity a second order factor. Even though intelligence, mathematical competence, and general creativity were positively related to mathematical creativity, only numerical intelligence and general creativity predicted unique variance of mathematical creativity. Additional analyses separating quantitative and qualitative aspects of mathematical creativity revealed differential relationships to intelligence components and general creativity. This exploratory study provides first evidence that intelligence and general creativity are important predictors for mathematical creativity in adults, whereas mathematical competence seems to be not as important for mathematical creativity in adults as in children.

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“…The promotion of mathematical creativity is usually closely linked to problem-solving and problem-posing, both of which are often embedded in comprehensive theory-building processes (Assmus & Fritzlar, 2018 ). Generally, the development of creativity requires cognitively demanding mathematical tasks that entail high-level cognitive processes (Leikin & Elgrably, 2020 ).…”

Section: Literature Survey Theoretical Framework Research Context and Research Questionsmentioning

confidence: 99%

Can mathematical modelling work as a creativity-demanding activity? An empirical study in China

Kaiser

2021

ZDM Mathematics Education

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Creativity has been identified as a key characteristic that allows students to adapt smoothly to rapid societal and economic changes in the real world. However, Chinese students appear to perform less well in mathematical problem-solving and problem-posing abilities, which are strongly connected to mathematical creativity. Mathematical modelling has recently been introduced as one of the six core competencies in the Chinese mathematical curriculum and is built on students’ ability to solve real-world problems using mathematical means. As mathematical modelling is characterised by openness regarding the understanding of complex real-world problems and the complex relationship between the real world and mathematics, for the strengthening of creativity, mathematical modelling activities seem to be adequate to accomplish this purpose. In this paper, we describe a study with 71 upper secondary school students, 50 pre-service mathematics teachers, and 66 in-service mathematics teachers, based on an extended didactical framework regarding mathematical modelling as a creativity-demanding activity. The results of the study indicate a significant correlation between modelling competencies and creativity aspects. Especially significant correlations between the adequacy of the modelling approaches and the two creativity aspects of usefulness and fluency could be identified, as well as a significant negative correlation between usefulness and originality. The results of the correlational analysis of relationships among the four criteria were not always consistent in the three participant groups. Overall, the results have implications for the promotion of creativity for various expertise groups and demonstrate the dependency of the modelling activities on the mathematical knowledge of the participants and the mathematical topic with which they are dealing.

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Mathematical Giftedness and Creativity in Primary Grades

Cited by 16 publications

References 22 publications

Creativity in students’ modelling competencies: conceptualisation and measurement

Creativity in students’ modelling competencies: conceptualisation and measurement

Mathematical Creativity in Adults: Its Measurement and Its Relation to Intelligence, Mathematical Competence and General Creativity

Can mathematical modelling work as a creativity-demanding activity? An empirical study in China

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