Connecting mathematical creativity to mathematical ability

This study aims to investigate whether there is a relationship between mathematical ability and mathematical creativity, and to examine the structure of this relationship. Furthermore, in order to validate the relationship between the two constructs, we will trace groups of students that differ across mathematical ability and investigate the relationships amongst these students’ performance on a mathematical ability test and the components of mathematical creativity. Data were collected by administering two tests, a mathematical ability and a mathematical creativity test, to 359 elementary school students. Mathematical ability was considered as a multidimensional construct, including quantitative ability (number sense and pre-algebraic reasoning), causal ability (examination of cause–effect relations), spatial ability (paper folding, perspective and spatial rotation abilities), qualitative ability (processing of similarity and difference relations) and inductive/deductive ability. Mathematical creativity was defined as a domain-specific characteristic, enabling individuals to be characterized by fluency, flexibility and originality in the domain of mathematics. The data analysis revealed that there is a positive correlation between mathematical creativity and mathematical ability. Moreover, confirmatory factor analysis suggested that mathematical creativity is a subcomponent of mathematical ability. Further, latent class analysis showed that three different categories of students can be identified varying in mathematical ability. These groups of students varying in mathematical ability also reflected three categories of students varying in mathematical creativity.     

Recognising mathematical creativity in schoolchildren

Examples of tasks designed to recognise creative thinking within mathematics, used with 11–12-year-old pupuls, are described. The first construct empoyed in the design of these tasks is the ability to overcome fixation. Sometimes pupils demonstrate content-universe fixation, by restricting their thinking about a problem to an insufficient or inappropriate range of elements. Other times they show algorithmic fixation by continuing to adhere to a routine procedure or stereotype response even when this becomes inefficient or inappropriate. The second construct employed is that of divergent production, indicated by flexibility and originality in mathematical tasks to which a large number of appropriate responses are possible. Examples of three categories of such tasks are described: (1) problem-solving, (2) problem-posing, and (3) redefinition. Examples of pupils’ responses to various tasks are used to argue that they do indeed reveal thinking that can justifiably be described as creative. The relationship to conventional mathematics attainment is discussed-mathematics attainment is seen to limit but not to determine mathematical creativity.     

The methods of fostering creativity through mathematical problem solving

Which methods could be used to foster mathematical creativity in school situations? The following topics are treated with the respect to this question: 1. “Open-ended approach” and “From problem to problem”, 2. Relation to mathematical creativity, 3. Teacher’s belief and the mathematics textbook.     

Fostering creativity through instruction rich in mathematical problem solving and problem posing

Although creativity is often viewed as being associated with the notions of “genius” or exceptional ability, it can be productive for mathematics educators to view creativity instead as an orientation or disposition toward mathematical activity that can be fostered broadly in the general school population. In this article, it is argued that inquiry-oriented mathematics instruction which includes problem-solving and problem-posing tasks and activities can assist students to develop more creative approaches to mathematics. Through the use of such tasks and activities, teachers can increase their students’ capacity with respect to the core dimensions of creativity, namely, fluency, flexibility, and novelty. Because the instructional techniques discussed in this article have been used successfully with students all over the world, there is little reason to believe that creativity-enriched mathematics instruction cannot be used with a broad range of students in order to increase their representational and strategic fluency and flexibility, and their appreciation for novel problems, solution methods, or solutions.     

Comparisons of mathematical creativity,some personality and biographical factors of middle school dropouts and stayins

Middle school dropouts and stayins were compared on mathematical creativity, some personality and biographical factors. Verbal and non‐verbal mathematical creativity tests, a Hindi adaptation of the Thorndike dimensions of temperament test and a biographical inventory were used on 70 dropouts and 100 stayins male students, aged 11+ to 13+ years, randomly selected, from Sultanpur District, India. The results showed that: (1) mathematical creativity of dropouts was found to be lower than stayins; (2) dropouts were found to be sociable, accepting, reflective, lethargic and casual in nature whereas stayins were found to be solitary, critical, practical, premeditated, active and responsible in nature; and (3) the level of family income, professional background of the family, parents’ education, standard of living, interest‐patterns, attitude and level of aspiration of the stayins were found to be higher than of the dropouts.     

The mathematical tourist

The Mathematical Intelligencer -