Recent research at the University of Turku reveals a novel factor, spontaneous focus on quantitative relations that plays a role in the development of mathematical thinking. According to the study children with a tendency to focus spontaneously on quantitative relations might have an advantage in school mathematics.
Spontaneous Focusing on Quantitative Relations
While children have a variety of mathematical competencies, some show a greater tendency to focus spontaneously on quantitative relations. Researcher, MA Jake McMullen discovered that this tendency shows even in situations that are not explicitly mathematical and is a factor in developing mathematics skills.
“We were interested in expanding our groups’ previous research on children’s focusing on exact number and how it contributes to early counting and numerical skills. We supposed that looking at how children spontaneously focus their attention on the relationships between numbers and quantities might also be important for math development,” he says about discovering the research topic.
McMullen’s recent PhD dissertation at the University of Turku essentially defined Spontaneous Focus on Quantitative Relations (SFOR) and examined its role in the development of rational number conceptual knowledge.
Impact on Mathematical Development
McMullen developed methods for measuring spontaneous focusing on quantitative relations in primary school children and examined it in relation to the development of rational number conceptual knowledge.
He gathered data from research settings where children participated in different activities. “The studies that made up my dissertation involved feeding stuffed animals pieces of bread or spoons of rice, or describing how sets of objects had changed,” he says and adds that his post-doc studies will include scenarios and studies of real life activities in children’s everyday lives.
Although there was considerable variation between individuals, children who were more likely to recognize and use quantitative relations had advantages in mathematics, for example in arithmetic fluency. Also, follow-up studies revealed that SFOR tendency predicted fraction conceptual knowledge in fourth-graders.
While the impact on mathematical development is clear, McMullen says it is too early to say if spontaneous focusing predicts success in school mathematics.
“It seems to be a predictor of math development, especially knowledge of rational numbers, so we do think that it is helping with school math. Of course, we don’t expect it to be a sole determiner of success with school math, but it at least seems worth consideration when thinking about teaching and learning of math.”
In everyday life we all must make do with the mathematical competencies that we have. According to McMullen spontaneous focusing tendency might be quite common: “I would argue that everyone has some level of SFOR tendency, it’s just a matter of degree and different thresholds for recognizing opportunities to use quantitative relations in everyday situations. More evidence is still needed to determine if this is true.”
McMullen’s results suggest that children with spontaneous focusing tendency gain more and better practice with quantitative relations in everyday situations because of their natural tendency. This could be one explanation behind the observed effect on mathematical learning and development.
Teachers can support and strengthen spontaneous focusing tendency in children. Future research will help determine how this could be done effectively.
“We can’t say at this point exactly what we recommend to be done, in fact this is one of the major goals of our academy funded TULOS project. But, in general we would expect that teachers encouraging students to see these mathematical relations (and mathematics in general) in their everyday lives would help promote both SFOR and related math skills and knowledge. This is what my colleagues found when they did a study on enhancing children’s focusing on number,” McMullen says.
The PhD dissertation is openly accessible through the University of Turku’s electronic archives: McMullen (2014) Spontaneous Focusing on Quantitative Relations and the Development of Rational Number Conceptual Knowledge
McMullen will continue research on SFOR in the TULOS-project funded by the Academy of Finland.
Text: Maija Pollari.
