Can we count on early numerical abilities for early probabilistic reasoning abilities?

ABSTRACT

Previous research has shown that early numerical abilities are predictive of later mathematical achievement. In line with these previous studies, we investigated whether early numerical abilities are also associated with later probabilistic reasoning abilities. In the present study, we examined children’s numerical abilities in the second grade of preschool and their probabilistic reasoning abilities one and two years later. On the one hand, our results indicate that early numerical abilities assessed in the second grade of preschool predict the use of erroneous solving strategies to compare probabilities and create equal probabilities in the third grade of preschool. On the other hand, our results also indicate that the same early numerical abilities predict the use of more advanced or correct strategies when children are in the first grade of primary school. We discuss these seemingly contradicting findings in light of current research on probabilistic reasoning abilities.

KEYWORDS:

• Early numerical ability
• probabilistic reasoning
• preschool
• primary school

Declaration of interest statement

We wish to confirm that there are no known conflicts of interest related to this publication.

Additional information

Funding

This research was supported by Grant KU Leuven project [C16/16/001] “Development and stimulation of core mathematical competencies”.

Notes on contributors

Anne-Sophie Supply

Anne-Sophie Supply: As a PhD student at the Centre for Instructional Psychology and Technology at KU Leuven (Belgium), I take part in the large scale “Wis & Co” research project on the development and stimulation of children’s core mathematical competencies. Within this project, I focus on the development of probabilistic reasoning competencies in young children by longitudinally following a group of 5-9 year olds. The first main aim of the current PhD project is to longitudinally investigate children’s abilities to 1) distinguish certain from uncertain events, 2) compare two probabilities, and 3) establish a fair situation by generating equal probabilities. A second aim is to investigate whether it is possible to stimulate probabilistic reasoning at a younger age than is currently the case in Flemish schools by means of an intervention study.

Wim Van Dooren

Wim Van Dooren: I am associate professor at the Centre for Instructional Psychology and Technology at the University of Leuven. Most of my research is about mathematical teaching and learning, in a broad age range (from Kindergartners over primary and secondary school students to mathematical experts). This research addresses various mathematical topics: word problems, algebra, proportions, fractions, geometry, spatial thinking, probability, … I also do research on statistical reasoning and the difficulties that occur in interpreting graphs and the outcomes of statistical analyses. I am also involved in research on the link between physics and mathematics, as well as learners’ understanding of astronomical concepts. My focus is usually situated at the intersection of the content-specific domain, educational psychology and cognitive psychology. For example, I study the (positive and negative) role of intuitions in learning and reasoning on mathematical concepts. One point of attention in that research is how very young children can already reason about complex mathematical ideas if they are challenged. Another focus is on the role and the origins of specific misconceptions in learners, as they can have a strong impact on later learning. I also investigate the role external representations (drawings, schemes, graphs) can have in reasoning on certain concepts.

Patrick Onghena

Patrick Onghena: I am full professor at the Centre for Methodology of Educational Research at KU Leuven, Belgium. Most of my research is about methodology of educational research and about educational statistics. However, as a teacher of statistics, I also got interested in research about students’ misconceptions regarding probability and statistics, cognitive biases and the use of heuristics under uncertainty (e.g., in the Monty Hall Dilemma), and statistical reasoning. Recently, I shifted my research attention to probabilistic reasoning and precursors of probabilistic reasoning in preschoolers and primary school children because misconceptions regarding probability and statistics in adults and young adults appear to be deeply rooted and hard to change. A developmental and longitudinal perspective might shed some light on these roots, provide a broader understanding of the unresolved issues in research on statistics education, and give us some clues regarding the improvement of probabilistic reasoning and the avoidance of cognitive biases under uncertainty.