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Which line you choose at the supermarket helps researchers understand how math abilities develop. A new study published in the journal Behavioural and Brain Sciences by Dr. Tali Leibovich from the University of Western Ontario in Canada, and PhD students Naama Katzin and Maayan Harel and Prof. Avishai Henik from BGU's Psychology Department offers a new theory as to how the brain first learns basic math. Leibovich completed her PhD under Prof. Henik where they investigated mathematical ability.

“If we are able to understand how the brain learns math, and how it understands the concept of numbers and more complex math concepts that shape the world we live in, we will be able to teach math in a more intuitive and enjoyable way. The current study is the first step in achieving this goal,” says Dr. Leibovich.





Above: This example demonstrates the relationship between size and number: usually, more items will take up more space in the shopping cart, unless you have a few larger, denser items.





The dilemma about choosing the best checkout line at the grocery store is well known: how to choose the line that will allow us to wait for the shortest amount of time? The way we make such decisions reveals how basic math abilities are acquired. According to the most acceptable theory today, people are born with a “sense of numbers”, namely, with the ability to recognize different quantities, like the number of items in a shopping cart, and this ability improves with age. Early curricula in math and diagnostics tools for math-specific learning disabilities (i.e., dyscalculia) have been developed based on this theory.

However, the new paper challenges the prevalent “number sense” theory, and presents evidence supporting the claim that “number sense” is not innate, but is actually acquired. The key to this new theory is the relationship between number and size (e.g., area, density, perimeter, etc.). In the paper, the researchers present evidence that when people compare quantities, like in the case of shopping carts, the decision is based not only on the number of items but also on size: the total area the items occupy, their density, and so forth. Combining size and number allows us to make a faster and more efficient decision. The researchers argue that first understanding the relationship between size and number is critical for the development of higher math abilities.

This new theory could affect the way dyscalculia is diagnosed. Today dyscalculia can be diagnosed only in school-aged children. At this stage, however, children with dyscalculia are already lagging behind their peers.

“The new theory will allow us to develop diagnostic tools that do not require any formal math knowledge, thus allowing diagnosis and treatment of dyscalculia before school age,” says Dr. Leibovich.

The journal in which the paper was published is unique in that it invites experts to comment on the paper in order to encourage discourse that will advance research in the field. This paper joins a line of publications on the same subject, including a book edited by Prof. Henik (Continuous Issues in Numerical Cognition – How Many or How Much), and a new paper in the journal Current Directions in Psychological Science entitled “Size Perception and the Foundation of Numerical Processing.”

The study, "From 'sense of number' to 'sense of magnitude' - The role of continuous magnitudes in numerical cognition," was supported by the European Research Council (ERC) under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC Grant Agreement 295644 to AH.