On the structure of arithmetic facts in memory and its interaction with numerical magnitude representation
Final Report Abstract
This project aimed to study how basic arithmetic is memorised and used by the brain. In particular, we focused on how the brain store multiplication facts (i.e., the set of simple multiplications that are acquired during the first years of school; usually the multiplications from 1×1 to 10×10). The objective of this project was to test hypotheses concerning the cognitive architecture that underpins multiplication fact retrieval (i.e., solving simple multiplications through direct retrieval from memory). The main question was whether results of multiplication problems (e.g., 8×3) are retrieved as a holistic integrated entity (i.e., represented as a single element, e.g., 24) or as a componential structure (i.e., 2×10^1 + 4×10^0, that is 2 decades and 4 units). This componential structure reflects the syntax of the Hindu–Arabic numeral system, which represents numbers in base-10 positional notation. To answer this question, we analysed how multiplications are retrieved from memory. In a set of experiments, participants were asked to evaluate the correctness of multiplication equations presented on a computer screen (for example, 7×3=21 or 7×3=24). The proposed result (in this example, 21 or 24) was preceded by an unseen prime stimulus (i.e., a two-digit number). The visibility of the prime was reduced by presenting masking stimuli (e.g., four letters) before and after it. Although the masking induces a subjective lack of awareness (i.e., participants were not aware of its presence), a masked prime can influence behaviour. Results showed that the time required to evaluate the correctness of a multiplication equation was modulated by whether or not the decade of the prime was congruent with the decade product of the multiplication, regardless of other properties (such as the difficulty of the multiplication or its semantic relationships). This provides evidence for the idea that arithmetic knowledge is not represented holistically, but it is rather stored based on the syntax of the base-10 positional notation. Therefore, the componential structure of two-digit numbers seems to play a key role in the way arithmetic knowledge is stored and retrieved. The understanding of how basic mathematical knowledge is stored and retrieved from memory is essential for designing intervention programs aimed to assist children and adults with mathematical difficulties.
Publications
- (2018). The development of approximate addition and subtraction: the operational momentum effect monotonically increases between the ages of 8 and 12 years. European Workshop on Cognitive Neuropsychology, Bressanone, Italy
Didino, D., Pinheiro-Chagas, P., Haase, V. G., Wood, G., & Knops, A.
- (2019). Decade-consistency effect in multiplication: the influence of the place-value structure in the retrieval process. 21st Conference of the European Society for Cognitive Psychology, Tenerife, Spain
Didino, D. & Knops, A.
- (2019). Response: Commentary: The Developmental Trajectory of the Operational Momentum Effect. Frontiers in psychology, 10, 160
Didino, D., Pinheiro-Chagas, P., Wood, G., & Knops, A.
(See online at https://doi.org/10.3389/fpsyg.2019.00160) - (2019). The influence of semantic processing and response latency on the SNARC effect. Acta psychologica, 196, 75-86
Didino, D., Breil, C., & Knops, A.
(See online at https://doi.org/10.1016/j.actpsy.2019.04.008) - (2019). The role of semantic processing and response latency in the SNARC effect. Tagung Experimentell Arbeitender Psychologen, London, UK
Didino, D., Breil, C., & Knops, A.
