Final Report Summary - PISA (Procedures In Simple Arithmetic: neural implementation and development)
Summary Description of Project Objectives:
More than 20% of 15-year-old European students are low achievers in mathematics. Because low math competence can have dire economic and social effects, improving our knowledge of the neural mechanisms involved in arithmetic processing is critical to inform teaching and reduce low achievement. A central question in math education is whether calculation procedures should be emphasized over strategies based on retrieval during arithmetic learning. To date, studies suggest that calculation is less efficient than retrieval, at least for simple (i.e. single-digit) arithmetic problems. For example, single-digit problems for which subjects report using procedures are solved slower and less accurately than single-digit problems for which retrieval strategies are reported. Procedures are also linked to enhanced activity in fronto-parietal brain regions and this is thought to reflect effortful processing. These studies, however, might be misleading because (i) automatic procedures might be executed so fast that they cannot reach consciousness and (ii) enhanced activity in fronto-parietal regions during effortful calculation might not be related to procedures per se. The PISA project aimed to use functional magnetic resonance imaging (fMRI) to test the hypothesis that fronto-parietal regions may support automatized arithmetic procedures that can be as efficient as retrieval during arithmetic calculation. Specifically, we aimed to capitalize on the idea that, if problems are solved with procedural strategies, abstract automatic procedures should be activated by the simple presentation of an arithmetic sign, independently of the operands.
Description of Work Performed and Major Findings:
To test this hypothesis, we measured brain activity of adults and children while they were presented with single-digit addition and multiplication problems. In order to isolate activity associated with the arithmetic sign, we included trials during which only the arithmetic sign was presented. In those cases, participants were simply instructed to look at the arithmetic signs. We found the simple presentation of the addition sign (compared to the multiplication sign) was associated with enhanced activity and communication within a fronto-parietal network in adults. Several of these regions were involved in spatial attention, as demonstrated in an independent localizer task. Furthermore, the neural activity associated with the addition sign in a region of the prefrontal cortex predicted the size of an arithmetic priming effect measured in a behavioral task outside the scanner. In line with recent behavioral studies, this study demonstrates that addition signs are associated with automatic activation of procedures that may be spatial in nature and used to solve simple addition problems in adults. This indicates that arithmetic procedures can be automatized and that single-digit arithmetic learning does not necessarily involves a shift from procedural to retrieval strategies, but rather a shift from effortful to automatized procedures. In a subsequent developmental study conducted in children from 3rd to 10th grade, we showed that the emergence of associations between arithmetic signs and spatial procedures relies on hippocampal mechanisms. Specifically, hippocampal spatial mechanisms may help build associations between arithmetic operators and space in children, before these associated are encoded in fronto-parietal mechanisms. These results may prompt further research investigating the role of automatized procedures in arithmetic and have implication for math education.
Impact of the project:
This research will be of great and broad interest because of the fundamental role played by procedural knowledge during mathematics education. Although a wide range of teaching methods is used in countries of the EU, there is a general agreement that both fluency in recalling math facts and procedural skills are important. Yet, most cognitive studies to date point towards the superiority of fact retrieval over procedural strategies in simple arithmetic. Our results challenge this claim and provide the necessary groundwork for future studies that may investigate the extent to which automatization of procedures can be affected by teaching methods.
Our research may also greatly improve our understanding of dyscalculia, a learning disorder that affects the acquisition of numerical knowledge and arithmetic. The prevalence of children with dyscalculia is about 6% worldwide. The presents results suggest that impairments in hippocampal and fronto-parietal functioning might be associated with impaired automatization of arithmetic procedures. This might shed new light on the sources of math impairement in dyscalculic children.
More than 20% of 15-year-old European students are low achievers in mathematics. Because low math competence can have dire economic and social effects, improving our knowledge of the neural mechanisms involved in arithmetic processing is critical to inform teaching and reduce low achievement. A central question in math education is whether calculation procedures should be emphasized over strategies based on retrieval during arithmetic learning. To date, studies suggest that calculation is less efficient than retrieval, at least for simple (i.e. single-digit) arithmetic problems. For example, single-digit problems for which subjects report using procedures are solved slower and less accurately than single-digit problems for which retrieval strategies are reported. Procedures are also linked to enhanced activity in fronto-parietal brain regions and this is thought to reflect effortful processing. These studies, however, might be misleading because (i) automatic procedures might be executed so fast that they cannot reach consciousness and (ii) enhanced activity in fronto-parietal regions during effortful calculation might not be related to procedures per se. The PISA project aimed to use functional magnetic resonance imaging (fMRI) to test the hypothesis that fronto-parietal regions may support automatized arithmetic procedures that can be as efficient as retrieval during arithmetic calculation. Specifically, we aimed to capitalize on the idea that, if problems are solved with procedural strategies, abstract automatic procedures should be activated by the simple presentation of an arithmetic sign, independently of the operands.
Description of Work Performed and Major Findings:
To test this hypothesis, we measured brain activity of adults and children while they were presented with single-digit addition and multiplication problems. In order to isolate activity associated with the arithmetic sign, we included trials during which only the arithmetic sign was presented. In those cases, participants were simply instructed to look at the arithmetic signs. We found the simple presentation of the addition sign (compared to the multiplication sign) was associated with enhanced activity and communication within a fronto-parietal network in adults. Several of these regions were involved in spatial attention, as demonstrated in an independent localizer task. Furthermore, the neural activity associated with the addition sign in a region of the prefrontal cortex predicted the size of an arithmetic priming effect measured in a behavioral task outside the scanner. In line with recent behavioral studies, this study demonstrates that addition signs are associated with automatic activation of procedures that may be spatial in nature and used to solve simple addition problems in adults. This indicates that arithmetic procedures can be automatized and that single-digit arithmetic learning does not necessarily involves a shift from procedural to retrieval strategies, but rather a shift from effortful to automatized procedures. In a subsequent developmental study conducted in children from 3rd to 10th grade, we showed that the emergence of associations between arithmetic signs and spatial procedures relies on hippocampal mechanisms. Specifically, hippocampal spatial mechanisms may help build associations between arithmetic operators and space in children, before these associated are encoded in fronto-parietal mechanisms. These results may prompt further research investigating the role of automatized procedures in arithmetic and have implication for math education.
Impact of the project:
This research will be of great and broad interest because of the fundamental role played by procedural knowledge during mathematics education. Although a wide range of teaching methods is used in countries of the EU, there is a general agreement that both fluency in recalling math facts and procedural skills are important. Yet, most cognitive studies to date point towards the superiority of fact retrieval over procedural strategies in simple arithmetic. Our results challenge this claim and provide the necessary groundwork for future studies that may investigate the extent to which automatization of procedures can be affected by teaching methods.
Our research may also greatly improve our understanding of dyscalculia, a learning disorder that affects the acquisition of numerical knowledge and arithmetic. The prevalence of children with dyscalculia is about 6% worldwide. The presents results suggest that impairments in hippocampal and fronto-parietal functioning might be associated with impaired automatization of arithmetic procedures. This might shed new light on the sources of math impairement in dyscalculic children.