Infants’ sense of number - Investigating cognitive mechanisms and training interventions for learning mathematics early in life
The current project proposes that the Approximate Number System (ANS) can be trained already during the first year of life and that this will have a causal effect on later mathematical abilities. The ANS is a cognitive system -- present already in infancy -- that represents numerical magnitudes without the aid of symbols. In adults and children the acuity of the ANS is related to mathematical ability. Individuals with a more acute ANS are better at mathematics, suggesting that the ANS provides the basis for mathematical ability. Little is known about the development of the ANS in infancy. We will first investigate if the ANS can be trained, on a group level, during infancy, when the brain is still undergoing rapid development and re-organization. Then, we develop an individual difference measure of ANS acuity for infants, in order to individualize the ANS training. Finally, in a longitudinal study we investigate if individualized training targeted at the ANS during infancy causally affects mathematical ability later in life. This project is significant in that it will allow us both to assess if the ANS is modulated by experience and help us understand the mechanisms involved when children begin to learn mathematics. Further, the project is also significant in that it will develop early interventions with the long-term potential of making it easier for children to learn mathematics, especially for those who struggle because of learning deficits such as dyscalculia.
Final report
Purpose and development
The purpose of the project Infant's sense of number was to address how early cognitive mechanisms related to mathematics develop during infancy. Towards this purpose, we focus on three main aims. First, we sought to investigate functional and stable individual differences in infants' ability to estimate numerosity. Second, we aimed to examine the approximate number system's (ANS) role when older children learn mathematics. The project's third and final aim was to investigate if the ANS is malleable during infancy and if interventions can aid when learning mathematical concepts.
The primary purpose of the project has not changed during the project time. However, the scope of the project increased. Initially, we outlined a training intervention to be carried out on an eye-tracker. In addition to this intervention, results from a closely related project suggested that an intervention targeting active exploration of objects could affect infants' number discrimination abilities and other related constructs. Accordingly, we expanded the project by including additional training interventions to those described in the project plan.
Implementation
We focused on investigating possible functional and stable individual differences in infants' numerical abilities during the first half of the project. We developed eye-tracking procedures that can measure infants' abilities to discriminate numerical and magnitude information and carried out studies to investigate how such abilities develop during infancy (Lindskog et al., 2019; Schröder et al., 2021a). We also explored how individual abilities in numerical discrimination and discrimination of magnitudes were related to each other (Lindskog et al., 2021) to infants' play proficiency (Lindskog et al., 2021), and later mathematical abilities (Schröder et al., 2021b).
In the second part of the project, we turned our attention to the question of whether infants' numerical abilities are malleable and what type of intervention, if any, could influence the precision of such abilities. We have conducted two types of interventions. As outlined in the project plan, we investigated the possibility of influencing the acuity of the ANS through an adaptive training procedure implemented on an eye-tracker. Similar to recent studies on older children and adults, our preliminary results indicate that it is difficult to influence the ANS directly. Second, we investigated the possibility that a play-based intervention targeting children's active exploration could affect the ANS's acuity and other related constructs. The results showed that children's small form perception, an ability related to numerosity perception, benefited from the play intervention while their numerosity perception did not (Schröder et al., 2019).
Three main results and conclusions
The project has generated several interesting results and conclusions. The first main result is a documented relation between infants' non-symbolic number processing and processing of magnitudes within small geometric forms (Lindskog et al., 2021). There are several theoretical accounts as to the nature of the cognitive system underlying non-symbolic number processing. One account suggests this system to be an encapsulated core cognitive system. Another account suggests that non-symbolic number processing is part of a more extensive system that can process magnitudes in various situations. Our results add to this ongoing debate by indicating a connection between the processing of different types of magnitudes already from an early age. Although our findings cannot settle the debate, they are more consistent with the idea of a general magnitude system than an encapsulated number system.
Previous research has suggested that abstract concepts, both in general and mathematics, are grounded in perceptual experience derived from action. Several studies have shown the importance of motor skills and spatial ability for academic achievement in the STEM domains. Our second main result extends such findings by indicating a connection between infants' active exploration of their environment (and, more generally, their play proficiency) and their ability to process magnitudes. We find both that children's early play proficiency is related to their later ability to process magnitudes in small geometric forms (Lindskog et al., 2021) and that such abilities can be enhanced by a play intervention (Schröder et al., 2019). The results, taken together, indicate that opportunities for learning provided by play influence basic cognitive abilities connected to later mathematical abilities.
There are several theoretical accounts of what factors are essential for the development of formal mathematical abilities. The central hypothesis of the project, and indeed of much previous research, was that non-symbolic number processing is the foundation on which later knowledge of numbers is built. However, the third main result of the study gives a more nuanced picture. In a study investigating the role of non-symbolic number processing, language, and working memory for developing a natural number concept, we found language skills to play a more important role than non-symbolic number processing (Schröder et al., 2021b). These findings question the role of the ANS as foundational and suggest that learning number concepts is a process that requires other tools than an intuitive sense of number.
New research questions
The main new research question that the project has generated is what role infants' active exploration of their environment has in developing early cognitive abilities in general and early numerical abilities in particular. More generally, the research carried out within the project has resulted in a novel hypothesis, the opportunities for learning hypothesis, which suggests that children's play (of which active exploration is an important special case) provide nourishment to the developing mind.
Furthermore, when investigating children's early emerging natural number concept (Schröder et al., 2021b), we discovered that language skills played an important role. This finding is in line with previous research but extends it by showing that language is important very early on in this development. In contrast, children's non-symbolic number processing played a less important role. These findings have generated several new research questions related to the role language plays during the early stages of developing a natural number concept.
Dissemination of Results and Cooperation
The project's strategy has been to disseminate the results through publication in high-ranking, peer-reviewed journals. To date, two papers have been published (Lindskog et al., 2019; Schröder et al., 2019), both as open access. Manuscripts with results from the project that are in preparation or submitted to, but not yet accepted in, peer-review journals will also be published open access. Furthermore, as many details as possible of our studies (e.g., preregistration, study materials, data, analysis scripts, preprints, etc.) have been made openly available in a publicly accessible online repository (e.g., Open Science Framework, osf.io). The results from the project have also been disseminated at international scientific conferences, during invited popular talks, and through social media (e.g., Facebook, Twitter, etc.) and other media (e.g., Newspapers, Radio, etc.) outlets.
The purpose of the project Infant's sense of number was to address how early cognitive mechanisms related to mathematics develop during infancy. Towards this purpose, we focus on three main aims. First, we sought to investigate functional and stable individual differences in infants' ability to estimate numerosity. Second, we aimed to examine the approximate number system's (ANS) role when older children learn mathematics. The project's third and final aim was to investigate if the ANS is malleable during infancy and if interventions can aid when learning mathematical concepts.
The primary purpose of the project has not changed during the project time. However, the scope of the project increased. Initially, we outlined a training intervention to be carried out on an eye-tracker. In addition to this intervention, results from a closely related project suggested that an intervention targeting active exploration of objects could affect infants' number discrimination abilities and other related constructs. Accordingly, we expanded the project by including additional training interventions to those described in the project plan.
Implementation
We focused on investigating possible functional and stable individual differences in infants' numerical abilities during the first half of the project. We developed eye-tracking procedures that can measure infants' abilities to discriminate numerical and magnitude information and carried out studies to investigate how such abilities develop during infancy (Lindskog et al., 2019; Schröder et al., 2021a). We also explored how individual abilities in numerical discrimination and discrimination of magnitudes were related to each other (Lindskog et al., 2021) to infants' play proficiency (Lindskog et al., 2021), and later mathematical abilities (Schröder et al., 2021b).
In the second part of the project, we turned our attention to the question of whether infants' numerical abilities are malleable and what type of intervention, if any, could influence the precision of such abilities. We have conducted two types of interventions. As outlined in the project plan, we investigated the possibility of influencing the acuity of the ANS through an adaptive training procedure implemented on an eye-tracker. Similar to recent studies on older children and adults, our preliminary results indicate that it is difficult to influence the ANS directly. Second, we investigated the possibility that a play-based intervention targeting children's active exploration could affect the ANS's acuity and other related constructs. The results showed that children's small form perception, an ability related to numerosity perception, benefited from the play intervention while their numerosity perception did not (Schröder et al., 2019).
Three main results and conclusions
The project has generated several interesting results and conclusions. The first main result is a documented relation between infants' non-symbolic number processing and processing of magnitudes within small geometric forms (Lindskog et al., 2021). There are several theoretical accounts as to the nature of the cognitive system underlying non-symbolic number processing. One account suggests this system to be an encapsulated core cognitive system. Another account suggests that non-symbolic number processing is part of a more extensive system that can process magnitudes in various situations. Our results add to this ongoing debate by indicating a connection between the processing of different types of magnitudes already from an early age. Although our findings cannot settle the debate, they are more consistent with the idea of a general magnitude system than an encapsulated number system.
Previous research has suggested that abstract concepts, both in general and mathematics, are grounded in perceptual experience derived from action. Several studies have shown the importance of motor skills and spatial ability for academic achievement in the STEM domains. Our second main result extends such findings by indicating a connection between infants' active exploration of their environment (and, more generally, their play proficiency) and their ability to process magnitudes. We find both that children's early play proficiency is related to their later ability to process magnitudes in small geometric forms (Lindskog et al., 2021) and that such abilities can be enhanced by a play intervention (Schröder et al., 2019). The results, taken together, indicate that opportunities for learning provided by play influence basic cognitive abilities connected to later mathematical abilities.
There are several theoretical accounts of what factors are essential for the development of formal mathematical abilities. The central hypothesis of the project, and indeed of much previous research, was that non-symbolic number processing is the foundation on which later knowledge of numbers is built. However, the third main result of the study gives a more nuanced picture. In a study investigating the role of non-symbolic number processing, language, and working memory for developing a natural number concept, we found language skills to play a more important role than non-symbolic number processing (Schröder et al., 2021b). These findings question the role of the ANS as foundational and suggest that learning number concepts is a process that requires other tools than an intuitive sense of number.
New research questions
The main new research question that the project has generated is what role infants' active exploration of their environment has in developing early cognitive abilities in general and early numerical abilities in particular. More generally, the research carried out within the project has resulted in a novel hypothesis, the opportunities for learning hypothesis, which suggests that children's play (of which active exploration is an important special case) provide nourishment to the developing mind.
Furthermore, when investigating children's early emerging natural number concept (Schröder et al., 2021b), we discovered that language skills played an important role. This finding is in line with previous research but extends it by showing that language is important very early on in this development. In contrast, children's non-symbolic number processing played a less important role. These findings have generated several new research questions related to the role language plays during the early stages of developing a natural number concept.
Dissemination of Results and Cooperation
The project's strategy has been to disseminate the results through publication in high-ranking, peer-reviewed journals. To date, two papers have been published (Lindskog et al., 2019; Schröder et al., 2019), both as open access. Manuscripts with results from the project that are in preparation or submitted to, but not yet accepted in, peer-review journals will also be published open access. Furthermore, as many details as possible of our studies (e.g., preregistration, study materials, data, analysis scripts, preprints, etc.) have been made openly available in a publicly accessible online repository (e.g., Open Science Framework, osf.io). The results from the project have also been disseminated at international scientific conferences, during invited popular talks, and through social media (e.g., Facebook, Twitter, etc.) and other media (e.g., Newspapers, Radio, etc.) outlets.