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1. Measuring Emerging Number Knowledge in Toddlers

   https://doi.org/10.3389/fpsyg.2021.703598  

   Silver, Alex M.; Elliott, Leanne; Braham, Emily J.; Bachman, Heather J.; Votruba-Drzal, Elizabeth; Tamis-LeMonda, Catherine S.; Cabrera, Natasha; Libertus, Melissa E. (July 2021, Frontiers in Psychology)

   null (Ed.)

   Recent evidence suggests that infants and toddlers may recognize counting as numerically relevant long before they are able to count or understand the cardinal meaning of number words. The Give-N task, which asks children to produce sets of objects in different quantities, is commonly used to test children’s cardinal number knowledge and understanding of exact number words but does not capture children’s preliminary understanding of number words and is difficult to administer remotely. Here, we asked whether toddlers correctly map number words to the referred quantities in a two-alternative forced choice Point-to-X task (e.g., “Which has three?”). Two- to three-year-old toddlers ( N = 100) completed a Give-N task and a Point-to-X task through in-person testing or online via videoconferencing software. Across number-word trials in Point-to-X, toddlers pointed to the correct image more often than predicted by chance, indicating that they had some understanding of the prompted number word that allowed them to rule out incorrect responses, despite limited understanding of exact cardinal values. No differences in Point-to-X performance were seen for children tested in-person versus remotely. Children with better understanding of exact number words as indicated on the Give-N task also answered more trials correctly in Point-to-X. Critically, in-depth analyses of Point-to-X performance for children who were identified as 1- or 2-knowers on Give-N showed that 1-knowers do not show a preliminary understanding of numbers above their knower-level, whereas 2-knowers do. As researchers move to administering assessments remotely, the Point-to-X task promises to be an easy-to-administer alternative to Give-N for measuring children’s emerging number knowledge and capturing nuances in children’s number-word knowledge that Give-N may miss. 

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2. Counting to Infinity: Does Learning the Syntax of the Count List Predict Knowledge That Numbers Are Infinite?

   https://doi.org/10.1111/cogs.12875  

   Chu, Junyi; Cheung, Pierina; Schneider, Rose M.; Sullivan, Jessica; Barner, David (August 2020, Cognitive Science)

   Abstract By around the age of 5½, many children in the United States judge that numbers never end, and that it is always possible to add 1 to a set. These same children also generally perform well when asked to label the quantity of a set after one object is added (e.g., judging that a set labeled “five” should now be “six”). These findings suggest that children have implicit knowledge of the “successor function”: Every natural number,n, has a successor,n + 1. Here, we explored how children discover this recursive function, and whether it might be related to discovering productive morphological rules that govern language‐specific counting routines (e.g., the rules in English that represent base‐10 structure). We tested 4‐ and 5‐year‐old children’s knowledge of counting with three tasks, which we then related to (a) children’s belief that 1 can always be added to any number (the successor function) and (b) their belief that numbers never end (infinity). Children who exhibited knowledge of a productive counting rule were significantly more likely to believe that numbers are infinite (i.e., there is no largest number), though such counting knowledge was not directly linked to knowledge of the successor function, per se. Also, our findings suggest that children as young as 4 years of age are able to implement rules defined over their verbal count list to generate number words beyond their spontaneous counting range, an insight which may support reasoning over their acquired verbal count sequence to infer that numbers never end. 

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3. Verbal counting and the timing of number acquisition in an indigenous Amazonian group

   https://doi.org/10.1371/journal.pone.0270739  

   Boni, Isabelle; Jara-Ettinger, Julian; Sackstein, Sophie; Piantadosi, Steven T. (August 2022, PLOS ONE)

   Perlman, Marcus (Ed.)

   Children in industrialized cultures typically succeed on Give-N, a test of counting ability, by age 4. On the other hand, counting appears to be learned much later in the Tsimane’, an indigenous group in the Bolivian Amazon. This study tests three hypotheses for what may cause this difference in timing: (a) Tsimane’ children may be shy in providing behavioral responses to number tasks, (b) Tsimane’ children may not memorize the verbal list of number words early in acquisition, and/or (c) home environments may not support mathematical learning in the same way as in US samples, leading Tsimane’ children to primarily acquire mathematics through formalized schooling. Our results suggest that most of our subjects are not inhibited by shyness in responding to experimental tasks. We also find that Tsimane’ children (N = 100, ages 4-11) learn the verbal list later than US children, but even upon acquiring this list, still take time to pass Give-N tasks. We find that performance in counting varies across tasks and is related to formal schooling. These results highlight the importance of formal education, including instruction in the count list, in learning the meanings of the number words. 

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4. What Counts? Sources of Knowledge in Children’s Acquisition of the Successor Function

   https://doi.org/10.1111/cdev.13524  

   Schneider, Rose M.; Sullivan, Jessica; Guo, Kaiqi; Barner, David (January 2021, Child Development)

   Although many U.S. children can count sets by 4 years, it is not until 5½–6 years that they understand how counting relates to number—that is, that adding 1 to a set necessitates counting up one number. This study examined two knowledge sources that 3½‐ to 6‐year‐olds (N = 136) may leverage to acquire this “successor function”: (a) mastery of productive rules governing count list generation; and (b) training with “+1” math facts. Both productive counting and “+1” math facts were related to understanding that adding 1 to sets entails counting up one number in the count list; however, even children with robust successor knowledge struggled with its arithmetic expression, suggesting they do not generalize the successor function from “+1” math facts. 

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5. A tale of two lexica: Investigating computational pressures on word representation with neural networks

   https://doi.org/10.3389/frai.2023.1062230  

   Avcu, Enes; Hwang, Michael; Brown, Kevin Scott; Gow, David W. (March 2023, Frontiers in Artificial Intelligence)

   Introduction The notion of a single localized store of word representations has become increasingly less plausible as evidence has accumulated for the widely distributed neural representation of wordform grounded in motor, perceptual, and conceptual processes. Here, we attempt to combine machine learning methods and neurobiological frameworks to propose a computational model of brain systems potentially responsible for wordform representation. We tested the hypothesis that the functional specialization of word representation in the brain is driven partly by computational optimization. This hypothesis directly addresses the unique problem of mapping sound and articulation vs. mapping sound and meaning. Results We found that artificial neural networks trained on the mapping between sound and articulation performed poorly in recognizing the mapping between sound and meaning and vice versa. Moreover, a network trained on both tasks simultaneously could not discover the features required for efficient mapping between sound and higher-level cognitive states compared to the other two models. Furthermore, these networks developed internal representations reflecting specialized task-optimized functions without explicit training. Discussion Together, these findings demonstrate that different task-directed representations lead to more focused responses and better performance of a machine or algorithm and, hypothetically, the brain. Thus, we imply that the functional specialization of word representation mirrors a computational optimization strategy given the nature of the tasks that the human brain faces. 

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