Pre mathematics skills in infants: Numerosity as a game

Abstract

Pre literacy skills in young children have been well established. Explorations of the parallel concept of pre mathematic skills in young children are minimal. Recommendations for how to engage young children, specifically infants, in math have been limited to caregiver counting games. This colloquium presents an example of how an 11-month-old is able to demonstrate pre mathematics skills. This raises the question of beyond caregivers counting, what are early numerosity activities for preverbal infants?

James sat in the high chair looking intently at his mother. A typical 11-month-old little boy, he banged his hands on the high chair tray, causing his snack to bounce. He noticed the movement and giggled. His mother looked over and clicked her tongue at him making a sound twice. James paused and then clicked back at his mother twice. She smiled, and made one click sound in return. James responded with one click as well. The game continued, with the mother making a quantified number of clicks between one and six and James responding with a number of clicks ranging from one to many.

As the 11-month-old infant responds to his mother’s counting game of clicks, the question raised is, what skill is James demonstrating in regard to mathematics? Dehaene (2011) refers to the concept of numerical quantities as numerosity. In this instance, James is engaging in an activity that may be seen as a pre skill for counting by the identification of quantities of auditory sounds.

Pre mathematics skills in infants

It has been established that pre literacy skills are prevalent in children prior to school age and can be seen in infants. Milestones in children (infants to age three) include pretending to read, holding a book correctly, and engaging with the primary caregiver in book-sharing practices (Bennett-Armistead et al., 2007). Considering the activity of book-sharing as a pre literacy skill, we must begin to consider what are pre mathematics skills and what do they look like in infants? Building upon the idea of infants sharing books with their primary caregiver (an activity that fosters play and engagement with reading), are infants able to demonstrate a similar activity with numerosity? In the introduction, we observed James playing a game (tongue clicking) with his mother. In the game, clicks were made by the mother ranging from one to six with no specific pattern. James was able to respond and repeat the correct quantity of clicks with quantities of one to three. When the mother made four or more clicks, James struggled and responded with many clicks back, more than three but not the exact amount made by his mother. Other researchers have also begun to question what the skills are that children, often defined as infants, display prior to counting (Starkey and Cooper, 1980).

Past research

Prior research regarding mathematics skills with young children has looked at how infants are able to discriminate between quantities of items through visual representation. In 1980, Starkey and Cooper studied 16- to 30-week infants in order to determine if the infants could detect a difference in the number of dots (two and three) they were shown. Their research has been replicated with newborns ranging in age from 21 to 144 hours old, with smaller sets of numbers (Antell and Keating, 1983). The data found that newborns could tell a difference with small sets of numbers, two and three, but struggled with numbers larger than three. Further research has been built upon this line using similar procedures with older children (Izard et al., 2009). Strauss and Curtis (1981) found that 10- to 12-month-old infants were able to tell that a difference existed between the quantities two and three but were unable to tell the difference between four and five. More recent research (Sella et al., 2016) has looked at how young children (2.5 years of age) are able to apply precounting skills to mimic behavior. In this study, the children observed a puppet being fed tokens and then replicated the same behavior by feeding the puppet tokens in an amount ranging from one to six.

In the early stages of research on infants and mathematics abilities, Strauss and Curtis (1981) found that infants can identify numerosity visually, but noted a need for further research to test for numerosity verbally as a means to suggest a deeper awareness of number. James’s engagement in the game suggests a verbal recognition of counting in a rudimentary method. In order to respond with the correct number of clicks, it is necessary for James to have understood the quantity he heard. His verbal reply, in the form of clicks, demonstrates his basic numerosity of counting, without using symbols or words, to identify the number of items and respond with the same amount. Similar to Strauss and Curtis’s (1981) findings, James was able to identify and respond to one and two clicks with consistent accuracy. Three clicks were inconsistent in response and four or more clicks resulted in James making many clicks back. This finding is also consistent with Antell and Keating’s (1983) study of infants who similarly had difficulties with larger quantities than three.

Researchers have pointed to the idea that babies are born with an understanding of counting (Gelman and Gallistel, 1978). Mathematics studies on young children have focused on two approaches: Children’s ability to look at visuals of a quantity of items or children replicating a quantity of items when playing with toys. Within the research on mathematics skills in children, the investigations have been focused on subjects above age two (Sella et al., 2016; Zambryzcka, et al., 2017) or with infants using visual assessments (Brannon et al., 2004; Cordes and Brannon, 2009; Izard et al., 2009; Libertus and Brannon, 2010; Strauss and Curtis, 1981; Wynn et al., 2002; Xu, 2003; Xu and Spelke, 2000; Xu et al., 2005).

As we have agreed upon pre literacy skills in infants, perhaps it is time we engage in the discussion of pre mathematics, or specifically precounting (pre numerosity), skills in infants. Prior research has identified that infants, including newborns, do know something about mathematics skills. The question to begin to ask is what can parents and caregivers do to promote mathematics skills for infants? Eason and Levine (2017) explored ‘number talks’ and how often parents used number words with their children (ages 14- to 30-months-old). Other studies have been conducted with children ranging in age from over a year old to preschool age, while only one study to date has looked at infants 5- to 10-months-old (Goldstein et al., 2016). However, this research was more focused on how parents engage children with counting books compared to picture books. Counting as a skill requires a basic understanding of one-to-one correspondence, which typically develops in early childhood (Pepper and Hunting, 1998). The concept of infants playing games, in this case clicking to demonstrate pre numeracy skills, is an introduction to how infants can engage with counting.

Suggestions have been made that parents (caregivers) should reinforce early mathematics skills in the home with young children (Amente et al., 2017; Eason and Levine, 2017); however, there are limited suggestions for supporting infants beyond practicing skills such as basic counting and talking about numbers. The past research has focused on laboratory-style experiments and studies of infants’ abilities to determine differences in quantities of items, but has limited the role of parents or caregivers. In monitoring James, it has become apparent that his interactions with his mother could be laying the groundwork for James to explore numerosity and potentially establish precounting skills. Further research needs to be conducted with infants to identify what activities may promote pre mathematics, specifically pre numerosity skills.