Home Math Activities and Children’s Math Trajectories from Preschool to Primary School

Professor Zhang, Xiao   (Principal Investigator (PI))

Dr Hu Bi Ying   (Co-Investigator)

24

2020-06-30

2022-06-29

97060

Home Math Activities and Children’s Math Trajectories from Preschool to Primary School

home math activities, Mathematics, parental involvement

PsychologyEducation: Research on Teaching & Learning

201910159022

Seed Fund for PI Research – Basic Research

2019

Completed

Individual differences in math skills are evident at an early age prior to children’s entry into formal education, and children with poor early math skills often continue to fall behind their more competent peers (e.g., Aunola, Leskinen, Lerkkanen, & Nurmi, 2004). Identifying factors that affect the early acquisition of math skills can enhance our understanding of effective approaches to facilitating children’s development of these skills. In this study, we examine the extent to which parents’ involvement in math activities is associated with their children’s math growth trajectories from preschool to primary school. Researchers have identified two kinds of home math activities: formal and informal activities (LeFevre, Skwarchuk, Smith-Chant, Fast, Kamawar, & Bisanz, 2009). Formal math activities refer to experiences in which parents directly and intentionally teach their children math knowledge, such as explicit instruction of numbers, quantity, and arithmetic. In contrast, informal math activities involve games and real-world tasks in which children’s acquisition of math is likely to be incidental. Based on factor analysis, LeFevre et al. (2009) further divided formal math activities into number skills activities (e.g., counting objects, writing numbers) and book activities (e.g., reading number storybooks), and informal activities into number game activities (e.g., playing card or board games) and application activities (e.g., cooking, shopping). Over the past decade, a growing body of research has examined the relation between formal and informal math activities and young children’s math skills, and this research has yielded mixed results. In some studies, higher frequencies of formal math activities predicted better performance in several math domains, including general numeracy skills (LeFevre et al., 2010), symbolic number system knowledge (Skwarchuk et al., 2014), and arithmetic fluency (LeFevre et al., 2009). In other studies, however, no relation was found between formal activities and young children’s math skills. For instance, LeFevre et al. (2009) found that neither number skills nor number books activities were related to children’s math knowledge after controlling for demographic variables and home literacy activities. The case is more or less the same for informal math activities: some studies have showed links between such activities and children’s math skills, whereas others have not. LeFevre et al. (2009) found that both number game and application activities were related to children’s arithmetic fluency, and that engagement in number games was also related to math knowledge. In a study of Canadian and Greek 5-year-old children, however, LeFevre et al. (2010) reported that informal math activities were not related to numeracy knowledge. So far, virtually no model has been put forward to reconcile these contradictory findings and theorize the relation between home math activities and children’s math skills. The only exception is Skwarchuk et al.’s (2014) home numeracy model. In this model, Skwarchuk et al. distinguished between two types of math skills: (1) symbolic math knowledge or formal math skills, referring to knowledge involving the symbolic number system, such as writing Arabic digits; and (2) non-symbolic math knowledge or informal math skills, referring to the ability to represent and manipulate quantities without symbolism, such as object-based operations. The researchers argued that formal activities with an intentional focus on number system knowledge and arithmetic calculation provide children with opportunities to practice school-related math skills and thus help them acquire symbolic skills. In contrast, informal math activities such as number games involve little or no knowledge of the symbolic number system and therefore provide a basis for the development of non-symbolic math skills. Although Skwarchuk et al.’s model has received support from a few studies (Skwarchuk et al., 2014; LeFevre et al., 2010), many more studies have provided evidence that is inconsistent with the model. For example, LeFevre et al. (2009) andHuang et al. (2017) found that informal parent-child math activities were associated with young children’s symbolic math skills such as arithmetic fluency and written computation. We argue here that Skwarchuk et al.’s (2014) model has at least three limitations. First, their hypothesis that informal math activities predict non-symbolic math skills but not symbolic skills is inconsistent with theories of math development in which non-symbolic skills provide a critical foundation for the development of symbolic skills. As observed by many scholars (e.g., Gelman & Gallistel, 1978; Ginsburg, 1977), children’s development of symbolic math skills originates from their early experience with concrete objects. Specifically, they learn about numerical and arithmetic symbols by connecting them with the objects they represent. There is no denying that informal math activities can help children gain an understanding of non-symbolic quantities; however, such understanding, according to theories of math development, will eventually lead to solid knowledge of the symbolic number system. Second, Skwarchuk et al.’s (2014) model, which only considers games as informal math activities, ignores the role of other kinds of informal activities such as application activities, in children’s math learning. Math application activities provide children with opportunities to practice their math skills through solving real-world problems. Although game and application activities share common features in terms of stimulating learning – such as promoting active learning (Meltzoff, Kuhl, Movellan, & Sejnowski, 2009) and fostering deep engagement and staying on task (Benassi, Overson, & Hakala, 2014) – they differ in a crucial way. In contrast to games, application activities provide children with meaningful experiences that relate to their real lives. Ausubel (1968) distinguishes meaningful learning from rote learning and argues that true learning occurs in meaningful interactions with content that is related to children’s lives. For example, simple activities such as asking a child to set the table for dinner allow for potential real-world applications of math concepts (e.g., one-to-one correspondence) and, arguably, should promote effective learning. Thus, although game activities have been acknowledged as having a strong relation with young children’s math skills, there is good reason to assume that activities involving applied aspects of math may have an equally strong relation or an even stronger one. Finally, Skwarchuk et al. (2014) may overestimate the impact of formal activities on children’s math development. Parents often use the direct instruction method and take a primary rather than supportive role in their formal math activities with their children. Although direct instruction can result in better learning than free play, which contains no concrete learning goal (Alfieri, Brooks, Aldrich, & Tenenbaum, 2011), it often limits exploration, discourages active learning, and engages children in rote learning. According to Ausubel (1968), rote learning often lacks meaningful connection to what children already know and thus can easily fade from memory. Hence, the effect of early formal math activities, compared to informal activities, may more easily fade away once children are in primary school. Unfortunately, so far no attempt has been made to examine the long-term effect of early parent-child math activities on young children’s math trajectories through primary school.