Place value concepts and multi-digit numbers are the foundations of mathematics; however, many children struggle at acquiring this knowledge. Poor understanding of the place value concepts has been linked to difficulties in mathematics learning through the elementary and middle school grades, and it is present not only for children with learning disabilities but also for a large proportion of normally developing children. It is, thus, important to understand the developmental mechanisms of multi-digit number learning and potential sources of early experiences that allow some children to readily grasp the concepts while others continue to struggle. Recent research on place value concepts has suggested that children have partial knowledge of multi-digit numbers at the preschool period, before receiving formal training from schools. These precursors of multi-digit number knowledge can serve as important stepping-stones for children to master the concept of place value once entering schools. However, there are at least two gaps in our current understanding of the development of place value concepts. First, how does early understanding of multi-digit numbers relate to formal school training of the place value concepts? Second, how do children come to acquire partial knowledge of multi-digit numbers at such a young age in the first place? The goal of the proposed research aims at filling these gaps in the literature with three specific aims.
Aim 1 tests the hypothesis that early knowledge of multi-digit numbers is predictive of later school learning of the place value concepts. I propose to conduct a 3-year longitudinal study to measure children?s early understanding of multi-digit numbers at the start and end of kindergarten, 1st and 2nd grades. The study will test how early knowledge of number names and written numerals, as well as other individual difference measurements (e.g., age, gender, SES, number sense, home exposures to numbers), relate to the learning of base-10 principles in grade school.
Aim 2 tests the hypothesis that acquiring early knowledge of multi-digit numbers is a form of statistical learning, during which children extract latent structures that govern the mapping between number words and written numerals through sparse co-occurrence data. A training study is designed to give children casual experiences with multi-digit numbers in engaging and child- friendly activities (e.g., picture-book reading, ipad games). The same children in the statistical learning training will also be given formal school training afterward, allowing us to assess and provide causal evidence for the hypothesis that early knowledge prepares children for formal school training of the place value concepts. The knowledge gained from this research will have implications for: a) determining the role of early knowledge of multi-digit numbers in preparing children to learn about base-10 notation at schools; b) linking statistical learning from sparse co-occurrence data about number words and multi-digit numbers to early partial knowledge of place value; c) documenting how differences in early learning environment (or input) may contribute to developmental inequalities in later school performances.
The proposed research aims at understanding the early development of multi-digit numbers, its learning mechanisms and its impact on formal school training of place value concepts. The period of development studied here, from 3 to 5 years of age, is a period during which sizable individual differences in multi-digit number knowledge starts to emerge, which may contribute to early developmental inequalities that limit the development of some children even after entering school. The proposed work is relevant to public health in that it will shed light on how differences in early learning environment lead to individual differences in early understanding of multi-digit numbers, potentially serving as the foundation for future early mathematical training programs.