Yukari Okamoto

Comparisons of Children's Cognitive Representation of Number: China, France, Japan, Korea, Sweden, and the United States

Cross-national comparisons of mathematics achievement have shown differences in favour of Asian students. This study examined the idea that the superior mathematics performance of students from Japan, Korea, and China may be due, in part, to differences in cognitive representation of number that is affected by numerical language characteristics differentiating Asian and non-Asian language groups. First-graders from the Peoples Republic of China, Japan, Korea, France, Sweden, and the United States were asked to construct various numbers using Base 10 blocks. Chinese, Japanese, and Korean children showed a preference for using a construction of tens and ones to show numbers; place value appeared to be clearly represented in those constructions. French, Swedish, and US children, in contrast, showed a preference for using a collection of units, suggesting that they represent number as a grouping of counted objects. More Asianlanguage speakers than non-Asian-language speakers were also able to make two correct constructions for each number, which suggests greater flexibility of mental number manipulation. Thus, the unique characteristics of the Asian number language system may facilitate the teaching and learning of mathematics, especially computation, for speakers of those languages.

Maternal Stress and Efficacy for Latina Mothers with Infants in Neonatal Intensive Care

This study examined the levels of maternal stress and efficacy for Spanish- and English-speaking Latina mothers whose infants were in neonatal intensive care. Thirty-two Latina mothers participated in the study. Significant group differences were found between Spanish- and English-speaking Latina mothers. More stress was experienced by Spanish- than English-speaking Latina mothers in communicating with NICU staff, in general and learning about infant caregiving tasks, in particular. Maternal efficacy was not related to stress experienced by these mothers in the NICU. Implications for early interventions and future directions for research are discussed for Latina mothers and their newborn infants with special needs.

Prospective Secondary Mathematics Teachers’ Understanding and Cognitive Difficulties in Making Connections among Representations

This study investigates prospective secondary teachers’ cognitive difficulties and mathematical ideas involved in making connections among representations. We implemented a three-week teaching unit to help prospective secondary mathematics teachers develop understanding of big ideas that are critical to formulating connections among representations, in the context of conic curves. Qualitative analysis of data showed that most undergraduate mathematics majors and minors in this study struggled with variation, the Cartesian Connection, and other affiliated ideas such as graph as a locus of points. Furthermore, they were unable to identify basic metric relations encoded in algebraic expressions such as the distance between points, which further compounded their difficulties in making connections among representations. We argue that mathematics teacher education needs more focus on these ideas so that their graduates can successfully teach these big ideas in their future instruction.

Encoding “10ness” Improves First-Graders’ Estimation of Numerical Magnitudes

Understanding numerical magnitudes is a foundational skill that significantly impacts later learning of mathematics concepts. The current study tested the idea that encoding of “10ness” is crucial to improving children’s estimation of two-digit number magnitudes. We used commercially available base-10 blocks for this purpose. The children in the experimental condition were asked to construct two-digit numbers by laying down the precise combinations of 10- and 1-blocks horizontally (e.g., three 10-blocks and seven 1-blocks for 37). Two control conditions were also included. In one control condition, children used 1-blocks only. In another control condition, children used one 10-block and as many 1-blocks as necessary. After working with the experimenter for only 15 minutes twice, the children in the experimental condition were significantly more accurate on the estimation task than those in the control conditions. The findings confirmed the importance of encoding 10ness as a unit in making accurate estimates of two-digit number magnitudes. The importance of encoding other units in the base-10 system is discussed.

Children’s Developing Understanding of Number: Mind, Brain, and Culture

This chapter describes and extends Robbie Case’s contributions to the field of children’s numerical development. Case postulated a theory of numerical development that results from an integration of two schemas essential to understanding quantity relations. These schemas depict children’s intuitions about numerical concepts that involve counting objects and comparing quantities. A conceptual structure that supports a new way of thinking emerges from this integration – a qualitatively different way of viewing the quantitative world. This new structure is termed a central numerical structure, which serves as a focal hub for children’s understandings of a broad range of numerical activities and situations that are culturally defined. The current chapter takes these ideas in two directions: one is to explore the potential origins of the counting and quantity schemas and the other is to examine the development of central numerical structures in cultural contexts. The former presents an argument that the two, initial structures parallel the two “core” systems of number for infants: Recent findings from cognitive sciences and neurosciences show that infants may possess such systems of number that allow them to represent discrete numerosity (similar to the counting schema) and approximate numerical magnitudes (similar to the quantity schema). For the latter, the chapter presents evidence from two cross-national studies that showed equivalent patterns of development of central numerical structures between American and Japanese children, despite large achievement differences in mathematics. The chapter ends with an attempt to link recent developments in neurosciences to cognitive and cultural studies of the numerical mind.

Multidisciplinary perspectives on a video case of children designing and coding for robotics

Spatial reasoning plays a vital role in choice of and success in science, technology, engineering, and mathematics (STEM) careers, yet the topic is scarce in grade school curricula. We conjecture that this absence may be due to limited knowledge of how spatial reasoning is discussed and engaged across STEM professions. This study aimed to address that gap by asking 19 professionals to comment on a video that documented children’s progression through 5 days of building and programming robots. Their written opinions on the skills relevant to their careers demonstrated by the children revealed that spatial thinking and design thinking are central to what they see.RśuméLe raisonnement spatial joue un rôle essentiel dans la décision d’entreprendre une carrière STEM et de réussir dans les domaines concernés. Pourtant, ces matières sont peu représentées dans les curriculums à l’école primaire. Nous supposons que cette absence puisse être due à un manque de connaissances quant à la façon dont le raisonnement spatial est traité dans l’ensemble des professions STEM. Cette étude vise à combler ce manque en demandant à 19 professionnels de commenter une vidéo qui documente la progression d’enfants qui construisent et programment des robots pendant 5 jours. Les commentaires écrits des répondants sur les habiletés pertinentes illustrées par les élèves montrent que la pensée spatiale et la pensée conceptuelle sont fondamentales dans leur profession.

Resisting Suggestive Questions: Can Theory of Mind Help?

Abstract Childrens credibility as witnesses in court cases has become an important issue in recent years. When testifying, younger children are considered to be more susceptible to suggestion than are older children. The present study examined the possibility that knowledge of an interviewers mental states (intention and false belief, in this study) would influence the accuracy of young childrens reporting of a recently witnessed event. Five-year-old children were shown a short video clip, after which they were asked to free recall as well as respond to a list of specific questions. Results showed that children who were given knowledge of an interviewers intention resisted suggestive questioning, whereas children without mental-states knowledge were misled to report inaccurate information.