Response patterns of young children from two contrasting SES contexts to different numerical tasks with numbers 1–5

This study contributes to a multifaceted picture of young children’s emergent number knowledge by focusing on the variety of ways in which children express and use quantitative information. The authors’ aims are to (a) explore the extent to which quantifying collections 1–5 and using that information pose different levels of difficulty to children from 33 to 47?months old, (b) identify intra- and intertask response patterns, and (c) analyze the influence of socioeconomic status and age on these response patterns. Sixty-six children from two contrasting socioeconomic status groups (very low and middle) were asked to solve tasks with 1–5 elements in the context of a game. Using quantitative information turned out to be more complex than quantification. Intra- and intertask response patterns showed that children gradually come to understand the first five numerical values according to the numerical sequence in a much less strict way than that proposed by the cardinal-knowers model that posits that children progress in an orderly way in their number knowledge. Children in different ages and socioeconomic status groups were found to be more similar to each other when the whole arc of responses provided was considered than when solely correct performance was measured.     

Dissociation between magnitude comparison and relation identification across different formats for rational numbers

ABSTRACT

The present study examined whether a dissociation among formats for rational numbers (fractions, decimals, and percentages) can be obtained in tasks that require comparing a number to a non-symbolic quantity (discrete or else continuous). In Experiment 1, college students saw a discrete or else continuous image followed by a rational number, and had to decide which was numerically larger. In Experiment 2, participants saw the same displays but had to make a judgment about the type of ratio represented by the number. The magnitude task was performed more quickly using decimals (for both quantity types), whereas the relation task was performed more accurately with fractions (but only when the image showed discrete entities). The pattern observed for percentages was very similar to that for decimals. A dissociation between magnitude comparison and relational processing with rational numbers can be obtained when a symbolic number must be compared to a non-symbolic display.     

数字表征的表象赋义效应:来自数字线估计任务的证据

已有研究中数字线估计任务几乎都使用纯数字。本研究以二到六年级儿童为被试,采用纯数字任务和赋义数字任务来探索赋义表象对数字表征形式的影响。结果表明,对0~1000的数字赋义后,对数模型的解释力上升,而线性模型的解释力下降;表象大小对于赋义数字的估计影响显著,大表象赋义提高了对数模型解释力而降低了数字估计的准确性,小表象的影响比较微弱。