4-6岁儿童数学认知中的多元表征研究

本研究以早期儿童数学认知中的数、数运算以及模式三个维度为切入点,对来自上海市的120名4-6岁儿童采用个别面试法考察其数学认知中的多元表征,采用描述性统计、多元方差分析、卡方检验等方法探查儿童多元表征的发展特点、相互关系及影响因素。结果表明：4-6岁儿童已具备初步的数、数运算、模式的多元表征能力,其中数的多元表征能力最好;4-6岁儿童在数、模式的多元表征中未出现明显的年龄差异与性别差异,在数运算多元表征中有明显的年龄差异,无性别差异;儿童使用的表征形式数量随年龄增长相应增加,且更倾向于使用描绘性表征中的实物情境表征与教具模型表征;4-6岁儿童数、数运算、模式的多元表征能力之间存在一定的相关;除年龄之外,已有学习经验、学习材料的呈现样式也是影响儿童多元表征的可能性因素。     

家庭文化资本对幼儿数学学习的影响

本研究对来自上海市的590个中、大班幼儿家庭进行问卷调查,旨在了解家庭文化资本对幼儿数学学习的影响。结果表明：作为家庭客体化文化资本的家庭文化环境和作为家庭身体化文化资本的幼儿家长数学教导信念对幼儿的家庭数学学习经验有直接的影响作用;作为家庭制度化文化资本的家庭教育背景则通过家庭文化环境和幼儿家长的数学教导信念对幼儿家庭数学学习经验有间接的影响作用。     

Working memory and arithmetic calculation in children: the contributory roles of processing speed, short-term memory, and reading

The cognitive underpinnings of arithmetic calculation in children are noted to involve working memory; however, cognitive processes related to arithmetic calculation and working memory suggest that this relationship is more complex than stated previously. The purpose of this investigation was to examine the relative contributions of processing speed, short-term memory, working memory, and reading to arithmetic calculation in children. Results suggested four important findings. First, processing speed emerged as a significant contributor of arithmetic calculation only in relation to age-related differences in the general sample. Second, processing speed and short-term memory did not eliminate the contribution of working memory to arithmetic calculation. Third, individual working memory components--verbal working memory and visual-spatial working memory--each contributed unique variance to arithmetic calculation in the presence of all other variables. Fourth, a full model indicated that chronological age remained a significant contributor to arithmetic calculation in the presence of significant contributions from all other variables. Results are discussed in terms of directions for future research on working memory in arithmetic calculation.     

A microgenetic study of insightful problem solving

An eight-session microgenetic study of acquisition of an insightful problem-solving strategy was conducted. A total of 35 second graders who did not use this insightful strategy initially were assigned to two groups that differed in the frequency of problems likely to facilitate discovery and generalization of the strategy. Children in the facilitative problems group discovered the insightful strategy earlier, used it more often subsequently, and transferred it more often to novel problems than did those in the nonfacilitative problems group. Children generally discovered the insightful strategy on the most facilitative items and extended it progressively to items on which its advantages were smaller but still substantial. The results indicate that experience outside the experimental situation, as well as experience inside the experimental situation, influences use of new strategies.     

Children’s notions of the malleability of their academic competencies

This study set out to examine children’s notions of the malleability of their academic competencies and the relations of these notions to the child’s grade-level and gender and the parent’s educational level. In interviews of a total of 103 boys and girls of the third and the sixth grade, children of academically and vocationally educated parents were asked to rate their potential for improving their competencies in mathematics and Finnish. The children were asked to use intrapersonal and normative criteria in their ratings. The ratings were found to form distinct domains of the notions of malleability, as they did not correlate with each other. The children’s ratings of their current competencies, i.e. their academic self-concepts, turned out to be related to their normative ratings of the malleability of their competencies. The findings further suggested that the children’s notions of the malleability of their academic competencies became more pessimistic in the course of their school years.

Van Inwagen and the Quine-Putnam indispensability argument

In this paper I do two things: (1) I support the claim that there is still some confusion about just what the Quine-Putnam indispensability argument is and the way it employs Quinean meta-ontology and (2) I try to dispel some of this confusion by presenting the argument in a way which reveals its important meta-ontological features, and include these features explicitly as premises. As a means to these ends, I compare Peter van Inwagen’s argument for the existence of properties with Putnam’s presentation of the indispensability argument. Van Inwagen’s argument is a classic exercise in Quinean meta-ontology and yet he claims – despite his argument’s conspicuous similarities to the Quine-Putnam argument – that his own has a substantially different form. I argue, however, that there is no such difference between these two arguments even at a very high level of specificity; I show that there is a detailed generic indispensability argument that captures the single form of both. The arguments are identical in every way except for the kind of objects they argue for – an irrelevant difference for my purposes. Furthermore, Putnam’s and van Inwagen’s presentations make an assumption that is often mistakenly taken to be an important feature of the Quine-Putnam argument. Yet this assumption is only the implicit backdrop against which the argument is typically presented. This last point is brought into sharper relief by the fact that van Inwagen’s list of the four nominalistic responses to his argument is too short. His list is missing an important – and historically popular – fifth option.

Emotional and personality-related aspects of persistent career decision-making difficulties

This study focused on examining the persistent aspects of career decision-making difficulties, using the Emotional and Personality-related Career decision-making Difficulties scale (EPCD; [Saka, N., Gati, I., & Kelly, K.R. (in press). Emotional and personality-related aspects of career decision-making difficulties. Journal of Career Assessment]). The contribution of four personality measures—general indecisiveness, self-esteem, trait anxiety, and identity status—to the prediction of persistent career decision-making difficulties was tested on 747 students, using a longitudinal design. Results indicated that individuals with high EPCD scores at the beginning of the academic school year had less confidence in their choice and were less close to making a decision about the major into which they wanted to be admitted at the end of the year. The moderate correlations between the EPCD score and the four personality measures supported the validity of the EPCD. Implications for counseling and future research are discussed.     

From grammatical number to exact numbers: early meanings of 'one', 'two', and 'three' in English, Russian, and Japanese

This study examined whether singular/plural marking in a language helps children learn the meanings of the words 'one,' 'two,' and 'three.' First, CHILDES data in English, Russian (which marks singular/plural), and Japanese (which does not) were compared for frequency, variability, and contexts of number-word use. Then young children in the USA, Russia, and Japan were tested on Counting and Give-N tasks. More English and Russian learners knew the meaning of each number word than Japanese learners, regardless of whether singular/plural cues appeared in the task itself (e.g., "Give two apples" vs. "Give two"). These results suggest that the learning of "one," "two" and "three" is supported by the conceptual framework of grammatical number, rather than that of integers.     

Working memory deficit in children with mathematical difficulties: a general or specific deficit?

This study examined whether children with mathematical difficulties (MDs) or comorbid mathematical and reading difficulties have a working memory deficit and whether the hypothesized working memory deficit includes the whole working memory system or only specific components. In the study, 31 10-year-olds with MDs and 37 10-year-olds with both mathematical and reading difficulties were compared with 47 age-matched and 50 younger controls (9-year-olds) on a number of working memory tasks. Compared with the age-matched controls, both groups of children with MDs performed worse on tasks tapping the central executive (e.g., visual matrix span) and the phonological loop (e.g., word span). More important, the MD group performed worse than the younger controls on the counting span task, whereas the group with comorbid mathematical and reading difficulties performed worse on the counting span task and the visual matrix span task. These findings provide support for the assumption that children with MDs have a working memory deficit. More specifically, children with MDs have a central executive deficit connected to concurrent processing and storage of numerical and visual information.