Increasing Retention Without Increasing Study Time

ABSTRACT— Because people forget much of what they learn, students could benefit from learning strategies that yield long-lasting knowledge. Yet surprisingly little is known about how long-term retention is most efficiently achieved. Here we examine how retention is affected by two variables: the duration of a study session and the temporal distribution of study time across multiple sessions. Our results suggest that a single session devoted to the study of some material should continue long enough to ensure that mastery is achieved but that immediate further study of the same material is an inefficient use of time. Our data also show that the benefit of distributing a fixed amount of study time across two study sessions—the spacing effect —depends jointly on the interval between study sessions and the interval between study and test. We discuss the practical implications of both findings, especially in regard to mathematics learning.     

工作记忆在数学运算过程中的作用

Baddeley和Hitch(1974)提出的工作记忆模型被广泛地应用数学运算领域,但是已有研究还缺乏系统性。首先,当前的研究主要集中在加法和乘法两种运算上,较少涉及减法、除法和更为抽象的代数运算;第二,研究者对语音环路和中央执行系统的作用进行了较深入的研究,但常常忽略视空间模板的作用;第三,工作记忆在数学运算过程中的作用具有动态性,它受到一些外部因素、数学任务内在因素和个体认知因素（如认知策略）的影响;第四,几乎有关研究都肯定中央执行系统在数学运算过程中的重要作用,然而负荷于中央执行系统的次级任务所含成分或功能的复杂性,导致我们很难确定中央执行系统如何作用于数学运算。对这些问题的研究将是未来可能的研究方向     

初中生数学自我效能问卷的编制

根据国内外关于数学自我效能研究的文献,结合我国初中生数学学习的内容特点与实际背景情况,编制数学自我效能问卷。研究以初一与初二学生为对象,采用开放式问卷对188名学生和53名数学教师进行调查,首先编制出44个项目的初测问卷;采用封闭式问卷对479名学生的初测结果进行验证性因素分析与项目分析,形成了包含日常生活中数学任务的效能、数学相关课程的效能与数学学业问题解决效能三个维度的26个项目的正式问卷;最后对350名学生施测正式问卷。分析研究结果表明,该数学自我效能问卷的因素结构清晰,具有合理的信度和效度。     

Making Numbers Come to Life: Two Scoring Methods for Creativity in Aurora's Cartoon Numbers

Although creativity has long been recognized as an important aspect of mathematical thinking, both for the advancement of the field and in students' developing expertise in mathematics, assessments of student creativity in that domain have been limited in number and focus. This article presents an assessment developed for creativity that provides a score for mathematical creativity (MaC) in addition to a score for general creativity in the numeric domain, or what we might call numerical creativity (NuC). We developed different rating scales for each and then explored how each scoring method accounts for the students' mathematical/numerical and creative skills. The psychometric properties for both scoring approaches were examined. Each method was shown to reflect different relationships with other performance tests. In addition, it is proposed that MaC may provide useful insight into students' levels of adaptive expertise in mathematics, as reflected by their ability to apply mathematical knowledge (i.e., language, operations, concepts) to novel situations, representing an informative supplement to performance indicators of math achievement.     

Contrasting two models of academic self‐efficacy – domain‐specific versus cross‐domain – in children receiving and not receiving special instruction in mathematics

In social cognitive theory, self‐efficacy is domain‐specific. An alternative model, the cross‐domain influence model, would predict that self‐efficacy beliefs in one domain might influence performance in other domains. Research has also found that children who receive special instruction are not good at estimating their performance. The aim was to test two models of how self‐efficacy beliefs influence achievement, and to contrast children receiving special instruction in mathematics with normally‐achieving children. The participants were 73 fifth‐grade children who receive special instruction and 70 children who do not receive any special instruction. In year four and five, the children's skills in mathematics and reading were assessed by national curriculum tests, and in their fifth year, self‐efficacy in mathematics and reading were measured. Structural equation modeling showed that in domains where children do not receive special instruction in mathematics, self‐efficacy is a mediating variable between earlier and later achievement in the same domain. Achievement in mathematics was not mediated by self‐efficacy in mathematics for children who receive special instruction. For normal achieving children, earlier achievement in the language domain had an influence on later self‐efficacy in the mathematics domain, and self‐efficacy beliefs in different domains were correlated. Self‐efficacy is mostly domain specific, but may play a different role in academic performance depending on whether children receive special instruction. The results of the present study provided some support of the Cross‐Domain Influence Model for normal achieving children.     

The mathematics of sharing / Las matemáticas que realizan los niños al compartir

Abstract

The purpose of sharing is to construct equivalent sets, making it an ideal context for analysing important quantitative concepts such as counting, equivalence and cardinality. Two studies analysed how four- and five-year-olds shared blocks in equal sharing and reciprocity conditions and their number inferences about one set after counting the other. The researcher asked children to share double and single blocks between two characters. They succeeded more in building equivalent shares in an equal sharing than reciprocity condition. Most children who shared correctly also made appropriate number inferences. To examine whether perceptual cues helped children share the blocks, a second study used Canadian $1 and $2 coins. A double block is twice the size of a single, whereas there is no visual cue about the value relation between coins because they are the same size. Unexpectedly, children shared equally well with blocks and coins, and most children made number inferences.     

5～6岁不同数学能力水平儿童的执行功能差异研究

为了考察不同数学能力水平儿童的执行功能差异,根据331名学前儿童的数学能力得分选取了潜在数学学习困难儿童组、低分组、典型发展儿童组和数学优秀组等4个实验组。首先分析了各组儿童的执行功能差异特点,之后使用判别分析进一步探索了各执行功能子结构对儿童早期数学能力差异分组的贡献。结果表明:相对于典型发展儿童组,潜在数学学习困难儿童在执行功能的更新、抑制和转换方面普遍缺损;低分组儿童则仅表现出数字更新能力不足;数学优秀组在数字更新和有时间要求的认知转换方面比典型发展组有明显优势。进一步判别分析表明,对早期数学能力差异分组贡献最大的并非独立执行功能子结构,而是更新和转换的共同因素结构。     

‘Infinity Means it Goes on Forever’: Siblings' Informal Teaching of Mathematics

Sibling‐directed teaching of mathematical topics during naturalistic home interactions was investigated in 39 middle‐class sibling dyads at two time points. At time 1 (T1), siblings were 2 and 4 years of age, and at time 2 (T2), siblings were 4 and 6 years of age. Intentional sequences of sibling‐directed mathematical teaching were coded for (i) topics (e.g., number), (ii) contexts (e.g., play with materials/toys), and (iii) type of knowledge (conceptual and procedural). Siblings engaged in teaching number, geometry, and measurement at T1 and demonstrated preliminary evidence of teaching of grouping, relations, and operations at T2. Regarding context, at T1, mathematical teaching occurred most frequently during play with materials/toys, while at T2, games with rules were prominent. Teaching of conceptual or procedural knowledge varied over time and by topic and context. Findings are discussed in light of recent work on understanding children's mathematical knowledge as it develops in the informal family context. Copyright © 2015 John Wiley & Sons, Ltd.