Acalculia and Dyscalculia

Even though it is generally recognized that calculation ability represents a most important type of cognition, there is a significant paucity in the study of acalculia. In this paper the historical evolution of calculation abilities in humankind and the appearance of numerical concepts in child development are reviewed. Developmental calculation disturbances (developmental dyscalculia) are analyzed. It is proposed that calculation ability represents a multifactor skill, including verbal, spatial, memory, body knowledge, and executive function abilities. A general distinction between primary and secondary acalculias is presented, and different types of acquired calculation disturbances are analyzed. The association between acalculia and aphasia, apraxia and dementia is further considered, and special mention to the so-called Gerstmann syndrome is made. A model for the neuropsychological assessment of numerical abilities is proposed, and some general guidelines for the rehabilitation of calculation disturbances are presented.     

6—12岁儿童脑波超慢涨落功率与计算速度的关系

对176名6-12岁认知功能正常小学生进行脑波超慢涨落平均功率分布与计算速度关系的研究。结果表明：(1)计算速度快组和计算速度慢组中各年龄组的脑区平均功率符合额低枕高的前后梯度。计算速度慢组的逆转百分率高于计算速度快组。(2)在各年龄组中,计算速度快组和慢组功率前后逆转百分率的差异主要反映在右脑,右脑功率前后梯度逆转在不同计算组之间差异较大。(3)在计算速度快组和慢组中,左脑平均功率都小于右脑平均功率。计算速度快组和慢组脑波功率左右逆转百分率的差异主要反映在后脑,后脑功率左右逆转在逆转总数上计算速度快组多于计算速度慢组。     

Informal versus formal mathematics

We discuss Kunen’s algorithmic implementation of a proof for the Paris–Harrington theorem, and the author’s and da Costa’s proposed “exotic” formulation for the P = NP hypothesis. Out of those two examples we ponder the relation between mathematics within an axiomatic framework, and intuitive or informal mathematics. The author is Visiting Researcher at IEA/USP, Professor of Communications, Emeritus, at the Federal University in Rio de Janeiro, and a full member of the Brazilian Academy of Philosophy.     

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     

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.     

Site preference and alloying effect of Re atoms in the edge dislocation cores in Ni3Al

Using Cambridge sequential total energy package method based on the density functional theory, we investigated the site preference and alloying effect of Re atoms in the [1 0 0] (0 1 0) edge dislocation cores in Ni₃Al. Due to the introduction of a Re atom, the energetic and electronic structure of dislocation core systems have been changed a lot. The binding energy results suggest Re atom prefers Al site, especially the centre site in the centre-Al system, which can be explained by the results of Mulliken orbital population and density of states. When Re atom occupies the centre site in the centre-Al system, the DC system has the highest stability and stronger bonds formed between the Re atom and its nearest neighbouring atom due to hybridization of the Re-5d and Ni-3d orbitals.     

Functional mapping of left parietal areas involved in simple addition and multiplication. A single‐case study of qualitative analysis of errors

All electrostimulation studies on arithmetic have so far solely reported general errors. Nonetheless, a classification of the errors during stimulation can inform us about underlying arithmetic processes. The present electrostimulation study was performed in a case of left parietal glioma. The patient's erroneous responses suggested that calculation was mainly applied for addition and a combination of retrieval and calculation was mainly applied for multiplication. The findings of the present single‐case study encourage follow up with further data collection with the same paradigm.