Mathematics instruction in Head Start: Nature,extent, and contributions to children's learning

This study employed the most recent (2006) cohort of the nationally representative Family and Child Experiences Survey (FACES) to explore the nature of mathematics instruction in Head Start and the child, family, and teacher factors that contribute to children's mathematics learning over the preschool year. In total, 2501 preschoolers and their families, as well as their teachers (n = 335), participated in the study from fall 2006 to spring 2007. Results showed that teachers reported frequent mathematics instruction, although direct observations did not entirely confirm this frequency. A variety of factors predicted children's mathematics knowledge at Head Start entry, and several – including instructional quality – were linked to learning over time. No thresholds in instructional quality emerged. Overall, this study provides new information about classroom mathematics instruction and child learning among the nation's most vulnerable early learners.     

Learning potential and anxious tendency: Test anxiety as a bias factor in educational testing

Abstract

Contrary to conventional educational testing, in so-called dynamic assessment subjects are allowed to consult help during testing or are offered prior training. The differential results of both testing procedures are sometimes ascribed to the idea that dynamic tests reflect the breadth of the zone of proximal development on top of independent achievement. Alternative explanations claim that conventional tests are more strongly biased towards various characteristics of persons, which have a negative influence on performance, when compared to dynamic tests. In this study, it was hypothesised that static as well as dynamic assessment is biased towards anxious tendencies of subjects, but the former more strongly than the latter. In order to investigate this supposition, the performance of subjects on dynamic and static tests was systematically compared and related to measures of test anxiety in a longitudinal experiment. In the experiment, repeated measures of independent mathematics achievement as well as mathematics learning potential were gathered among students of secondary education in the Netherlands. Prior to every mathematics test, subjects filled out a test anxiety questionnaire. After every mathematics test, subjects filled out a general state anxiety questionnaire. The participating subjects were students from secondary education, either preparing for higher vocational training or university, aged approximately 15 years on average.

The results of the experiment showed that lack of self-confidence is an important constituent factor of test anxiety, apart from worry and emotionality. The data supported the assumption that such testing procedures are less biased towards anxiety than conventional tests, but it was not established that dynamic testing procedures render results that are not biased by test anxious tendencies.     

Matter,mathematics, and God

Between 1863 and 1928, positions regarding evolution and creationism debated in today's polls and popular culture first appeared in the Anglo-American world. By reviewing writings of T. H. Huxley, Alfred Russel Wallace, Helena P. Blavatsky, and H. P. Lovecraft, early formulations in today's culture wars and their relation to human curiosity or xenophobia become evident. Exploring these individuals in relation to one another is warranted since Blavatsky and Lovecraft, with their impact on popular culture in the twentieth century, often wrote in response to evolutionary writings, including those of Wallace and Huxley with their respective design-oriented and agnostic positions.     

Infinity in Mathematics and Theology

Abstract

“Infinity” and its derivatives are frequently used in mathematics and theology. Do these expressions denote the same thing in those distinct areas of scholarship? In this article the uses of “infinity” in mathematics and its uses in theology are examined and compared. One conclusion is that quite different concepts go under the heading of “infinity.” Although they must not be confused, there are some relations between mathematical and theological senses of infinity.     

The German Reformation and the Mathematization of the Created World

This article explores the emergence of mathematics and mathematical method as a means of defining authoritative truth in the thought of some scholars in the German Reformation. Against the background of Martin Luther's critique of Aristotelian philosophy, Philip Melanchthon presented mathematics as an ideal discipline for preparing the mind to understand God. His approach drew on the work of humanist mathematicians such as Regiomontanus. It finds resonances in the work of the Basel humanist Simon Grynaeus, and (in a less mathematically informed way) in the thought of Peter Ramus. These discussions about the divine nature and certainty of mathematical truth formed the context within which Johannes Kepler's Platonist astronomy emerged.     

Two Examples of How the History of Mathematics Can Inform Theology

In several of his writings, Bernard Lonergan emphasized the study of mathematics and especially its history as being important for philosophy and theology. In this article, I offer two examples of how the history of mathematics might inform theology. My first example explores the disparities between Euclid's Elements and Aquinas' Summa Contra Gentiles. My second example applies the idea of incompleteness to the “good and necessary consequence” clause of the Westminster Confession of Faith.     

Greed 1

Abstract

This paper discusses the supervisor's responsibility in addressing the vulnerability or wounds of the therapist. Supervisors have much to keep in mind as they conduct their work, not least the client for whose benefit supervision is deemed to be an essential aspect of good practice. Their responsibility towards the client often entails careful exploration of the experience of the counsellor, both through their counter-transferential response to the client and their own personal circumstances. The extent to which the supervisor has a mandate to discuss the psychological well-being, personal difficulties, or organizational conflicts of their supervisee depends on both contractual agreements and the working alliance. The need to recognize counter-transference responses is generic but when they highlight the internal conflicts of the counsellor, the supervisor must decide how far they can or should pursue the unravelling of such conflicts. Therapist difficulties (Schroder & Davis, 2004 Schröder, T. and Davis, J. 2004. Therapists' experience of difficulty in practice. Psychotherapy Research, 14: 328–345. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) provide a framework for understanding ways in which therapeutic practice is affected by the emotional response of the therapist.     

数学焦虑对工作记忆子系统及数学心算的影响分析

本研究从工作记忆容量的角度入手,探讨数学焦虑对工作记忆子系统及数学心算成绩的影响,并寻求三者之间关系的理论解释。本研究为3×2×2混合实验设计,即三组被试（高、中、低数学焦虑组）、工作记忆两个子系统（言语工作记忆和视空间工作记忆）和两种数学心算任务难度,并记录数学心算的反应时和正确率作为其成绩指标。结果表明在要求较高工作记忆容量的数学心算任务中,数学焦虑通过言语工作记忆和视空间工作记忆都会对数学心算成绩产生影响,其中视空间工作记忆是数学焦虑与复杂数学心算反应时之间的中介变量。     

Sensitivity to general and specific numerical features in typical achievers and children with mathematics learning disability

We examined the development of sensitivity to general and specific numerical features in typical achievers and in 6th and 8th graders with mathematics learning disability (MLD), using two effects in mental multiplication: operand-relatedness (i.e., difficulty in avoiding errors that are related to the operands via a shared multiplication row) and decade-consistency (i.e., difficulty in avoiding errors that are operand related and also share a decade with the true result). Responses to decade-consistent products were quick but erroneous. In line with the processing sequence in adults, children first became sensitive to the general numerical feature of operand-relatedness (typical achievers—from 3rd grade; children with MLD in 8th grade) and only later to the specific feature of decade-consistency (typical achievers—from 4th grade, but only from 6th grade in a mature pattern). Implications of the numerical sensitivity in children with MLD are discussed.     

Transcoding abilities in typical and atypical mathematics achievers: The role of working memory and procedural and lexical competencies

Transcoding between numerical systems is one of the most basic abilities acquired by children during their early school years. One important topic that requires further exploration is how mathematics proficiency can affect number transcoding. The aim of the current study was to investigate transcoding abilities (i.e., reading Arabic numerals and writing dictation) in Brazilian children with and without mathematics difficulties, focusing on different school grades. We observed that children with learning difficulties in mathematics demonstrated lower achievement in number transcoding in both early and middle elementary school. In early elementary school, difficulties were observed in both the basic numerical lexicon and the management of numerical syntax. In middle elementary school, difficulties appeared mainly in the transcoding of more complex numbers. An error analysis revealed that the children with mathematics difficulties struggled mainly with the acquisition of transcoding rules. Although we confirmed the previous evidence on the impact of working memory capacity on number transcoding, we found that it did not fully account for the observed group differences. The results are discussed in the context of a maturational lag in number transcoding ability in children with mathematics difficulties.