数学焦虑影响儿童的数量表征:认知抑制的调节作用

为了考察数学焦虑对儿童数量表征表现的可能影响及认知抑制的潜在调节作用,选取70名小学三年级儿童（高焦虑组36人,低焦虑组34人）为被试,在对抑制条件进行操控的情况下,要求其完成符号、非符号数量表征任务。结果发现,被试在两种数量表征任务中均出现距离效应,与符号数量比较任务相比,高焦虑组在非符号数量比较任务中的正确率显著低于低焦虑组,且高焦虑组表现出了更强的距离效应。鉴于非符号数量比较任务更能反映出个体近似数量系统（ANS）的敏锐性,上述结果意味着高数学焦虑儿童的数量表征更不精确,其在相对复杂问题上较差的表现或许源于基本数量能力缺陷。本研究还发现认知抑制能够调节数学焦虑对个体非符号数量表征的影响,抑制条件下高低焦虑组儿童在正确率指标上的差异大于非抑制条件,抑制条件的设置提高了个体对工作记忆资源的需求,此时焦虑情绪对认知资源的消耗会造成任务所需资源的不足,进而削弱高焦虑个体的认知效用。     

The developmental relations between spatial cognition and mathematics in primary school children

Spatial thinking is an important predictor of mathematics. However, existing data do not determine whether all spatial sub‐domains are equally important for mathematics outcomes nor whether mathematics–spatial associations vary through development. This study addresses these questions by exploring the developmental relations between mathematics and spatial skills in children aged 6–10 years (N = 155). We extend previous findings by assessing and comparing performance across Uttal et al.'s (2013), four spatial sub‐domains. Overall spatial skills explained 5%–14% of the variation across three mathematics performance measures (standardized mathematics skills, approximate number sense and number line estimation skills), beyond other known predictors of mathematics including vocabulary and gender. Spatial scaling (extrinsic‐static sub‐domain) was a significant predictor of all mathematics outcomes, across all ages, highlighting its importance for mathematics in middle childhood. Other spatial sub‐domains were differentially associated with mathematics in a task‐ and age‐dependent manner. Mental rotation (intrinsic‐dynamic skills) was a significant predictor of mathematics at 6 and 7 years only which suggests that at approximately 8 years of age there is a transition period regarding the spatial skills that are important for mathematics. Taken together, the results support the investigation of spatial training, particularly targeting spatial scaling, as a means of improving both spatial and mathematical thinking.     

The Bernreuter Personality Inventory as a Measure of Student Adjustment

Abstract

In this study salience, importance, and multidimensional aspects of spontaneous social identities were examined. A Social Identity Survey was developed and administered to an ethnically diverse sample of American undergraduate students. Freely generated, social identities were rank ordered for importance and rated along four conceptually-derived dimensions: emotion, evaluation, importance, and stability. Results showed pattern differences among three groups of highly salient social identities: (a) gender, religion, and ethnicity; (b) academic major and student; and (c) hobbies and athletics. Ethnic differences suggest that mainstream Americans attributed less importance to the gender and ethnic identities in comparison with Asians and Hispanics.     

How Gödel Relates Platonism to Mathematics

It is well known that Gödel takes his realistic world view as closely related to mathematics, especially to his own work in the foundations of mathematics. He reports, publicly as well as privately, that Platonism is fundamental to his major work in logic and set theory, and suggests that this philosophical position can be seen as a product of reflections on mathematics. These views of Gödel, however, are often regarded as being insufficiently formulated or argued for. In this article, the author tries to consider some points which are related to the understanding of the Gödelian mode of the interaction between mathematics and philosophy.     

Mathematics and Theology: A Stroll through the Garden of Mathaphors

Mathematics has long been considered the language of science and has even been acknowledged as the universal language of the future. Yet mathematics also plays a less-recognized religious role in that metaphors drawn from mathematics (mathaphors) can influence our spiritual perspectives by helping us to entertain new religious ideas and to challenge old ones. Mathaphors are therefore useful tools in matheology (the study of mathematics and theology). This essay explores ten ways in which contemporary mathaphors affect our spiritual lives. Specifically, mathaphors are: changing our metaphors for God; challenging our human role in the universe; helping us accept ambiguity; revamping our understanding of the one and the many; revising our thoughts about free will and determinism; moving us toward pluralistic, multi-world views; pushing the envelope on what consciousness is; altering our expectations for afterlife; offering the hope of a more compassionate future; encouraging faith perspectives that are always incomplete and in process.     

Constructivism and the Role of Skills in Mathematics Instruction for Academically At-Risk Secondary Students

Summary

Instructional uses of technology in special education have evolved considerably over the last two decades. Many researchers have moved away from stand alone uses (e.g., computer assisted instruction) toward an array of different technologies that serve as tools in complex learning environments. A change in thinking about teaching and learning has also occurred, as researchers have moved away from didactic instructional methods to constructivist approaches. Yet constructivism remains problematic for many in the field, in part because of the traditional emphasis on skills in day-to-day instruction. This article describes how skills instruction can be an important feature of constructivism for teaching special education students.     

Memory abilities in generally gifted and excelling-in-mathematics adolescents

This paper presents part of a multidimensional examination of mathematical giftedness. The present study examined the memory mechanisms associated with general giftedness (G) and excellence in mathematics (E) in four groups of 10th–12th grade students (16–18 years old) varying in levels of G and E. The participants first underwent the Raven test for general ability evaluation and SAT-M — the mathematical excellence tests in order to design the study groups. Afterwards, the students were tested on a battery of three memory tests including tests for short-term (STM) and working memory (WM). The results reveal that the G factor is related to high STM for both phonological loop and phonological central executive mechanisms. It was also found that the E factor is associated with high visual–spatial memory (VSM), in particular with the visual central executive mechanism. An interaction effect was found between G and E factors regarding WM. The central executive mechanism appeared to be related to both G and E factors. In addition, gender differences were shown within the groups. Male participants performed better than their female counterparts on a phonological storage task and a phonological central executive mechanism task. The results can contribute to the theoretical knowledge regarding similarities and differences in memory mechanisms in G and E groups.     

Conceptually congruent actions can promote thought

Can action support thought? Previous work suggests that it can. Here, we examined whether actions that are conceptually congruent with thinking facilitate thinking and whether direct action facilitates performance. We found that young children performed addition, a discrete one-to-one math task, better when using discrete one-to-one actions that matched the number of objects than when using discrete actions that matched the number of sums to be added. They performed number line estimation, a continuous math task, better when using a continuous action in which the time and distance of the action were commensurate with the quantity to be estimated, than when using a discrete action that marked a proportional distance. Action congruence facilitated performance beyond spatial congruence. Furthermore, direct manipulation led to better performance than mediated manipulation. Finding advantages of congruent mappings of thought to action supports the Spraction Theory, which asserts that thought is internalized action, and that re-externalizing thought through congruent actions facilitates thought.     

Examining the Relationship Between Gender DIF and Language Complexity in Mathematics Assessments

This study investigated whether the linguistic complexity of items leads to gender differential item functioning (DIF) on mathematics assessments. Two forms of a mathematics test were developed. The first form consisted of algebra items based on mathematical expressions, terms, and equations. In the second form, the same items were written as word problems without changing their contents and solutions. The test forms were given to a sample of 671 sixth-grade students from 10 middle schools in Turkey. The tests were administered to the students with a 4-week interval. Explanatory item response modeling and logistic regression approaches were used to examine gender DIF. Several word problems were flagged as having gender DIF in favor of female examinees, whereas mathematically expressed forms of the same items did not function differently across male and female examinees. The verbal content of word problems seems to influence the way males and females respond to items.     

初中生感知到的同伴支持与数学学习投入—基于变量为中心和个体为中心的分析

为考察同伴支持对初中生数学学习投入的影响机制,采用问卷法对1177名七、八年级学生感知到的同伴支持、数学认同、数学焦虑和数学学习投入进行测查。结果发现：同伴支持不仅能直接预测初中生的数学学习投入,还通过数学认同经数学焦虑的链式中介作用来预测数学学习投入;对数学认同和数学焦虑的得分进行潜剖面分析,可将学生分为高认同-低焦虑、中认同-中焦虑和低认同-高焦虑三组,同伴支持可预测学生的不同亚组,三组学生的数学学习投入得分存在显著差异。上述发现为促进基础教育阶段学生数学学习投入的教育实践提供了理论依据。