学科领域知识与数学学习的知识表征研究

根据领域知识的结构特点对初中数学学科知识作出改编和重组,形成数学学科领域知识单元进行教学实验,以215名普通初中二年级学生为被试,通过自编问卷和深度访谈考察学科领域知识对知识表征的影响,并探讨了知识表征与数学学业成绩之间的关系。研究发现:(1)学科领域知识可以显著提高学生数学陈述性知识表征全面性和总体水平;(2)学科领域知识可以显著提高学生的程序性知识表征全面性、自动化、组织性和总体水平;(3)认知结构三要素、陈述性知识表征及程序性知识表征与数学成绩显著相关;(4)学优生的陈述性知识表征准确性、总体水平和程序性知识表征组织性、总体水平显著高于中等生和学困生。     

成就目标定向与小学生数学学习投入的关系:学业拖延和数学焦虑的中介作用

采用问卷法对708名小学高年级学生进行调查,以考察成就目标定向、学业拖延、数学焦虑与数学学习投入之间的关系,结果显示：（1）掌握定向和表现-接近定向均能直接正向预测数学学习投入,而表现-回避定向的直接预测作用不显著;（2）掌握定向、表现-接近定向和表现-回避定向均能通过学业拖延来间接预测数学学习投入;（3）掌握定向和表现-回避定向均能通过数学焦虑来间接预测数学学习投入,但表现-接近定向不能通过数学焦虑来间接预测数学学习投入;（4）三种成就目标定向均能通过学业拖延经数学焦虑的多重中介作用来预测数学学习投入。这表明成就目标定向不仅能直接预测,还能通过学业拖延和数学焦虑的多重中介作用,来间接预测小学生数学学习投入。     

听障儿童抑制控制能力特点及其与数学基本能力的关系

采用Flanker实验范式与中国小学生数学基本能力测试量表,以97名听障儿童与97名健听儿童为被试,考察听障儿童抑制控制能力与其数学基本能力的关系。结果发现：（1）听障儿童抑制控制能力水平显著低于健听儿童;（2）听障儿童数学基本能力显著低于健听儿童;（3）听障儿童抑制控制能力与数学基本能力之间相关显著,且抑制控制能力能够预测听障儿童的逻辑思维与空间–视觉能力。     

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.     

儿童早期工作记忆与数学学习的关系

以往研究认为工作记忆对数学学习很重要,但是以往工作记忆和早期数学学习的关系研究结果并不一致。本研究运用元分析的方法回顾了33篇独立研究,含307项相关系数作为效应值,总被试量为42423名平均年龄3~8岁的儿童,旨在探讨工作记忆的3个主成分PL(语音回路)、VSSP(视觉空间画板)、CE(中央执行)与数学学习不同方面之间的关系,以及样本年龄对工作记忆和数学学习相关程度的调节作用。结果显示:工作记忆与数学学习确实存在强相关,工作记忆子成分中,CE与数学学习平均相关的程度最强。并且,CE与数学学习不同方面之间的相关程度不存在显著差异,PL、VSSP与数运算的相关程度比数概念更强,存在显著差异。样本年龄对CE、PL与数学学习之间相关关系存在显著调节作用,对VSSP与数学学习之间的相关关系不存在显著调节作用。文献梳理还发现,以往研究对数学学习的考察,大都聚焦数概念、数运算的内容,未来研究需要关注几何与空间、测量等方面内容。     

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.     

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.     

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.