数学家庭作业动机量表在中国青少年群体中的信效度检验

目的:在中国青少年中对数学家庭作业动机量表进行修订并考察其信效度。方法:采用方便取样选取762名青少年,对数学家庭作业动机量表进行项目分析、探索性因素分析、验证性因素分析、测量等值性检验以及信效度分析。结果:中文版数学家庭作业动机量表包括认同调节、内部动机、外在调节和内摄调节4个因素,并具有跨性别和跨年龄组的测量等值性以及良好的效标效度和信度。结论:修订后的数学家庭作业动机量表具有良好的心理测量学指标,可以作为测量和评估中国青少年数学家庭作业动机的有效工具。     

A Negationless Interpretation of Intuitionistic Theories. I

The present work contains an axiomatic treatment of some parts of the restricted version of intuitionistic mathematics advocated by G. F. C. Griss, also known as negationless intuitionistic mathematics. Formal systems NPC, NA, and FIM ^N for negationless predicate logic, arithmetic, and analysis are proposed. Our Theorem 4 in Section 2 asserts the translatability of Heyting's arithmetic HAinto NA. The result can in fact be extended to a large class of intuitionistic theories based on HAand their negationless counterparts. For instance, in Section 3 this is shown for Kleene's system of intuitionistic analysis FIMand our FIM ^N . This revised version was published online in June 2006 with corrections to the Cover Date.     

Who benefits the most? Teacher expectations and their relation with students’ achievement in mathematics in primary school

Over the past 50 years, many studies have investigated the impact of teacher expectations on student achievement and indicated small to moderate effects. Currently, it is still unclear which student-related factors (e.g. socioeconomic status, or gender) moderate the expectation effect. There is still a need to gain a better understanding of the relation between teacher expectations and students' characteristics. The present study aims to examine the accuracy of teacher expectations as well as student-related moderators of the expectation effects on students' achievement. The analyses are based on data from a longitudinal study including 28 primary school teachers and their students (N = 509). The results show that high expectations of teachers correlated positively with student achievement in mathematics, although no significant moderating effects were found. These findings strengthen the importance of ensuring high teacher expectations for all students.     

高中生数学元认知水平调查问卷的设计与编制*

对于元认知能力的评价和测试一直以来都是研究的难点,特别是就数学学科而言,已有研究多围绕数学问题解决过程中元认知监控水平的评价以及能力的培养展开,鲜有全面评价学生数学学习元认知水平的问卷。同时,没有针对高中生编制的元认知水平调查问卷。故本研究在已有研究的基础上,对已有的问卷进行修正和完善,通过征求专家意见与样本测试和数据分析,形成《高中生数学元认知水平调查问卷》。该问卷具有较好的内容效度和结构效度。信度方面,问卷整体的内部信度为0.952,分半信度为0.931,重测信度为0.946,说明问卷具有很好的内部一致性和测量稳定性。     

高效率数学学习高中生数学成绩的影响路径

为探究高效率数学学习高中生的数学学习成绩的影响因素的不同作用效果,以及这些影响因素间存在的作用路径,通过目标抽样,选取102名高中生为被试开展调查研究。通过数据分析,并依托AMOS软件的模型界定搜寻功能进行路径分析,获得研究结论：（1）数学元认知、数学非智力因素、智力因素、数学学习策略和数学素养这5个变量对高效率数学学习高中生的数学学习成绩的作用效果值依次递减。（2）5个变量通过两条主要路径影响高效率数学学习高中生的数学学习成绩,一是智力因素与数学素养构成的影响路径,二是数学元认知、数学非智力因素以及数学学习策略构成的影响路径。     

Racing dragons and remembering aliens: Benefits of playing number and working memory games on kindergartners' numerical knowledge

Sources that contribute to variation in mathematical achievement include both numerical knowledge and general underlying cognitive processing abilities. The current study tested the benefits of tablet‐based training games that targeted each of these areas for improving the mathematical knowledge of kindergarten‐age children. We hypothesized that playing a number‐based game targeting numerical magnitude knowledge would improve children's broader numerical skills. We also hypothesized that the benefits of playing a working memory (WM) game would transfer to children's numerical knowledge given its important underlying role in mathematics achievement. Kindergarteners from diverse backgrounds (n = 148; 52% girls; M_age = 71.87 months) were randomly assigned to either play a number‐based game, a WM game, or a control game on a tablet for 10 sessions. Structural equation modeling was used to model children's learning gains in mathematics and WM across time. Overall, our results suggest that playing the number game improved kindergarten children's numerical knowledge at the latent level, and these improvements remained stable as assessed 1 month later. However, children in the WM group did not improve their numerical knowledge compared to children in the control condition. Playing both the number game and WM game improved children's WM at the latent level. Importantly, the WM group continued to improve their WM for at least a month after playing the games. The results demonstrate that computerized games that target both domain‐specific and domain‐general skills can benefit a broad range of kindergarten‐aged children.     

First demonstration of effective spatial training for near transfer to spatial performance and far transfer to a range of mathematics skills at 8 years

There is evidence that spatial thinking is malleable, and that spatial and mathematical skills are associated (Mix et al. [2016] Journal of Experimental Psychology: General, 145, 1206; Mix et al. [2017] Journal of Cognition and Development, 18, 465; Uttal et al. [2013] Psychological Bulletin, 139, 352). However, few studies have investigated transfer of spatial training gains to mathematics outcomes in children, and no known studies have compared different modes of spatial instruction (explicit vs. implicit instruction). Based on a sample of 250 participants, this study compared the effectiveness of explicit and implicit spatial instruction in eliciting near transfer (to the specific spatial skills trained), intermediate transfer (to untrained spatial skills) and far transfer (to mathematics domains) at age 8. Spatial scaling and mental rotation skills were chosen as training targets as previous studies have found, and proposed explanations for, associations between these skills and mathematics in children of this age (Journal of Experimental Psychology: General, 145, 2016 and 1206). In this study, spatial training led to near, intermediate and far transfer of gains. Mental visualization and proportional reasoning were proposed to explain far transfer from mental rotation and spatial scaling skills respectively. For most outcomes, except for geometry, there was no difference in the effectiveness of implicit (practice with feedback) compared to explicit instruction (instructional videos). From a theoretical perspective, the study identified a specific causal effect of spatial skills on mathematics skills in children. Practically, the results also highlight the potential of instructional videos as a method of introducing spatial thinking into the classroom.     

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。     

Understanding linear and exponential growth: Searching for the roots in 6- to 9-year-olds

Previous studies have suggested that children as young as 9 years old have developed an understanding of non-linear growth processes prior to formal education. The present experiment aimed at investigating this competency in even younger samples (i.e., in kindergartners, first, and third graders, ages 6, 7 and 9, respectively). Children (N = 90) solved non-verbal inductive reasoning tasks by forecasting linear and exponential growth. While children of all ages forecasted linear growth adequately, exponential growth was also estimated remarkably well. Surprisingly, kindergartners and third graders showed similar high achievement concerning the magnitude and curve shape of forecasts, whereas first graders performed significantly worse. We concluded that primary knowledge of both linearity and non-linearity exists even in kindergartners. However, children's understanding is quite fragile, as their performance was strongly affected by task sequence: Children underestimated exponential growth when the previous task required a forecast of linear growth, and overestimated linear growth when the previous task required forecasting of exponential growth.     

Hilbert's epsilon as an operator of indefinite committed choice

Hilbert and Bernays avoided overspecification of Hilbert's ε-operator. They axiomatized only what was relevant for their proof-theoretic investigations. Semantically, this left the ε-operator underspecified. After briefly reviewing the literature on semantics of Hilbert's epsilon operator, we propose a new semantics with the following features: We avoid overspecification (such as right-uniqueness), but admit indefinite choice, committed choice, and classical logics. Moreover, our semantics for the ε simplifies proof search and is natural in the sense that it mirrors some cases of referential interpretation of indefinite articles in natural language.