The construct and measurement of spontaneous attention to a number

The Spontaneous Attention to a Number (SAN) construct serves a different purpose than Hannula-Sormunen and colleagues’ Spontaneous Focus on Number (SFON) construct. As an extension of Eleanor J. Gibson’s differentiation theory, the premise of SAN is that children’s step-wise construction of small number concepts enables them to perceptually differentiate among increasingly larger numbers—to distinguish reliably between “oneness” or “twoness” and larger numbers, then between “threeness” and “larger numbers,” and eventually between “fourness” and larger numbers. In contrast, SFON refers to the tendency to attend to numbers in general—an attentional process that, unlike SAN, is separate from enumeration skill. Not surprisingly, then, although the prototype for both the SAN and SFON tasks is Nancy C. Jordan and colleagues’ non-directive nonverbal number task, the independent development of the SAN and SFON tasks resulted in key differences in how they are administered and scored and to whom they are administered.     

The role of planning in different mathematical skills

Despite the fact that planning has been found to be a significant predictor of reading (particularly of reading comprehension), much less is known about its contribution to mathematics. The purpose of this study was to examine the role of two levels of planning (operation planning and action planning) in three mathematical skills (calculation fluency, math problem-solving, and math reasoning). Eighty Grade 2 children from Shanghai, China were assessed on measures of nonverbal cognitive ability (nonverbal matrices), working memory (digit span backwards and N-back), operation planning (matching numbers, planned codes, and planned search), action planning (crack the code), and mathematics (calculation fluency, math problem-solving, and math reasoning). The results of regression analyses showed that both levels of planning accounted for unique variance in mathematics over and above the effects of nonverbal cognitive ability and working memory. The effects of action planning were particularly strong in math problem-solving. These findings suggest that measures of planning could be used along with measures of working memory to detect children at-risk for mathematics disabilities and that intervention programmes targeting planning could be developed to boost children's mathematics performance.     

教师变量对小学生数学学习观影响的多层线性分析

32名小学数学教师与这些教师所教班级的1691名学生参与了本研究.两个测量工具评价了教师的数学学科知识与学科教学知识,对教师的55节数学课进行了录像;并按照学习任务的认知水平与课堂对话的特点进行了编码,采用问卷法测查了学生对数学学习的看法与态度.多水平分析表明:教师的学科教学知识、课堂学习任务的认知水平、课堂师生对话的权威来源与教师运用学生想法的程度对学生数学学习观具有显著预测作用;教师的学科知识对学生数学学习观的预测未达到显著性水平.     

Teaching math skills to at-risk students using home-based peer tutoring

Home-based peer tutoring was used to teach math skills to 4 girls with deficits in mathematics and histories of abuse or neglect. Girls living in the same home formed tutoring dyads, and each participant served as both the peer tutor and the tutee during the course of the study. At the initiation of the tutoring intervention, an expert tutor provided multiple 3-min tutoring sessions to the designated peer tutor on three or four mathematics skills. The peer tutor concurrently provided 3-min tutoring sessions on the same skills to the tutee using a multiple baseline design. Results showed that participants improved their performance on all target skills. Additional interventions were implemented for some skills to improve accuracy further. Maintenance tests were also administered after 3 to 5 months of no practice on the skills. Results showed that tutors and tutees maintained their accuracy on 7 of the 12 skills assessed.     

数学焦虑对心算加工的影响

近20年来,研究者逐渐注意到心算加工会受到数学焦虑的影响。文章主要介绍了数学焦虑的涵义、测量及其对心算加工的影响和理论解释。数学焦虑对心算的影响与问题大小效应关系密切。数学焦虑对简单心算问题的影响不大,随着问题难度的增加,数学焦虑效应逐渐明显。此外,数学焦虑还影响着心算的编码、提取以及策略选择等过程。目前的研究多倾向证明加工效能理论,同时抑制理论也是个可选择的理论解释,只是尚缺乏验证研究     

How to Measure and Explain Achievement Change in Large-Scale Assessments: A Rejoinder

In this rejoinder, we discuss substantive and methodological validity issues of large-scale assessments of trends in student achievement, commenting on the discussion paper by Van den Heuvel-Panhuizen, Robitzsch, Treffers, and Köller (2009). We focus on methodological challenges in deciding what to measure, how to measure it, and how to foster stability. Next, we discuss what to do with trends that are found. Finally, we reflect on how the research findings were received.     

数学日记对数学学习有效性的实验研究

本研究对高中数学学科进行实验研究,以探讨数学日记对主观数学学习效能感与客观数学成绩的影响.结果显示数学日记能显著提高学生的数学学习效能感,有助于数学学习成绩的提高,尤其对数学差生更具有显著作用;同时数学日记还能使学生对数学学习的信念与数学学习的实效协调起来,获得一致性效应.结论是数学日记能使学生形成一种有效性的学习.     

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.