算术应用题的分类结果与数学成绩关系研究

以算术应用题为材料,探讨了不同年级、不同数学成绩学生对算术应用题的分类结果及其与数学成绩的关系。结果表明:不同年级学生对算术应用题分类结果差异显著;数学成绩优生与数学成绩差生对算术应用题分类结果存在差异。     

Improved set‐size labeling mediates the effect of a counting intervention on children's understanding of cardinality

How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively, it may delay development by decreasing the need for a comprehensive abstract principle to understand and label exact numerosities (Piantadosi et al., 2012). In this study, preschoolers (N = 106, M_age = 4;8) were randomly assigned to one of three conditions: (a) count‐and‐label, wherein children spent 6 weeks both counting and labeling sets arranged in canonical patterns like pips on a die; (b) label‐first,wherein children spent the first 3 weeks learning to label the set sizes without counting before spending 3 weeks identical to the count‐and‐label condition; (c) print referencing control. Both counting conditions improved understanding of cardinality through increases in children's ability to label set sizes without counting. In addition to this indirect effect, there was a direct effect of the count‐and‐label condition on progress toward understanding of cardinality. Results highlight the roles of set labeling and equifinality in the development of children's understanding of number concepts.     

两种类型数学困难儿童的执行水平

使用Crack the Code任务考察单纯型与混合型数学困难小学儿童的执行水平,结果发现:单纯型数学困难儿童在对认知资源要求较高的任务上的执行水平显著低于数学优良生,但在认知要求较低的任务上二者之间没有显著差异;混合型数学困难儿童执行水平最低,在两个难度水平执行任务上的表现均显著差于数学优良生、单纯型数学困难儿童.小学儿童执行水平年级差异似乎主要表现在认知负荷较高的任务上,1年级学生与3、5年级学生的执行水平存在显著差异.     

小学一年级数感不良儿童的筛查与动态干预

首先编制测查小学一年级儿童数感发展水平的测验, 以筛查出数感发展不良儿童并进行数量转换和数量估计的动态干预。将数感不良儿童分为干预组(29人)和控制组(27人), 并以数感正常儿童作为对照组(40人), 以比较干预训练对儿童数感水平和与之密切相关的计算流畅性的促进作用。同时进一步考查数感和计算流畅性的作用方向。结果发现：(1)所编制的儿童数感发展测验信效度良好, 能有效评估一年级儿童的数感水平; (2)数感不良儿童经干预后, 其数感水平较控制组有了明显改善, 计算流畅性水平也显著提高, 甚至达到正常组儿童的水平; (3)数感对计算流畅性有明显的预测作用, 是计算流畅性的基础。     

Student Preference for Explicit Timing and Interspersal Procedures as a Function of Math Problem Completion Rates: Testing the Discrete Task Completion Hypothesis

A within-subjects design was used to compare explicit timing and interspersal with college students. Students were given 3 minutes to complete problems on the explicit timing assignment (25 problems, 3 digits –3 digits) and the interspersal assignment (25 similar problems and 10 problems, 1 digit –1 digit). Results indicated that: (a) students completed more total problems during interspersal for both trials, (b) students completed more target problems during explicit timing for the second trial, and (c) students only preferred interspersal for the first trial. The data from trial one fit the discrete task completion hypothesis and matching law, yet the data from trial two do not match as closely (Skinner, 2002). Discussion focuses on continued need for more research on academic interventions, comparing academic interventions, the discrete task completion hypothesis, and the matching law.     

An Experimental Analysis of Mathematics Instructional Components: Examining the Effects of Student-Selected Versus Empirically-Selected Interventions

Within the context of an experimental analysis, the current study examined the effects of student- and empirically-selected interventions on the mathematics computational fluency of three elementary-aged students. For all of the participants, the empirically-selected intervention resulted in higher levels of computational fluency then the student-selected intervention. These results suggest that empirically-selected interventions may enhance the mathematics computational fluency of students experiencing mathematics problems. However, individual responsiveness to empirically-selected interventions suggests the importance of conducting brief experimental analyses to determine the most efficacious intervention. The implication of these results for intervention selection and incorporating choice-making opportunities into academic interventions are discussed.     

Solution Strategies and Achievement in Dutch Complex Arithmetic: Latent Variable Modeling of Change

In the Netherlands, national assessments at the end of primary school (Grade 6) show a decline of achievement on problems of complex or written arithmetic over the last two decades. The present study aims at contributing to an explanation of the large achievement decrease on complex division, by investigating the strategies students used in solving the division problems in the two most recent assessments carried out in 1997 and in 2004. The students’ strategies were classified into four categories. A data set resulted with two types of repeated observations within students: the nominal strategies and the dichotomous achievement scores (correct/incorrect) on the items administered.It is argued that latent variable modeling methodology is appropriate to analyze these data. First, latent class analyses with year of assessment as a covariate were carried out on the multivariate nominal strategy variables. Results showed a shift from application of the traditional long division algorithm in 1997, to the less accurate strategy of stating an answer without writing down any notes or calculations in 2004, especially for boys. Second, explanatory IRT analyses showed that the three main strategies were significantly less accurate in 2004 than they were in 1997.     

珠心算训练儿童加法心算的ERP早成分研究

采用事件相关电位(ERP)的方法,对32名儿童进行了双位数加法心算实验,探讨了珠心算训练方式对儿童加法心算加工早期感知觉的影响。研究结果表明,与非珠心算训练儿童相比,在加法心算过程的早期阶段,珠心算训练儿童枕部P1、额中央区的N1波幅增大,而颞枕区N170以及额中央区P2波幅减小。本研究结果发现珠心算训练对儿童心算过程的早期感知有显著影响。     

Self-recording and goal-setting: Effects on on-task and math productivity of low-achieving Korean elementary school students

Using an alternating treatments design, we investigated the effects of self-recording and goal-setting on the on-task behavior and the mathematics productivity of five low-achieving elementary school students in a group of eleven students in Korea. We also examined which intervention students preferred after they experienced self-recording and goal-setting. Visual analyses of the data showed (a) increases in students' on-task and mathematics productivity levels contingent upon the implementation of both self-recording and goal-setting, (b) no differential effects of the two interventions, and (c) students' general preference of goal-setting to self recording. We interpreted these results as indicating that both self-recording and goal-setting are effective self-management strategies, but practitioners must consider the features of the interventions before selecting one from them, and future researchers must examine the effect of combining the two procedures.     

Can Constructive Mathematics be Applied in Physics?

The nature of modern constructive mathematics, and its applications, actual and potential, to classical and quantum physics, are discussed.