【作者】 张莹；

【导师】 邓赐平；

【作者基本信息】 华东师范大学 ， 发展与教育心理学， 2011， 硕士

【摘要】 计算能力是小学生数学教学的基础内容,心算能力是计算能力的一个重要体现。一方面,关于心算的认知研究是数认知领域的重要选题；另一方面,对于儿童心算能力发展的考察也是基础认知研究与学校教学应用的结合点。因此,本研究选择小学生心算为研究对象,考察心算各加工阶段的特点,小学生心算的发展,以及心算能力与其他基本认知能力间的关联。尽管对于心算的考察有着诸多的研究视角和方法,本研究选择小学生整数加减乘除心算为研究对象。具体来说,本研究1.通过不同的认知任务考察心算不同加工阶段(表征、提取、执行)的特点,以及儿童在不同加工阶段的发展；2.通过心算测验考察儿童心算发展的特点；3.考察小学生基本认知能力(工作记忆、PASS模型中的4个认知过程、注意不同方面)与心算能力的关联。本研究中被试为上海市某普通小学三、四、五年级各一个班级的学生共计102人,男生49人,女生53人。研究表明：1.心算加工在表征、提取及程序执行几个阶段上有各自的特点。在表征阶段,被试所犯符号输入错误可能高于操作数错误；在输入阶段信息输入越清晰,整个加工过程所用时间就越短。在提取阶段,被试提取乘法算术事实好于提取加法算术事实。在提取阶段,过快的提取常常造成提取错误。在执行阶段,进位的执行需要在个位时存储进位操作,在十位时执行该操作,更多的加工操作会使整个加工的正确率降低,反应时变长。2.从三年级到五年级,学生心算能力显著提高,这种提高主要体现在速度上。学生的表征和提取加工显著提高,这两个阶段上的年级差异也体现在速度上。学生的执行加工也有显著提升,体现在加法执行的正确率和反应时均有显著提高；乘法执行的正确率有显著提高。3.工作记忆广度方面,句子广度、复杂空间广度正确率和简单空间广度反应时对心算成绩有显著的预测作用。PASS模型中4个认知过程中,仅有注意过程对心算得分有显著的预测作用；而注意的各个方面(持续性注意、选择性注意、执行控制／转换)对心算均有一定的预测作用。更多还原

【Abstract】 Calculation skill is the basic content of mathematics education in primary school, and mental arithmetic ability is important representation of calculation skill. On the one hand, cognitive research on mental arithmetic is one of the important topics in the numerical cognition domain; on the other hand, the study of children’s mental arithmetic is also the point of integration between the fundamental cognition research and school applications. Therefore, the study chose pupils’mental arithmetic ability as the object, exploring the characteristics of mental arithmetic in different processing stages, the development of mental arithmetic ability and the relationship between mental arithmetic ability and those fundamental cognitive abilities.Although there are various perspectives and methods on mental arithmetic study, this study chose four arithmetic operations of integer as the object. In details, this study aimed at:1. Using different cognitive tasks, exploring the characteristics of different cognitive processing stages (representing, retrieval, executing) during mental calculation and the children’s development at different stages; 2. Using mental calculation test, studying the developmental characteristics of the children’s mental arithmetic ability; 3. Finding the relationship between mental arithmetic ability and those fundamental cognitive abilities (working memory, four cognitive processes in PASS model, different aspects of attention).Participants of the study are recruited from an ordinary primary school in Shanghai. Total 102 pupils come from three classes from Grade 3 to Grade 5,49 boys and 53 girls.The results indicated that:1. Mental calculation processing show different characteristics in different processing stages. In representing phase, the participants commits more operator errors than operand errors and it takes more processing time if the input information is unclear and unsharp. In retrieval phase, the participants retrieve multiplication facts better than addition facts. In executing phase, problems with carrying operation needs take more time to execute, storing the carry needs at units calculation and executing carry operation at tens calculation.2. From third grade to fifth grade, the pupils’ mental calculation ability improves significantly, and this improvement is embodied in processing speed rather than accuracy. On representing phase and retrieval phase, the developmental improvement is reflected in the speed. On executing phase, the developmental improvement is reflected both in speed and accuracy.3. With regard to working memory spans, sentence span, the accuracy of complex spatial span and the speed of simple spatial span predicts mental arithmetic ability significantly. In terms of PASS model, only attention process predicts mental calculation significantly. As for various aspects of attention, they all have a certain extent predictive effect on mental calculation.更多还原