5～10岁儿童策略优越性及策略选择的个体差异的研究

本研究选取5～10岁的儿童被试144名,使用不同的加法问题测查策略的优越性以及儿童策略选择的个体差异。结果发现：1、在解决加法问题中,各种策略使用率存在显著差异。五岁到七岁儿童计算简单加法问题时使用提取策略,从大数开始数策略和凑十策略的反应时和正确率优于其它策略。2、五岁到六岁儿童使用策略的反应时个体差异不显著,但优生和中等生使用的策略种类明显比差生多;七岁到十岁儿童的策略选择个体差异也不显著,但优生使用提取策略和凑十策略的反应时明显要低于差生。     

8～11岁儿童解决加法等值问题的策略发展特点

本研究选取142名8～11岁儿童进行了加法等值问题测试,采用口头报告的方法考察了儿童解决加法等值问题的策略发展特点。研究表明:(1)儿童在解决加法等值问题中,策略具有多样性;(2)儿童在策略使用的数量上没有显著的年级差异,但在不同学习成绩的被试之间存在明显的不同;(3)总体上看儿童对正确策略的使用基本上都是随着年级的增加在逐渐提高,而对错误策略的使用却相反。     

题目类型对加法认知策略选择影响的比较研究

随机选取小学二、三年级数学学习不良组儿童各30名,数学学习正常组儿童各30名,采用实验法、观察法和口语报告法相结合的方式,考察了两类儿童在解决简单加法题目、复杂加法题目和连加加法题目时,问题结构类型对两类儿童加法策略选择的影响。结果发现,在不同类型加法题目中,小学二、三年级儿童的策略使用表现出对题目的适应性,数学学习正常儿童的适应性特点更加明显。     

5～6岁幼儿加法策略选择及执行特点

以220名5～6岁幼儿为被试,采用个别测查法,考察了幼儿策略选择和策略执行的发展特点.结果表明: (1)5～6岁幼儿能运用多种策略解决加法算术题,包括5种基本加法类型与3种数数亚类型. (2)幼儿主要选择支持性策略. (3)5～6岁幼儿策略执行呈多样性特点,各策略的执行正确率与速度不相同. (4)题目难度对幼儿的策略选择与执行存在影响.     

儿童内包量概念发展的实验研究

以2～5年级学生为被试．系统探讨了儿童速度、浓度内包量概念的发展。研究发现：(1)儿童的内包量概念发展要经历四个阶段;(2)儿童速度概念的形成早于其浓度概念的形成;(3)凋整任务在儿童解决速度内包量问题中优于比较任务;(4)儿童解决内包量概念问题的策略经历从单维向双维、从比差的加法法则向乘法法则的转变。     

5-6岁儿童多单位量比较能力的发展特点

通过计算机呈现任务和记录反应,对5岁、5岁半和6岁儿童解决多单位量比较问题的正确率和反应时进行了考察。研究结果表明:(1)6岁之前的儿童难以正确解决多单位量比较问题,从6岁开始,儿童开始逐渐掌握这种问题的解决方法;(2)在解决多单位量比较问题时,儿童采用了比较较高级单位的策略,而没有对每个单个物体进行计算;(3)进位规则没有对儿童解决多单位量比较问题的正确率和反应时产生显著影响。     

3～5岁儿童基于能力特质进行信任判断的策略及其发展

研究采用对偶选择的范式考察了3～5岁儿童基于能力特质进行信任判断的策略。让144名3～5岁儿童在面对能力强和不挑食这两类人时做出信任判断。结果发现3～4岁儿童的信任判断受老师评价偏向的影响,他们的信任选择与老师评价偏向一致。5岁儿童的信任判断则不受老师评价偏向的影响。这些结果表明3～4岁儿童信任判断的策略是依据特质效价,5岁儿童的策略是依据特质意义。     

小学一～三年级儿童加减法策略选择的发展特点研究

随机选取90名小学一～三年级的儿童为被试,采用实验法和访谈法对儿童解决加减法算术题的策略发展特点进行了探讨。结果发现:1儿童能运用多种策略解决加减法算术题,在解决两个数的算术题时用到了13种策略,在解决三个数的算术题时用到了8种策略。2儿童在解决同一道题时大多能同时运用两种或两种以上的策略。3随着年龄的增长,儿童使用策略的总目呈简约化发展的趋势。4在解决两个数的算术题时,不同年级的儿童在使用出声策略、拆十策略、手势策略、逆算策略、数数策略的次数上差异显著,随着年级的增长其使用频率逐渐降低。5儿童在解决三个数的算术题时,各年级儿童使用出声策略、手势策略、对位策略差异显著,随着年级的增长其使用频率逐渐增高。     

4~8岁儿童认知风格的发展及其对问题解决的影响

认知风格是个体获取和加工信息的一贯模式,影响诸多认知活动。本研究测量了98名4-8岁儿童的认知风格和积木拼图中的问题解决行为,主要发现:（1）4-8岁儿童总体上表现为整体型认知风格,但分析型认知风格随着年龄增长在逐渐发展;（2）认知风格影响问题解决策略：越偏整体型认知风格的儿童越多使用主体参照策略（即先拼主体图形再补充其他部分）,并且越少使用线索推断策略（按照行/列的线索顺序依次拼图）和局部定位策略（根据某一局部图案的具体位置摆放积木）。本实验首次探索了低龄儿童认知风格的年龄差异,发现认知风格在发展早期就已影响问题解决行为。研究结果有助于理解儿童认知风格的发展及其作用,为儿童问题解决能力的培养实践提供一定的理论依据。     

4-5岁幼儿数数行为的规则性与策略化应用特点的研究

本研究的主要目的是考察4-5岁儿童数数行为的规则性和策略化应用特点。研究选取了104名幼儿园中班儿童(年龄范围4-5岁),男女各半,采用现场实验法进行了逐一测查,测查任务为标准计数任务和数字复制任务。结果发现:4-5岁儿童的数数行为已经遵循一些数数规则,如固定顺序原则、一一对应原则和基数原则;但该年龄段的儿童还不会自发地把数数作为问题解决的策略应用于比较两组物体数目的问题上。     

Stability and change in children's division strategies

Age-related changes in children's performance on simple division problems (e.g., 6/2, 72/9) were investigated by asking children in Grades 4 through 7 to solve 32 simple division problems. Differences in performance were found across grade, with younger children performing more slowly and less accurately than older children. Problem size effects were also found in that children were faster and more accurate on small problems than on large problems. Two strategies changed across age, with children in Grade 4 relying heavily on the strategy of "addition" (adding the divisor until the dividend was reached) to solve the problems and children in Grades 5 through 7 relying primarily on the strategy of "multiplication" (recasting the division problem as a multiplication problem) to solve the problems. Surprisingly, the frequency of direct retrieval (retrieving the answer directly from memory) did not increase across grade and never became the dominant strategy of choice. Reasons for why retrieval use remains infrequent and age invariant are discussed. Overall, the results suggest that division is a unique operation and that the continued study of division may have implications for further understanding of how procedural and conceptual knowledge of arithmetic develops.     

不同任务类型条件下4～6年级儿童比例推理策略的表现

随机选取小学4~6年级被试86名,从辅助策略、比例推理策略的策略选择和策略效用三方面,通过五种类型的天平任务考察儿童比例推理策略的表现。结果表明:(1)儿童最常使用手指动作辅助加工基本数量信息。辅助策略的使用率随年龄增长而减少,五年级开始使用出声思维,反映出元认知能力的发展。(2)在正式学习比例知识之前,各年级儿童都能使用两种以上策略,也能根据任务难度自发产生新策略,具备策略选择的多样性和适应性。其中,三个年级均能使用定性比例推理策略(双维策略,IIIA策略,补偿策略),表明儿童初步认识了距离和重量两个维度的共变关系。此外,六年级儿童能使用"运货车策略"将冲突问题灵活地化解为简单问题。(3)儿童的错误策略表现为:在冲突任务中盲目使用补偿策略、简单策略或加法策略。(4)分层回归分析表明,在控制年龄后,儿童的一般推理能力越高,其对重量策略的依赖性越低,且可能更容易发掘距离维度的意义,其使用运货车策略的频次更多。此外,一般推理能力对解决冲突类天平任务的正确次数有正向预测作用。     

Children’s strategies in complex arithmetic

Strategies used to solve two-digit addition problems (e.g., 27 + 48, Experiment 1) and two-digit subtraction problems (e.g., 73 – 59, Experiment 2) were investigated in adults and in children from Grades 3, 5, and 7. Participants were tested in choice and no-choice conditions. Results showed that (a) participants used the full decomposition strategy more often than the partial decomposition strategy to solve addition problems but used both strategies equally often to solve subtraction problems; (b) strategy use and execution were influenced by participants’ age, problem features, relative strategy performance, and whether the problems were displayed horizontally or vertically; and (c) age-related changes in complex arithmetic concern relative strategy use and execution as well as the relative influences of problem characteristics, strategy characteristics, and problem presentation on strategy choices and strategy performance. Implications of these findings for understanding age-related changes in strategic aspects of complex arithmetic performance are discussed.     

Context Effects in Children's Selection and Use of Simple Arithmetic Strategies

Six- and 7-year-old children computed moves on a board game from dice over 3 sessions (game context) and also solved simple, aurally presented addition problems (academic context), corresponding to the dice rolls made in the game. Children displayed multiple and variable use of addition strategies in both the game and academic contexts, although there were significant differences in the strategies used and patterns of performance between the 2 contexts. Children used more sophisticated strategies and made more errors during the academic than the game context. The relation between strategy use, variability, and errors also varied between the 2 conditions, as did the selection of strategies children used for solving identical addition problems. These findings support selectionist models of cognitive development and illustrate the potent role of context in young children's strategy use.     

Strategy choices in simple and complex addition: Contributions of working memory and counting knowledge for children with mathematical disability

Groups of first-grade (mean age = 82 months), third-grade (mean age = 107 months), and fifth-grade (mean age = 131 months) children with a learning disability in mathematics (MD, n = 58) and their normally achieving peers (n = 91) were administered tasks that assessed their knowledge of counting principles, working memory, and the strategies used to solve simple (4+3) and complex (16+8) addition problems. In all grades, the children with MD showed a working memory deficit, and in first grade, the children with MD used less sophisticated strategies and committed more errors while solving simple and complex addition problems. The group differences in strategy usage and accuracy were related, in part, to the group difference in working memory and to group and individual differences in counting knowledge. Across grade-level and group, the switch from simple to complex addition problems resulted in a shift in the mix of problem-solving strategies. Individual differences in the strategy mix and in the strategy shift were related, in part, to individual differences in working memory capacity and counting knowledge.     

Children’s use of multiple and variable addition strategies in a game context

Developmental and contextual effects on children’s addition strategies were assessed in preschool, kindergarten and first‐grade children’s strategy use while playing a board game (‘Chutes and Ladders’), using one or two dice to compute moves. Children of all ages displayed multiple‐ and variable‐strategy use, and there was a progression toward more sophisticated strategy use with age. Different patterns of strategy use in the two‐dice condition were observed as a function of whether children began the game with one versus two dice and for children who could recognize (as opposed to having to count) die roles of ‘5’ and ‘6’ in the one‐die condition. An examination of latencies indicated that more noncounting (start‐up) time was required to execute the MIN than the SUM strategy. Children showed significantly greater speed and accuracy when adding numbers during the game than in the math problems that followed. The findings reflect young children’s flexible use of strategies and extend Siegler’s adaptive strategy choice model to the development of simple addition strategies in an everyday context.     

数字记忆广度对策略应用模式的影响──中美儿童计算能力差异的比较研究

本研究旨在了解中美儿童在策略运用模式上的差异是否与数字记忆广度有关。为此,分别测验了中美幼儿园儿童的加法技能,数字记忆广度,并通过一组计算机呈现的加法作业评估儿童使用的解题策略。结果表明,中国儿童的基本算术技能和数学记忆广度均超过同龄的美国儿童。在解题时,中国儿童多使用效率较高的言语计算策略,美国儿童则多采用计数手指策略,在言语计数策略和检索策略的加工速度上中国儿童也超过美国儿童。相关分析表明．策略应用模式的文化差异与数字记忆广度有关。比较大的工作记忆容量增加了数字线索可利用的资源,为儿童早期言语计数能力的发展提供了有利条件。     

比较研究-影响中美儿童计算能力差异的认知因素

本研究要确定中美儿童基本计算技能的差异是否与他们使用的解题策略和基本加工过程的速度有关。为此,对中美两国的一年级儿童进行了书面计算能力测验,以及一组计算机呈现的加法作业。中国儿童在计算能力测验上表现出3:1的操作优势。中美儿童使用的解题策略种类一样,但是,中国儿童在策略综合运用的发展程度上超过美国儿童,检索策略的加工速度也超过美国儿童。显然,策略运用和加工速度的差异促成了中国儿童在计算能力测验上的优势.