问题解决中图式与策略的关系:来自表征复杂性模型的说明

采用口语报告法收集了26名小学三年级儿童解决两道复杂的算术应用题时的口语报告和作业资料,探讨了问题解决中图式与策略的关系。结果发现,对二者关系的解释要以问题表征复杂性为中介：如果被试的关系图式水平较高,表征复杂性(特别是表征深度)也会较大,相应会选择领域专门性更强的快捷策略;如果缺乏必需的关系图式。表征深度就降低,甚至不能正确表征问题,这时只好使用常规策略甚至错误策略。这个结论适用于有多种表征和解题方式的问题中。     

对一个初级运动系统的认知

本研究设计了一个模拟的初级运动系统,让14名五至十岁的被试解决该系统中的车速比较问题,通过收集和分析被试解题的原始材料,结果发现:(1)被试解题中存在两类不同性质的错误:知识性错误和策略性错误;(2)在这些被试的解题行为中,存在着四种不同的策略,这些不同的解题策略,在一定程度上反映了被试的认知发展水平。根据这些结果,作者对问题解决中的知识和策略的性质及其关系,作了进一步的讨论。     

运用部分记分模型研究不同解题策略问题

1问题的提出在许多心理和教育测验中通常采用二值记分的方法，即答对1题得1分，答错1题得0分。但是人们可以发现，对于同一道题目，不同的被试可能会采用不同的解题策略。有些策略指导下的解题步骤比较繁琐，有些策略却能引导被试巧妙而简洁地得到问题的解，这和被试对问题的认知水平有关。显然对于用不同策略答对同一道题目的被试给予相同的分数是不合理的，那么应该如何确定不同解题策略水平之间的差异呢‘！假设对于某一道题目有两种不同的策略，一种是较低水平的，另一种是较高水平的，我们若给采用较低水平策略答对题目的被试得1分，那…     

未意识到错误影响错误后调整的电生理证据

现有研究一致认为意识到错误可引起错误后调整, 但是未意识到错误能否促使个体进行错误后调整尚存争议。本实验采用基于go/no-go范式的错误意识任务考察上述问题, 并根据被试对自己按键反应正误主观报告将no-go错误反应分为意识到错误和未意识到错误。行为结果发现, 意识到错误和未意识到错误后正确率均显著高于正确击中试次(正确go试次)后正确率; 但是, 意识到错误后试次反应时显著快于正确击中后反应时, 未意识到错误后反应时显著慢于正确击中后反应时。该结果表明两类错误均优化了错误后行为表现, 但是意识到错误后被试调整速度加快, 未意识到错误后被试调整速度减慢。进而, 时频分析发现意识到错误相较于未意识到错误诱发显著更强的alpha波能量。并且, 前者在错误意识主观报告前已诱发alpha波, 后者在错误意识主观报告反应后诱发alpha波。该结果表明意识到错误一直处于持续的注意监控中, 而未意识到错误是任务引起的暂时注意控制。因此, 本实验说明错误意识影响错误后调整, 意识到错误可能采用类似主动性控制的策略调节错误后行为, 而未意识到错误可能采用类似反应性控制的策略调节错误后行为。     

表征变化及其影响因素的微观发生研究

Karmiloff-Smith的表征重述理论认为表征重述是人类获取知识的重要途径,并且表征变化的过程包括程序、元程序和概念化三个阶段。采用微观发生法（包括前测、练习和迁移3个阶段,共8个期间）,以数字分解组合任务为研究材料,探讨了120名小学一、二年级儿童问题解决中的表征变化及所受年龄和练习模式等因素的影响。结果表明,前测中存在发展性差异,即二年级儿童达到概念化阶段的人数显著多于一年级儿童,但前测处于程序阶段的儿童接受5次解题练习过程中以及在近迁移题目上都没有表现出年级差异,而在远迁移题目上二年级儿童的完成情况好于一年级儿童。练习模式对表征变化的影响主要体现在三个方面：（1）从变化的路线看,与简单模式相比,复杂模式更能促进儿童的表征发生变化,而且这时儿童表征变化的路线更丰富,表征变化发生循环的人数比例也更高。（2）从变化的速度看,复杂模式下儿童在插入难题的两次练习期间表征变化比较迅速,其余期间变化较小;简单模式下儿童在第二次和第三次练习期间表征变化比较迅速,随后变化比较平稳。（3）从变化的广度看,练习中所获表征能力（在最后三次练习中达到元程序或概念化阶段）的推广,无论是在近迁移题还是远迁移题上两种练习模式之下的被试没有明显差异;但两组被试在近迁移题上的表现均好于远迁移题     

提取练习在记忆保持与迁移中的优势效应：基于认知负荷理论的解释

提取练习比建构概念图更有利于记忆保持和迁移的研究结果尚存在争议。依据认知负荷的3个成分,设计两个实验探究前期知识水平与策略复杂性对以上两种学习策略有效性的影响。结果表明：(1)前期知识水平的主效应不显著,但是与学习策略之间存在交互作用：在提取练习策略条件下,高前期知识水平的被试与低前期知识水平的被试在记忆保持和迁移上的正确率没有显著差异,但是在建构概念图策略条件下,高前期知识水平的被试在记忆保持和迁移上的正确率显著地高于低前期知识水平的被试;(2)当降低概念图的难度后,被试使用建构部分概念图策略产生的认知负荷与使用提取练习策略相比显著降低,并且其在学习阶段学习到的知识量显著地高于使用提取练习策略的结果,但是在最终测试上,其记忆保持与迁移的正确率与使用提取练习策略并没有显著差异,策略的复杂性增加了学习者的额外负荷,但是对策略有效性的发挥却不具有决定性影响。以上结果说明提取练习策略之所以比建构概念图策略更具优势,不是因为其策略本身更易掌握,而是因为其与建构概念图策略相比不受学习者前期知识水平的影响。这意味着认知负荷理论可以很好地解释提取练习在记忆保持与迁移中产生优势效应的内部机制,并进一步证实提取练习与精细编码不同,具有独特的加工机制。     

解决几何问题的思惟过程

本研究探讨了初中学生解几何题的思惟过程。所用的方法是要求被试证题时出声想,收集他们证题时的口语材料,并对这些材料作了初步的分析。 结果表明: 一、几何问题解决过程往往包含有假设验证的过程。其中,被试如果能从问题的情境中正确地辨认出某种模式,就能唤起与解题有关的知识。 二、两组被试在解题的时间和过程方面有一些差异。甲组被试(解题经验较多)解题的平均时间是乙组被试的三分之一。甲组被试能很快地把他原来熟悉的模式辨认出来。乙组被试(相当于初学者)多半要作一些无效的尝试才有可能正确地认出模式。甲组被试比乙组被试善于交替运用逆推和顺推的搜索策略以及其他有效的策略和办法。     

运用规则空间模型识别解题中的认知错误

运用规则空间模型识别学生解题中的认知错误,该模型将认知心理学,项目反应理论和数据库的代数理论相结合,将被试的二值反应模式映射为笛卡尔乘积空间的一组序偶,然后计算被试和错误规则在该空间的代表性位置之间的马氏距离,并通过贝叶斯决策准则划分被试的错误类型,根据６４４名中学生对３０个数学题目的反应,识别出其中８６％的学生可以被划分人１８种认知错误类型中。     

问题表征过程的一项研究

问题表征是解决问题时理解问题的方式．本研究选用智力数学题为实验作业,通过详细分析３４名大学生被试的问题表征环节及他们问题解决的结果,探讨问题表征中的信息加工过程及其对问题解决结果的影响．实验结果表明：（１）正确的问题表征是解决问题的必要前提,在错误的或者不完整的问题空间中进行搜索不可能求得问题的正确解．（２）问题表征是对问题信息的提取和理解的过程,问题规则在问题表征中起重要作用．（３）在问题表征过程中,导致建构出错误的或者不完整的问题空间的因素包括：信息遗漏（未能将问题的有关信息全部提取出来）,信息误解（对某些问题信息做了错误的分析和理解）,隐喻干扰（问题信息中潜在的歧义性使被试困惑或误导被试的解题思路）等．     

说明文形式图式阅读策略训练提高初中生阅读水平的实验研究

本研究以两所中学的136名初二学生为实验被试．采取平衡组实验设计,编制专门的(实验教程)．以专门训练与日常教学渗透相结合和专门集中训练两种方式进行说明文形式图式阅读策略训练。实验结果表明：1。说明文形式图式阅读策略训练可提高学生的阅读理解水平;2。策略训练对优生、中等生的帮助更大;3。在迁移效果上,阅读策略的专门训练与教学渗透相结合的训练明显优于专门的集中训练。4。在本实验的延迟测验条件下．对策略的运用,激活组显着优于未激活组。     

数学等值概念获得的过渡性学习者认知发展的实验研究

就数学等值概念获得而言,一般地,过渡性学习者在解决简单问题作业时趋向于使用一种正确策略,而当题目较难时则使用几种不同的错误策略。经过针对性的指导（或输入适当信息）后极易掌握此概念,表现为使用一种正确且充分的策略。同时,“言语一手势失匹配”可能不是过渡性学习者的必然的认知特征。     

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。     

Spontaneous gestures influence strategy choices in problem solving

Do gestures merely reflect problem-solving processes, or do they play a functional role in problem solving? We hypothesized that gestures highlight and structure perceptual-motor information, and thereby make such information more likely to be used in problem solving. Participants in two experiments solved problems requiring the prediction of gear movement, either with gesture allowed or with gesture prohibited. Such problems can be correctly solved using either a perceptual-motor strategy (simulation of gear movements) or an abstract strategy (the parity strategy). Participants in the gesture-allowed condition were more likely to use perceptual-motor strategies than were participants in the gesture-prohibited condition. Gesture promoted use of perceptual-motor strategies both for participants who talked aloud while solving the problems (Experiment 1) and for participants who solved the problems silently (Experiment 2). Thus, spontaneous gestures influence strategy choices in problem solving.     

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。     

Metacognition and mathematics strategy use

The role of children's metacognitive knowledge in their mathematics strategy use was studied by a longitudinal examination of second graders' effort attributions, metacognition for mathematics, and strategy use while solving mathematics problems. Children's correct use of retrieval, internal and external strategies, and the prevalence of strategy use were assessed in September and the following January. Effort attributions for success and failure were also assessed at both points in time. In January, metacognitive knowledge about mathematics strategies was measured. Second graders possess metacognitive knowledge about mathematics strategies, and this knowledge is correlated most strongly with the tendency to use internal strategies in September and correct internal strategy use in September. Effort attributions measured at both timepoints were significantly related to metacognition. Effort attributions in January also correlated with the tendency to use internal strategies in January. In general, the results are consistent with self-system theories, which posit that metacognition, motivation, and strategy use work together to promote learning.     

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.     

Mental models in word problem-solving: A comparison between American and Korean sixth-grade students

Mental model analysis was conducted in word problem solving using American (n = 42) and Korean (n = 44) sixth-graders. Two levels of mental models–the problem model and the mathematical model–constructed in the process of word problem solving were investigated. Categories for correct and incorrect models were developed to be used in think-aloud protocol analysis. The majority of students who constructed correct problem models classified the problems rapidly according to solution procedures as they read the problems, or restated the problems focusing on the specific words relating them to other statements in the problems. However, significant differences were found between American and Korean sixth-graders' in some categories of problem and mathematical models. While many Korean sixth-graders' problem-solving process steps were proceduralized, this was not the case for American sixth-graders, even for those who had a readily accessible knowledge base of basic mathematical facts.     

Why do children lack the flexibility to innovate tools?

Despite being proficient tool users, young children have surprising difficulty in innovating tools (making novel tools to solve problems). Two experiments found that 4- to 7-year-olds had difficulty on two tool innovation problems and explored reasons for this inflexibility. Experiment 1 (N = 51) showed that children’s performance was unaffected by the need to switch away from previously correct strategies. Experiment 2 (N = 92) suggested that children’s difficulty could not easily be explained by task pragmatics or permission issues. Both experiments found evidence that some children perseverated on a single incorrect strategy, but such perseveration was insufficient to explain children’s tendency not to innovate tools. We suggest that children’s difficulty lies not with switching, task pragmatics, or behavioral perseveration but rather with solving the fundamentally “ill-structured” nature of tool innovation problems.     

You’ll see what you mean: Students encode equations based on their knowledge of arithmetic

This study investigated the roles of problem structure and strategy use in problem encoding. Fourth-grade students solved and explained a set of typical addition problems (e.g., ) and mathematical equivalence problems (e.g., or ). Next, they completed an encoding task in which they reconstructed addition and equivalence problems after viewing each for 5 s. Equivalence problems of the form overlap with a perceptual pattern found in traditional arithmetic problems (i.e., answer blank in final position), and students’ encoding was poorest on problems of this type. Individual differences in encoding the equivalence problems were related to variations in strategy use. Some students solved blank-final equivalence problems using the standard arithmetic strategy of performing all given operations on all given numbers. These students made more errors in encoding problem structure, but fewer errors in encoding the numbers, than did students who solved the problems using correct or other incorrect strategies. Moreover, students who expressed many strategies for solving the blank-final equivalence problems made fewer errors in encoding problem structure, but more errors in encoding the numbers, than did students who expressed only a single strategy. Results highlight that encoding is intended to guide action and that prior experience can simultaneously facilitate and interfere with accurate encoding.