小学2-4年级儿童数学应用题表征策略对其解决不规则问题影响的研究

本研究运用实验法和临床访谈法对某普通小学的123名2-4年级学生进行了不规则数学应用题测验,以考察数学学优生和学差生在解决这些应用题时表征策略的差异。结果表明：（1）从2-4年级儿童解答条件多余和条件不足应用题上看,学优生的成绩要好于学差生,口头报告分析显示学优生较多地使用问题模型策略对问题进行表征,而学差生较多使用直接转换策略对问题进行表征;（2）在三年级时,条件多余和条件不足应用题的解题正确率有所提高,但到四年级时,正确率却有所下降;（3）在解决条件多余和条件不足应用题中,性别差异不显著。     

大学生解决物理问题的表征层次的实验研究

设计了两个实验,探讨优、差生物理问题表征层次的特点。结果表明,优、差生物理问题表征层次有差异。优生侧重于科学理论表征,表现为以物理原理分类,在科学理论表征层次上多为正向推理：差生则受初始表征的影响,以表面特征分类,在科学理论表征层次上多为逆向推理。     

比较应用题的问题表征策略研究

采用2×2×4三因素混合实验设计,对不同年级学生解比较应用题过程中的各种指标进行分析,结果表明:学生解比较应用题时的问题表征策略存在显著的年级差异;数学成绩优生、差生存在不同的问题表征策略;题目呈现方式对学生的问题表征策略有显著影响。     

优差生亲子沟通与认知和情绪压力的关系

研究对优生、差生与其父母围绕数学问题解决而展开的沟通过程进行观察,并采用量表法测量其感受到的认知和情绪压力,以考察两变量之间的关系及优、差生在两者得分上的差异。结果发现：（1）优生无论在沟通行为次数上,还是在沟通行为类型上都表现出一些积极特征;（2）优生的二级认知压力显著高于差生,一级认知压力和情绪压力显著低于差生;（3）督促、指责等消极沟通行为都与一级认知压力和情绪压力存在正相关,而积极沟通行为,如方法指导等则与一级认知压力、情绪压力呈显著负相关;一级认知压力与正确提议比例之间存在显著负相关。     

解题反思对数学学业优差生解题过程的影响

考察解题反思对数学学业优生和差生解题结果及所用策略的不同影响。选取初一至初三年级的数学学业优生和差生为被试,以一套连加数问题为实验材料,进行一对一的测试,前后进行两次测试。对反思组优差生(优生12人,差生10人)和无反思组优差生(优生14人,差生14人)解题过程的比较,发现:1)解题后立即进行反思能够提高差生的解题正确率,但是延长解题时间;2)先前的解题反思对优生和差生后续解题时的正确率和解题时间均不产生明显影响;3)解题后立即进行反思能够促进优生和差生使用高效策略,放弃低效策略;4)先前的解题反思在后续解题中仍然促进学生使用高效策略,对优生的促进作用比对差生更明显。     

小学2～4年级儿童数学应用题表征策略差异的研究

本研究运用实验法和临床访谈法对某普通小学的123名2～4年级学生进行了数学应用题测验,以考察数学学优生和学差生在解决比较应用题时表征策略的差异。结果表明:(1)从2～4年级儿童解答一致和不一致应用题上看,学优生较多地使用问题模型策略对问题进行表征,学差生较多地使用直接转换策略对问题进行表征;(2)除学差女生的解题正确率低于学差男生的正确率,学差女生自我报告中直接转换策略的使用多于学差男生外,在其它方面,性别差异并不显著;(3)随着年级的升高,学优生在使用问题模型策略上越来越成熟,学差生并没有学会使用更加有效的问题模型表征策略,仍然停留在直接转换策略上,但他们在关于策略使用的认识上有所提高。     

小学三年级数学学优生与学困生解决比较问题的差异

运用实验法和临床访谈法研究了数学学优生与学困生在解决比较问题时的差异及元认知对解题成绩的影响。被试为40名小学三年级学生。比较问题分为一致问题和不一致问题。元认知包括元认知知识和元认知监控技能。结果表明：(1)学优生与学困生解决比较问题的成绩差异显著,学优生在一致问题和不一致问题上的解题成绩均优于学困生。这种差异与其解题时所运用的表征策略有关。(2)学生在解决比较问题中出现的主要错误为转换错误,在不一致问题中出现的错误多于一致问题中出现的错误。(3)学优生与学困生在元认知知识和监控技能上均有显著差异,元认知监控技能对解决比较问题的成绩有显著预测作用。     

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．     

不同亚型数学学习困难儿童应用题问题表征过程的研究

采用自编数学应用题解决能力测验题对小学四年级单纯型数困儿童、混合型数困儿童和普通儿童问题理解阶段、问题整合阶段的差异,以及问题表征能力与数学问题解决之间的关系进行探究。结果表明：（1）单纯型与混合型数困儿童有效识别信息的能力弱,难于利用相关信息和排除干扰信息。（2）单纯型数困儿童比混合型数困儿童更擅于运用图式表征策略。（3）图式表征策略能促进数困儿童应用题的解决。     

换位棋问题规则的表征与解题正确率间关系的研究

本研究通过对被试求解换位棋过程的记录与分析,重点研究了问题表征在换位棋求解过程中的作用。实验结果表明：（1）正确表征问题规则是解题的必要前提.对问题规则信息的误解和遗漏,是影响解题正确率的重要因素。其中对非隐含问题规则的错误表征也占全部错误表征的很大比率。（2）“关键结构”的发现是解决换位棋的必要条件,对问题规则的错误表征影响“关键结构”的发现.（3）前置问题的解决经验对目标问题的正确表征无显著的影响作用。     

小学生数学问题解决中视觉空间表征的研究

本研究区分了两类数学应用题:非视觉化题目与视觉化题目,采用数学测验与个别访谈相结合的方法,考察了54名小学四、五、六年级不同学业水平学生的视觉空间表征。结果表明:图式表征在非视觉化题目与视觉化题目上都极大地促进了问题解决,图像表征妨碍非视觉化题目的解决但与视觉化题目的解决无关,并提出图式表征和图像表征在两类题目上有不同的含义。六年级学生的解题成绩及图式表征有显著的提高,但图像表征与年级因素无关。差生的图式表征能力很差,而在视觉化题目上使用图像表征显著地多于优生及中等生。在非视觉化题目的非视觉空间表征与图式表征之间的转换灵活性上,优生表现了明显的优势。     

Representing Space and Objects in Monkeys and Apes

Primate foraging can be construed as a set of interconnected problems that include finding food, selecting efficient travel routes, anticipating the positions of moving prey, and manipulating, and occasionally, extracting food items using tools. The evidence reviewed in this paper strongly suggests that both monkeys and apes use three types of representation (i.e., static, dynamic, and relational) to solve various problems. Static representations involve recalling certain features of the environment, dynamic representations involve imagining changes in the trajectories of moving objects, and relational representations involve encoding the properties of objects in relation to other objects. Contrary to previous claims, no clear differences were found between the representational skills of monkeys and apes. Current evidence also suggests that primates may be better at representing general compared to specific problem features. Finally, we have characterized the domains of space and objects as complementary and indicated future lines of research in these domains.     

Categorization and representation of physics problems by experts and novices

The representation of physics problems in relation to the organization of physics knowledge is investigated in experts and novices. Four experiments examine (a) the existence of problem categories as a basis for representation; (b) differences in the categories used by experts and novices; (c) differences in the knowledge associated with the categories; and (d) features in the problems that contribute to problem categorization and representation. Results from sorting tasks and protocols reveal that experts and novices begin their problem representations with specifiably different problem categories, and completion of the representations depends on the knowledge associated with the categories. For, the experts initially abstract physics principles to approach and solve a problem representation, whereas novices base their representation and approaches on the problem's literal features.     

Students' Coordination of Knowledge When Learning to Model Physical Situations

In this article, I present a study in which 12 pairs of 8th-grade students solved problems about a physical device with algebra. The device, called a winch, instantiates motions that can be modeled by pairs of simultaneous linear functions. The following question motivated the study: How can students generate algebraic models without direct instruction from more experienced others? The first main result of the study is that students have and can use criteria for judging when 1 algebraic expression is better than another. Thus, students can use criteria to regulate their problem-solving activity. The second main result is that constructing knowledge for modeling with algebra can require students to coordinate criteria for algebraic representations with several other types of knowledge that I also identify in the article. These results contribute to research on students' algebraic modeling, cognitive processes and knowledge structures for using mathematical representations, and the development of mathematical knowledge.     

The influence of depression symptoms on exploratory decision-making

People with symptoms of depression show impairments in decision-making. One explanation is that they have difficulty maintaining rich representations of the task environment. We test this hypothesis in the context of exploratory choice. We analyze depressive and non-depressive participants’ exploration strategies by comparing their choices to two computational models: (1) an “Ideal Actor” model that reflectively updates beliefs and plans ahead, employing a rich representation of the environment and (2) a “Naïve Reinforcement Learning” (RL) model that updates beliefs reflexively utilizing a minimal task representation. Relative to non-depressive participants, we find that depressive participants’ choices are better described by the simple RL model. Further, depressive participants were more exploratory than non-depressives in their decision-making. Depressive symptoms appear to influence basic mechanisms supporting choice behavior by reducing use of rich task representations and hindering performance during exploratory decision-making.     

手指的感知、运动以及数量表征对数字认知的促进作用

手指是儿童在习得数字符号之前最常使用的表征数量的工具,大量研究都表明手指在数字认知中具有促进作用。但是,目前仍不清楚手指在数字认知中的作用机制。综述从手指感知、手指运动以及手指数量表征三个方面总结了手指在数字认知中所起的作用。手指感知可能通过影响儿童的数量表征能力间接地影响其它数学能力;与表征量有关的手指运动可能促进了数量大小的加工。关于手指数量表征在数字认知中的作用存在两种有争议的观点：一种认为手指数量表征促进了儿童由非符号数量表征向符号数量表征的转化;另一种认为手指数量表征可能是一种数量语义表征方式。未来应该在发展、作用机制、性别差异等方向继续开展研究,进一步探讨手指在数字认知中所起的作用。     

代数应用题视觉化表征的理论模型及影响因素

视觉化表征是代数应用题表征的一大类型, 在问题解决过程中起着重要作用。视觉化表征的理论主要有视觉-逻辑二维模型、理解-转换模型、表象表征理论和图式-图像表征论, 四种理论模型各有其特殊的方法学意义。代数应用题的视觉化表征主要受到题目视觉化程度和认知负载等刺激因素以及自我效能感等认知因素的影响, 最后, 本文指出了在代数应用题视觉化表征理论、研究方法和影响因素探索中的进步以及发展空间。     

The structure of vocational interests in Germany: Different methodologies, different conclusions

The cross-cultural generalizability of vocational interest structures has received significant attention in recent years. This article adds to this research in four respects. First, data from a context that has not previously been investigated (Germany) was analyzed. Second, students at different stages of their educational career were examined. Third, the interest structure in male and females was compared. Fourth, two methods—the randomization test of hypothesized order relations (RTOR) and confirmatory factor analysis (CFA)—were applied to three competing structural conceptions: Holland’s circular representation, Gati’s hierarchical model, and Rounds and Tracey’s alternative hierarchical model. RTOR supported all three representations, whereas CFA supported only Holland’s model. CFAs indicated that the interest structure is reasonably invariant between high school and university students, but that the configurations for high school females and males differ. Substantive and methodological implications are discussed.