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。     

小学生表征数学应用题策略的实验研究

通过一个2(成功与否)×2(提示与否)×2(题型)的混合实验设计,对小学五年级学生解决和差应用题的表征策略进行了研究.结果表明:(1)与比较应用题的表征相类似,小学生对和差应用题的表征也存在着直译策略和问题模型策略;(2)不成功组解题者在表征和差应用题时倾向于运用直译策略,而成功组的解题者更倾向于运用问题模型策略,这导致了成功者与不成功者在列式上的差异,特别是在不一致题型上表现得更明显;(3)在读题前给以“请注意理解这道题的意思”这样简单的提示,对不成功的解题者对和差问题的正确表征并不能起到作用;(4)成功的和差应用题解题者和不成功的解题者在列式正确性的自我评价上存在显著差异.     

算术应用题表征策略的眼动研究

采用EyelinkⅡ眼动记录仪,以21名大学生为被试,探讨了大学生解决三步比较应用题的表征策略。实验设计为2(正确率:高、低)×2(题型:一致、不一致)×2(无关信息:插入、未插入)的三因素混合实验。结果表明:(1)大学生被试解三步式比较应用题存在直译策略和问题模型策略;(2)解题正确率高者解难度较大的应用题时倾向于对应用题情境进行加工,即采用问题模型策略,正确率低者未表现出这一倾向,往往采用直译策略。     

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。     

小学二年级两类数学困难学生应用题表征策略的差异

本研究主要采用实验法和临床访谈法对某小学二年级单纯型数困儿童与混合型数困儿童进行一致/环一致应用题测验,以考察两类数困生在解决此类应用题时表征策略的差异.结果表明:(1)正常组学生较多地使用问题模型策略,数困组较多地使用直译策略;正常组在列式成绩显著优于数困组,列式时间显著少于数困组.(2)在两种表征策略(直泽表征、问题模型表征)上,单困组与双困组没有显著差异.(3)在列式成绩、列式时间上,单困组与双困组没有显著差异.(4)简单提示对三类学生的表征策略、列式成绩及列式时间均没有产生显著的影响.     

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。     

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。     

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。     

中学生学习策略应用特点的研究

运用中学生学习策略量表对442名初、高中学生进行测试,考察中学生应用学习策略的一般特点。结果表明：（1）中学生学习策略量表具有良好的信度、效度;（2）中学生在应用学习策略方面有随年级增长而下降的趋势。在调控策略的运用上女生显著多于男生,而在认知策略的运用上男生多于女生。深层加工策略和反馈调节策略存在年级与性别的交互作用;（3）初二和高二年级学习优、差生之间在学习策略上存在显著的差异,其中,深层加工、检索应用策略和反馈调节策略在各年级的优、差生之间都存在显著差异。     

优、差生非智力因素发展研究

本文从发展的角度研究小学、初中至高中阶段优生、差生非智力因素的发展趋势 ,并探讨智力、非智力因素与优生、差生学习成绩的关系。结果显示 :(1)优生、差生的非智力因素发展水平不同 ,但发展顺序一致 ,初二是非智力因素发展的转折期 ;(2 )非智力因素在优生中普遍高于同年级差生 ;并对优生、差生学习成绩影响差异显著 ;(3)智力因素与非智力因素呈显著正相关 ,它们共同影响学习成绩。就被试总体而言 :智力因素对学习成绩的贡献率为 2 2 % ,非智力因素的贡献率为 59%。     

小学生应用题表征的类型和特点

以124名小学六年级学生为被试。采用应用题解决问卷考查了我国小学生应用题表征的类型和特点。结果表明小学生应用题的表征方式有复述内容、图式表征、图片表征、直译表征、语义结构分析等;成功解题者和不成功解题者对各种表征方式的使用次数上没有显着差异;成功解题者和不成功解题者在各种表征方式下的解题成绩有显着差异,成功解题者在图式表征、直译表征和语义结构分析表征下的成绩显着优于不成功解题者。     

关于数学应用题心理表征策略的新理论

本文主要阐述了数学应用题心理表征中的两种策略一直接转换策略和问题模型策略,介绍了两种策略的认知过程,并对两种策略的区分方法进行了探讨,最后总结说明了研究数学心理表征在理论和实践中的意义。     

文本表述和结构对小学生数学应用题表征的影响

以450名小学生为被试,探讨了文本表述和结构对小学生数学应用题表征成绩的影响。采用2(难度)×2(题材熟悉度)×5(措辞类型)×3(年级)四因素混合设计。结果表明:不同文本表述和结构对小学生解决数学应用题的影响不因年级的不同而不同;概念性措辞问题和情境性措辞问题都促进了小学生数学应用题的表征成绩;在容易问题中,额外信息对表征成绩影响较大;在较难问题中,数学运算关系难度对表征成绩影响较大;当解决文本背景较简单的标准措辞问题时,题材熟悉度对小学生的理解产生较大影响;文本长度对问题解决的影响取决于所增加的文本是否对理解问题的句法关系和语义情景有益。     

数学焦虑对初中生数学应用题成绩的影响

通过对筛选出的391名初中1～3年级学生进行《数学应用题问卷》、《数学焦虑问卷》测试,探讨了数学焦虑对初中数优生、数困生数学应用题成绩的影响。结果发现：1）应用题成绩性别差异不显著,性别不是影响应用题成绩的主要因素;2）数优生的焦虑程度远远低于数困生;3）数学焦虑的年级差异不显著;4）数学焦虑的性别差异不显著;5）数学焦虑对应用题成绩具有一定的预测作用。     

Learning new problem-solving strategies leads to changes in problem representation

Children sometimes solve problems incorrectly because they fail to represent key features of the problems. One potential source of improvements in children's problem representations is learning new problem-solving strategies. Ninety-one 3rd- and 4th-grade students solved mathematical equivalence problems (e.g., 3 + 4 + 6 = 3 + __) and completed a representation assessment in which they briefly viewed similar problems and either reconstructed each problem or identified it in a set of alternatives. Experimental groups then received a lesson about one or both of two solution strategies, the equalize strategy and the add–subtract strategy. A control group received no instruction. All children completed posttest assessments of representation and problem solving. Children taught the equalize strategy improved their problem representations more than those not taught it. This pattern did not hold for the add–subtract strategy. These results indicate that learning new strategies is one source of changes in problem representation. However, some strategies are more effective than others at promoting accurate problem representation.     

Sex differences in elaborative strategies: a developmental analysis.

The present study examined sex differences in the use of elaboration in paired associate learning in adolescence and young adulthood. In Experiment 1, 48 eighth grade and 48 tenth grade students were asked to recall 24 word pairs, half of which were high frequency pairs, and half low frequency pairs. After recall, students reported the type of strategy used for each word pair (reading the pairs carefully, rehearsing the words, using imagery or constructing a verbal connection). Females used elaborative strategies more often, were more likely to recall elaborated pairs, and recalled more word pairs than males at both ages. These effects were observed in both high and low frequency word pairs. There was also a main effect of frequency, with elaboration more common with high frequency word pairs. In Experiment 2, college students performed the same paired-associates learning task, but with the added instruction to describe their elaborations in a sentence. At this age, there was a sex by materials interaction, with sex differences in strategy use only present with low frequency word pairs. These findings indicate that sex differences diminish under more favorable task conditions that encourage strategy use (high frequency word pairs) as males and females become more proficient strategy users, but remain under less favorable circumstances. An examination of the types of elaborations generated by college students indicated although males and females produced similar types of elaborations to the word pairs, sex differences in the recallability of low frequency words appeared with less interactive and more idiosyncratic elaborations.     

Arithmetic word problem solving: a Situation Strategy First framework

Before instruction, children solve many arithmetic word problems with informal strategies based on the situation described in the problem. A Situation Strategy First framework is introduced that posits that initial representation of the problem activates a situation-based strategy even after instruction: only when it is not efficient for providing the numerical solution is the representation of the problem modified so that the relevant arithmetic knowledge might be used. Three experiments were conducted with Year 3 and Year 4 children. Subtraction, multiplication and division problems were created in two versions involving the same wording but different numerical values. The first version could be mentally solved with a Situation strategy (Si version) and the second with a Mental Arithmetic strategy (MA version). Results show that Si-problems are easier than MA-problems even after instruction, and, when children were asked to report their strategy by writing a number sentence, equations that directly model the situation were predominant for Si-problems but not for MA ones. Implications of the Situation Strategy First framework regarding the relation between conceptual and procedural knowledge and the development of arithmetic knowledge are discussed.     

Task‐Related Factors that Influence the Spontaneous Use of Diagrams in Math Word Problems

Diagrams are effective tools for problem solving. However, previous findings indicate that students generally do not use diagrams spontaneously. This study examined task‐related factors that may influence the spontaneity of diagram use. Experiment 1 compared two possible explanations: the first, that the length‐relatedness of the story context of the problem (i.e. whether it involves the measurement of length) determines the likelihood of diagram use; and the second, that the cognitive cost of transforming the situation described in the word problem to an abstract diagrammatic representation is the more important factor. Four math word problems, differing in their story context and structure, were administered to eighth‐grade Japanese students (n = 125) to solve. The results provide support for the cognitive transformation cost explanation. The results of experiment 2, in which the problems were administered to students in both Japan (n = 291) and New Zealand (n = 323), confirm this finding. Copyright © 2011 John Wiley & Sons, Ltd.     

大中学生英语阅读的元认知策略发展及其民族差异比较

采用英语阅读的元认知意识问卷对云南省大学生,昆明汉族、丽江地区的纳西族和彝族中学生进行测查。结果表明：(1)大中学生英语阅读的元认知策略水平随着年级的升高呈现出提高的趋势,从中学到大学是元认知策略水平快速发展的时期;(2)男女大中学生英语阅读的元认知策略水平整体上具有一致性,但在中学阶段却呈现出女生略优于男生的趋势,到了大学,男女两性发展基本平衡;(3)汉族与纳西族中学生英语阅读的元认知策略水平整体上具有一致性,彝族中学生英语阅读的元认知策略水平呈现出优于汉族和纳西族的趋势。