等值分数概念的理解

等值分数是表示具有相等值的分数,它建立在两个量具有确定比例关系的基础上。研究表明,儿童在接受正式教学之前,就具有了等值分数的非正式知识,但仍然在概念理解上存在很大的困难,主要有两方面的原因:一是受自身运算思维发展水平的制约,未获得乘法思维和守恒观念;二是缺乏对等值分数不同语义的理解。在今后研究中,需进一步探讨从非正式知识到正式概念之间的发展路径,尝试开展等值分数的早期教学实验,并需要结合多种语义背景来考查儿童的概念发展水平。     

五、六年级小学生对分数的意义和性质的理解

本研究采用面积、线段、集合和数线的表征方式为试题,对小学五、六年级学生掌握分数的意义和性质的情况作了调查。研究结果显示:小学五、六年级学生能够掌握分数所代表的部分和整体的意义,但还不能很好地掌握分数所代表的测量的意义和等值分数的概念。六年级学生的等值分数的概念较五年级学生有显著的发展。研究结果对我们考察和思考目前的小学分数教学有所启示     

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。     

关于儿童对部份与整体关系认知发展的实验研究——5～10岁儿童分数认识的发展

数学中的部份与整体关系是儿童掌握数学概念的一个重要环节。儿童对这种关系的认识水平反映出他的思维水平,同时也是他掌握数学概念的手段和途径。分数从其本身性质来看,就是一个部份与整体关系的问题。小学数学教科书在讲到分数的意义时,首先就开宗明义地说:“把整体‘1’平均分成若干份,表示这样一份或几份的数,叫做分数。”我们在以前所做的四个有关实验的基础上,概括提出了儿童掌握部份和整体关系的十二项指标,并据以进一步探索儿童对数的部份与整体关系认识的发展过程和规律。本研究是从5—10岁儿童对分数概念的认识来进行实验,并期望能对小学分数的数学提供心理学参考依据。     

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。     

怒族、傈僳族和景颇族儿童认知发展研究

采用《中小学生思维发展水平测验量表》,对怒族、傈僳族和景颇族三种少数民族390名儿童进行调查研究。结果发现：1．儿童认知发展的阶段性基本支持皮亚杰认知发展的阶段性理论,形式思维水平在13～16岁尚未形成稳定的认知结构;2．在发展的年龄上,儿童认知发展水平出现明显的“滞后”现象;3．儿童在初中一年级出现认知发展的加速期;4．三种少数民族儿童认知发展整体上不存在显著性的跨文化差异;5．认知发展在性别差异上主要体现在动作协调一空间定位能力上。     

单独作业组与相互作用组儿童空间表象掌握的对比研究

研究目的近年来,皮亚杰的理论受到挑战,人们批评皮亚杰虽然强调社会因素对于认识发展的作用,但在实验中并未真正加以研究。具体到三山课题上,已有的研究多是在儿童单独作业条件下分析儿童关于三山课题认识发展的过程、自我中心现象的变化趋势以及知觉经验在儿童掌握空间表象中的作用。而儿童间的相互作用对儿童掌握空间表象是否存在影响,至今尚未见到过实验研究报告。本实验试图通过对儿童在单独作业和相互作用两种条件下进行训练,然后对比两组儿童对空间表象的掌握情况,分析两组间是否存在差异,为进一步完善皮亚杰的儿童空间认知发展理论提供实验上的依据。研究方法被试随机抽取一至四年级学生200名,其中一年级40名,二年级50名,三年级50名,四年级60名,按所在年级分成四个年级组。初试后,将各年级回答错误的儿童,按等组法的原则分成单独作业组与相互作用组两组。两组儿童的初试成绩不存在差异。     

3～6年级儿童整数数量表征与分数数量表征的关系

研究主要探讨了整数数量表征和分数数量表征的关系以及年级对两者关系的影响。实验对155名三至六年级儿童进行0~1分数数字线估计任务和0~1000整数数字线估计任务的测量。结果发现:(1)对于整数数字线估计,所有年级儿童均主要采取了线性表征;(2)对于分数数字线估计,五六年级儿童主要采取了线性表征,三四年级儿童没有明显的线性表征或对数表征的倾向;(3)整数数量表征和分数数量表征呈显著正相关,不过年级对两者的关系产生了影响,表现在只有五六年级儿童的整数数字线估计对分数数字线估计有显著预测作用。     

核等值：一种观察分数等值体系

核等值流程包括：预平滑、估计分数概率、连续化、等值、评估等值结果。该方法兼具线性等值与等百分位等值的优点, 各环节扩展性与包容性较强; 采用平滑与连续化处理, 可降低等值随机误差; 等值差异标准误等其所特有的概念为结果评估提供可靠的工具。连续化与带宽选择方法等因素均可影响其表现; 基于核等值的新方法为等值发展提供了新颖的视角。未来可关注核等值体系的扩充与完善、流程的更新、等值方法的结合和比较等方向。     

儿童数字估计的表征模式与发展

探讨中国儿童数字估计的表征模式与发展趋势。包括两个实验,均采用数字线估计任务,实验一以92名幼儿园、一年级及二年级儿童为被试,考察其在0~100范围的数字估计,结果显示,幼儿园儿童在数字估计更多地采用对数表征,而一二年级的儿童在数字估计中更多地采用线性表征;实验二以86名一、三、五年级儿童为被试,考察其在0~1000范围的数字估计,结果显示,一年级儿童有一半采用对数表征,另一半采用线性表征,而三五年级儿童大多采用线性表征。中国儿童的数字估计表现出与美国儿童相同的发展模式,都是由不精确的对数表征逐步向精确的线性表征发展;人的数表征有多种形式,即使在同一年龄阶段,也会因任务难度的不同而选择不同的表征模式。中国儿童精确数字估计能力的出现要早于美国儿童。     

Development of proportional reasoning: where young children go wrong

Previous studies have found that children have difficulty solving proportional reasoning problems involving discrete units until 10 to 12 years of age, but can solve parallel problems involving continuous quantities by 6 years of age. The present studies examine where children go wrong in processing proportions that involve discrete quantities. A computerized proportional equivalence choice task was administered to kindergartners through 4th-graders in Study 1, and to 1st- and 3rd-graders in Study 2. Both studies involved 4 between-subjects conditions that were formed by pairing continuous and discrete target proportions with continuous and discrete choice alternatives. In Study 1, target and choice alternatives were presented simultaneously; in Study 2, target and choice alternatives were presented sequentially. In both studies, children performed significantly worse when both the target and choice alternatives were represented with discrete quantities than when either or both of the proportions involved continuous quantities. Taken together, these findings indicate that children go astray on proportional reasoning problems involving discrete units only when a numerical match is possible, suggesting that their difficulty is due to an overextension of numerical equivalence concepts to proportional equivalence problems.     

数字线和离散物体任务训练对儿童整数偏向的影响

通过数字线任务和离散物体任务对81名拥有错误整数偏向的儿童进行干预,再进行分数比较任务,以考查不同干预对错误整数偏向的影响以及分数在心理数字线上的表征方式。结果表明：（1）离散物体组儿童在干预任务中表现较好,在分数比较任务中得分也显著高于数字线组儿童,但反应时要慢于数字线组儿童。（2）正确比较分数时,两组均出现正确整数偏向,但错误的整数偏向依然存在,二者在整数系统扩展到有理数系统这个过渡期同时存在。     

皮质醇日常节律与儿童问题行为及心理社会因素的关系

HPA轴(下丘脑?垂体?肾上腺皮质轴, hypothalamic-pituitary-adrenal cortex axis)是人体应对压力的重要神经内分泌系统, 其终产物皮质醇常作为测量压力的生物学指标。目前的研究多通过皮质醇日常节律表示静息状态下HPA轴的活动, 而日常节律因其较高的稳定性和可靠性成为儿童生理健康评估的最佳指标。儿童期迅速发育的神经内分泌系统与儿童的行为相互作用, 并受到多种心理社会因素的影响。以往研究主要关注皮质醇日常节律与儿童问题行为及心理社会因素的关系, 未来研究应讨论逆境条件下影响儿童成长的危险性因素和保护性因素, 并探索环境对儿童行为影响可能存在的内分泌机制。     

Talking about proportion: Fraction labels impact numerical interference in non‐symbolic proportional reasoning

Across two experiments, we investigated how verbal labels impact the way young children attend to proportional information, well before the introduction of formal fraction education. Five‐ to seven‐year‐old children were introduced to equivalent non‐symbolic proportions labeled in one of three ways: (a) a single, categorical label for multiple fractions (both 3/4 and 6/8 referred to as “blick”), (b) labels that focused on the numerator [e.g., 3/4 labeled as “three blicks” (Experiment 1) or “three‐fourths” (Experiment 2)], or (c) labels that had a complete part‐whole structure (“three‐out‐of‐four”). Children then completed measures of non‐symbolic proportional reasoning that pitted whole‐number information against proportional information for novel proportions. Across both experiments, children who heard the categorical labels were more likely to match non‐symbolic displays based on proportion than children in any of the other conditions, who demonstrated higher levels of numerical interference. These findings suggest that fraction labels have the potential to shape children's attention to proportional information even in the context of non‐symbolic part‐whole displays and for children who are not familiar with formal fraction symbols. We discuss these findings in terms of children's developing understanding of proportional reasoning and its implications for fraction education.     

人际关系状况与学龄前流动儿童的问题行为

以北京市40所幼儿园的336个班级的3430名儿童为被试, 构建多层线性模型, 分析亲子关系、班级师幼关系氛围对学龄前城市和流动儿童问题行为的影响。发现亲子冲突和班级师幼冲突氛围显著正向预测儿童的内、外向问题行为; 班级师幼亲密和冲突氛围对城市儿童内向问题行为的预测作用相比流动儿童更大; 班级师幼冲突氛围对亲子冲突高的流动儿童的外向问题行为的消极作用降低, 高亲子亲密缓解了班级师幼冲突氛围对流动儿童内向问题行为的消极作用。     

小学低年级儿童口语词汇知识的发展轨迹及其影响因素

以149名小学生为研究对象, 对其口语词汇知识进行了历时3年的5次追踪测试, 采用潜变量增长模型探索了小学1~3年级学生汉语口语词汇知识的发展轨迹, 并考察了语音意识、同形语素意识、复合语素意识和家庭社会经济地位对口语词汇知识发展轨迹的影响。结果发现：(1) 1~3年级学生口语词汇知识发展轨迹呈曲线形式, 其中前两年呈线性发展, 三年级时呈加速发展, 发展速度是前期发展的两倍, 起始水平和发展速度均存在显著的个体差异; (2)语音意识、同形语素意识、复合语素意识和家庭社会经济地位均可以正向预测学生口语词汇知识的起始水平; (3)只有同形语素意识和家庭社会经济地位可以正向预测学生口语词汇知识的发展速度。     

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.     

Spatial Proportional Reasoning Is Associated With Formal Knowledge About Fractions

Proportional reasoning involves thinking about parts and wholes (i.e., about fractional quantities). Yet, research on proportional reasoning and fraction learning has proceeded separately. This study assessed proportional reasoning and formal fraction knowledge in 8- to 10-year-olds. Participants (N = 52) saw combinations of cherry juice and water in displays that highlighted either part–whole or part–part relations. Their task was to indicate on a continuous rating scale how much each mixture would taste of cherries. Ratings suggested the use of a proportional integration rule for both kinds of displays, although more robustly and accurately for part–whole displays. The findings indicate that children may be more likely to scale proportional components when being presented with part–whole as compared with part–part displays. Crucially, ratings for part–whole problems correlated with fraction knowledge, even after controlling for age, suggesting that a sense of spatial proportions is associated with an understanding of fractional quantities.