发展性计算障碍儿童的数量转换缺陷

本研究拟考察发展性计算障碍儿童的认知缺陷成因。实验1要求被试在三种形式(点/点,数/数,点/数)下进行数量比较,实验2仅将点集替换为汉字数字词。结果表明障碍组和正常组在数/数、点/数和汉字/汉字比较任务上的成绩存在显著差异,而在点/点和汉字/汉字比较上没有差异。据此推论,计算障碍儿童符号加工能力受到损伤,符号与非符号数量转换能力存在缺陷,但非符号加工能力和不同符号间数量转换没有缺陷,支持语义提取缺陷假设。     

建构反应题中能力估计准确性的影响因素:评分者人数和项目个数的交互作用

采用康春花、孙小坚和曾平飞(2016)提出的等级反应多水平侧面模型探讨了评分者人数和项目个数对被试能力估计准确性的影响。模拟研究的结果表明:(1)随着项目个数的增加,估计值与真值之间的相关也不断增加;(2)评分者人数和项目个数在平均绝对偏差(MAB)和误差均方根(RMSE)上的主效应均显著,两者间的交互效应也显著;(3)简单效应分析发现,当项目较少时,3个评分者条件下的能力估计准确性最好; 随着项目个数的增加,4个评分者的估计误差迅速下降,且表现变为最好。     

Prospective Elementary Teachers Learning to Reason Flexibly with Sums and Differences: Number Sense Development Viewed Through the Lens of Collective Activity

I present a viable learning trajectory for prospective elementary teachers’ number sense development with a focus on whole-number place value, addition, and subtraction. I document a chronology of classroom mathematical practices in a Number and Operations course. The findings provide insights into prospective elementary teachers’ number sense development. These include the role of standard algorithms and their relationship to the evolution of classroom mathematical practices that involve reasoning flexibly about number composition, sums, and differences.     

Matrix training of preliteracy skills with preschoolers with autism

Matrix training is a generative approach to instruction in which words are arranged in a matrix so that some multiword phrases are taught and others emerge without direct teaching. We taught 4 preschoolers with autism to follow instructions to perform action-picture combinations (e.g., circle the pepper, underline the deer). Each matrix contained 6 actions on 1 axis and 6 pictures on the other axis. We used most-to-least prompting to train the instructions along the diagonal of each matrix and probed the untrained combinations. For 2 participants, untrained responding emerged after the minimum amount of training. The other 2 participants required further training before untrained combinations emerged. At the end of the study, 3 of the 4 participants performed the trained actions with previously known pictures, letters, and numbers. This study demonstrated that matrix training is an efficient approach to teaching language and literacy skills to children with autism.     

“多少”概念发展的研究

采用数量判定任务,分别用2～30和5～100范围内点子图为刺激,研究个体“多”和“少”概念的发展。结果发现：在5～100点子条件下,随年龄的增长,个体“多”概念的判断值、“少”概念的判断值、“多”“少”概念的临界值均显著增大;7～9岁是个体“多少”概念发展的转折期;个体对“多少”概念的认知具有相对性;在本实验的两种条件下,随年龄增长,个体“多”概念的判断值、“少”概念的判断值、“多”“少”概念的临界值逐渐趋于刺激点子数最大值的2/3、1/3、1/2,“多”概念与“少”概念判断的不确定距离逐渐趋于刺激点子数最大变化范围的1/3或略小于1/3。     

How do we convert a number into a finger trajectory?

How do we understand two-digit numbers such as 42? Models of multi-digit number comprehension differ widely. Some postulate that the decades and units digits are processed separately and possibly serially. Others hypothesize a holistic process which maps the entire 2-digit string onto a magnitude, represented as a position on a number line. In educated adults, the number line is thought to be linear, but the “number sense” hypothesis proposes that a logarithmic scale underlies our intuitions of number size, and that this compressive representation may still be dormant in the adult brain. We investigated these issues by asking adults to point to the location of two-digit numbers on a number line while their finger location was continuously monitored. Finger trajectories revealed a linear scale, yet with a transient logarithmic effect suggesting the activation of a compressive and holistic quantity representation. Units and decades digits were processed in parallel, without any difference in left-to-right vs. right-to-left readers. The late part of the trajectory was influenced by spatial reference points placed at the left end, middle, and right end of the line. Altogether, finger trajectory analysis provides a precise cognitive decomposition of the sequence of stages used in converting a number to a quantity and then a position.     

Numerical approximation abilities correlate with and predict informal but not formal mathematics abilities

Previous research has found a relationship between individual differences in children’s precision when nonverbally approximating quantities and their school mathematics performance. School mathematics performance emerges from both informal (e.g., counting) and formal (e.g., knowledge of mathematics facts) abilities. It remains unknown whether approximation precision relates to both of these types of mathematics abilities. In the current study, we assessed the precision of numerical approximation in 85 3- to 7-year-old children four times over a span of 2 years. In addition, at the final time point, we tested children’s informal and formal mathematics abilities using the Test of Early Mathematics Ability (TEMA-3). We found that children’s numerical approximation precision correlated with and predicted their informal, but not formal, mathematics abilities when controlling for age and IQ. These results add to our growing understanding of the relationship between an unlearned nonsymbolic system of quantity representation and the system of mathematics reasoning that children come to master through instruction.     

Temperature-dependent crack surface tension

The fracture surface energy is calculated for a one-dimensional, exactly solvable model of a crack. The temperature dependence of the crack surface tension is determined on the basis of a self-consistent Einstein approach. It is found that lattice vibrations result in a strong reduction in the crack surface tension.     

幼儿在集合比较中运用数数的实验研究

本研究中运用了两个实验探讨数数干预和测查条件对儿童在集合比较中运用数数的影响。干预对3岁儿童(M=3：9)没有影响。在平均年龄为4岁4个月时．干预组儿童比控制组儿童更倾向于用数数比较集合．自然组儿童也比传统组更倾向于用数数。许多4岁儿童在无干预时不用数数可能是因为,1)不知数数比视觉性比较更有效,或2)他们在集合比较中的数数极易受测查情景因素的影响。儿童在集合比较中的数数运用与他们的数数水平密切关联。