人类基本数学能力的进化证据

数学能力是人类重要的高级认知能力。人类的基本数学能力从进化上而言是一种适应性的表现,对个体的生存和繁衍有重要的意义。近年来比较心理学研究发现,成年人、婴儿的基本数学能力的行为表现和脑神经机制与其它物种相似,分子遗传学研究表明基本数学能力具有一定的遗传性。这些发现有助于人们更深刻地理解基本数学能力的本质及发生发展机制。     

Critiquing Statistics in Student and Professional Worlds

This article compares students' critiques within a class discussion about an invented statistic to STEM professionals' critiques from interviews to better understand how the situated meanings of a statistic are similar and different across student and professional worlds. We discuss similarities and differences in how participants constructed meaning for the statistic, and argue that disciplinary practices in schooling will always have an approximate, and somewhat indeterminate, relation to the figured worlds of professional practice.     

比例推理的过度使用及其认知机制:一项发展性的负启动研究

从抑制控制模型出发,采用负启动范式探究过度使用比例推理的认知机制。研究包括3个实验,以小学生、中学生和大学生为被试,分别考察了抑制控制在解决缺值应用题、图片推理任务中的作用,以及数字比(整数比、非整数比)是否对抑制控制过程有影响。结果发现:小学生、中学生和大学生在两类实验任务中均出现了负启动效应,但负启动量不存在年级差异;在图片推理任务中,不同数字比类型下的负启动量具有显著差异。研究结果支持了抑制控制模型的观点,即成功解决问题不仅需要掌握问题的内在逻辑,更需要对不恰当策略进行抑制;在解决问题的过程中,无论是儿童、青少年还是成人都需要抑制控制的参与,三者在抑制控制效率上没有差异;数字比类型对抑制过程有影响,但仅限于图片推理问题。     

中医“证概念”符号化的倡议与中医诊疗标量化的探讨

中医学是以“概念为单元”的功能医学,经络是功能网络。中医的“证”是外在的、变化着的、阶段性的。随着病的变化,证也在变化,质在变,量也在变。它有整体可控性,用模糊数学给中医的证候标量化,以便临床选方用药,“以数据治”。概念语言符号化,使中医古老的语形结构换上新衣,方便与当代科技沟通,进入网络传播,这或许是中医逐步走向现代化的一个切入点,一座桥梁。     

An Investigation of Incremental Effects of Interspersing Math Items on Task-Related Behavior

The purpose of this study was to replicate and extend research on task interspersal. The authors investigated whether changes in on-task behavior of two middle school students were functionally related to changes in the relative percentages of easy and difficult items on math worksheets. They found that the participants remained on task longer while completing worksheets with 33 and 67% interspersed easy problems than while completing worksheets without the interspersed easy problems. Participants’ accuracy in answering the target problems was not affected, however, by the interspersal procedure. The authors concluded that interspersing easy items on independent math seatwork assignments can increase on-task behavior.     

The Interplay among Stereotypes, Performance-Avoidance Goals, and Women's Math Performance Expectations

This project was designed to examine whether and how achievement goals contribute to the effect of gender stereotypes on women's low expectancies for success on math tasks. Study 1 confirmed predictions from the Stereotyped Task Engagement Process (STEP) model (Smith, 2004) by demonstrating that, compared to a counter-stereotype situation, women reminded of the gender-stereotype endorsed performance-avoidance goals. Study 2 tested whether performance-goal adoption differed between men and women. Results showed that, compared to men, women in a stereotype salient math situation were more likely to endorse performance-avoidance achievement goals. This performance-avoidance goal adoption in turn, accounted for the negative relationship between participants' gender and performance expectations for a standardized math test.     

算术应用题的分类结果与数学成绩关系研究

以算术应用题为材料,探讨了不同年级、不同数学成绩学生对算术应用题的分类结果及其与数学成绩的关系。结果表明:不同年级学生对算术应用题分类结果差异显著;数学成绩优生与数学成绩差生对算术应用题分类结果存在差异。     

Improved set‐size labeling mediates the effect of a counting intervention on children's understanding of cardinality

How does improving children's ability to label set sizes without counting affect the development of understanding of the cardinality principle? It may accelerate development by facilitating subsequent alignment and comparison of the cardinal label for a given set and the last word counted when counting that set (Mix et al., 2012). Alternatively, it may delay development by decreasing the need for a comprehensive abstract principle to understand and label exact numerosities (Piantadosi et al., 2012). In this study, preschoolers (N = 106, M_age = 4;8) were randomly assigned to one of three conditions: (a) count‐and‐label, wherein children spent 6 weeks both counting and labeling sets arranged in canonical patterns like pips on a die; (b) label‐first,wherein children spent the first 3 weeks learning to label the set sizes without counting before spending 3 weeks identical to the count‐and‐label condition; (c) print referencing control. Both counting conditions improved understanding of cardinality through increases in children's ability to label set sizes without counting. In addition to this indirect effect, there was a direct effect of the count‐and‐label condition on progress toward understanding of cardinality. Results highlight the roles of set labeling and equifinality in the development of children's understanding of number concepts.     

两种类型数学困难儿童的执行水平

使用Crack the Code任务考察单纯型与混合型数学困难小学儿童的执行水平,结果发现:单纯型数学困难儿童在对认知资源要求较高的任务上的执行水平显著低于数学优良生,但在认知要求较低的任务上二者之间没有显著差异;混合型数学困难儿童执行水平最低,在两个难度水平执行任务上的表现均显著差于数学优良生、单纯型数学困难儿童.小学儿童执行水平年级差异似乎主要表现在认知负荷较高的任务上,1年级学生与3、5年级学生的执行水平存在显著差异.     

Student Preference for Explicit Timing and Interspersal Procedures as a Function of Math Problem Completion Rates: Testing the Discrete Task Completion Hypothesis

A within-subjects design was used to compare explicit timing and interspersal with college students. Students were given 3 minutes to complete problems on the explicit timing assignment (25 problems, 3 digits –3 digits) and the interspersal assignment (25 similar problems and 10 problems, 1 digit –1 digit). Results indicated that: (a) students completed more total problems during interspersal for both trials, (b) students completed more target problems during explicit timing for the second trial, and (c) students only preferred interspersal for the first trial. The data from trial one fit the discrete task completion hypothesis and matching law, yet the data from trial two do not match as closely (Skinner, 2002). Discussion focuses on continued need for more research on academic interventions, comparing academic interventions, the discrete task completion hypothesis, and the matching law.