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.     

Who can escape the natural number bias in rational number tasks? A study involving students and experts

Many learners have difficulties with rational number tasks because they persistently rely on their natural number knowledge, which is not always applicable. Studies show that such a natural number bias can mislead not only children but also educated adults. It is still unclear whether and under what conditions mathematical expertise enables people to be completely unaffected by such a bias on tasks in which people with less expertise are clearly biased. We compared the performance of eighth‐grade students and expert mathematicians on the same set of algebraic expression problems that addressed the effect of arithmetic operations (multiplication and division). Using accuracy and response time measures, we found clear evidence for a natural number bias in students but no traces of a bias in experts. The data suggested that whereas students based their answers on their intuitions about natural numbers, expert mathematicians relied on their skilled intuitions about algebraic expressions. We conclude that it is possible for experts to be unaffected by the natural number bias on rational number tasks when they use strategies that do not involve natural numbers.     

系统思维在糖尿病防治中的应用

随着人们生活水平的提高,糖尿病日益成为威胁人类健康的主要疾病。在整体观的指导下,人们对于糖尿病采取综合全面的治疗。同时,整体优化的原则在防治中被充分运用。近年来,我国建立了2型糖尿病发病因素分析方式与概率预测模型。     

大学生SCL－90测试结果的研究

采用ＳＣＬ－９０临床症状自评量表,对随机抽取的安徽大学１－４年级２００名学生进行测试,结果表明：大学生心理健康总体水平低于全国成人常模;生源于城市和农村的大学生相比,总体差异不显著;生源于应届高中毕业生和历届高中毕业的大学生相比,在恐怖和精神病性两因子上,前者的均分显著高于后者;男女大学生相比,女大学生在抑郁和恐怖两个因子上的均分显著高于男大学生。     

外框数目、线索数目和线索类型对返回抑制的影响

采用被试内重复测量设计和经典的线索—靶子实验范式,考查了外框数目（4和8）、线索数目（1和3）、不同线索类型（on-off线索（即线索出现后消失）、onset线索（即线索持续呈现））对返回抑制的影响,发现靶子潜在位置数目越多反应时越长,返回抑制量越小;线索数目越少反应时越长,返回抑制量越大;onset线索反应时长于on-off线索,onset线索产生的返回抑制量大于on-off线索。这表明空间工作记忆负载和记忆痕迹会影响返回抑制。     

易学思想与中国传统建筑

本文从卦象、易数与阴阳合德三方面论述了易学思想与中国传统建筑之间不可分割的联系,中国建筑作为中华文明的重要组成部分,其本源是来自<周易>,与易学思想的发展变化密切相关.     

探索道路上的十年——“现代小学数学”教学实验

本文是对十年来的“现代小学数学”教学实验的初步总结。实验结果表明:1.把作为主体认识对象的客体(小学数学知识)的建构与对主体对客体认识的发展规律的研究有机发结合起来,这一研究小学生数学思维发展的总体设计是可行的、有效的;2.有意识地揭示小学数学知识内在的辩征关系以萌发小学生的辩证思维,不仅有必要,而且有可能;3.心理学研研人员与教学研究人员和广大教师相结合,是进行教学实验的一条比较理想的途径。     

《河图》五行数与《周易》四象数之间的关系

<河图>的五行成数不能与<周易>四象数混同."六、七、八、九"四数在<周易>与<河图>中的含义并不一致;五行成数实际存在两种说法,先秦文献中使用的土的成数是"五",而不是"十",因而五行数到"九"为止;土有成数"十"最初见于汉代,实际是五行学说在<易>理指导下发展的产物.     

《周易》自然哲学与生命实践

《周易》蕴涵的自然哲学思想,可谓是一种以生命为隐喻,宇宙论、本体论、价值论统一的生成哲学,它基于道德实践与认识实践统一的生命实践。文章根据《周易》"经"、"传"本身之内涵,按现代哲学表述方法,从源于道德之宇宙论,三才圆通之本体论,知行不二之实践论,生成整体之方法论等方面,阐明中国式自然哲学的特性与意义。指出正是这种独特的自然哲学,不仅开启了中国文化超越的价值之源,为中国古代科学提供了形而上学基础,而且应在21世纪伟大历史转型和中西对话中,共同创造人类不同文化"殊途同归"、"和而不同"的世界生成之序。     

Taurek, Numbers and Probabilities

In his paper, “Should the Numbers Count?" John Taurek imagines that we are in a position such that we can either save a group of five people, or we can save one individual, David. We cannot save David and the five. This is because they each require a life-saving drug. However, David needs all of the drug if he is to survive, while the other five need only a fifth each. Typically, people have argued as if there was a choice to be made: either numbers matter, in which case we should save the greater number, or numbers don't matter, but rather there is moral value in giving each person an equal chance of survival, and therefore we should toss a coin. My claim is that we do not have to make a choice in this way. Rather, numbers do matter, but it doesn't follow that we should always save the greater number. And likewise, there is moral value in giving each person an equal chance of survival, but it doesn't follow that we should always toss a coin. In addition, I argue that a similar approach can be applied to situations in which we can save one person or another, but the chances of success are different.     

整数构成对分数加工的影响

本研究通过两个实验考察了整数构成对分数加工的影响。实验一重复了Bonato等(2007)的研究,要求25名被试比较1/5与1/1、1/2、1/3、1/4、1/6、1/7、1/8、1/9等分数的大小,结果发现被试采用了成分加工策略,即通过比较分母判断分数的大小。实验二改变了分数的整数构成,让24名被试比较1/5与1/1、2/4、3/9、4/16、4/24、3/21、2/16、1/9等分数的大小。这些分数与实验一中的分数实数值相等但整数构成不同。结果表明被试既采取了成分策略,又采取了整体策略,即比较分数的实数值,不过成分策略比整体策略的作用更大。这些结果表明,分数加工具有成分和整体两种策略,具体使用哪种策略与分数的整数构成密切相关。     

负数的空间表征引起的空间注意转移

本研究采用数字线索提示的刺激探测任务, 通过三个实验探讨负数的低水平加工能否,以及怎样引起空间注意的转移。实验一探讨只有负数单独呈现作为线索时能否引起空间注意的转移。结果表明：对负数绝对值大小的加工能引起空间注意的转移。实验二进一步探讨在正数、负数和零混合作为线索时能否引起空间注意的转移。结果表明：对负数数量大小的加工能引起空间注意的转移。实验三再次用正数, 负数和0三种数字混合作为探测刺激前的线索, 但仅对负数和零作为提示线索之后的探测刺激进行反应, 又一次得到了由有效提示线索所引发的对数字数量大小加工引起的空间注意的转移。本研究表明, 对负数的低水平加工可以引起空间注意的转移, 然而, 是对绝对值的加工还是数量大小的加工引起注意转移依赖于共同参与的其它数字加工产生的影响。     

邵雍易数哲学探微

本文将分五个部分以论邵雍之易数思想：首先,以天地之数和圆方之数作为天地源起之象征,并以此二数分为十六大位,以穷究天地体用之变化。其次,以阴阳奇偶之数作为天圆地方之数的基础,并以阴阳刚柔之四象、八卦配合干支之数,参以天地变化之数和体四月三之原则,以导出象征生灵万有之动植通数。再次,结合前两部分所探讨之天圆地方变化十六位数和阴阳刚柔奇偶动植通数,以呈现出一体用生物运行具象之数,以此代表天地万物的流行生化之象《天主运行,地主生化》。再次,将天行刚健之数进一步具体细分为元会运世之数．以成就邵雍独创之历法纪年。同时,将地生柔顺之数进一步体现于律吕声音之多元性和差异性来表现动植生物之不齐与参差。最后,以此五类大数施行、旁通而统贯于自然界与人文界之一切万有,以作为邵雍易学中穷理之学的终结。     

数字表征的表象赋义效应:来自数字线估计任务的证据

已有研究中数字线估计任务几乎都使用纯数字。本研究以二到六年级儿童为被试,采用纯数字任务和赋义数字任务来探索赋义表象对数字表征形式的影响。结果表明,对0~1000的数字赋义后,对数模型的解释力上升,而线性模型的解释力下降;表象大小对于赋义数字的估计影响显著,大表象赋义提高了对数模型解释力而降低了数字估计的准确性,小表象的影响比较微弱。     

关于数字卦与六十四卦符号体系之形成问题

将见于商周器物上的数字卦与传逝文献的有关记载结合起来分析,商周时期应已存在用两个符号记写的六十四卦体系;周初陶拍所见易卦与传本《周易》相同的非覆即反的排列方法,也表明当时的筮书应是用两个确定的符号记写的;六十四卦应如文献所记是由八卦重合而成的,而这种八卦形成的前提同样是将其记写符号确定为两个;构成八卦的阴阳爻应是按阴阳观念将偶数记成“一一”,将奇数记戚“—”的产物。     

A Note on Finiteness in the Predicative Foundations of Arithmetic

Recently, Feferman and Hellman (and Aczel) showed how to establish the existence and categoricity of a natural number system by predicative means given the primitive notion of a finite set of individuals and given also a suitable pairing function operating on individuals. This short paper shows that this existence and categoricity result does not rely (even indirectly) on finite-set induction, thereby sustaining Feferman and Hellman's point in favor of the view that natural number induction can be derived from a very weak fragment of finite-set theory, so weak that finite-set induction is not assumed. Many basic features of finiteness fail to hold in these weak fragments, conspicuously the principle that finite sets are in one-one correspondence with a proper initial segments of a (any) natural number structure. In the last part of the paper, we propose two prima facie evident principles for finite sets that, when added to these fragments, entail this principle.