小学2～4年级儿童数学应用题表征策略差异的研究

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年级学生进行了数学应用题测验,以考察数学学优生和学差生在解决比较应用题时表征策略的差异。结果表明:(1)从2～4年级儿童解答一致和不一致应用题上看,学优生较多地使用问题模型策略对问题进行表征,学差生较多地使用直接转换策略对问题进行表征;(2)除学差女生的解题正确率低于学差男生的正确率,学差女生自我报告中直接转换策略的使用多于学差男生外,在其它方面,性别差异并不显著;(3)随着年级的升高,学优生在使用问题模型策略上越来越成熟,学差生并没有学会使用更加有效的问题模型表征策略,仍然停留在直接转换策略上,但他们在关于策略使用的认识上有所提高。     

心算加工年老化及其机制研究

以１７２名２０－７９岁成人为被式对心算加工的年老化过程及其机制进行了研究。任务为连续减法心算,依难度分为５种：１０００－１,１０００－３,１０００－１３及１０００－１７。结果表明,年龄与心算难度存在明显的交互作用,且随着年龄增加,不同难度心算效率均以幂函数形式降低。     

心算活动机制的研究

心算是一种重要的思维活动,是认知心理学的研究主题之一。心算活动具有明显的问题大小效应,其加工过程与工作记忆和长时记忆存在密切关系。此外,对心算的加工机制进行跨学科（认知心理学、神经科学等）的综合研究,是今后心算研究的主要方向。     

心算加工年老化及其机制研究

以172名20－79岁成人为被试对心算加工的年老化过程及其机制进行了研究。任务为连续减法心算,依难度分为5种：1000－1、1000－3、1000－7、1000－13及1000－17。结果表明,年龄与心算难度存在明显的交互作用,且随着年龄增加,不同难度心算效率均以幂函数形式降低。结构方程建模分析发现心算加工年老化过程存在两个中介作用因子,即速度因子和非速度因子,且速度因子对非速度因子存在明显的正效应。     

Empiricism,probability, and knowledge of arithmetic: A preliminary defense

The topic of this paper is our knowledge of the natural numbers, and in particular, our knowledge of the basic axioms for the natural numbers, namely the Peano axioms. The thesis defended in this paper is that knowledge of these axioms may be gained by recourse to judgments of probability. While considerations of probability have come to the forefront in recent epistemology, it seems safe to say that the thesis defended here is heterodox from the vantage point of traditional philosophy of mathematics. So this paper focuses on providing a preliminary defense of this thesis, in that it focuses on responding to several objections. Some of these objections are from the classical literature, such as Frege's concern about indiscernibility and circularity (Section 2.1), while other are more recent, such as Baker's concern about the unreliability of small samplings in the setting of arithmetic (Section 2.2). Another family of objections suggests that we simply do not have access to probability assignments in the setting of arithmetic, either due to issues related to the ω-rule (Section 3.1) or to the non-computability and non-continuity of probability assignments (Section 3.2). Articulating these objections and the responses to them involves developing some non-trivial results on probability assignments (Appendix A–Appendix C), such as a forcing argument to establish the existence of continuous probability assignments that may be computably approximated (Theorem 4 Appendix B). In the concluding section, two problems for future work are discussed: developing the source of arithmetical confirmation and responding to the probabilistic liar.     

Frequency of finger looking during finger counting is related to children's working memory capacities

Finger counting can be useful in solving arithmetic problems, noticeably because it reduces the working memory demand of mental calculations. However, proprioceptive information might not be sufficient to keep track of the number of fingers raised during problem solving, and visual input may play an important role in this process. The present study was designed to address this question and shows that 8-year-old children look at their fingers in 60% of the trials during finger counting when solving additive problems. Moreover, our results reveal that the frequency of finger looking is negatively correlated with working memory capacities and is higher for more difficult problems. These findings suggest that finger looking is recruited in managing the cognitive demand of the arithmetic task, probably by providing additional external cues to monitor the number of steps that have to be incremented during finger counting.     

The Effect of Interpolated Motor Activity on the Short-Term Retention of Movement Distance and End-Location

The effect of an interpolated movement on the recall of a blind, lever-positioning movement was assessed separately for the reproduction cues of distance and end-location. Both cues showed the context effect of assimilation, that is, the end-location of the interpolated movement caused directional biasing of the algebraic or constant error (CE) for location reproduction while the length of the interpolated movement caused similar directional biasing for distance reproduction. Variability about algebraic error (VE) was used to assess forgetting. There was no change in VE for location reproduction, and an increase in VE for distance reproduction was limited to the relatively large movements. Thus, an interpolated movement that does not have to be remembered does not cause interference with the retention of location information, but does cause some interference with the retention of distance information. The findings are discussed in relation to a model of motor short-term memory which incorporates both CE and VE.     

Error adaptation in mental arithmetic

Until now, error and conflict adaptation have been studied extensively using simple laboratory tasks. A common finding is that responses slow down after errors. According to the conflict monitoring theory, performance should also improve after an error. However, this is usually not observed. In this study, we investigated whether the characteristics of the experimental paradigms normally used could explain this absence. More precisely, these paradigms have in common that behavioural adaptation has little room to be expressed. We therefore studied error and conflict adaptation effects in a task that encounters the richness of everyday life's behavioural adaptation—namely, mental arithmetic, where multiple solution strategies are available. In accordance with our hypothesis, we observed that posterror accuracy increases after errors in mental arithmetic. No support for conflict adaptation in mental arithmetic was found. Implications for current theories of conflict and error monitoring are discussed.     

High-performers use the phonological loop less to process mental arithmetic during working memory tasks

This study investigated the effects of three working memory components—the central executive, phonological loop, and visuospatial sketchpad—on performance differences in complex mental arithmetic between individuals. Using the dual-task method, we examined how performance during two-digit addition was affected by load on the central executive (random tapping condition), phonological loop (articulatory suppression condition), and visuospatial sketchpad (spatial tapping condition) compared to that under no load (control condition) in high- and low-performers of complex mental arithmetic in Experiment 1. Low-performers showed an increase in errors under the random tapping and articulatory suppression conditions, whereas high-performers showed an increase of errors only under the random tapping condition. In Experiment 2, we conducted similar experiments on only the high-performers but used a shorter presentation time of each number. We found the same pattern for performing complex mental arithmetic as seen in Experiment 1. These results indicate that high-performers might reduce their dependence on the phonological loop, because the central executive enables them to choose a strategy in which they use less working memory capacity.