小学一～三年级儿童加减法策略选择的发展特点研究

随机选取90名小学一～三年级的儿童为被试,采用实验法和访谈法对儿童解决加减法算术题的策略发展特点进行了探讨。结果发现:1儿童能运用多种策略解决加减法算术题,在解决两个数的算术题时用到了13种策略,在解决三个数的算术题时用到了8种策略。2儿童在解决同一道题时大多能同时运用两种或两种以上的策略。3随着年龄的增长,儿童使用策略的总目呈简约化发展的趋势。4在解决两个数的算术题时,不同年级的儿童在使用出声策略、拆十策略、手势策略、逆算策略、数数策略的次数上差异显著,随着年级的增长其使用频率逐渐降低。5儿童在解决三个数的算术题时,各年级儿童使用出声策略、手势策略、对位策略差异显著,随着年级的增长其使用频率逐渐增高。     

When Hyperpropositions Meet ...

With each proposition P we associate a set of proposition (a hyperproposition) which determines the order in which one may retreat from accepting P, if one cannot fully hold on to P. We first describe the structure of hyperpropositions. Then we describe two operations on propositions, subtraction and merge, which can be modelled in terms of hyperpropositions. Subtraction is an operation that takes away part of the content of a proposition. Merge is an operation that determines the maximal consistent content of two propositions considered jointly. The merge operation gives rise to an inference relation which is, in a certain sense, optimally paraconsistent.     

Age and outcome allocation: A new test of the subtractive model

The no, moderate, and large differences between shares of outcome allocated to the high and low performers are interpreted as the respective rules of equality, ordinal equity, and proportional equity. The ability to employ the proportional rule is also believed to develop around the age of 13 years. The authors hypothesized that: (i) the rule of outcome allocation is subtraction; and (ii) age differences in outcome allocation are mediated by age differences in perceived inputs. In an experiment on Chinese aged 8–20 years, measures of perceived inputs were taken after or before outcome allocation. Results from the input-allocation order supported the hypotheses. Obviously, age effects in outcome allocations by Asians can sometimes be mediated by age differences in the ability to perceive the inputs accurately.     

The role of perceptual and cognitive processes in addition-subtraction studies with 5-month-old infants

After a brief familiarization period to either one or two toys 5-month-olds gave a clear preference for perceptually novel displays, suggesting that replicable findings of greater looking at an unexpected arithmetic outcome in addition/subtraction experiments cannot easily be attributed to simple familiarity preferences.     

聋生和听力正常学生解决加减文字题的眼动比较研究

采用EyetinkⅡ眼动记录仪,探讨了聋生与解题正确率高的听力正常学生表征和解决加减文字题的差异。被试为小学3年级学生．聋生12名．听力正常学生8名。研究结果表明：（1）在解决加减文字题时,聋生与解题正确率高的听力正常学生在阅读方式、关注关键信息上有显著差异,很多聋生阅读没规律．漏看文字题的关键信息;（2）聋生解决加减文字题的困难与其不能正确表征文字题的文本有关。     

Retention and treatment failure in Classwide Peer Tutoring: Implications for further research

Knowledge of basic arithmetic facts aids in the acquisition and speed of performance of arithmetic operations. A peer mediated instructional procedure, Classwide Peer Tutoring (CWPT), has been shown to increase the rates and accuracy of students responses to academic tasks and to improve student performance on a variety of academic tasks. The present investigation evaluated the retention of 100 subtraction items by primary grade-age children with mild disabilities using CWPT for 10 weeks. Short- and long-term retention of items, and rate of correct responding were assessed. Results indicated that the students' average pretest score was 58.0% correct, and their average weekly posttest score was 87.12 correct, a 27% improvement in accuracy. Short- and longer-term retention measured on posttests was 88.7 % and 85.0% correct, respectively. Improvement in students rate of accurate responding to subtraction items practiced during CWPT was obtained. Student failure to learn particular items was not attributable to fewer opportunities to practice these items, less accurate practice, or item difficulty. Students reported positive evaluation of CWPT and perceived positive social and self esteem outcomes. Directions for future research focusing on retention and analysis of treatment failure are suggested.     

Influence of the large–small split effect on strategy choice in complex subtraction

Two main theories have been used to explain the arithmetic split effect: decision‐making process theory and strategy choice theory. Using the inequality paradigm, previous studies have confirmed that individuals tend to adopt a plausibility‐checking strategy and a whole‐calculation strategy to solve large and small split problems in complex addition arithmetic, respectively. This supports strategy choice theory, but it is unknown whether this theory also explains performance in solving different split problems in complex subtraction arithmetic. This study used small, intermediate and large split sizes, with each split condition being further divided into problems requiring and not requiring borrowing. The reaction times (RTs) for large and intermediate splits were significantly shorter than those for small splits, while accuracy was significantly higher for large and middle splits than for small splits, reflecting no speed–accuracy trade‐off. Further, RTs and accuracy differed significantly between the borrow and no‐borrow conditions only for small splits. This study indicates that strategy choice theory is suitable to explain the split effect in complex subtraction arithmetic. That is, individuals tend to choose the plausibility‐checking strategy or the whole‐calculation strategy according to the split size.     

Errors in subtractions: judged and observed frequencies

In a first study 10 adults, aged 24-44 years, solved all 105 subtraction problems in the form M - N = , where 0 < or = M < or = 13, 0 < or = N < or = 13 and N < or = M. Each participant solved every problem 10 times and in total there were 10 500 answers. Answers, response latencies and errors were registered. Retrospective verbal reports were also given, indicating how a solution was reached: (1) via a (conscious) reconstructive cognitive process or (2) via an (unconscious) reproductive (retrieval) process. The participants made 291 errors (2.8%) when solving the subtractions in study 1. The rate of self-correction was very high, 92%. In a second study 27 undergraduate students estimated overall error rates, including self-corrected errors for the 105 subtraction problems used in the first study. Judged and actual error rates were compared. The participants systematically underestimated error rates for error prone problems and overestimated error rates for error free problems. The participants were fairly accurate when they predicted problems that were most error prone, with a hit rate of 0.67 for the (18) problems predicted as the most error prone ones. In contrast, predictions of which problems were error free were very poor with a hit rate of only 0.20 of the problems predicted as error free really having no errors in study 1. The correlation between judged error rates and frequencies for actually made errors was 0.69 for answers belonging to reconstructive solutions. In contrast, there was no significant correlation between judged and actual error rates at all for retrieved solutions, possibly reflecting the inaccessibility to consciousness of quick retrieval processes.     

解答加减文字题中情境复杂性对问题难度的影响

过去人们基于语言复杂性探讨加减文字题的难度成因,本研究将探讨情境复杂性对问题难度的影响。被试为北京市一城区小学二年级共108名学生（男52,女56）,平均年龄8岁4个月。采用2(问题类型：“给”问题和“拿”问题)×2(事件类型：增多事件和减少事件)混合设计。对于“给”问题,增多题中各语句的主语不一致,减少题中一致,对于“拿”问题则相反。根据语言复杂性解释,因为各语句的主语一致有利于加工,“给”问题有减少题加工优势,“拿”问题有增多题加工优势;根据情境复杂性解释,因为减少情境有利于加工,两类问题均有减少题加工优势。实验表明不论“给”问题还是“拿”问题,均有减少题的加工优势,支持情境复杂性解释     

加减文字题解决研究概述

加减文字题指应用加减法运算解答的简单数学应用题。基本类型有合并题、变化题和比较题。人们主要采用四种方法研究解题过程：解答问题、回忆和构造问题、建立计算机模型和眼动记录。过去研究发现语义类型、年龄、难以理解的词句、问题陈述的简约性、题材个人化、问题陈述结构、数量大小、未知集类型和解答问题的方式等因素显著影响解题过程。人们对解题过程提出了两种理论模型,一是数学知识应用模型,一是语言理解模型