The Cognitive Process of Chinese Abacus Arithmetic

Based on the literature review about abacus arithmetic, this study proposes a model of the cognitive process of Chinese abacus arithmetic. This model describes three methods for solving abacus arithmetic problems: retrieval method, procedure method, and mental arithmetic method and three external factors that affect the choice of those methods: level of expertise, level of difficulty, and type of operation. The experiment in the study invited 36 participants including 12 vocational high-school students as junior experts, 12 ordinary high-school students as novices, and 12 bank clerks as senior experts to validate the 3 × 3 × 2 experiment. The results of this study indicate that (1) the retrieval method, procedure method, and mental arithmetic method are the three main calculation methods of abacus arithmetic, each of them having some variations; (2) experts tend to use the retrieval method, while novices tend to use the mental arithmetic method; (3) the retrieval method and mental arithmetic method are applied more for simple operations and addition problems, while the procedure method is applied more for complicated operations and subtraction problems.     

CAS理论在珠心算教学中的应用

传统的珠心算教学在教学发展过程中遇到瓶颈,珠心算教学系统的复杂性导致珠心算教学陷入困境,而系统科学的发展促进珠心算和各学科课程的融合和整合。首先从CAS理论入手,论证其在珠心算教学中应用的复杂性及可行性,并结合实际教学中存在的问题,提出在珠心算教学中应该注意的问题。     

珠心算神经生理机制研究及启智方案初探

珠心算是珠算式心算的简称,近几年,随着技术手段的不断进步．对珠心算的神经生理机制研究己取得丰硕的成果．本文分别从视觉空间,大脑两半球．数字运算的脑机制三个方面介绍了近几年珠心算的神经生理机制研究的成果,并指出．应该其基础上探索完善的启智培养方案。并给出了方案的总体假设。     

A LONGITUDINAL STUDY OF THE DEVELOPMENT OF MATHEMATICS STRATEGIES AND UNDERLYING COUNTING SCHEMES

The purpose of this study was to determine whether patterns of strategy use in second, third and fourth grade children’s arithmetic supported Steffe’s model of numerical development. In addition to student-generated strategies, we looked at commonly taught algorithms not considered in Steffe’s model to determine whether these algorithms reflected underlying schemes. 206 children were assessed on their strategy use while solving arithmetic problems in the second grade, the third grade and again in the fourth grade. Factor analyses indicated some support for Steffe’s model, but there were exceptions. Not all children progressed in their number knowledge and strategies as a function of schooling and schooling appeared to affect the types of strategies children use independent of underlying schemes.     

Inhibiting interference from prior knowledge: Arithmetic intrusions in algebra word problem solving

In Singapore, 6–12 year-old students are taught to solve algebra word problems with a mix of arithmetic and pre-algebraic strategies; 13–17 year-olds are typically encouraged to replace these strategies with letter-symbolic algebra. We examined whether algebra problem-solving proficiency amongst beginning learners of letter-symbolic algebra is correlated with the ability to inhibit intrusions from the earlier arithmetic strategies. Similar to typical school practice in Singapore, we asked 14 year-old students (N = 157) to use only letter-symbolic algebra to solve 9 algebra word problems. After having controlled for algebraic knowledge, working memory, and intelligence, better inhibitory ability still predicted fewer arithmetic intrusions and higher problem solving accuracy. Path analysis revealed 2 types of inhibition. Inhibition-of-reified-processes predicted accuracy through arithmetic intrusions. Inhibition-of-recently-learned-associations predicted accuracy through intelligence. Findings suggest establishing pedagogical links between arithmetic and algebraic methods may facilitate students' transition to letter-symbolic algebra.     

Promoting basic arithmetic competence in early school years–using a response to intervention model

This study investigated whether mathematics education based on a multi-tiered response to intervention (RTI) model can support students' arithmetic competence in primary schools in Sweden. The intent was to identify and support students at risk of failure. In this study, 113 students participated in the intervention, and 30 students participated in the control group. Both groups were followed from Grade 1 to the end of Grade 2 and compared. During the first semester in Grade 1, all students were taught basic addition and subtraction with explicit instructions in Tier 1. Those who did not respond to Tier 1 after one semester were provided support within Tier 2 during the second semester. The same was repeated in grade 2 and the students that did not respond to Tier 2 were supported within Tier 3. At the end of Grade 2, students in the intervention group performed significantly higher on the basic arithmetic competence in the number range 1–9 than the control group. No significant difference was found in a test measuring basic arithmetic competence in the number range 10–19. This study shows that using multi-tiered RTI might be sufficient to identify and support students at risk in early arithmetic competence.     

论珠心算在小学数学计算教学中的作用

计算能力是人类终身必备的基本能力,培养学生的计算能力应该是学校数学教学的主要任务之一。珠心算与笔算有着紧密的联系和内在规律。珠心算是在脑中运用象数思维的模型进行快速计算的方法,而笔算是借助阿拉伯数码来计算的模型。珠心算是从左向右运算的,与人的思维方式相应,符合人脑反映的顺逆关系,又与读数、写数、看数顺序一致,因而优于从低位向高位计算的笔算。在小学低年级数学计算教学中,利用珠心算能大大加快学生的计算速度,比笔算的运算过程直观、形象、快捷。     

小学生关系性思维的测试与分析

代数思维被认为是数学的“核心思想”,关系性思维与“代数思维”密切相关。有研究表明,有意识地培养学生的关系性思维,有助于学生从算术学习过渡到代数学习。文章对小学生关系性思维的特点进行了分析,并借助测试工具,对四、五、六年级小学生解决“23＋15=26＋口”这样的等式问题的思维方式进行了研究。这次测试反映出,小学生在解决上述等式问题时所表现出的关系性思维水平,并不因年级的升高表现更优。     

对话·辨析·能力——“基于学生中心”的理论性课程教学模式初探

长期以来高校汉语言文学专业理论性课程的灌输式教学导致教学效果低下,原因在于这种教学模式忽视了学生的作用。“师生对话一理论辨析一能力养成”三位一体的教学模式,是一种“基于学生中心”的理论性课程教学模式,既顺应了当前教育学理论的发展,也符合学生生理心理特点,更突出了教育的目的最终是为了实现“不教”。     

THE EFFECTS OF TESTING UPON ATTITUDE TOWARDS THE METHOD AND CONTENT OF INSTRUCTION

Senior high school mathematics students were taught computer arithmetic via self-instructional materials. Following instruction they were randomly assigned to one of two groups. One group was tested with a norm-referenced measure made up of items having moderate difficulty and high correlations with each other; the other group was tested with a criterion-referenced measure designed to assess attainment of specific behavioral objectives. Student attitude toward the content of instruction and toward the mode of instruction was assessed immediately following. Significantly more positive attitude toward the subject matter of instruction was associated with the use of the criterion-referenced measure. Differences in attitude toward mode of instruction were not significant.     

Schematising activities in early childhood education

The purpose of this study was to determine the importance of introducing schematising to children in early childhood and to determine whether schematising can be taught to children. This was done using a longitudinal, quantitative study with a quasi-experimental design (N = 133). In this study, the use of schematising was taught to an experimental group of children to determine if it is possible to realise significantly improved results in schematising tasks for an experimental group in comparison to a control group of children who were not taught schematising. Pupils in the experimental group demonstrated significantly better results on schematising, which cannot be explained by maturation. In our future research, we will investigate the mathematical performances of these experimental and control groups in the next grade of the primary school curriculum.     

The effect of Newsday's science education series program on selected ninth-grade students' comprehension of science reading material

Reading is a communication process that is crucial to students in science. Printed text materials are the most widely used teacher aids in the classroom. But reading as a major focus of science instruction has been out of favor with the mainstream of science education since the late 1950s. Despite this, few would deny the value of reading skills in a science class. The purpose of the present investigation was to determine how the use of Newsday's Science Education Series Program affected selected ninth-grade students' comprehension of science reading material. Analysis of covariance showed that students with standardized reading and mathematics scores at least two years above grade level who were taught using newspaper science articles alone had Degrees of Reading Power posttest scores higher at the 0.05 level of significance compared to students taught using Newsday's Science Education Series Program or using only the science article's content as part of class lessons. Students with standardized reading and mathematics scores on grade level taught using Newsday's Science Education Series Program had Degrees of Reading Power posttest scores higher at the 0.01 level of significance compared to students taught by either of the other methods.     

Gender effects for student perception of the classroom psychosocial environment

A future shortage of science teachers has been predicted, and since women are presently underrepresented in the sciences, they are a good potential source for future science teachers. Unfortunately women appear to become less interested in science as they continue in school. Because the classroom psychosocial environment has been shown to be related to learning outcomes, it may contribute to women's lack of interest in sciences. This study compared the classroom environments perceived by fourth grade, seventh grade and high school boys and girls in classes taught by males and females to determine if any perceptual differences existed. The three, two factor MANOVAS (teacher gender by student gender) showed no differences for fourth grade students, one for seventh grade students and three for high school students. The seventh grade boys and girls perceived classes taught by females as having more friction than classes taught by males and high school boys and girls perceived classes taught by females as being more difficult than classes taught by males. Further, for the high school students it appears that classes are perceived more favorably when the opposite genders are combined. These perceptual differences combined with role modeling may contribute to the lack of women in science. More research is necessary to determine causal relationships.     

Linguistic and Spatial Skills Predict Early Arithmetic Development via Counting Sequence Knowledge

Utilizing a longitudinal sample of Finnish children (ages 6–10), two studies examined how early linguistic (spoken vs. written) and spatial skills predict later development of arithmetic, and whether counting sequence knowledge mediates these associations. In Study 1 (N = 1,880), letter knowledge and spatial visualization, measured in kindergarten, predicted the level of arithmetic in first grade, and later growth through third grade. Study 2 (n = 378) further showed that these associations were mediated by counting sequence knowledge measured in first grade. These studies add to the literature by demonstrating the importance of written language for arithmetic development. The findings are consistent with the hypothesis that linguistic and spatial skills can improve arithmetic development by enhancing children's number‐related knowledge.     

Learning to spell: variability, choice, and change in children's strategy use

We examined whether the overlapping waves model, originally developed to account for strategy choices in arithmetic, could also account for strategy choices in spelling. The contrast was of particular interest because arithmetic is an algorithmic domain (a domain that includes strategies that always yield correct answers if executed properly), whereas spelling is not. Thirty first-grade students spelled words under 2 conditions, and 23 of these students were retested in second grade. Trial-by-trial analysis of strategy use was used to identify which strategies first and second graders used, how adaptively they chose among them, how effective the strategies were, and what changes occurred from first to second grade along each dimension. The model proved useful for understanding the development of spelling, despite the fact that explicit use of backup strategies had a minimal impact on accuracy. Implications for understanding adaptive strategy choices in algorithmic and nonalgorithmic domains are discussed.     

Partial Fractions via Calculus

The standard technique taught in calculus courses for partial fraction expansions uses undetermined coefficients to generate a system of linear equations; we present a derivative-based technique that calculus and differential equations instructors can use to reinforce connections to calculus. Simple algebra shows that we can use the derivative to calculate coefficients, reinforcing calculus connections. For irreducible quadratic factors, the simple derivative formula with complex arithmetic gives the coefficients, helping students gain facility with complex numbers. For higher multiplicity factors, we can use higher derivative formulas taken from the Laurent expansion. We conclude with examples of using the technique in different courses, highlighting precalculus and calculus classes.     

湖北省现场统计研究会2010年学术年会会议论文选——基于区组设计的建模评分方式研究

数学建模竞赛试卷的评分方式的合理性与公正性一直是大家关注的焦点.传统的评分方式的最大弊端在于阅卷老师的差异会对试卷的最终得分有一定的影响.根据区组设计的思想,对每位阅卷教师的差异性进行提取,并应用方差分析法进行假设检验.若不同阅卷老师的评分没有显著性差异,就可以用传统的算术平均法计算得分;否则,就应该对学生的试卷得分进行调整,以消除不同阅卷老师评分的差异性,从而保证公平.     

电子算盘训练器的设计

针对珠算教学中出现的问题,本着提高教学管理的效率、实现学生的自我测试和评价的目的,设计了带USB接口的珠算训练器。对电子算盘训练器的上位机、下位机、系统数据库和系统功能进行了详细的设计。     

高职院校开设珠算课的意义

随着计算机的不断普及，珠算以其特有的算理和化作为一种计算工具不仅没有消失，而且在小规模运算时，更多的人越来越愿意使用算盘，因此，有必要对珠算重新认识。同时，高校开设珠算课不仅仅是掌握一种计算技能的需要，更是提高学生素质的手段。