Impact of Children’s math self-concept,math self-efficacy,math anxiety,and teacher competencies on math development

We examined to what extent children’s development of arithmetic fluency and mathematical problem-solving was influenced by their math self-concept, math self-efficacy, and math anxiety but also teacher competence, specifically: actual teaching behavior, self-efficacy, and mathematical teaching knowledge. Participants were 610 children and 31 teachers of grade four. Multi-level analyses showed children’s math self-concept to be a positive predictor of arithmetic fluency and actual teaching behavior to be a negative predictor. The development of mathematical problem-solving was predicted: positively by mathematical teaching knowledge; negatively by actual teaching behavior and teachers’ self-efficacy; and not at all by the child factors of math self-concept, math self-efficacy, or math anxiety. Promoting the self-confidence of young children is essential for their mathematical development. More research into the relationship between teaching behaviors and children’s math development is needed.     

Mathematical history,philosophy and education

History of mathematics occupies itself describing processes of growth and development, whereas philosophy of mathematics is concerned with questions of justification. Both play an essential role within the educational context. But there is a problem because genuine historical studies necessitate ever greater particularity whereas mathematics and philosophy require generality and abstraction. The paper offers some methodological reflections about these matters together with two case studies from nineteenth century history of arithmetic and integration theory, respectively, which try to strike a balance between the directly opposed requirements.     

Representation of problem-solving procedures: A comparative look at China, Singapore, and US mathematics textbooks

This study examined how selected school mathematics textbooks in China, Singapore, and USA at the lower secondary grade level represent problem-solving procedures. The analysis of problem-solving procedures was carried out in two layers – general strategies, which adopted Pólya’s four-stage problem-solving model, and specific strategies, which consisted of 17 different problem-solving heuristics such as ‘acting it out,’ ‘looking for a pattern,’ ‘working backwards,’ etc. Both similarities and differences in the representation of problem-solving procedures in the textbooks across the three countries were revealed and compared. The possible reasons for the similarities and especially for the differences were explored. Suggestions about how to improve the representation of problem-solving in mathematics textbooks were provided at the end of the study.

数列通项式求解方法

求数列通项式，在中等学校数学教学中是一个难点，又占有一定的重要位置．笔者就数列通项式的求解方法归纳整理为累加法、递推式法、数学归纳法和待定系数法，提出了典型例子，并就待定系数法进行了较深入的探讨．     

小学生数学能力培养探析

培养数学能力是国内外数学教学改革的发展趋势，也是中小学数学教学的重要任务。正确认识小学生数学能力的内涵，重视小学生数学能力的培养，探索数学能力培养的途径已成为提高小学生数学教学质量的当务之急。     

学生数学能力培养之我见

就“培养学生的数学能力 ,提高学生的素质”这一问题 ,从数学知识的传授、数学知识的应用这两个方面进行阐述 ,提出在注重数学知识传授的基础上进行数学建模教学的方法 .     

The completeness property of the set of real numbers in the transition from calculus to analysis

This paper focuses on teaching and learning the set of real numbers R and its completeness property at the university level. It studies, in particular, the opportunities for understanding this property that students are offered in four undergraduate correlative courses in Calculus and Analysis. The theoretical framework used in the study draws on concepts developed in the Anthropological Theory of Didactics, especially the notions of praxeology and mathematical organization. The paper shows different expectations concerning the same notion (R and its completeness) through different school levels, and intends to bring up some reflections about the transition from Calculus to Analysis.

论新课程标准下数学教师的素质

2l世纪已进入信息社会，新一代公民要有较高的数学素养．作为培养新一代公民的当代数学教师，值此新课程标准实施之际，应如何迎接基础教育大改革新形势的挑战呢?本文试图回答这一问题，提出了对数学教师素质的一些新要求．     

“奥数”兴衰的利益逻辑

奥数在中国潮起潮落,关键在于利益的嵌入。这种利益以机会、条件与资源的形式分布到奥数场域中。利益的存在引发奥数场域中主要的利益相关者——学生、学校、培训与出版机构的利益博弈,并且导致教育付出不对称的利益代价,伤害了教育本身。要消除全民奥数,避免奥数沦为利益博弈的工具,回归教育的本真,需要依赖教育、制度与行政层面的作为来缩减利益空间、规范利益分配、遏止不当得利。     

Adaptive number knowledge and its relation to arithmetic and pre-algebra knowledge

Traditionally measured skills with arithmetic are not related to later algebra success at levels that would be expected given the close conceptual relation between arithmetic and algebra. However, adaptivity with arithmetic may be one aspect of arithmetic competences that can account for additional variation in algebra attainment. With this in mind, the present study aims to present evidence for the existence and relevance of a newly acknowledged component of adaptivity with arithmetic, namely, adaptive number knowledge. In particular, we aim to examine whether there are substantial individual differences in adaptive number knowledge and to what extent these differences are related to arithmetic and pre-algebra skills and knowledge. Adaptive number knowledge is defined as the well-connected knowledge of numerical characteristics and relations. A large sample of 1065 Finnish late primary school students completed measures of adaptive number knowledge, arithmetic conceptual knowledge, and arithmetic fluency. Three months later they completed a measure of pre-algebra skills. Substantial individual differences in adaptive number knowledge were identified using latent profile analysis. The identified profiles were related to concurrent arithmetic skills and knowledge. As well, adaptive number knowledge was found to predict later pre-algebra skills, even after taking into account arithmetic conceptual knowledge and arithmetic fluency. These results suggest that adaptive number knowledge is a relevant component of mathematical development, and may help account for disparities in algebra development.