混合溶液中质量分数求值判定式的推导与应用

通过具体实例分析论述了混合溶液中质量分数的求值问题，在对常规解法进行剖析的同时，从理论上建立了新的解题方法。     

游戏化学习体验的质性分析研究

基于游戏化学习体验的基本理论框架,通过对学生游戏化学习体验的质性分析,本文探究了游戏化学习体验中认知体验与主体性体验的核心内容。本研究基于对多种资料的分析,归纳了游戏化学习过程中认知体验的过程要素,包含知识探究、学习迁移和认知成果;建构了主体性体验的核心要素,包括学习过程中的情绪状态、游戏与学习动机和反思意愿。对游戏化学习体验的核心内容的探究有助于理解游戏化学习行为,了解学生游戏化学习体验的个体差异,为教育游戏的设计和评估提供了重要参考。     

关于4个Lucas数乘积和的恒等变换注记

研究了4个Lucas数乘积和的恒等变换问题，给出了r次(r=2s)恒等变换公式．     

缺失数据下遗传重组率估计的EM方法

EM算法是在不完全信息资料下实现参数估计的一种通用迭代方法，其在现代科学的许多领域已有着广泛的应用。文章导出了双位点不同标记类型，包括共显性-共显性，共显性-显性和显性-显性三种模式下，部分个体缺失标记基因型时，重组率估计率的EM算法。用编制的SAS／IML程序进行了Monte Carlo模拟研究，验证了文章所述方法在遗传连锁分析中的有效性和实用性。     

Drawing on a Theoretical Model to Study Students’ Understandings of Fractions

Teaching and learning fractions has traditionally been one of the most problematic areas in primary school mathematics. Several studies have suggested that one of the main factors contributing to this complexity is that fractions comprise a multifaceted notion encompassing five interrelated subconstructs (i.e., part-whole, ratio, operator, quotient, and measure). Kieren was the first to establish that the concept of fractions is not a single construct, but consists of several interrelated subconstructs. Later on, in the early 1980s, Behr et al. built on Kieren’s conceptualization and suggested a theoretical model linking the five subconstructs of fractions to the operations of fractions, fraction equivalence, and problem solving. In the present study we used this theoretical model as a reference point to investigate students’ constructions of the different subconstructs of fractions. In particular, using structural equation modeling techniques to analyze data of 646 fifth and sixth graders’ performance on fractions, we examined the associations among the different subconstructs of fractions as well as the extent to which these subconstructs explain students’ performance on fraction operations and fraction equivalence. To a great extent, the data provided support to the associations included in the model, although, they also suggested some additional associations between the notions of the model. We discuss these findings taking into consideration the context in which the study was conducted and we provide implications for the teaching of fractions and suggestions for further research.     

二元对称型向量有理插值算法

本文构造了二元对称型向量有理插值的递推算法，并以矩阵的初等变换作为工具建立了插值系数的矩阵算法。     

一个分数序列的若干性质

利用一个简单的不等式构造了以[0,1]区间上的一个分数序列，并给出了该分数序列的若干性质．     

几个常用有理分式的分解公式

给出了几个常用有理分式分解成部分分式之和的分解公式和证明。     

Lucas数分式之和

设Un,Vn是Lucas数,研究了Lucas数分式变换之和,得到了封闭形恒等式.     

An Experiment in Teaching Ratio and Proportion

This paper summarizes our analysis of the complexity of ratio problems at Grades 6 and 7, and reports a two-year experiment related to the teaching and learning of rational numbers and proportionality in these grades. Two classes were followed and observed. Part of the teaching material was common to both classes, mainly the objectives and the corpus of ratio problems in a physical context. But in one class, here called “Partial-experiment”, the learning environment was exclusively a paper-pencil one and the teacher followed his usual method in designing and conducting teaching sequences. In the other class, here called “Full-experiment”, the teaching was based on a framework, emerging from our analysis of complexity of ratio problems, involving precise guidelines and a specific computer environment. Using a pre-test and a post-test, we observed clear progress in both classes compared to a sample of “standard” pupils. Our comparative pupil-oriented study indicates more complete improvement in the “full-experiment” class, i.e., a better acquisition of fractions and their use for solving usual proportionality problems. The average pupil’s progress is greater in the “full experiment”, with the pupils who were initially high- or low-level attainers benefiting the most from the “full-experiment”.