Persona-Based Journaling: Striving for Authenticity in Representing the Problem-Solving Process

Students’ mathematical problem-solving experiences are fraught with failed attempts, wrong turns, and partial successes that move in fits and jerks, oscillating between periods of inactivity, stalled progress, rapid advancement, and epiphanies. Students’ problem-solving journals, however, do not always reflect this rather organic process. Without proper guidance, some students tend to ‘smooth’ out their experiences and produce journal writing that is less reflective of the process and more representative of their product. In this article, I present research on the effectiveness of a persona-based framework for guiding students’ journaling to reflect the erratic to-and-fro of the problem-solving process more accurately. This framework incorporates the use of three personas—the narrator, the mathematician, and the participant—in telling the tale of the problem-solving process. Results indicate that this persona-based framework is effective in producing more representative journals.     

The effects of informational complexity and working memory on problem-solving efficiency

This study investigated the influence of informational complexity and working memory capacity on problem-solving efficiency. We examined two predictions of thesituational efficiency hypothesis, which states that the efficiency of problem solving varies as a function of situational constraints. One prediction is that informational complexity affects problem-solving efficiency. A second prediction is that working memory capacity affects problem-solving efficiency. Students completed a working memory task and solved abstract and concrete syllogisms. Participants solved abstract syllogisms more accurately than concrete syllogisms and spent more time solving abstract syllogisms. Thus participants demonstrated greater problem-solving efficiency when solving concrete syllogisms. Results indicate that there is a trade-off between problem-solving accuracy and problem-solving time when information differs with respect to informational complexity, a phenomenon we refer to as theefficiency paradox. Working memory capacity did not affect accuracy or efficiency. The results support the conclusion that problem-solving efficiency is situational and a function of the complexity of information. Educational implications and directions for future research are suggested.     

肺水肿与民族因素间的多元线性回归分析

基于多元线性回归分析的理论,通过建立数学模型,对肺水肿发病人数与民族因素之间的多元线性关系进行探讨。文章通过SPSS软件对青海海西州地区肺水肿发病例监测登记资料进行统计分析,建立了多元线性回归模型。最后,对所得到的回归方程进行显著性检验。     

改进的变分迭代法在Fokker-Planck方程中的应用

讨论将改进的变分迭代法应用于Fokker-Planck方程或者其相似的方程并求精确解.通过其简便的计算得到方程的解,与Adomian分裂法对比可知变分迭代法求收敛解的速度比后者要快速、简单.     

小波阈值方法在Laplace方程中的应用

把Laplace方程的柯西问题化为算子方程来考虑,右端项是非精确数据。运用小波对偶最小二乘法,得到了阶最佳的收敛性稳定性分析和非线性自适应。     

问题解决模式与场依存性认知方式的相关研究

以往关于问题解决模式的研究并没有揭示出不同个体解决同一问题时认知行为的内部差异及其与场依存性认知方式的相关性.提出盲目式、产生式、范畴式三种认知模式,综合运用认知作业分析法、心理测验法、个案访谈法来揭示不同个体在同一问题解决中认知模式的差异及与场依存性认知方式的相关性.结果发现各种问题解决认知模式的个案数具有非常显著性的差异;认知模式的总体分布没有表现出性别上的显著差异;认知模式与场依存性认知方式显著相关.因此可得出结论:不同个体解决同一问题时认知行为存在显著的内部差异;认知模式与场依存性认知方式具有显著相关性;认知模式的总体分布在性别上的差异不显著.     

双变量模型的二阶差分方程的分析与应用

说明怎样运用二阶差分方程法分析双变量模型,其中每一个变量既是滞后一期的该变量的函数,又是滞后一期的另一个变量的函数,旨在为当今社会经济的发展提供理论和实践依据。     

关于不定方程x（x+d）（x+2d）（x+3d）=p2ky（y+d）（y+2d）（y+3d）

设p是素数,k为自然数,d>1为奇数。该文运用初等方法证明了不定方程x(x+d)(x+2d)(x+3d)=p2ky(y+d)(y+2d)(y+3d)没有正整数解。     

非线性Schroeginger方程的包络波形式新的精确解

采用一种双曲函数和一类新的辅助常微分方程相结合的方法给出非线性Schroeglnger方程的包络波形式的精确解．这种方法也可用于其他非线性发展方程的新的孤立波解．     

电大生《经济数学基础》课程学习困难的成因分析

本文对电大生《经济数学基础》课程学习困难的成因进行了分析,并对教师在该课程教学中要注意的问题提出了几点建议。