转化法在数学解题中的应用

本文通过例题说明转化法在数学解题中的应用     

Teaching Critical Thinking and Problem Defining Skills

Critical thinking and skills in defining problems have been among the goals of a computers and society course that had its credits reduced and student number increased. In an attempt to prevent worsening the students' learning, four measures were taken. The results actually improved from a failure rate of 21.5% to 0.7%. This was mainly due to tighter project structure and additional student work. Reduced course material and improved teacher preparation did not seem to have any effect, while more focused project teaching may have contributed to the decreased failure rate. Further improvements may be gained through time estimation in the problem definition process.     

解数学题的基本方法只有两种吗?

本文从揭示解数学题这一过程的实质入手,科学地指出解数学题的基本方法恰有三种,而不是通常所认为的只有综合法和分析法两种,并指出了RMI法也只是第三种基本方法中的一种。     

动态生成观下高等数学解题预设分析

基于动态生成教学理念,以数学解题教学设计为入手点,利用解题预设的典型案例,对如何进行教学预设,如何更有效地改进数学解题教学,如何更有效地促进动态资源的生成进行初步研究,生动地诠释了“动态生成观”在数学解题教学中的应用。     

矢量数性积在解题中的应用探讨

矢量数性积是矢量代数中的一种运算 ,它沟通了矢量与代数间的转换关系 ,同时它也有效地解决了几何度量和角度问题。通过实例的分析和求解 ,阐述了矢量数性积在解题中具有非常广泛的应用。     

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.     

幼儿科教活动中提问所存在的问题及解决策略

由于幼儿注意力容易分散,行动的目的性和预见性差,因此需要教师对幼儿教育要寓教于乐。提问是教师设疑、激趣的好方法,但是在科学教育活动中,教师的提问也有使用不当的时候,影响了幼儿学习的效果。探讨教师提问所存在的问题并提出有效的解决策略。     

三角函数解题中隐含信息的挖掘

通过举例对比分析,在解题过程中要充分利用隐含条件,注意各象限内相应的三角函数的符号,使学生正确地解决问题.     

The impact of learner characteristics on information utilization strategies, cognitive load experienced, and performance in hypermedia learning

Against the background of an adaptation of Cognitive Load Theory to learner-controlled settings we investigated the impact of learner characteristics on information utilization strategies, cognitive load, and learning outcomes in a hypermedia environment. Based on the data of 79 students, five clusters of students were identified according to their learner characteristics by means of a cluster analysis. Further analyses showed that learners with more favorable characteristics (i.e., higher prior knowledge, more complex epistemological beliefs, more positive attitudes towards mathematics, better cognitive and metacognitive strategy use) tended to show a more adaptive example utilization behavior, reported less cognitive load, and solved more problems correctly than learners with less favorable characteristics.     

Chemistry problem solving instruction: a comparison of three computer-based formats for learning from hierarchical network problem representations

Within the cognitive load theory framework, we designed and compared three alternative instructional solution formats that can be derived from a common static hierarchical network representation depicting problem structure. The interactive-solution format permitted students to search in self-controlled manner for solution steps, static-solution format displayed all solutions steps, and no-solution format did not have solution steps. When we matched instructional time across the formats, in relation to the complex molarity problems rather than the dilution problems, differential transfer performance existed between the static-solution or no-solution formats and the interactive-solution format, but not between the static-solution format and no-solution format. The manner in which learners interact with the static-solution and no-solution formats depends on their level of expertise in the chemistry domain. With considerable learner expertise, provision of solution steps may be redundant incurring extraneous cognitive load. Absence of the solution steps may not have left sufficient cognitive capacity for germane cognitive load as some beginning learners lacked the prior knowledge to deduce the solution steps. Searching for solution steps presumably incurred extraneous cognitive load which interfered with learning and hence, in the interactive-solution format, it outweighed the benefit of engaging in self-regulated interaction with the content. Hence, cognitive load theory is a promising tool to predict the mental load associated with learning from the three alternative computer-based instructional formats.