共查询到20条相似文献，搜索用时 203 毫秒
1.
王新民 《中国数学教育(高中版)》2013,(18):38-39
"圆面分割问题"蕴含着丰富的数学思想方法,通过归纳、类比与演绎三个维度的分析,揭示了该问题的基本量性结构,提出了两种具有数学特点的归纳思维模式:要素归纳模式与递推归纳模式.利用所提出的思维模式与所获得的结论对其他分割问题给出了较为简捷、具有一致性的解答思路. 相似文献
2.
王新民 《中国数学教育(高中版)》2013,(9):38-39
“圆面分割问题”蕴含着丰富的数学思想方法,通过归纳、类比与演绎三个维度的分析,揭示了该问题的基本量性结构,提出了两种具有数学特点的归纳思维模式：要素归纳模式与递推归纳模式．利用所提出的思维模式与所获得的结论对其他分割问题给出了较为简捷、具有一致性的解答思路． 相似文献
3.
数学思维方式与学生的数学创新能力紧密相关 ,作为数学教师应当在教学活动中 ,精心设计问题的情境和教学方法 ,重视数学思维方式的渗透 :归纳与猜想、类比与猜想、推广与猜想 相似文献
4.
数学猜想是通过对所研究的问题进行观察、实验、分析、比较、类比、联想、归纳等 ,并依据已有的材料和知识作出符合一定的经验与事实的推测性想象的一种思维方法 .数学猜想的形成是对研究对象联系已有知识与经验进行形象性的分解、选择、加工、改造的整合过程 .数学之中处处都有猜想 ,学习数学定理、公式时可猜想定理公式、猜证法 ,再研究证明 ;对于一个数学问题可猜解题思路、解题方法以及答案的形式、范围、数值 ,再探索解决 .数学猜想是学生不断认识数学知识结构 ,完善知识系统 ,形成知识板块的一种学习方法 ,又是解决数学问题、简缩思维… 相似文献
5.
数学教学的核心是发展学生的数学思维.新课程改革的根本在于要带给学生充实的思维过程.教学可以通过观察联想、类比迁移、突破定势、变式训练、归纳反思等方式,提高学生的数学思维能力. 相似文献
6.
李庆社 《语数外学习(初中版)》2011,(4):24-26
猜想是通过对所研究的问题进行观察、实验、分析、联想、类比、归纳等,作出符合一定的推测性想象的思维方法.现结合一些具体例子,就如何猜想一些问题的答案予以归纳总结. 相似文献
7.
所谓组合性思维就是将一些基本思维，如：比较思维、分析思维、综合思维、有序思维、逆向思维、归纳思维、演绎思维、类比思维、发散思维、集中思维、想象思维等，让学生根据数学认知或练习材料的特点有机组合起来的思维。它对发展学生的思维能力有重要意义。 相似文献
8.
9.
林文琴 《新课程导学(上)》2023,(29):57-60
类比迁移是以已知信息为基础,运用联想的方法解决新问题,并从中归纳新信息的一种思维方法。将类比迁移用于小学数学教学过程中,对提升学生的数学思维水平,提高学生的数学学习效率有着积极意义。文章结合“分数乘除法”一课的教学案例,分析类比迁移在小学数学教学中的应用策略,指出教师可以通过分析教材、优化内容、综合教法、完善评价等方式发挥类比迁移的教学作用。同时,文章基于实际教学案例提出几点教学反思,希望为进一步提升小学数学教学质量提供参考。 相似文献
10.
本文讨论了中学数学要培养学生的几种数学思维方式,包括归纳思想、函数思想、统计观念,类比思想及数学建模能力的培养等。 相似文献
11.
研究采用问题解决作业单和认知作业分析法考察了71名高中生解决学科问题时的图式归纳和迁移情况。结果表明：（1）在问题结构相同的情况下，增加问题表面相似性能促进问题解决迁移；（2）近类比条件有助于同一学科领域问题的迁移，而远类比条件可能更有助于跨学科领域问题的迁移；（3）近类比条件下，图式归纳水平对学科问题迁移的影响不大，远类比条件下，较高的图式归纳水平有助于学科问题解决的迁移。 相似文献
12.
类比迁移是一种重要的迁移现象.在数学中,两个不同知识系统或两个不同问题之间的共同要素以及学习者头脑中的认知结构是影响类比迁移的两个主要因素;两个可类比的系统存在直接和间接两种关系,具有直接关系的两个系统存在着意义完全明确的类比关系,因此可直接进行类比推理,具有间接关系的两个系统,则需要对类比系统进行变换或重整化处理,建构一个中介系统;在类比迁移过程中,两个系统的共同要素是诱因,而过程性知识则起着支配作用。 相似文献
13.
数学归纳法的发展历程 总被引：1，自引：0，他引：1
冯进 《常熟理工学院学报》2008,22(8):19-26
数学归纳法是数学中的一个重要的证明方法,也是中学数学的一个重要内容．本文根据新的研究史料,给出了数学归纳法发展的一个较完整的面貌．指出了个别数学内容的发展与整个学科发展是互相促进、相互影响的,数学归纳法的发展几乎经历了整个数学的发展历程,从而也从一个侧面给出数学发展的缩影． 相似文献
14.
Ruth Stavy 《科学教学研究杂志》1991,28(4):305-313
A new approach to change misconceptions of students is to build on ideas which match their students' existing intuitive knowledge. This can be done by analogy. The use of an analogical relation between the known and the unknown can help students learn new information and discard or modify misconceptions. Previous studies have confirmed this result in such areas as mathematics. The present study examined the use of analogical instruction to overcome misconceptions about conservation of matter. Students who understood the concept of conservation of matter when iodine was evaporated were able to transfer their understanding to the evaporation of acetone. This indicates that teaching by analogy can be an effective tool in science. The author is now studying the relative effectiveness of conflict training and learning by analogy. 相似文献
15.
Analogical reasoning is believed to be an efficient means of problem solving and construction of knowledge during the search
for and the analysis of new mathematical objects. However, there is growing concern that despite everyday usage, learners
are unable to transfer analogical reasoning to learning situations. This study aims at facilitating analogy use for conjecturing
in discourse-rich mathematics classrooms. We reconceptualized one of the traditional perspectives on analogical reasoning,
called classical analogy, as a more dynamic one by providing learners with the opportunity to choose a target object and its
property. While shifting attention to particular aspects of mathematical activity, we observed and analyzed how students became
aware of hidden relational similarities and utilized them while weakening others to make conjectures. The detailed analysis
of the constructs and processes of several similarity-making and conjecturing activities supports the significance of reconceived
classical analogy use in mathematics classrooms. 相似文献
16.
王祥 《南昌教育学院学报》2013,(9):133+138
在进行高等数学的具体授课过程中切实转变教育观念,将培养学生的创新精神和探索精神作为重点来抓,是实现学生数学素养全面提高的重要方法。高等数学作为现今大学科目设置的一门基础课程,授课教师在进行教学活动理应通过有意识的引导,培养学生尽快形成并熟练运用逆向思维能力、类比思维能力、归纳思维能力进行高等数学学习,为学生实现数学素质的全面提高奠定坚实基础。 相似文献
17.
数学本质·认识论·数学观——简评"对数学本质的认识" 总被引：11，自引：8，他引：11
数学本质是一个认识论问题，涉及经验知识与理论知识的关系，从其它角度提出质疑是文不对题的。数学本质是数学观的重要表现，它影响或决定着数学研究方法。研究数学本质是数学教育工作者的一个重要课题，不是“没有必要”的；培养学生树立正确的数学观是数学教师的一项重要任务，不是“无关紧要的”。数学发展的动力是实践，而不是归纳法。 相似文献
18.
Although there has been considerable research into knowledge transfer for over a century, there remains a need for specific, validated techniques for teaching for transfer. This article reports on classroom-based research in which students learned about complex systems and climate change with agent-based computer models using two different instructional approaches based on productive failure (PF). In both PF approaches, students initially explored a problem space on their own and then received teacher-led instruction. One treatment group used climate computer models whereas the other group engaged in analogical comparisons between the same climate computer models and complexity computer models in different domains. The study found both groups demonstrated significant learning gains by posttest on assessments of declarative and explanatory knowledge and on within domain near transfer. However, students in the two models treatment group performed at a significantly higher level on an across domain far transfer problem solving task. Theoretical and practical implications are considered. 相似文献
19.
During one school year, data were collected for vocational education students while they worked collaboratively on open-ended mathematics problems. In collaboration with participating teachers, instructional activities were designed with a twofold goal of modelling the process of problem solving and improving collaboration. Instructional activities were based on scaffolding instruction and included modelling problem solving, stimulating reflection, and giving feedback on the process of collaboration. These activities were gradually developed and implemented in collaboration with teachers who participated in the study. The main research question in this study was whether student collaboration while working in small groups creates a learning context where students work on open-ended problems and where instructional activities are aimed at stimulating collaborative problem solving in mathematics.To answer the research question, an experiment was undertaken in two classes in different schools. Two groups of students were videotaped while they tried to solve mathematics problems collaboratively. Observational data were analysed with a schema that was developed as part of this research. Analyses of the data showed that, in both groups, collaboration-oriented patterns increased during the school year. It is argued that the approach of gradual implementation of instructional activities that are designed in cooperation with participating teachers is effective in stimulating collaborative problem solving. 相似文献
20.
Mercedes Garc��a Salvador Llinares Gloria S��nchez-Matamoros 《International Journal of Science and Mathematics Education》2011,9(5):1023-1045
This paper reports on different underlying structures of the derivative schema of three undergraduate students that were considered
to be at the trans level of development of the derivative schema (action–process–object–schema). The derivative schema is
characterized in terms of the students’ ability to explicitly transfer the relationship between a function and its first derivative
to the derivative function and the second derivative. This conscious shift of properties of derivatives is differently manifested
by the students in the trans level of development of the derivative schema and can be considered evidence of the different
characteristics of the thematization of derivative schema. From here we suggest that there are different underlying structures
in the constructed schema due to the consciousness in which students use the relations between a function and its derivative. 相似文献