Mathematics in Children's Thinking

The human mind inevitably comprehends the world in mathematical terms (among others). Children's informal and invented mathematics contains on an implicit level many of the mathematical ideas that teachers want to promote on a formal and explicit level. These ideas may be innate, constructed for the purpose of adaptation, or picked up from an environment that is rich in mathematical structure, regardless of culture. Teachers should attempt to uncover the mathematical ideas contained in their students' thinking because much, but not all, of the mathematics curriculum is immanent in children's informal and invented knowledge. This mathematical perspective requires a focus not only on the child's constructive process but also on the mathematical content underlying the child's thinking. Teachers then can use these crude ideas as a foundation on which to construct a significant portion of classroom pedagogy. In doing this, teachers should recognize that children's invented strategies are not an end in themselves. Instead, the ultimate goal is to facilitate children's progressive mathematization of their immanent ideas. Children need to understand mathematics in deep, formal, and conventional ways.     

数学思想方法在高等数学教育中的作用

从高等数学教育改革的角度,阐述了数学思想方法的含义和高等数学中的基本数学思想方法,论述了在高等数学教育中加强数学思想方法教学的重要性.     

Cultural Influences on Children's Probabilistic Thinking

This study investigated selected cultural influences on probabilistic thinking of 11–12-year-old children in England. Language, beliefs and experience are shown to influence the children's “informal knowledge” of probability, i.e., the intuitive knowledge they bring to school and use in thinking about probabilistic situations presented in school. Some of the pupils' responses in interviews and in a questionnaire were consistent with the “outcome approach” and with the use of certain heuristics: “representativeness”; “availability”; “equiprobability.” A significant proportion of pupils revealed superstitions. Standard “random devices” such as dice were regarded by some children as subject to personal, religious or causative influences. In a comparison between two culturally-contrasted subgroups in the same school, we found significant differences in scores on probability tests, even when taking account of numerical and non-verbal ability. But the differences between the two groups could almost entirely be explained by differences in language ability.     

Prospective Elementary Teachers' Perceptions of Gender Differences in Children's Attitudes Toward Mathematics

Prospective elementary teachers hold preconceived ideas about elementary school students' attitudes toward mathematics. We found that there exists a gender bias with prospective teachers expecting girls to have negative attitudes toward mathematics and boys more likely to have positive attitudes toward mathematics. We found that these expectations exist for both prospective teachers in a traditional undergraduate degree program and prospective teachers in an alternative licensure graduate degree program. We also found that these expectations do change with the completion of a mathematics methods course and classroom experiences.     

推行高等数学目标教学法 培养创造性数学思维能力

阐述了高等数学教学改革的必要性和迫切性 .提出了一种新的教学方法 :目标教学法 ,给出了它的内容和具体实施方案 .论述了培养学生创造性思维的必要性和重要性 .结合例子 ,叙述了在教学过程中培养学生发散思维和逆向思维的方法 .通过教学实践 ,论证了此教学法取得了很好效果 ,并具有很好的推广价值     

试谈高等数学教学中的几种思维模式

在理论与实践上探讨在高等数学教学中如何启迪学生的数学思维 ,培养学生思维结构的合理性和思维的创新性     

Book review of Thinking Practices in Mathematics and Science Learning

The goal of this project, an animation-based tutor for algebra word problems, is to build instructional software to improve estimation, reasoning, and problem-solving skills. In this study, we focused on the 2nd (task completion) module, which uses tank-filling problems in which the unknown variable is the time it will take to fill a tank. Students build on the answers to a simple (no leak) problem to estimate, and then calculate, answers to problems in which there is a leak in the bottom of the tank, a leak in the side of the tank, and a delay in starting one of the pipes. We evaluated the software in an intermediate algebra class consisting of a diverse group of students at a community college. We use the findings to discuss what works (estimation and the solution of the simpler problems) and to make recommendations on how to improve use of the decomposition method for solving the more complex problems.     

在高等代数教学中渗透数学史知识的思考

高等代数是一门内容丰富、思想独特、方法技巧较强的一门基础课程.在授课过程中,适当地渗透数学史知识,有助于学生兴趣的培养,有助于学生理解数学的思想、方法和精神,有助于培养他们抽象思维能力、逻辑推理能力、分析问题和解决问题能力.     

对数学创新能力的认识与思考

培养学生数学创新能力是当前数学教育的一个重要目标.数学创新能力的内涵可以从潜在的认知过程和显现的认知结果两个方面去认识.因此,对学生数学创新能力的培养可从以下三个方面去展开:一是培养学生有条件的质疑精神;二是教师具有良好创新素质;三是革新教学方法,实施情境—问题教学模式.     

林业院校数学教学中存在的问题与思考

分析了现行林业院校数学教学中存在的主要问题 ,认为合理地设置数学课程和学时数是保证教学质量的前提 ,开设数学实验课和建立数学实践教学基地是培养学生应用数学能力的主要手段 .加强师资队伍建设、开展教研活动和学术交流及采用多媒体辅助教学能促进教学水平的提高 .     

关于高等数学作业的思考与实践

简要分析了作业与教学的关系;指出了传统的高等数学作业存在的一些问题;结合具体实践,提出了高等数学作业改革的一些办法.     

数学教学中创造性思维能力的培养

本文从创造性思维的五个特点出发 ,介绍了如何在数学教学中培养学生创造思维能力 .     

关于大学数学的创造性思维教学模式的探讨

传统的注入式大学数学教学已无法适应现代社会的发展,培养学生创造性思维的能力,建立全新的大学数学教学模式,已成为大学数学教学的首要任务.本文对此做了一些初步的探讨.