数学探究学习最终发生在课堂上。
Mathematics inquiry learning ultimately takes place in classroom.
以问题为起点进行数学探究学习。
The problem is the initial point of mathematics inquiry learning.
第二部分：高中数学探究教学的概述；
The second part: High school mathematics inquisition teaching outline;
第五部分：高中数学探究教学实施的条件和原则；
The fifth part: High school mathematics inquisition teaching implementation condition and principle;
数学探究教学在具体实施中存在诸多问题，且教学效果不理想。
In practice, there were many questions in explorative teaching of mathematics.
因此，笔者试图从理论到实践方面来探讨中学数学探究性学习。
Therefore, I try to probe into inquiry study in learning mathematics in middle schools from theoretical and practical aspects.
高中阶段至少各应安排一次较完整的数学建模、数学探究活动。
During high school, we should at least assign a thorough mathematical modeling and mathematical exploration activity.
几何画板是目前国内应用于数学探究式教学中的优秀软件平台。
The Study of Classroom Teaching and Learning of Mathematical Inquiring Teaching in Middle School Based on the Geometers Sketchpad;
第三部分结合案例探讨CAI课件在中学数学探究式教学中的应用策略；
Part 3, discuses the strategies to use CAI in inquiring teaching in seconding mathematics using two cases.
因此，关于高中数学探究学习的相关理论与实践是值得我们深入研究的问题。
Therefore, the study about high school math to explore the theory and practice related to the merits in-depth examination of the problem.
教学是一种特殊的认识活动，认识论的视角有助于深化对数学探究教学的认识。
The perspective of the epistemology is helpful to deepen the cognition of mathematics inquiry teaching.
数学课题学习通常通过数学建模、数学实验、数学探究学习和数学主题阅读等方式来实现。
Math task study is usually implemented by making math models, math experiments, math research study and math motif reading.
本研究旨在给一线教师提供开展数学探究的一种新思路，提供一种可借鉴的数学探究教学模式。
This study was designed to give front-line teachers to explore math launched a new line of thought, providing a reference model to explore math.
数学建模、数学探究、数学实验、数学调查、数学制作与设计、数学主题阅读是课题学习的常见形式。
Mathematics modeling, mathematical inquiry, mathematics experiments, mathematics investigation, mathematics execution and designing, mathematical topic reading are high-frequent methods.
本文基于数学发现的经验性，分析了数学中有探究性的一面，指出数学探究教学在数学学科中的必要性。
This paper, based on the empirical feature of mathematical discovery, analyzes the explorable feature of mathematics and points out the necessity of explorative teaching in mathematics.
基于对窄化和泛化现象的反思，进行数学探究学习的理论构建和实践探索，是本课题研究的突破口和推进轴。
The theoretical and practical study on the inquiry learning of mathematics which is based on these phenomena should be considered as the breakthrough of the paper.
而另外一些深入探究了数学计算过程，但只面向熟悉代数的读者。
Yet others go into mathematical procedures, but assume that the reader is adept in using algebra.
波究瓦德发现他必须创建一个新的数学模式来使用循环量子引力理论，以便更加精确地探究大弹跳之前的宇宙。
Bojowald found he had to create a new mathematical model to use with the theory of Loop Quantum Gravity in order to explore the universe before the Big Bounce with more precision.
让我们先来探究一下最近邻背后的数学理论，以便能更好地理解这个过程并了解此技术的某些限制。
Let's delve into the math a little bit, so you can understand the process and also see some of the limitations of this technique.
为了了解更多，研究者决定探究一下孩子们的数学成绩和他们与生俱来的无需计算就能估计与比较数量的能力之间的关系。
To learn more, researchers decided to explore the relationship between children's mathematics achievement and their innate ability to estimate and compare quantities without counting.
这是一个数学的形象化软件用于抽象代数课堂。用户可以交互直观的探究很多的有限组。
Group Explorer is mathematical visualization software for the abstract algebra classroom. Users can explore dozens of finite groups (and morphisms among them) visually and interactively.
他认为，通过简洁优雅的数学方程就可以探究基础物理理论。到如今，在研究物质本质的弦理论中，这一思想得到了广泛的采纳。
His view that fundamental physics could be gleaned from elegant mathematics now permeates a whole field of inquiry into the reality of nature, string theory.
“五环节数学教学模式”把教学过程化分为五个环节：精讲、探究、反思、反馈、留疑。
In the teaching process of maths, I applied "five links" teaching model: intensive teaching, explore, self-analysis, feedback, and doubt.
本文就数学教学中如何实施探究性学习做初步探讨。
The paper makes an initial study on how to carry out research learning model in mathematics teaching.
经过筛选和加工，其中有的可以作为“探究性课题”，成为数学课堂教学的学习材料。
After selecting and processing, a part of them, as the research-based tasks, could become the materials of teaching mathematical knowledge in classroom.
在这几年中我通过几次的培训和不断探究，总结以下几点数学教学经验，供给同仁参考。
I pass several times in this several years of training with continuously investigation, summary the following what time mathematics teaching experience, supply colleague reference.
大学数学教育研究，究其实质是要探究大学水平的数学的教和学的问题。
The college mathematics education research, in essence, is to probe into teaching and learning mathematics at the college level.
数学研究性学习的特点体现在：较高的抽象性、广阔的开放性、较深刻的探究性以及非常有利于培养钻研精神。
The basic characteristic of mathematical research based learning is that it is abstract and opened and exploratory and good for developing the studying spirit.
数学研究性学习的特点体现在：较高的抽象性、广阔的开放性、较深刻的探究性以及非常有利于培养钻研精神。
The basic characteristic of mathematical research based learning is that it is abstract and opened and exploratory and good for developing the studying spirit.
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