关系映射反演方法作为一种重要的数学方法,它能将复杂的函数问题进行拆分和转化,使问题化生为熟、化繁为简。因此,本文从数学思想方法的角度出发研究了关系映射反演原则在高中函数问题中的应用,不仅能为一线教师的解题教学提供一定的参考价值,也有利于培养学生的数学思维能力,提高学生的解题能力。As an important mathematical method, the relational mapping inversion method can break down and transform complex function problems, making them more familiar and simplified. Therefore, this article studies the application of the principle of relational mapping inversion in high school function problems from the perspective of mathematical thinking methods. It not only provides certain reference value for frontline teachers’ problem-solving teaching, but also helps cultivate students’ mathematical thinking ability and improve their problem-solving ability.
随着核心素养导向的高中数学课程改革不断深化,探索科学有效的教学方法成为数学教育研究的重要课题。RMI (表示–映射–反演)原则作为一种系统化的数学方法论,强调通过数学表示、映射转换和反演求解的思维过程,将复杂问题转化为可解决的模型,对提升学生的数学思维能力具有重要作用。本文基于RMI原则,系统探讨其在高中数学教学中的应用模式与实践路径。With the deepening of the core literature-oriented senior high school mathematics curriculum reform, the exploration of scientific and effective teaching methods has become an important topic in mathematics education research. As a systematic mathematical methodology, RMI (Representation-Map-Inversion) principle emphasizes the thinking process of mathematical representation, mapping transformation and inversion solution to transform complex problems into solvable models, which plays an important role in improving students’ mathematical thinking ability. Based on RMI principle, this paper systematically discusses its application model and practice path in high school mathematics teaching.
本文探讨了在中学数学课堂中渗透数学文化的实践路径,阐明了数学文化融入教学的重要性及其具体策略。通过结合数学史料、生活实例和丰富的数学活动,提升学生对数学本质的理解和对学科的兴趣,促使学生全面发展。本研究旨在为中学数学教师提供有效的教学参考,促进数学教学的创新与发展。This article explores the practical path of infiltrating mathematical culture into middle school mathematics classrooms, and elucidates the importance and specific strategies of integrating mathematical culture into teaching. By combining mathematical historical materials, life examples, and rich mathematical activities, we aim to enhance students’ understanding of the essence of mathematics and their interest in the subject, promoting their comprehensive development. This study aims to provide effective teaching references for middle school mathematics teachers and promote innovation and development in mathematics teaching.
教学评价是教师获取学生学情信息、优化教学策略的重要依据。通过系统分析教学过程与学习成效,教师能够精准把握学生认知特征、思维偏好及课堂互动表现,从而针对性地调整教学方向。当前中学数学教学中,传统评价方式多聚焦知识掌握程度,忽视对学生逻辑推理、创新思维等素养的培育。在构建数学教学评价体系时,需突破传统仅关注知识掌握度的局限,将发展性评价作为提升学生核心素养的关键路径。此类评价并非以任务达成为单一导向,而是通过动态化、个性化的评估机制,有效激发学生数学学习内驱力,增强其面对复杂问题的探究信心。在实操层面,教师需结合数学学科特性,促使学生在自我审视与合作交流中发现知识盲区,完善认知结构。实践表明,系统性发展性评价能显著提升学生数学学习效能,其关键在于形成“评价–诊断–教学改进”闭环,最终实现从知识传递向素养培育的范式转变。Teaching evaluation is an important basis for teachers to obtain students’ learning information and optimize teaching strategies. Through systematic analysis of teaching process and learning effect, teachers can accurately grasp students’ cognitive characteristics, thinking preferences and classroom interaction performance, so as to adjust the teaching direction. In the current middle school mathematics teaching, the traditional evaluation methods mainly focus on knowledge mastery, ignoring the cultivation of students’ logical reasoning, innovative thinking and other qualities. In the construction of mathematics teaching evaluation system, it is necessary to break through the traditional limitation of only focusing on knowledge mastery, and take developmental evaluation as the key path to improve students’ core literacy. This kind of evaluation is not based on the single orientation of task achievement, but through the dynamic and personalized evaluation mechanism, it c
