Taking the Chinese remainder theorem as an example, this paper carries out the teaching case study of ideological and political education in the course of Elementary Number Theory which contains rich ideological and political elements, which provides a good foundation for the ideological and political teaching of classroom.

数学建模作为六大数学核心素养之一,其重要性不言而喻.如何有效开展数学建模活动,实现数学建模素养的落地生根是广大一线教师面临的难题.基于此,从DELC教学模式出发,以"鞋码与身高"教学为例,设计完整的数学建模活动,以期促进学生深度学习,为一线教师教学提供参考.

随着科学技术的迅猛发展,全面发展的人才已成为社会发展的宝贵资源.《普通高中数学课程标准(2017年版)》指出,数学素养是现代社会每一个人应该具备的基本素养,其中的直观想象素养是数学核心素养的基础,而提升学生的直观想象素养是传统教学的难点、痛点.文章以外接球的切瓜模型为支撑点,适时、适当、适切地引用GeoGebra软件辅助教学,使学生通过视觉方法与几何方法的交互作用,理解几何知识的本质,提高数形结合能力,帮助学生扩展思维阈限,把提升学生的直观想象素养落于实处.

问题解决教学是落实《义务教育数学课程标准(2022 年版)》提出的数学核心素养的有效路径.以初中数学"电话计费问题"教学为例,循着大师的足迹前行,设计了波利亚理论下课堂实施的四个环节:梳理条件、以图示意、理解题目;数据悟律、分解问题、拟定方案;构建方程、执行方案、得出结论;回顾反思、深化概念、发展能力.学生在有效的教学设计与实施中,学会用数学的眼光观察,用数学的头脑思考,用数学的语言表达,逐渐成长为能主动解决问题的高素养的人才,也揭示了遵循教育理论指导教学实践提升核心素养的有效策略.

《义务教育数学课程标准(2022年版)》等系列课标的发布意味着本轮课改进入一个新的阶段,核心素养和跨学科已然成为本阶段的重要议题."综合与实践"是义务教育阶段数学学科中跨学科主题学习的主要领域,也是发展数学核心素养的重要载体.对比《全日制义务教育数学课程标准(实验稿)》《义务教育数学课程标准(2011年版)》《义务教育数学课程标准(2022年版)》中"综合与实践"的内容,提出以主动参与为主旨,以问题解决为抓手,以课标内容为指导,以促进四基培养、四能发展和素养形成,进而帮助一线教师更好地实施该领域的内容.

The key to improve the quality of basic education classroom teaching lies in transforming the developmental purport of the classroom, converting the classroom from concept to practice with a panoramic view, and forming a classroom culture that matches the pursuits of cultivating talents in the era. The in-depth classroom teaching is a kind of development-orient classroom that respects the identity of students as subjects, attaches importance to giving full play to the cultivation of talents through subjects, emphasizes the improvement of students’ learning thinking level, understanding realm and overall gain, enhances the multi-dimensional interaction of relevant subjects in the classroom, and pursues the improvement of internal quality. It has the essential characteristics of manifesting attributes for human, exploring the value of knowledge education and giving play to the function of discipline education. The realization of in-depth classroom construction depends on the creative processing of knowledge, the learning pattern of students, the educational function of the discipline, to promote the growth of knowledge thinking, adjust the overall rhythm of the classroom, and improve teachers’ educational ability.

By discussing how to distinct the non-uniqueness of ordinary differential equation starting value,and prompting the result,this essay has obtained the non-uniqueness distinction principle of difference differential equation.