初中数学课程知识图谱的构建与应用——以《平行四边形》为例

课程知识图谱是教育知识图谱中的一种类型,是用可视化的图谱方式来呈现课程中的知识点间的丰富关系,它可以整合大量的课程数据,为学习者提供个性化学习的技术手段。八年级下册数学在初中数学中扮演着重要的角色。这一阶段的学习不仅可以对之前所学知识进行巩固和深化,更可以为后续的学习打下基础,通过八年级下册数学课程的学习,学生可以提高解题能力和逻辑思维能力。课程知识图谱不仅可以辅助教师去完成备课、教研、试卷分析等工作,还能反映学生当前的知识掌握情况,为他们提供个性化的学习路径规划,助力他们更有效地学习。文章以人教版八年级下册数学课程中的《平行四边形》为例,构造了课程知识图谱,探讨了课程知识图谱在教学中的应用。Curriculum knowledge mapping is a type of educational knowledge mapping, which is a visual mapping to present the rich relationships between knowledge points in a curriculum, and it can integrate a large amount of curriculum data to provide learners with technical tools for personalised learning. Lower 8th grade mathematics plays an important role in middle school mathematics. This stage of learning can not only consolidate and deepen the knowledge learned before, but also lay the foundation for subsequent learning, through the learning of the eighth grade lower mathematics course, students can improve their problem solving ability and logical thinking ability. Curriculum knowledge mapping can not only assist teachers in preparing lessons, conducting research, and analyzing test papers, but also reflect students’ current knowledge mastery, providing them with personalized learning path planning and helping them learn more effectively. The article takes the Parallelogram in the second book of the eighth grade mathematics curriculum of the Renjiao version as an example, constructs a curriculum knowledge map, and discusses the application of the curriculum knowledge map in teaching.

矩阵乘积的加权最小二乘广义逆的反序律研究

加权广义逆是矩阵理论与应用中不可或缺的一部分,它在线性偏微分方程、多元统计分析、线性控制理论等领域有着广泛的应用.本文利用广义Schur补的极大极小秩这一方法研究了一些矩阵乘积的加权广义逆的反序律,给出了矩阵乘积的加权广义逆的反序律A_(3){1,3M_(3)}A_(2){1,3M_(2)}A_(1){1,3M_(1)}■(A_(1)A_(2)A_(3)){1,3M_(1)} 和 A_(3){1, 4M_(4)}A_(2){1, 4M_(3)}A_(1){1, 4M_(2)}■(A_(1)A_(2)A_(3)){1,4M_(4)}成立的充分必要条件.