中文摘要：

介绍了基于SPOC和翻转课堂的线性代数混合式教学的实践．实践过程包括三个阶段：课程准备与资源建设、教学过程设计与组织、教学评价与形成性反馈．从课程知识体系、知识点、计算方法三个方面，构建思维导图范例，以廓清课程知识体系和学习主线．提出重视知识单元设计，强调基于专业背景的案例拓展教学，以实现探究式、分层个性化学习，全面提升教学效果和学生综合素质．

英文摘要：

The blended teaching and learning model based on SPOC and flipped classroom is designed for Linear Algebra. Firstly, three stages, namely the preparing and construction of course resources, the design and organizational strategy of teaching process, the feedback and assessment mechanism are introduced. Secondly, various examples of mind maps are carried out to classify knowledge system. Finally, Knowledge unit organization and practical applications to different majors for personalized learning are emphasized in case teaching to improve learners＇ inquiry ability and enhance teaching effect.