Teaching and learning mathematics at the university based on an integrated(conceptual-procedural) approach

We proposed teaching practices based on the educational strategy of Inquiry-based learning (IBL). These practices include (i) determining learning objectives to focus students' attention and motivate them to achieve them; (ii) solving problems with high cognitive demands that encourage students to search, research, solve problems, and make connections; (iii) engaging students in productive work on knowledge construction and fostering meaningful mathematical discourse; (iv) procedural fluency training based on conceptual understanding.We also confirmed the effectiveness of the integrated conceptual and procedural approach through an experiment.本研究提出了基于探究式学习（Inquiry-based Learning, IBL）教育策略的教学实践体系，具体包含以下四项内容：（一）明确学习目标，以聚焦学生注意力并激励其达成目标；（二）设计高认知要求的问题任务，引导学生开展探索、调研、解题及建立知识关联的活动；（三）推动学生参与知识建构的高质量实践，并营造富有意义的数学交流氛围；（四）依托概念性理解开展程序性流畅性训练。本研究还通过实验验证了概念与程序融合式教学方法的有效性。