Contributing Factors To Achieve The High Cognitive Level Of Mathematical Teaching And Strategies To Achieve It

The paper includes four sections. Firstly, based on many years' of teaching experience in junior high schools, one provides a comprehensive analysis about the characteristics of three levels of mathematics learning proposed by current scholars: mechanic memorization, learning by explanation, and explorative understanding. Secondly, from the framework of three levels, one documents potential problems in the classroom teaching in junior high schools and finds the gap between the new concepts and the actual teaching practice. Additionally, the overall teaching standard needs to be improved, which is consistent with the case studies conducted in foreign countries that active learning in mathematics benefit the students the most by encouraging thinking and exploration while teaching for low levels of understanding won't produce effective learning. Thirdly, from extensive teaching experience and education theory, I find four main factors that can affect the level of understanding in mathematics teaching: (1) the interaction of learning and the mood of minds; (2) the presentation of contents and structure; (3) the relationship between behavior and psychology; (4) feedback and further adjustment. These factors influence the development of students' understanding in all phases of mathematics teaching. Lastly, I identify eight strategies that can achieve the active learning in teaching junior high...