The dissertation is a result of an action research on improving mathematics teachers' classroom teaching and facilitating their professional development. The author bring forward a teaching belief which is based on the understanding of mathematics, the state quo of mathematics teaching in China and the emphasis on "mathematics essence" by some experts in mathematics or mathematics education field, called "Classroom Teaching Driven by Primitive Mathematics Idea"(abbreviated as CTDPMI). It is guided by quasi-empiricism mathematics belief, call for that mathematics teaching should root in students' common sense and experience, surpass too much pursuit of skilled mathematics and embed the core of situated mathematics; let students master the essence of mathematics what taught by teachers, through the quasi-mathematician activities--mathematical supposing, rational reasoning, (error-trial) exploring, validating, proving et al, and reorganize students' new common sense and experience.The research objects are two primary school teachers' teaching of "Division with a complement" and two junior high school teachers' teaching of "Pythagorean theorem", here the "two" means mat one is a novice and the other is an experienced teacher. Each teacher was asked to teach the same theme for three times. The first time of teaching is generally a natural one; the second, attempting CTDPMI, and the third, improving CTDPMI. The research question is: What's the difference, change or similarity between novice and experienced teachers in their practice of CTDPMI?In the study, qualitative research is the basic way. From the end of the first natural teaching, four teachers, their colleagues and researchers prepared, reviewed and discussed the lesson all together. The author attended the teaching research activities all the while, and collected data by video-taped classroom, interviewing each teacher after her lesson, reflective diary and audio-taped teaching research activities. Some tools were used to analyze the collected data: The Mathematics Tasks Framework, Guide For Tasks Analysis and Factors Associated With Maintenance And Decline Of High-level Cognitive Demands in QUASAR project, Pittsburgh University, some techniques of video-taped analysis and discourse semantic analysis. The researching results were presented inEast China Normal Universitytransverse and longitudinal way. The transverse comparison aimed at the difference and similarity between novice and experienced teachers in each time of teaching, and the longitudinal comparison aimed at the change of each teacher m her three times of teaching.In the transverse comparison, three common grounds were found in each time of teaching. In the first time of teaching, (1) mere was a certain routine way, procedurized pattern of teaching; (2) the product of knowledge was emphasized and process of mathematics was neglected, and yet essence; (3) teachers highly depended on their experiences but short of reflection on their teaching design. In the second time of teaching, (1) it seemed teaching was given a "belief burden"; (2) but the process of knowledge and students' mathematical activities were emphasized; (3) teachers depended on the collective ideas about teaching too much. In the third time of teaching, (1) they had same or similar teaching process, and the taches of teaching were integrated and consistent; (2) the students' acquirement was stressed; (3) the teaching was a result of the collective wits.In the longitudinal comparison, two signified phenomena were found: all the teachers' three times of teaching had the same changingprocess--from the beginning "paying attention to textbook and personalexperience", to the next "paying more attention on new belief and others experience", and to last "paying high attention on acquirement of the students in the realized classroom". The second phenomenon was that novice and experienced teachers little by little have the surprising similarity or common ground in teaching taches and time distribution in the whole process of the t