The Practice Research On How To Develop Student's Reflective Abilities In Middle Schools Mathematics Teaching

Rethinking is the reflection of learning. Mathematical rethinking refers to a math learner's acquisition, self-assessment, self-observation, self-exploration, and self-adjustment during his or her learning process and result. A learner's math knowledge, skills and content are the core of mathematical rethinking. Mathematical rethinking knowledge includes narrative knowledge, programming knowledge, and processing knowledge. Mathematical skills include experience, theory, analysis, assessment, strategy, and practice. Mathematical rethinking happens in pre-mathematical activities, during- mathematical activities, and post- mathematical activities, which have a close connection with the communication and reflection of both the teacher's and the students'rethinking.Mathematical rethinking abilities belong to the original mathematical ability. But in the meantime, other abilities are closely connected with them. They provide basis, promotion, and improvement for each other. Mathematical abilities have lived through periods of unconscious rethinking, passive rethinking, and active rethinking. Many factors have impacts on mathematical rethinking, among which are presentation of text books, methodology, and teaching assessment.This research article focus on the nurture of senior high school students'mathematical rethinking abilities, passing on traditional mathematical teaching methods, making mathematical rethinking teaching practical, paying attention to the nurture and adjustment of acquisition, improving the students'rethinking abilities of solving mathematical problems, providing more opportunities for students to reason and correct mistakes. The nurture consists of three aspects: stimulation, giving examples, and training. The interactivities between teachers and students will promote and recycle the three aspects. Ways and approaches of nurture are to expose thinking process, to make use of a teaching method of questions, to use a question chain to assess and then promote rethinking. Giving assessment helps to make rethinking.This article research adopts an action research, which makes a comparison between two different classes. One is for rethinking teaching; the other is for operation teaching. To establish a set of effective teaching patterns of mathematical rethinking, the three aspects of nurture should be planned, practiced, monitored, rethought, and adjusted. Class observations, after-school work, checking students'record in assessment forms, carrying out questionnaires, group discussions, and interviews help to collect relevant information and data.The conclusions of the research include: 1. A short period of rethinking teaching and operation teaching have a little influence on students'general performances in math tests, but have an obvious influence on both top level and low level students.2. Rethinking has no direct or little influence on increasing students'interest in math or lessening their stress in math tests.3. Rethinking helps to strengthen students'confidence in math learning, self-study ability and ability of prediction.4. Persistence, time, and methods are three key factors that affect students'rethhinking.5. Exposing thinking process, giving assignments, and assessments works well on nurturing students'rethinking abilities. However, more practical and more specific approaches need to be found and improved.Some defects have been found with this research itself, and they are considered at the end of the article.