| Questioning, as so widespread in our life, often takes place so easy and smooth. We take question only when we face a problem and have to question. Questioning occurs naturally because we take questioning in the question. We are questioning because we have problems; We have problems because we are thinking. Thus questioning ,problem and thinking move by turns in circle. Does questioning take place so easy and smooth when questioning becomes an action of teaching in classroom? In classroom, there are two types of thinkers, one is "Forerunner" and the other is "Latecomers". But "Forerunner" has knowledge earlier than "latecomers" .So when they meet together in classroom, "Forerunner" is one who knows everything. There are not any problems that "Forerunner" is not able to answer. So "Forerunner" has not questions to ask "Latecomers" but "Latecomers" have questions to ask "Forerunner". On the opposite, in the most cases, "Forerunner" has many questions to ask "Latecomers" while "Latecomers" has no questions to ask "Forerunner". However, can "Latecomers", as the unknown, take questioning to carry the teaching forward in the mathematical classroom? Obviously , it is not possible. It is a paradox of questioning in mathematical classroom. The paradox has brought some phenomena. For example, "What has been known is to be questioned , and what has not been known is not to be questioned", "Questioning becomes a mere formality", "Teaching is just for show", etc..However, in educational history, Confucius and Socrates have been called "an exemplary teacher for all ages". Their "Heuristic" or "the art of intellectual midwifery" all are orientated by questioning. Their questioning is mostly teacher-asking. Another, questioning is an interactive processing. Classroom is where students grow up. But the growing bases on the interaction between the peoples. Lastly, as mentioned before, questioning means thinking, and questioning is understanding. So questioning in classroom has been paid more attention in educational theory and practice. Mathematics is "abstract" and "sur-experienced" "in ideal world". Mathematics is mastered only by thinking, and known only by thinking, and surpassed other branch of learning. Our forefathers have said "Learning starts from thinking , thinking from question". So question is important in learning mathematics. Overall, one side is that questioning in classroom is the paradox, the other side is that learning mathematics demands questions to be put on the center. To put them together , questioning in mathematical classroom would be in "dialogue". Dialogue requires to be developed around question. Dialogue is not only a way of mathematical teaching but also a principle too. This research is based on this thought.This dissertation includes five parts.Part One : Introduction .This part briefly gives the basic view ,the value, the methods, the processing , and the outcomes of the research . The research to the questioning hi mathematical classroom has the ontology value. The value includesthree aspects: the education and the teaching--questioning is common in theclassroom , the nature of mathematics --mathematics is question-able , thephilosophy of science--questioning is a basic way of the action in science. Theresearch has some realistic value , that is , which turns the way from emphasizing on the technique of questioning in the past research to on the essence of questioning . It tries to correct the mistakes in the theory and the practice of questioning in the past In the methods, it uses the observation, the interview and the analysis-based-situation in qualitative research, and uses the rational thought, too. The research goes from practice to theory ,from the perceptual to the rational, from "acting" to "thinking".Part Two : To review from the history of the questioning research in mathematical classroom . This part finds that the past researches stress on the functions ,the roles and the technique of questioning and on the numbers ,the characters and the "wait t...
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