A Research For Instinctive Cognition To Infinity Of Primary And Middle School Students

It's easy to find the importance of infinity in Primary or Middle School Math teaching. On one hand, it contains abstract features, like natural numbers, infinite circulating decimal (though it can be replaced by fractions, infinity of its connotation is irreplaceable.) and irrational number ? . On the other hand, infinite expend of lines and ductibility of planes in daily life have the features of visibility.According to those above, infinity plays a very important role in students' learning process, so researching their recognition to infinity is with positive meaning. The author researches instinct to infinity of Primary and Middle School students, trying to declaim post current development of cognition and recognition to infinity among Chinese students, which is beneficial to the construction of relative courses and materials, as well as teaching fulfillment. It has a directly promoting function in improving level of studying relative contents of these students, and it also supplies a reference to the improvement of Primary and Middle School students' teaching.This research will analyze Primary and Middle School students' thinking features and the relationship among aspects influencing thinking, connecting basis of instinct theory in cognitive psychology. It will use interview and measure instrument of instinctive thinking about infinity (case study), unitary equation methods to counting analysis of numbers, it can test the rationality among elements, at the meantime, analysis of research results, truly embodying testees' current status of cognition to infinity in Math learning is included.As to the problems reflected from research, author connects theory and practice in Math course revolution of current compulsory education, promoting some solutions and approaches, which represent personal opinions and suggestion.Research shows:Testees have an instinct to infinity, because normally their answers are not random. Some students continuously repeat what have been taught (e.g. there are boundless dots in an interzone), but some don't, the difference proves instinct to infinity will change easily, depending on predictable and relative influence. The changeability of instinct can be explained as inner paradox whether they will accept "infinity" as a psychological reality.There is an important hypothesis among current researches, that is instinct, especially to "infinity" does not rely on the influence of age. Our discovery proves this kind of predict partially.Te positions of "finite" and "infinite" do not rely on directions determined by what we call "abstract" and "concrete".Actually, instinctive reflection to infinity if related to cultivating thinking in Math, so teaching should utilize instinctive thinking in material system. It should also include lively Math innovative thinking activities, showing process teaching. Then it makes students experience "Math in developing", promoting their interest in learning, encouraging their creativity and gradually improve their instinctive thinking level.