Curriculum And Teaching Research On The Concept Of Rational Number And Reasonlessness

This group of relative concept which concludes rational number and irrational number in the extension number system is the basis of content in mathematics curriculum, but the students don’t understand quite well for this part of study. In this thesis, by studying the existing curriculum, comparing the content and analyzing the teaching part from textbooks, it provides the teaching strategies for teachers. In this way, it indeed encourages students to truly understand two concepts.According to the comparative study of research foundation and the course content, I make the following conclusion:curriculum content about rational concept in Personal Teaching edition is more enriched while the layout of irrational number in Beijing Normal University Version has more features. But at the same time, this comparison also reflects some deficiency of our textbook. From the point of the macro level:(1) pay more attention to the operation instruction instead of concept teaching; (2) the arrangement of the contents of irrational number is not enough. From the point of the specific level:(1) the decimal cycle forms are not mentioned in the course of rational number concepts; (2) during the understanding of the concept, students are not able to fully understand the significance of the concept of ρ; (3) the transition and connection of rational numbers and decimals are q not perfect; (4) in the textbook, irrational concept’s not being commensurable has not been paid attention completely. In terms of the problems after the comparison between rational numbers and irrational numbers course, the following teaching strategies are put in the teaching preparation stage and teaching implementation stage. Teaching preparation strategy:(1) the organization strategy of knowledge in the textbook; (2) the analysis strategy of knowledge structure of teaching materials. Teaching implementation strategies:(1) the comprehensive strategy of introduction of the contents, avoiding the recognition is not complete; (2) the associative strategy of the internal concept, deepen the understanding of the concrete concept; (3) the development strategy of following knowledge, finding the appropriate cognitive perspective; (4) the connective strategy by the link among subjects, demonstrating meaning of the concept of number; (5) multi-angle concept strategy, forming the basic structure of number system; (6) the check-comprehension strategy of the concept map, improving the overall concept.Finally, in accordance with the teaching strategies which have been mentioned before, offer the concrete teaching design of rational numbers and irrational numbers.