Research On The Radical Quadratic Factor Concept Understanding For Student In Grade Nine, Ten

Radical quadratic factor is in the student has grasped the content which the square root, in the arithmetic square root's foundation further studies. In essence, radical quadratic factor is a kind of arithmetic square root said, through the radical quadratic factor learning, to further improve the learning algebra concepts and operations, For further study equation, function and the computation good foundation in algebra.This article through to the Zhejiang Pinghu's 160 student's questionnaire surveys and the individual interview, examined the student to radical quadratic factor definition understanding, radical quadratic factor nature grasping as well as radical quadratic factor application keeps abreast of the situation, draws the following conclusion:First, students'understanding level of definition of the concept of the radical quadratic factor is different. Percentage of the students in the previous structure level, single-structure level, multi-level structure accounts for 53.75%,37.50%,8.75% respectively. Students to radical quadratic factor of the concept of diversity, mainly presented representation without/wrong representation types, not entirely correct image representation, the correct image which are not completely correct representation for the radical quadratic factor performance that nonnegative part, take the square root mean, a kind of the infinite decimals open square computation, examples, which are free of fault representation than the largest/, each class has more than half; Secondly, students from a symbolic Angle to understand more radical, sometimes even the quadratic radical equal to the square root of secondary;Second, students to radical quadratic factor concept cognitive basic does not exist gender differences, but in low levels of gender differences in cognitive level, i.e. the girl on the square root, the concept of arithmetic square root, cube root of memory, the direct operation related concepts, the negative's simple application, that in low levels of understanding better than boys, but with cognitive levels rise, girls advantage gradually blurred;Third, there are grade differences exists in radical quadratic factor on application, namely, the application of the radical quadratic factor, superior is better than junior, but there are no significant differences in senior and junior about the radical quadratic factor related concepts, second nature of radical quadratic factor.In view of the above conclusions proposed the following four Suggestions:First, it should pay great attention to the construction of radical quadratic factor concepts in radical quadratic factor's teaching, follow from concrete to the abstract when do introduction, from known the teaching principles which proceeds in an orderly way to unknown, when soon completes the concept teaching, helps the student to establish the concept of radical quadratic factor;Second, it should pay attention to the following two aspects when strengthening radical quadratic factor double nonnegativity analysis:on one hand that should be emphasized in radical quadratic factor the number and radical itself does not prescribe for negative reasons in teaching, the other hand is aimed at double the negative for special practice, especially the books and exercise books to summarize and analyze the related topics;Third, in order to improve the accuracy of application of radical quadratic factor problems, make some supplements in teaching (for example:the absolute value of nature, factoring decomposition commonly used method, solution inequality and inequality the basic way of the fraction of the implied meaning of teaching condition etc).Forth, pay attention in radical quadratic factor teaching mathematics thinking method seepage, especially gathers the thought and the classified discussion idea, specifically:First, in radical quadratic factor concept's formation, the developing process takes the set thought the seepage, lets the student understand in the root number the part is a whole; Second, in the concept, in the nature application takes seriously to classify the discussion thought the seepage, lets the student explain completely the topic, analyzes thoroughly.