| "Cross multiplication", As a simple method of factorization, a kind of mathematical thought and tool, which was canceled as teaching content by < mathematics curriculum standard for compulsory education > in 2000,has ever arouse great controversy in the field of mathematics education field for many years. Whether the decide is reasonable or not, there are endless argument, a lot of experts and scholars has their own opinions,different opinions.Based on existing research, start from the junior high school mathematics "cross multiplication" teaching and learning of the actual situation of, Urumqi city were randomly selected for different levels of two junior high school and high school students and teachers as the research object, by questionnaire sur vey, test surveys and interviews from students and teachers, double level of junior high school and high school were investigated, through investigation and Study on the junior high school mathematics "cross multiplication" teaches with study the present situation that the following conclusions:(1)Among respondents, 100% students from grade school said "cross multiplication" in math class, the first grade students in 100% high school said "cross multiplication" in math class 88.52% of the students said, had added in the junior middle school mathematics teachers, 11.48% junior high school students have not learned but the high school mathematics teachers. The interview added at the beginning of high school mathematics teachers have said they would "cross multiplication" in the teaching process. Although the standard of < > "cross multiplication factor" decomposition is not required, but the junior middle school mathematics teachers in the process of its decomposition on the factor of knowledge as a teaching supplement, high school mathematics teachers in the process of its knowledge link as the teaching of knowledge is a common phenomenon.(2)On the whole, the junior middle school students, 92% of students in the test volume selection using cross multiplication "problem solving. High school students, 91.87% of students in the test volume in selection using cross multiplication" problem solving.(3)Subjective willingness to choose to "cross multiplication" and formula method, 49.51% of junior high school students the students said he can skillfully use "cross multiplication" problem-solving. 43.6% of high school students said he can skillfully use "cross multiplication of solving problems.(4) The "cross multiplication formula" and actual choice and the level of mastery, junior high school students in a class of two quadratic polynomial decomposition problem, "cross multiplication" use rate and accuracy rate are much higher than the formula; in the solution of quadratic equation with one unknown class of topics, use rate increased the formula method, "using cross multiplication" ratio decreased, but still higher than the overall formula usage rate of two methods was comparable to the one yuan quadratic function; in the topic, "cross multiplication rate" only still occupies the main position, the two methods was comparable to the high school students. In the solution of equations on the topic, "using cross multiplication" rate and accuracy rate are higher than the formula; in the solution of a two kind of inequality problem, the correct rate formula and "cross multiplication" declined, but on the whole, or "cross multiplication" right The rate is still higher than that of the formula method. In solving the function definition domain, the "cross multiplication" is still the main selection method, and the correct rate of "cross multiplication" is still higher than that of the formula method."Cross multiplication" in the process of teaching and learning is not difficult, and in the cultivation of students’ basic skills and ability, mathematics curriculum of basic philosophy angle has an indispensable role, treatment of cross multiplication "in the current junior high school mathematics textbook is not reasonable, should be" cross multiplication "as the teaching content added to the materials. |
