subject: On the Mathematics Teaching in High School Mathematics Teaching [print this page] On the Mathematics Teaching in High School Mathematics Teaching
Abstract: In high school mathematics teaching, teaching has become widely used. This paper describes what is and Mathematics Teaching and Mathematics Teaching in the role, and then combined with teaching practical example of the Mathematics Teaching in High School Mathematics Teaching, finally, summarizes the changes in mathematics teaching in the teaching should be noted problems.
Keywords: High School Mathematics Teaching I. What is Mathematics Teaching Called Mathematics Teaching, refers to the process of mathematics teaching the concept, nature, theorems, formulas, and the problem from different angles and at different levels and in different circumstances, different backgrounds and make effective changes in their condition or form change, while the essential characteristics are unchanged.
2, Mathematics Teaching in High School Mathematics Teaching Examples
Example 1: If the new grant Theorem "a + b 2", where a, b R +, (if and only if a = b when taking "=" number) theorem, the stress conditions used in Theorem is: "One is the second set three equal." Textbook Exercise for change through the following teaching:
The original question: Given x> 0, y the minimum requirements. (High School "Mathematics (PEP)," New Teaching material Compulsory (5) P100 Practice Question 1)
Variant 1: x R, the function y has a minimum it? Why?
Variant 2: Given x> 0, the minimum demand y;
Variant 3: x> 3, the minimum value of the function y 2 it?
Of Inequality is a key high school, but students in the use, it is easy to forget the conditions of Theorem use "is the second set of a three-equal." Therefore, after-school exercise in teaching from the start, using the original title in terms of specialization about the general conditions, to have specific characteristics in terms of making subject is unique. Design practice to answer the three variants to enable students to deepen understanding of the conditions of the theorem and master the proper use of the theorems laid a more solid basis.
Example 2: Original title: in the ellipse of one point P, making it the focus of the connection with the two perpendicular to each other.
Variant 1: The two focuses of the ellipse is F1, F2, point P is a fixed point on it, when F1PF2 as the obtuse angle, the point P of the horizontal range is ___________
Analysis: Inspired by the original question, whether it is obtuse, or acute, is to angle for the reference solution to the problem a lot, but the most simple geometric method. Shown to coordinate origin O as the center of a circle to | F1F2 | Draw a circle with a diameter of elliptical cross in A, B, C, D four points on the circumference by the diameter of the angle is right angle can see: When the points P in A, B , C, D 4:00 pm, F1PF2 for the right angle, when the point P in the ellipse or arc on the arc AB CD when, F1PF2 an obtuse; acute angle of the situation is self-evident, easy to request the range of abscissa of point P be
. Variant 2: F1, F2 is the Oval C: two focus on the C PF1 PF2 to meet the number of points for the __________ P
Analysis: The problem only seek to determine the coordinates of points, the number of points, but the solution is the same, but seek to | F1F2 | diameter of the circle and the ellipse the intersection number, apparently to | F1F2 | as diameter of the circle equation, and elliptic C: tangent to ellipse minor axis endpoint, so the number of points P to 2.
Variant 3: Let the two elliptical focus F1 (-C, 0), F2 (C, 0), C> 0, and the ellipse of a point P, so PF1 and PF2 vertical, realistic number of m, range.
