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Master mathematical thought to pay attention to innovation thinking
From;    Author:Stand originally
Course of study is taken an examination of to already ended in this year, from this year of Shanghai in in taking an examination of maths to press an axis to inscribe, what inspiration do we get? Sum up well, this to us the educational education henceforth and exam of enter a higher school coach waiting for the job will be very beneficial.

Above all we will see this problem, try to analyse and be solved again next.

Example: (maths was studied in Shanghai 2005 last problem the 25th problem) in △ ABC, ∠ ABC=90 ° , AB=4, BC=3, o is one on edge AC moves a point, with 0 make semicircle for the centre of a circle, as tangent as edge AB at nodding D, hand in line segment OC at nodding E, ED of the ⊥ that make EP hands in ray AB at nodding P, hand in ray CB at nodding F. (1) if pursue, seek testimony: AEP of △ of △ ADE ∽ ;

(2) set OA= , when AP= , beg about function relation, draw up its definition region;

(3) when BF=1, beg the length of line segment AP. Analysis: This problem starting point is not high, but the demand is more overall. Be computation of one number of channels and form, algebra and geometrical proof, similar triangle decide the omnibus examination questions that begs solution, the Pythagorean therom and function, circle and triangle to compare photograph union with equation of analysis of property, draw and row. At the same time check the most serious maths thought in maths of junior high school: The mathematical thought such as the idea that several form combine, thought of classified discussion and geometrical movement change. The subject is like ever not was acquainted again, blended in dynamic geometry change and changeless, in asking the student is moved, beg static, jing Zhongsai changes, have certain difficulty, but begin is easy still. The subject has 3 to ask, be equivalent to 3 step, this kind of appropriate matting gave examinee wider entry, be helpful for examinee the play of normal level. And through layer upon layer set ask, ascend the stairs, progressively development, can make one share outstanding student maths level gets reflecting, in rising, take an examination of -- , the function of choose of exam of enter a higher school.

(1) asking is a foundation, beg two triangles likeness, want concatenate OD only, find out easily have two horn correspondence equal, can conclude. Starting point is low, begin is easy, great majority student can be compared give easily solve.

(2) ask and (3) asking solution, after by several form union requests the relation that gives function, want to be good at observation and inferential judgement already, want accurate calculation again, should analyse meticulously in the round more. Want to use the idea that the classification in maths discusses adequately above all, careful careful is inscribed, capture line segment and ray the distinction of these two concepts, two kinds of case when considering O of the centre of a circle to change in the motion on AC, make EP ⊥ ED hands in line segment AB to cross AB extension line at nodding P and EF at nodding P, discuss respectively solve, can reach right answer.
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