Mathematics is often regarded as a bunch of formulas and theorems. Taking Pythagorean Theorem as an example, it links geometry and algebra well, and it is a mathematical knowledge point that we must learn. The pythagorean theorem that children learn is most likely like this: a? +b？ =c？ But is this the essence of Pythagorean theorem? Of course not. If you just study like this, many children may not even know what A, B and C are.
We have forgotten three things that we should know most in mathematics learning: first, the connection between mathematics knowledge and life; Second, the ins and outs of mathematical knowledge; Third, the essence and thinking method of mathematical spirit.
1 Mathematics has such a connection with life.
Many people only know how to remember the Pythagorean theorem, but they can't use it skillfully. The problem is that we don't know what the Pythagorean theorem has to do with life, and we can't really understand its essence.
It is said that Dayu controls water and determines the direction of water flow according to the terrain, which is the result of the application of Pythagorean theorem. For another example, in home decoration, in order to judge whether a corner is a standard right angle, workers will measure 30cm and 40cm from the corner to two walls and mark them on a point, and then measure whether the distance between these two points is 50cm. If there is an error, it means that the angle is not a right angle, which is also the result of applying Pythagorean theorem.
2 Explore the ins and outs of knowledge
After understanding the application of Pythagorean theorem in real life, are you curious about its "origin"? Pythagorean theorem is called Pythagorean theorem in the west. Pythagoras can find this theorem because he is good at thinking about the details of life, instead of sitting in the room at the desk, thinking hard with paper and pen.
Pythagoras was once invited to a party. The master's luxurious palace is covered with square marble floor tiles. Pythagoras found that drawing a square with the diagonal of a floor tile as the edge is exactly equal to the sum of the areas of two floor tiles. He was curious, so he made another square with the rectangular diagonal of two floor tiles. He found that the area of a square is equal to the area of five floor tiles.
So far, Pythagoras has made a bold assumption: the square of the hypotenuse of any right triangle is exactly equal to the sum of the squares of the other two sides. This is the origin of Pythagorean theorem.
3 the essence of mathematical thought
Just now, we also talked about the process of exploring Pythagorean theorem, which fully embodies an important mathematical idea-"the combination of numbers and shapes": transforming the "shape" of a right triangle into the "number" between three sides. At the same time, it also embodies the mathematical thought of "from special to general". First, it explores the relationship among the three sides of a special right triangle, and then from special to general, it explores the relationship among the three sides of a general right triangle. There is also the transformation from the exploration edge to the exploration area and so on. These all reflect the mystery of mathematical thought.