One of Job's main research fields: HPM. How to integrate the history of dropping out of school into teaching practice according to teaching difficulties and cognitive obstacles, and give play to educational value? What is the relationship between HPM and the professional development of primary school teachers?
Theoretical framework of mathematics teaching from the perspective of HPM;
One view is: HPM
Two Bridges: Mathematics History and Mathematics Teaching? × (History and Reality, Mathematics and Humanities)
Three-dimensional goals: knowledge and skills; Process and method; Emotional attitudes and values (knowledge, belief and ability);
Four ways: attachment, copy, adaptation and reconstruction.
Five principles: interest, scientificity, effectiveness, learnability and novelty.
Six types of value
It is mentioned that Yue Zengcheng's tutor Professor Wang Xiaoqin's "Mathematics Teaching in Primary Schools from the Perspective of HPM" mentioned different ways to deal with resources, that is, several ways to integrate mathematics culture into mathematics classroom.
That is to say, what should I do to obtain the resources of mathematics culture or mathematics reading?
1. Additional type? Show pictures of mathematicians, tell math stories, etc. , and the teaching content will not be greatly affected after removal.
Example: Tell the story that Descartes showed the position of flies when he taught the method of showing position; When teaching "understanding of large numbers", tell the story of Archimedes counting sand; Tell Kepler's story when deducing the formula of circular area.
Link 1: Descartes' story about the location of flies
Legend has it that one day, young Descartes lay in bed and let his thoughts wander in the abstract world. Forgot to introduce. Descartes had the habit of 1 1 getting up in the morning because of his weak body. At this time, a fly, a fly that would be recorded in human history if it had a name, buzzed and danced, constantly changing its resting position on the ceiling. Descartes stared at the fly for a while, maybe he had the idea of driving that annoying fly away. However, Descartes was a mathematician and philosopher. He turned the idea into a mathematical problem, not an action: how to locate the fly accurately?
If you choose a certain point (such as a corner) as a reference point, you can locate flies by counting several ceilings in the east-west direction and several ceilings in the north-south direction. In other words, as long as you choose a reference point and two directions (not necessarily vertical and non-overlapping), you can use two numbers to locate points on the plane. This is the concept of Cartesian coordinate system.
With Cartesian coordinate system, geometry and algebra are linked, and the mathematical field of analytic geometry has emerged since then. With the foundation of algebraic analysis of geometry, geometry can develop in the direction of high dimension, abstraction and curved space. Analytic geometry combines the analytic tools of algebra with the visualization of geometry, and provides a method to visualize algebraic equations. There is an old saying in China, "If Zhong Ni is not born in the sky, it will last forever.". Imagine what human natural science would be like today without rectangular coordinate system.
Conceptual background of coordinate system:
This paper introduces the story class of mathematics culture, which only arouses students' love for mathematics.
2. Plagiarism directly uses historical math problems and solutions.
When teaching travel itinerary, we directly adopt the problem of geese meeting in Nine Chapters of Arithmetic or the problem of two ships meeting in Calculation Book. The lattice algorithm is directly introduced into the teaching of two-digit multiplication. Is it a carpet? )
Shen Goose came to meet:
In Nine Chapters Arithmetic, one of the "Ten Classic Arithmetic Books" in ancient China, there is a famous passage "Ducks and geese meet". The original title is: "There is a seven-day trip from the South China Sea to the North Sea today; These geese set off from the North Sea and arrived in the South China Sea on the 9th. The geese are rising today. When will we meet? " It takes seven days for ducklings to fly from the South China Sea to the North China Sea, and nine days for geese to fly from the North China Sea to the South China Sea. Now they take off from the South China Sea and the North Sea of China at the same time. How many days can they meet?
My solution is: time = distance/speed and.
The problem of linkage double grid algorithm;
Lattice algorithm, also known as "carpet laying", is a mathematical algorithm discovered in Italy more than 500 years ago. Later, it was introduced to China at the same time as the pen calculation in the Ming Dynasty. This algorithm needs to be calculated one by one and then added.
Let's take 46×75 as an example. What we do is to divide it into four formulas: 40×5, 6×5, 40×70 and 6×70, and get 200, 30, 2800 and 420 respectively, and then add up all the numbers to get 3450. So many formulas are worked out one by one, and then added together, which is slow and easy to write, so everyone thinks the calculation is really annoying.
3. Write mathematical stories according to historical materials and appropriately adapt historical thinking methods.
For example, according to the proposition 37 "The area between a triangle with the same base and the same two parallel lines is equal" in the Elements of Geometry, a question is put forward: There are two triangles with the same base between the two parallel lines, from which it can be concluded that the areas of the two triangles are equal (the exercise "Polygon area" in the first volume of the fifth grade of People's Education Press (Mathematics)) on page 95.
4. refactoring? Draw lessons from or reconstruct the history of the occurrence and development of knowledge.
According to the order of "quality-quantity-relationship", reproduce the history of angle concept; Reconstruct the history of the circle in the order of "appreciating the circle-drawing it-recognizing it-using it". (We will sort this out separately. )
Reflect the source of knowledge; Extension of methods; Emotional embellishment; The effect of practice.
Curriculum development process: