A Conceptual Understanding And Teaching Elementary Simple Equation

Equation contains a rich history, it has experienced such a long evolution and finally formed the unity of "appearance" and "name" and "using numbers to indicate letters". Recognizing the origin and evolution of equations can have a better understanding of it. From the word origin of equation,we can understand that why it is called equation; from the history of equation,we can know its earliest form; from the history of equation, we can comprehend that equation is not equivalent to the equation; from the evolution of the expression of equation, we can grasp the three-stage of equation expressions.Different origins of arithmetic and algebra lead different results in both research fields and the core of thinking. It is because of the difference between algebra and arithmetic that leads students to experience two changes when they are learning the equations. Firstly, adding of letters and its chain reactions--unknowns involved in operations; secondly, the role shift of "=". These changes explain why students listed the "arithmetic type equation"(218-33)÷2=x and resolve the equation like "3x+5=26=26-5=21=21-3=7". Through "using numbers to indicate letters ","unknowns involved in operations" and "understanding of the equal sign" can help students adapt to the changes from arithmetic to algebra. The method of solving equations by a vertical notation and the application of mathematical model of Singapore primary school’s mathematics curriculum give us some new opportunities, but also lead us focus more on the traditional inheritance.