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The role of the common intuitive model in multiplication.
- Apr 11, 2018 -

     In order to help students understand the math better, teachers should be good at selecting multiple methods. There are physical prototype, intuitive model, knowledge and so on. The physical prototype refers to the physical materials with certain structure, such as "yuan, jiao, min" and other measuring units such as RMB, "kilometer, meter and decimeter". The intuitive model refers to the operation materials and visual materials with certain structure, such as sticks, counters, rectangles or circles, and number lines. A few of the intuitive models used in the multiplication are different because they are different in their "structure".

  1. The area model of "not having a decimal relationship".

Such as idea, "have no decimal relationship" of the lattice model, this model is helpful to understand the meaning of multiplication, caused the students into different parts and produce a variety of methods, so when students are encouraged to algorithm diversity is a valuable model. Of course, by using this model, not all students can naturally "break down the multiplier into 10 and a few", which requires the teacher to choose the guide.

  2. The area model of "having a decimal relationship".

Such as small sticks to a bundle of ten, this model will help students understand the meaning of multiplication, but due to its decimal relationship obviously is not easy to cause a variety of methods of students, but to guide students to multiplier "split into 10 and a few" are of great help/very helpful.

  3. Counter model.

Using the counter model to represent 12*4, it is clear that this model has a clear relationship with 10, which is abstract compared with the decimal model.

  4. Linear model.

Domestic textbooks seldom use numerical line models in the study of integer multiplication, which may be related to the fact that multidigit multiplication is difficult to express superiority. But the number line model has its own value, which is reflected in the following aspects: first, the points and Numbers on the line can establish corresponding relation; Second, the size of the visual comparison; Thirdly, it is a model of Numbers, which can be counted by number (multiplication), and can be reciprocal (division); Fourth, it is helpful for students to understand the meaning of times.