| Calculating rectangular area is one of the classic mathematics teaching content in the primary school. It was included both in the first textbook of modern geometry "The Purpose of Learning Geometry" and in the first textbook of new China "Initial / Senior Primary School Arithmetic".Rectangular area calculation formula seems simple, but it is important and fundamental in the primary school stage for learning of calculating all planar graphs, and it is the first lesson for primary school students to learn area calculation. In daily teaching, teachers will usually set the formula calculation as the teaching goal, and use mechanical memorizing and tremendous practicing as a way of learning for the pupils. As such, students will become calculating machines and only know it but not the why.In order to know the study situation of the students, the author conducted a survey regarding "rectangular area calculation" and an analysis on the after-class homework covering the grade-three students in three primary schools located in Shangcheng District of Hangzhou. Through the investigation and analysis, the author finds that it is not optimistic for students’ studying and learning "rectangular area calculation", and it is relatively common that the students are lack of understanding of the formula’s meaning. The students only know the rectangular area calculation formula but not the why.To further pursue the reasons, the author analyzes from two angles of understanding the textbooks and comparing the teaching methods. Through the analysis, the author finds that the experimental textbooks with the new curriculum standards reform the presentation way of "examples & explanations” to the way by providing scenarios pictures and activity diagrams, which are of rich learning contents and in a lively teaching form. However, we need to look into the contents and forms and study and understand the knowledge structures, objectives of the contents and learning methods. In addition, as the structure and contents of different textbooks are with distinctive features, if we can make comparisons and absorb the advantages from others, we may set out a teaching instructional design that will make the students easier to understand the area calculation formula. From the study of different teaching instructional designs, the author has a more clear understanding on the teaching goal, arrangement of learning steps and cognitive theory concerning the rectangular area calculations, and sets up a new teaching instructional design.After comparing and analyzing the current 6 major versions of textbooks and 77 types of typical teaching instructional designs, according to the van Hiele model of learning geometry the author forms a new teaching instructional design. The new teaching instructional design includes the following distinctive features:(1) designing a new leaning sequence of three steps and five stages, that is, "formation of representation, verification by operation, and understanding through application", to progressively and entirely promote the students to understand the rectangular area calculation formula;(2) arranging learning approaches of "discovering from inquiries, and verification by operation", to discover and obtain the area formula in the intuition, imagination and experiments for deepening the understanding, so that the students may know why; and(3) accumulating the experiences in the activity of reasoning through the series of studies, to enjoy funs of discovering mathematical formula.This teaching instructional design was applied in several trial classes in ordinary primary schools, experimental primary schools, and rural primary schools, and was achieved remarkable success. Also, its content was fully published on the magazine of "Primary School Mathematics Teacher" by Shanghai Education Press. From a practical point of view, this design has solved the dilemma of teaching students to understand the area formula, and may provide reference value for the front-line teachers. |
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