Instruction Research Of Optimized Formula For Difference Of Squares

Formula for the difference of squares, which is the first formula in the junior middle school, is a special type of multiplication of polynomials which is translated naturally by students who grasp the multiplication of polynomials. It is a typical example of transforming from commonness to specialty and has an important role in the junior middle school teaching. It is found through listening to and studying on the lessons that a number of students, who have been taught formula for the difference of squares, cannot clearly understand its origin and forming, have fuzzy memories about its structure and do not digest its intrinsic character, which result in teaching of difference of squares doesn’t function fully as the typical example.As mathematics possesses extreme abstraction, it is difficult for students to study directly the mathematics formula. To enhance the study efficiency and effectiveness, studying mathematics through multiple aspects, which is also studying mathematics by the learning idea of mathematical multi-representations, has the priority. The learning idea by applying multi-representations in teaching makes learners understanding deeply mathematical objects and grasping its essence.The current research is expanded through theory and practice. On the one hand, the instruction strategy of optimizing formula for the difference of squares is proposed based on multi-representations, which offers a theory explanation for improving instruction of difference of squares and formula teaching practice and enriches mathematical studying and teaching theories. On the other hand, the research validates the meaning and value of optimizing instruction of difference of squares in practice and makes students obtain profound understanding through the transformation among the various representational forms of mathematical formula and the translation among the different representational systems, which improves studying effectiveness.The results in the current researches are:In terms of theory research:the current topic discusses profoundly the instruction strategy of multi-representations in optimizing learning of difference of squares based on learning theory of multi-representations which is carried out by theory speculation mainly and experience conclusion partly with the consideration of the characters of formula for the difference of squares:(1) representation of information selection strategy;(2) representation of sequence design strategy;(3) information package strategy;(4) scaffold strategy;(5) strategy cognition strategy;(6) variant teaching strategy;(7) graphic organizer strategy。In terms of practice research:the current topic researches and analyzes the cognitive load, studying effectiveness and learning efficiency of the instruction strategy of multi-representations teaching for the formula for the difference of squares through teaching experimentations integrated by questionnaires and interviews. The experimentation researches show:optimized multi-representations instruction strategy has obvious guiding meanings and reference values for improving the learning of formula for the difference of squares. In comparison to traditional instructions, the strategy obviously enhances the studying effectiveness and efficiency and reduces the cognitive load of learning the formula for the difference of squares.The current research enriches instruction strategy of multi-representations learning and instruction design of courses similar to "formula for the difference of squares" in theory and validates the meanings and values of multi-representations instruction strategy in practice, which offers theoretical and practical reference of improving formula teaching similar to "formula for the difference of squares".