Research On Probability Concept Teaching Method Based On APOS Theory

On the basis of constructivism, America scholar Ed Dubinsky proposes the APOS theory, which mainly aims at researching the learning process of the concept. He points out the learning of new concept has four steps including Action, Process, Object, Scheme. APOS theory thinks that in learning mathematical concept, the students construct themselves internal knowledge system finally with the help of knowledge they have had and the reflection and summary and the activities designed by teacher under the background of social reality.based on Probability of the third book of Compulsory Mathematics published by Beijing Normal University, the thesis mainly studies these three questions:(1) The understanding of the Probability’s importance among the students of senior high school.(2)The cognition of the Probability and the main problems existed in study among the students of senior school.(3) discuss about the teaching design based on the APOS theory.Out of the purpose of knowing the situation and problems existed in learning Probability of the students in senior high school, we investigated the students in class (13) and class (14) grade 2 and interviewed the math teachers in some senior high school in Ankang city. Linking with educational experiences and cases in educational practice, we arrived at the current basic teaching method in math class of the Probability. Finally, starting from the students’ cognition degree, we made the class teaching design of "the Frequency and Probability ", "the distinction of Classical Probability and calculation formula of Probability" and "simulated method-application of Probability" under the guide of APOS theory.Our practice show that the APOS theory has the important significance to the Probability teaching, which can improve the teaching methods and the class effect, better help students construct the knowledge system of Probability and more deeply understand the concept of Probability and store the concept of Probability in the cognitive structure by a comprehensive psychological schema.The main differences between the teaching design guided by APOS theory and the traditional teaching design are:the former that highlights the body status of student and pays attention to the students’ participation to the math activities has four stages that every stage has students’ participation, which through participation and teacher’s guide and reflection and summary makes students themselves explore the forming process of the concept. On the contrary, the latter that highlights the teacher’s teaching only let the students accept the knowledge and leave less time for students to take part in the activities and think.In order to make better use of APOS theory in educational practice, the study proposes five suggestions:(1) to take the real examples in the process of teaching so that students can feel the practical value of math. (2) to creatively use the text book and elaborate the teaching content. (3)to use the multimedia technology properly. (4) Pay attention to the exploring process in the teaching of mathematical concept. (5) Focus on the penetration of mathematical thinking methods in the class.