Research On The Teaching Design Of "A Fraction Of Cognition" Based On APOS Theory

Fraction is one of the core concepts of primary school mathematics.“ a fraction of cognition” is the beginning of the fraction unit,it is also the starting point to understand the concept of fraction.Existing research findings,there is a general obstacle for students to understand the concept of a fraction,it has something to do with the teacher's teaching at the beginning of fraction.Teachers' teaching of this course is mostly based on experience,lack of theoretical guidance,and most of the teaching design has no feedback on teaching quality.Because the concept of fraction has process-object duality,it conforms to the characteristics of APOS theory.Therefore,under the guidance of APOS theory,this paper makes a systematic teaching design for the course of "a fraction of cognition",and further optimize the design in the teaching practice.First,this paper interprets the subject content of "a fraction of cognition",sorts out the curriculum standards of different periods in our country,compares different versions of teaching materials,and uses interview method to investigate the learning actuality.Based on the understanding of mathematics,curriculum and students,the first draft of teaching design "a fraction of cognition" is formed under the guidance of APOS theory.Meanwhile,make test paper as teaching evaluation tool.Then,the teaching design is revised in instructional design.In class A,teaching is carried out according to the first draft of the design,test papers are distributed,and students' learning disabilities are analyzed based on test papers and interviews.The results show that students have different levels of understanding defects in the meaning of average score,a fraction and overall 1.A small number of students lack the awareness of using fraction to express quantity,so they understand "number of shares" as "number of shares".Based on this,revise the design and form the official draft of teaching design.Adopt comparative teaching,take class B as the experimental class to carry out teaching according to the official draft,distribute test papers and collect feedback information of teaching effect.Sort out the grades of class A and class B,the conclusion is as follows: the total score of class B is better than that of class A,the vast majority of students can understand the relationship between the overall 1,the numerator and the denominator.More students are able to use rotation,translation and other methods to find "number of copies".Only very few students still use integers to expressthe quantitative relationship between the whole and the part.The above results show that the revised teaching design improves the teaching effect.Through the above research,we finally get an APOS theory which is helpful for students' mastery of knowledge and the teaching design of "a fraction of cognition" suitable for teachers.In order to help students better understand the concept of a fraction,and provide a feasible teaching reference for teachers.