Research On The Level Of Primary School Mathematics Teachers' Understanding Of Mathematics Concepts Based On The APOS Theory

In order to improve the quality of students' mathematical learning,an important measure is to improve the quality of teachers' mathematical knowledge firstly.In primary school mathematics,most of the knowledge learned by students is the concept or conceptual knowledge,so front-line teachers should have a profound understanding of primary school mathematics concepts.APOS theory is a constructivist learning theory put forward by Dubinsky for the learning process of mathematical concepts.It shows that students have to go through four stages of operation,process,object and schema when they construct mathematical concepts.Similarly,the theory is applicable to the analysis of teachers' understanding level of mathematical concepts.The understanding level of mathematical concept of teachers was studied in this paper,which was based on APOS theory.The mistakes made by students in mathematical learning are important resources for students' learning,they are also important for teachers to carry out teaching.In the process of teaching,it is one of the basic teaching activities for mathematics teachers to analyze students' problem-solving errors,attribute and correct students' mathematical errors.Therefore,teachers must have professional subject knowledge in order to be able to carry out teaching.It can be seen that teachers must have professional knowledge to deal with students' errors accurately.By analyzing the ways that teachers deal with students' mathematics errors,the level of teachers' understanding of mathematics knowledge was studied in this paper.Starting from dealing with students' mathematical errors,this paper took the calculation errors which are related for two important concepts place value and area in the first learning period of primary school as the carrier,and used the methods of questionnaire and interview to carry out a research and investigation on the level of mathematical concept understanding of 60 primary school mathematics teachers at the front line of teaching.By analyzing the attribution and correction strategies of math teachers to students' mathematical errors,this paper studies the level of their understanding of mathematical concepts with the help of APOS theory.The main conclusions are as follows:(1)From the perspective of abdication subtraction,primary school mathematics teachers have different understanding of the concept of place value.Correspondingly,the proportion of teachers who are at the level of action,process,object and schema accounts for 5%,45.00%,40.00% and 10.00%,respectively.(2)From the perspective of multiplying two digits by two digits,primary school mathematics teachers have different understanding of the concept of place value.Correspondingly,the proportion of teachers who are at the level of action,process,object and schema accounts for 5%,46.67%,40.00% and 10.00%,respectively.(3)From the perspective of comparing the size of irregular figure area,the understanding degree of primary school mathematics teachers on the concept of area is different.Correspondingly,the proportion of teachers who are at the level of action,process,object and schema accounts for 6.67%,50.00%,35.00% and 8.33%,respectively.Finally,according to the conclusion of this study,the author gives some suggestions to promote the level of primary school teachers' mathematical concept understanding from three aspects: pre-service education,post-service teaching and professional development:(1)reveal the essence of mathematics,strengthen the concept understanding.(2)carry out teaching reflection,establish the concept system.(3)combine theory with practice,promote professional development.