Analysis And Research Of Infiltration Algebra Thought In Elementary School Arithmetic Teaching

The new curriculum standard proposed that teachers should play a leading role in the class to make students understand and master the basic mathematical knowledge and skills,and at the same time,highlight the mathematical thoughts and methods.The prominent idea of mathematics thoughts should be said to be a major feature of the development of mathematics education.Algebraic thinking is an important mathematical thought.It is necessary for students to comprehend some basic mathematical thinking methods in mathematics classes of the elementary school,which can help students understand the essence of mathematics concepts,formulas,rules and so on.Therefore,this study focus on the infiltration of algebraic thinking in the arithmetic teaching of elementary school.The study chose "the division with remainder" as the case of classroom observation,aiming at analyzing the behavior of infiltrating algebraic thinking of teachers with the teaching video of six teachers and the class records.The analytical framework for classroom observation has two dimensions,each of which has three indicators:(1)the breadth and depth of the interpretation of the teaching content-teachers can use a variety of characterization methods;teachers can guide students to focus on the relationship of mathematics concept;teachers can guide students to use different methods to explore and solve the problems;(2)the organization of teaching content and teacher-student interaction-teachers can design a variety of class activities;teachers' questions can lead students' deep thinking;teachers' feedback can promote students' deep understanding of content.According to this framework,the teaching of six teachers is analyzed and scored.And Anderson's cognitive target classification is modified to cater to the characteristics of primary mathematics curriculum.On the basis of four dimensions: remembering,understanding,applying,analyze,the correspondence between the indicators and cognitive targets is analyzed,which can also examine the correspondence between process and objectives.The main teaching objectives of “the division with remainder” is to let the students understand the meaning of the remainder and the division with remainder,explore the relationship between the remainder and the divisor,and use the remainder to solve some simple practical problems.Through classroom observation,the six teachers are basically able to complete the teaching objectives,that is,most students can master the basic knowledge and skills.The analysis framework used in the study is to analyze whether the teaching has the idea of infiltration algebra.After observing,analyzing and scoring,it is found that teachers have different performance in the idea of infiltration algebra.So the teaching of "division with remainder" can be divided into two categories: one is based on the teaching of basic knowledge and skills;the other is based on the idea of infiltrating algebraic thinking.Teachers with the previous tendency in the teaching pay more attention to the basic knowledge,such as the concept of the remainder,explaining the meaning of formulas in the specific situation.But they are not concerned about the relationship between the different concepts.And they pay less attention to guide students into exploring the problem in a variety of ways.Teachers based on the idea of infiltrating algebraic thinking are able to use different characterization methods to present concepts,helping students to understand.And when students are interpreting and translating different representations,they can get a powerful thinking tool.What's more,teachers will pay more attention to guide students to focus on the relationship between the concepts.In guiding students,teachers with algebraic thinking tend to devise a variety of classroom activities,leave students with opportunities to explore problems in a variety of ways.This can not only to develop students' problem-solving skills,but also to enable students to associate knowledge with reality.In the interaction between teachers and students,teachers will pay more attention to trigger students' thinking activities through their questions and feedback,such as conjecture,imagination,comparison,induction,analysis,etc.,all of which are the embodiment of infiltrating algebraic thinking.