Research On Algebra Teaching Design In Junior High School Based On FREUDENTHAL'S Educational Ideas

Algebra in junior high school is the basic content and important part of mathematics in the junior high school,and it nearly accounts for 34% of junior high school mathematics.It serves as a link between primary school and high school algebra study.Algebra in junior high school synthesize the characteristics of abstraction and logic,which can effectively exercise the abstract thinking ability of junior high school students.In the new curriculum reform of the 21 st century,the “compulsory education mathematics curriculum standard(2011 edition)” has clearly put forward the core concepts of application consciousness,innovation consciousness,symbol consciousness and reasoning ability.However,the teaching method of mathematics in China is still mainly taught by experience,which has not been able to meet the requirements of modern people for algebra learning.Therefore,a new educational method of mathematics needs to be introduced.Freudenthal,a Dutch mathematics educator,puts forward the ideas of reality,mathematization and re-creation of mathematics education,which can stimulate students' learning motivation,improve their mathematical thinking ability,and develop students' ability to explore and innovate.It has important significance for improving algebra teaching in a junior high school in our country.At present,based on the Freudenthal's mathematics education ideas,the algebra teaching researches of junior high school in our country mostly focus on the stage of theoretical exploration,while the practical operation is relatively few and lacks of systematicness.So it is necessary to carry out more research on algebra teaching design in junior high school under the guidance of the Freudenthal's mathematics education ideas.In this paper,based on Freudenthal's educational ideas,the algebra teaching in junior high school is studied through literature analysis,interview and questionnaire survey.The main research contents are as follows:(1)summarizing the Freudenthal's educational ideas and the algebra teaching methods in junior high school;(2)based on the Freudenthal's educational ideas,theoretically exploring the algebra teaching design in the junior high school,such as analyzing Freudenthal's educational ideas,analyzing the relationships between Freudenthal's educational ideas and algebra teaching in junior high school,and analyzing the educational values of the algebra teaching in junior high school;(3)based on the Freudenthal's educational ideas,designing the algebra teaching in junior high school.Firstly,analyzing the contents of algebra teaching in junior high school,proposing the teaching design strategies,designing the teaching cases.Then,using interview and questionnaire survey to study the implementation of these cases.Finally,verifying and analyzing the teaching cases.According to the study,the design strategies of algebra teaching in junior high school based on the Freudenthal's educational ideas mainly include: creating suitable realistic situations,and paying attention to the applicability of algebra and the difference of individual;synthetically using the reasonable reasoning and deductive reasoning to realize mathematization;emphasizing the subjectivity of students and paying attention to students' practical inquiry under the teachers' guidance;improving the reflective ability in the process of algebra teaching.In the study of teaching design of "inverse proportional function",the teachers' interviews and the students' questionnaires all show that Freudenthal's educational ideas can effectively improve the learning efficiency,can make the students feel more fun in the process of mathematization and re-creation,can enhance the students' interest and motivation in mathematics learning,can cultivate the students' abstract thinking and logical reasoning ability of analogy and induction.Therefore,the validity of Freudenthal's educational ideas is verified.