Research On The Integration Of Mathematics History Into The Teaching Of Univariate Linear Equations In Junior High Schools

In elementary school,students are only initially exposed to simple equations,while formal and systematic learning of equations is in middle school.At the beginning of the equation chapter,the quadratic equation is the beginning of the formation of equation ideas and the key period for mastering modeling ideas,which is very crucial for students' subsequent algebraic learning.However,most middle school teachers give the definition and solution of quadratic equations directly when teaching,paying less attention to the historical formation and development process of this knowledge,which to a certain extent affects middle school students' understanding and mastery of equation ideas.By integrating the history of mathematics into the teaching of quadratic equations in junior high school,students can deeply understand the relevant concepts and laws,perceive the charm of equation ideas,and realize the smooth transformation from arithmetic thinking to algebraic thinking.Based on combing HPM research and research on the teaching of quadratic equations and other related literature,a questionnaire survey was conducted among teachers and students in four secondary schools in Tianjin,and interviews were conducted with three representative teachers to understand the reality of integrating the history of mathematics into the teaching of quadratic equations.The results show that the history of mathematics,as a vivid teaching resource and learning material,has not been given a corresponding opportunity to appear in the actual teaching of quadratic equations and play the new role given in the context of quality education.The main problems are as follows:(1)teachers think the history of quadratic equations is important,but do not deeply understand its importance and level;(2)teachers' knowledge of the history of mathematics is high,but their vision of the history of mathematics is narrow;(3)teachers understand the requirement of integrating the history of mathematics in the curriculum,but there is a deficiency in the actual frequency of using the history of quadratic equations and the degree of tapping into it;(4)students have a slightly single way to draw on the history of quadratic equations and their understanding of it is not optimistic;(5)students recognize more the interesting function of the history of quadratic equations,and do not understand quadratic equations in terms of its deep cognitive function.After an in-depth analysis,the causes of these problems are mainly the following:(1)the concept is not profound;(2)the vision is not comprehensive;(3)the timing is not clear;(4)the method is not scientific;(5)the learning is not active.To address the causes of these problems,we proposed the following strategies for integrating the history of mathematics into the teaching of quadratic equations:(1)to firmly establish the teaching concept of "studentoriented and educating people through history";(2)to select a wide range of materials inside and outside the textbook and to identify the value of historical materials in-depth;(3)to find the right rhythm in the classroom and to penetrate the history of mathematics in-depth;(4)to adopt a diversified approach and to integrate the history of mathematics in depth and organically.Then a teaching case of integrating the history of mathematics into the concept of quadratic equations is given with the proposed strategies.