The Application Of Polya's "How To Solve Problems Table" In The Teaching Of Logarithmic Function

The logarithm was created and developed to solve the tedious calculations in astronomy,navigation,trade,and engineering.It not only had a profound influence on various natural sciences and mathematics in the 16 th and 17 th centuries,but also covers an essential part in these subjects nowadays.Therefore,there are explicit requirements on the teaching of logarithmic function in many countries,so as in China.The logarithmic function plays a certain role in the national college entrance examination.However,as for such important mathematics knowledge,student’s understanding and command of it are not as optimistic as expected.In this case,the author tries to teach logarithmic function from different angles,in order to draw lessons from various teaching experiences.The American-Hungarian mathematician and math educator Polya,with a profound knowledge of mathematics teaching,devoted his entire life to mathematics and mathematics teaching research.He advocated to use heuristic methods to guide students to revisit the discovery process of mathematics.The table from his classic masterpiece How to Solve It is the consummation of his teaching experience,embodying his teaching efforts on the past several decades.Thus,the author starts to explore whether or not the table from How to Solve It can be applied to the teaching of logarithmic function.If it is applicable,then how to apply and what benefits can be achieved?This study intends to first analyze students’ learning status of logarithmic function,the connotation of Polya’s table from How to Solve It,as well as the logarithm and characteristics of logarithmic function.Then the study proceeds to discuss the analytical results dialectically,to further illustrate the feasibility of applying Polya’s table to logarithmic function teaching.Finally,according to the analytical results,the author puts forward a method of applying Polya’s table in the teaching of logarithmic function.Based on this method,the author conducts two related new lessons and comes up with three related teaching designs on how to solve problems.Besides,after the teaching practice,the author also analyzes the teaching effects through several in-depth interviews.Based on this study,the author finds that: 1.the table from How to Solve It as well as itsimplication of mathematics are instructive not only for the teaching of problem-solving,but also for a new lesson;2.the use of Polya’s table in teaching can enhance students’ understanding of the concept of logarithm and the nature of its operations to a certain extent,which somewhat helps students to get rid of creating formulas related to logarithm by themselves;3.inspired by questions in Polya’s table,the teachers can mobilize students’ learning enthusiasm and also improve students’ effectiveness of participating in the lectures.