The Influence That The Logarithmic Function Question Feature On Analogical Transfer Of Its Solutions

The study designs two experiments.In experiment 1 adopt 2(class types:experimental class and innovative class)× 3(student types:excellent students,middle students and students with academic difficulties)× 8(transfer levels:8 different transfer levels)a mixed design of three factors,class types and student types are inter-subject variables,transfer levels is intra-subject variable,and the study variable is transfer performance.The purpose of this study is to explore the influence of the similarity between the transfer levels of logarithmic function test questions and examples on the analogical transfer of the solutions when the students in senior one are in different class types and student types.In experiment 2 adopt 2(class types:experimental class and innovative class)× 2(the values of m:m>1 and 0<m<1)×3(the values of Δ:Δ>0、Δ=0 and Δ<0).The values of m and the values of Δ are intra-subject variable,class types is inter-subject variable,and the study variable is transfer performance.The purpose of this study is to explore the influence of the similarity between the values of m and Δ in the test questions and the examples of logarithmic function on the analogical transfer of solutions when the students of senior one are in different class types.Results of experiment 1:When the students in Grade 1 of high school are the subjects,the main effect of the transfer levels is significant,and the interaction effect of both the transfer levels and the class types is significant.The simple effect analysis is made further on the transfer levels at the level of two different class types,and the results showed that at the level of experimental class,the transfer levels has a significant effect on the analogical transfer of functional y=logm(ax2+bx+c)solutions;at the level of innovation class,the transfer levels has a significant effect on the analogical transfer of functional y=logm(ax2+bx+c)solutions.The interaction effect of both student types and the transfer levels is not significant,and the interaction effect of transfer levels and class types and student types is not significant,either.The main effect of class types and student types is significant.Results of experiment 2:When the students in Grade 1 are the subjects,the main effect of m isn’t significant,and the interaction effect of both the values of m and the class type isn’t significant,either.The main effect of the values of Δ is significant,and the interaction effect of both the values of Δ and the class types is also significant.The simple effect analysis is made further on the values of Δ at the level of two different class types.And the results showed at the level of experimental class,the values of Δ hasn’t Δ significant effect on the analogical transfer of the functional y=logm(ax2+bx+c)solutions,at the level of the innovation class,the values of Δ has Δ significant influence on the analogical transfer performance of function y=logm(ax2+bx+c)solutions and there are differences in class types.The interaction effect of both the values of m and the values of Δ is also significant.which shows that the values of Δ has Δ significant influence on the analogical transfer performance of function y=logm(ax2+bx+c)solutions and there are differences in the values of m.The simple effect analysis of the values of Δ at the two levels of the values of m is further carried out,and the results showed that at the value level of m>1,the values ofΔ has Δ significant influence on the analogical transfer of function y=logm(ax2+bx+c)solutions;and at the value level of 0<m<1,the values of Δ has Δ significant influence on the analogical transfer of function y=logm(ax2+bx+c)solutions.The interaction effect of the values of m and the values of Δ and the class types isn’t significant.The main effect of class types is also significant.According to the research results,the following conclusions are drawn:(1)when the subject is Δ freshman in high school,The feature of migration level has Δ significant impact on analogical transfer of functional y=logm(ax2+bx+c)solutions,not only on the accessibility and extraction of function y=logm(ax2+bx+c)solution methods,but also on its application,and there are significant differences in class types.(2)When the subject is a senior high school freshman,the surface feature of the values of m hasn’t Δ significant influence on analogical transfer of function y=logm(ax2+bx+c)solution,and has no influence on access,extraction and application of function solution methods,and there is no significant difference in class types.(3)When the subject is Δ senior high school freshman,the structural feature of the values of Δ has Δ significant impact on the analog transfer of function y=logm(ax2+bx+c)solutions,which not only affects the accessibility and extraction of functional solution,but also plays Δ role in its application,and there are significant differences in class types.(4)When the subject is Δ senior high school freshman,class types and student types have Δ significant influence on analogical transfer of function y=logm(ax2+bx+c)solution,which will affect the accessibility,extraction and application of function solution methods.(5)Whether the subjects are students who rely on surface content or students who can generalize structural features,the similarity of surface content and structural features of the sample and logarithmic function has different degrees of influence on the analogical transfer of their solutions.Based on the research results and conclusions,the following teaching recommendations are made:first,the teaching suggestions for solving function y=logm(ax2+bx+c)include:(1)Pay attention to the concept teaching of logarithmic function,and make clear the value range of the definition domain and range of the logarithmic function;(2)Pay attention to the teaching of function y=logm(ax2+bx+c)substitution disassembly and strengthen the drawing training of complex functions;(3)Set sample questions for discriminant Δ and pay attention to the cultivation of mathematical thoughts and methods;(4)Strengthen the variation exercises of logarithmic functions to train students’ mathematical abstract thinking.The second is to promote the thinking of analogical transfer in mathematical problem solving in teaching,including(1)Strengthening the awareness of goal,correctly representing the problem,and promoting the transfer;(2)Reveal the abstract relation from the sample questions,and classify and summarize the typical example questions.