An Empirical Study On The Bankward Transfer Of Derivative To Slope Concept From AoT Perspective

Learning transfer refers to the influence of one kind of learning on another kind of learning,and reverse transfer refers to the influence produced in the process of acquiring new knowledge and summarizing and reasoning the previous knowledge.The occurrence of learning transfer often means the deepening of understanding and lays the foundation for innovative thinking,so learning transfer is the booster of the continuous development of core literacy.The development of the perspective of situational transfer begins to pay attention to the view of transfer from the perspective of "actor" or "learner",focusing on the individual construction of similar relations between activities and the process of distinguishing differences.This view is abbreviated as "The Actor-Oriented Transfer Perspective"(AOT).Scholars who hold this view tend to measure student migration through real problem situations with similar disciplinary(or interdisciplinary)connotations.According to the backward transfer theory,it is assumed that the existing concept layer is extended when students learn the derivative,the relationship between the two concepts of slope and derivative is established,the concept of slope of a line is extended to "slope of a curve",and the concept of slope in calculus and function attribute is obtained.Given that there are few studies on backward transfer from the perspective of AOT by domestic scholars,this study attempts to investigate the influence of students’ learning of new knowledge on previous knowledge.Specifically,students’ understanding of slope concept before and after learning derivative and the change of understanding level are taken as evidence of the occurrence of reverse transfer.Therefore,the research question is put forward: Do students have reverse transfer of slope concept before and after learning derivative? On the basis of literature research,the evidence of students’ reverse migration is collected from two aspects.Conceptualizations is a specific representation associated with a specific fundamental feature of a concept in a specific context(Ricardo et al.,2020).Firstly,in order to investigate whether the slope conceptualization of students changes before and after learning derivatives,the "Slope Conceptualization Questionnaire for High School students" was compiled according to the 11 slope conceptualization categories determined by Nagle et al.(2013a)85sophomore students in a key high school were selected to conduct a questionnaire survey before and after learning derivatives.A total of 1368 units of analysis were provided before and after the students’ answers to the four tasks.The slope conceptualization category was used to independently code the participants’ answers.The frequency of each conceptualization used by the students for the four tasks was counted,and the changes of the students’ slope conceptualization in the four tasks and the overall situation were analyzed.Secondly,in order to further investigate whether students’ understanding level of slope function attributes changes after learning derivatives,a test volume of slope understanding level for high school students is designed according to APOS slope understanding framework proposed by Nagle et al.(2019)and interviews with teachers.For the convenience of the study,different from the first study,but at the same level of the research object,170 students from a key high school were selected for the test paper survey before and after learning the derivative.A total of 164 sets of questionnaires were collected,of which 156 were valid,with an effective rate of 95.1%.SPSS26.0 statistical software was used to process the data.Using the methods of drawing the overall basic graph,paired sample T test,rapid cluster analysis and so on,the data analysis of students’ performance in the activity,process and object stage was carried out,and the change of students’ understanding level in the three stages and the overall level was quantitatively analyzed.Based on the above research,the following conclusions can be drawn:(1)The survey on students’ slope conceptualization found that the frequency of students’ use of slope concept’s function attribute concept and calculus concept increased,and positive and reverse transfer occurred in the learning process.(2)The investigation on the understanding level of slope function attribute shows that students’ understanding level of slope function attribute is improved,and positive and negative transfer occurs in the learning process.Firstly,the graphic statistical analysis of the students’ scores shows that the scores of the post-test are higher than those of the pre-test,and the overall scores of the students are higher than those of the pre-test.Secondly,the paired sample T-test for each stage of the students’ scores found that the p values of the three pairs were all less than 0.05,with significant differences.Finally,rapid clustering is used to analyze the results of each stage of the students,and it is found that the increase of concentrated scores in each stage means that the students’ understanding of each stage increases.Based on the results of the two surveys,it is found that after learning derivatives,students have a positive inverse transfer to the concept of slope,adding a new concept layer of slope,and the thickness of the concept layer of the function attribute of slope concept increases.Finally,according to the research conclusion,some suggestions are put forward for students’ learning and teachers’ teaching.