Teaching Research On On The Learning Progression Of Function Concept In High School Based On APOS Theory

This study takes "high school functions" as the core concept,and constructs a top-down model of high school function learning by using a validation-based learning progression model.Through the study of learning progression theory and literature related to function concept learning,a hypothetical learning progression model for high school function concepts is constructed based on APOS theory,mathematics curriculum standards and textbooks.Test questions were developed based on the features of each progression level and the hypothetical learning progression model was validated using the Rasch model.The progression levels were analyzed in terms of difficulty values and score rates,and the results of student and teacher interviews were combined to revise the high school function concept learning progression model and obtain the final high school function concept learning progression model.To construct a teaching strategy for teaching function concepts based on the learning progression model of high school function concepts,and to implement the teaching design and practice in order to verify the effectiveness of teaching based on learning progression.Research indicates:(1)The learning progression model of high school function concept is divided into 5 stages and 9 levels,i.e.preparatory stage,advanced level 1:mastering the concept of functions(variables say),advanced level 2: mastering simple functional relations;operational phase,advanced level 3: understanding correspondence,using set language;process stage,advanced level 4: understanding the three elements of functions,advanced level 5: understanding the conceptual nature of a function;object stage,advanced level 6: understanding of symbolic connotations,advanced level 7:mastering three representations of functions;graphical stage,advanced level 8: deep understanding of function concepts,advanced level 9: application of functions;(2)Based on the application of learning progressions in teaching,teaching strategies were constructed;and instructional design was carried out,which proved to be effective in teaching practice.The teaching strategies are:(1)teaching by learning,following the learning path;(2)reviewing old knowledge,unifying the starting point of progression;(3)building a teaching scaffold according to the progression model;(4)teaching by variation,highlighting the essence of the concept;(5)reflecting and summarizing,forming a concept schema;(6)According to the advanced level of study,the formative assessment is realized.