Research On High School Students’ Learning Progressions For Exponential Function

This dissertation applies learning progressions(LPs)to the study of high school students’ progress in learning exponential function.My research mainly consists of the requirements on exponential function in The Curriculum Standards of Secondary School Mathematics(Curriculum Standards)and contents in three different versions of textbooks.The vertical levels of achievements in the model are constructed in terms of the key competencies of mathematics.The model eventually unveils high school students’ understandings of exponential function concepts and help instruct teaching and assessment.This dissertation adopts validation LPs as study structure,which is divided into three stages:(1)Preparation: using text analysis to construct hypothetical LPs.Specifically,setting up learning goals and levels of achievements by means of analyzing contents on exponential function in Curriculum Standards,literature and textbooks,and then construct pre-test.(2)Validation: making interviews and launching pre-test and formal test to obtain quantitative data validating hypothetical LPs.Sample ranging from Senior 1 to Senior 3 is selected among three high schools,53 for pre-test and 248 for formal test.Data later is analysed in partial credit model(PCM),a kind of Rasch model.(3)Optimization: using outcomes in previous stages to adjust the hypothetical LPs and building high school students’ LPs in exponential function as a result.To be specific,the hypothetical LPs are adjusted in analyzing scores of every item,interviews to subjects and experts and related literature.The results give out the keypoints in every level of achievements in order to guide teaching and assessment on learning in exponential function.Throughout analysis of data and interviews,the conclusions are listed as below:(1)secondary students’ LPs in exponential function can be divided into three stages(Abstraction,Reasoning,Modelling)and six levels of achievements.(2)The tendency of gap between levels of achievements goes fast from the beginging and slows down in the end.Specifically,the crossing which is across the highest range in difficulty from level 1 to level 2 is easier at first.However,starting with level 4 in reasoning phase,it becomes more and more difficult to cross upward,and the gap between levels of achievements changes less and less.(3)In terms of grades,there is statistically significant difference in both the mean of person measure and the performance between Senior 2 and Senior 1.So do Senior 2 and Senior 3.The reason why Senior 2 students perform poor is likely the retroactive interference or forgetting.(4)In general,gender most unlikely has statistically significant impact on the ability to learn exponential functions.At a lower level of achievements,females are basically ahead of males in ability.However,when entering the reasoning and abstraction phase,in tems of the mean of person measure,males gradually surpass females.Finally,according to the keypoints and obstacles in students’ performance during the LPs,the dissertation gives out the suggestions and paths to learning and teaching.To be specific,the keypoints at each stage are: mastering the "correspondence" and exponential power operation,managing exponential function concepts and symbols interpretation,and the understanding of functions from model perspective.The obstacles at each stage are: identifying the function relationships,mastering properties of exponential operations,identifying the class of exponential functions,and abstract function relationships from situations.