Study On Constructing Assessment Model Of Geometrical Intuitive Ability For Primary School Students

Geometrical intuitive ability,as one basic literacy of citizens,is an important component of mathematical literacy.Since the 21 st century,most of countries have paid much attention on cultivating the geometrical intuitive ability of primary and secondary students,and designing mathematics curriculum for that purpose.Empirical study on students’ geometrical intuitive ability is also an important research project in China under the background of advocating empirical research in Chinese educational fields and "geometrical intuition" mentioned as the core concept in "Curriculum Standard for Compulsory Education Mathematics(2011)".However,the majority of previous research focuses on exploring the definitions of geometrical intuitive ability,teaching strategies,problem-solving and status quo investigation and so on.There lack research on the operational definition,assessment indicators and assessment models of geometrical intuitive ability.This will result in lack of research basis on mathematical curriculum and material development,classroom teaching,students’ learning assessment for cultivating students’ geometrical intuitive ability.Based on these considerations,this study identifies the two following research questions:Question one: To explore the operational definition of the geometrical intuitive ability of primary school students,and explore its assessment indicators.Question two: To construct the assessment model of the geometrical intuitive ability of primary school students and test its’ reliability and validity.Drawing on the existing research ideas and methods on constructing assessment model in educational research,this study both employs qualitative and quantitative research methods,including literature study,interview,test survey,questionnaire survey,exploratory factor analysis,confirmatory factor analysis,single factor analysis of variance,and independent sample T-test.Questionnaire surveys are conducted to mathematics education experts,primary school mathematics teachers and teaching researchers from Beijing,Tianjin,Zhejiang,Inner Mongolia,Chongqing,Guizhou,Hainan,Jilin and Shandong,and test students from more than 10 primary schools in eastern,central and western China.Based on the literature study and empirical investigation,the operational definition,the assessment indicators,the assessment model,and the test tool are studied,and the assessment model is tested through empirical data.The study process and conclusions are as follows:(1)The concept of geometrical intuitive ability of primary school students is clarified.Through literature study and empirical investigation,the concept of geometrical intuitive ability of primary school students has been finalized.It refers to a kind of the ability of students understanding graphics and using graphics to describe and analyze a mathematical problem,to obtain a direct perception and overall understanding of the problem.(2)The construction of operational definition and preliminary exploration of assessment indicators of geometrical intuitive ability.The operational definition of geometrical intuitive ability of primary school students is constructed,and tentatively divided into 5 first—class indicators,based on the analysis of literature,"Curriculum Standard for Compulsory Education Mathematics(2011)",primary school mathematics textbooks and experts’ opinions.By data analysis of 520 primary school students,the Cronbach’s Alpha coefficient of the questionnaire is 0.624.Through exploratory analysis,the 5 first-class indicators are clustered into 3 first-class indicators,and each first-class indicator contains 3 second-class indicators.The first-class indicators include the knowledge of graphic formation,using graphics to describe problems,and using graphics to analyze problems.The second-class indicators include abstracting graphics from specific objects,knowing graphics and using symbols to represent graphics,forming graphical images and drawing basic graphics,using graphics to represent numbers and their operations,using graphics to represent geometric problems,using graphics to represent realistic problems,exploring problems with the help of graphics,establishing numerical relationships by graphics,and using graphics to solve problems.(3)The degree of recognition and confirmatory analysis of assessment indicators,and the construction of assessment model.A questionnaire surveying people’s opinions about assessment indicators is administered to 563 mathematics educational experts,in-service mathematics teachers and teaching researchers.The Cranach’s Alpha coefficient of this questionnaire is 0.852.The results show that the degree of recognition of the importance and the legitimacy of nine assessment indicators is relatively high,which are more than 4.17 sores.The confirmatory factor analysis shows that the fitting degree of the default model and the sample data is good,and three potential variables are closely related to the nine observed variables,and their mutual influence reaches a significant level.Based on the theories and methods of constructing the model framework,the objective assignment method and the subjective assignment method,the study attempts to use factor analysis method and expert scoring method to construct the assessment model of geometrical intuitive ability of primary school students:(10)(10)(28)4.03.03.0CBAY,therein,Y stands for “geometrical intuitive ability of primary school students ”,A stands for “knowledge of graphic formation”,B stands for “using graphics to describe problems”,C stands for“using graphics to analyze problems”.(4)Testing the assessment model and analyzing the characteristics of the geometrical intuitive ability of primary school students.The result of the questionnaire survey about the assessment indicators and the assessment model is consistent with the experts’ experience and understanding.1093 students from grades 4 to 6,are tested and the Cronbach’s Alpha coefficient of the test is 0.616.The results show that there is a positive correlation between the development of students’ geometrical intuition and mathematical achievement.The average levels of students’ geometrical intuitive ability gradually improve with the growth of grade.The students’ achievement in grades 4,5 and 6 has no significant gender differences,while urban students’ achievement is higher than that of rural students.These results show the findings using the assessment model have consistency with relevant domestic and foreign research results and reflect the actual situation.Therefore,these results indicate that the constructed assessment model is reliable,reasonable and operational.In addition,the study also finds that primary school students perform better in “graphics and geometry” and “statistics and probability”,but demonstrates lower ability in “number and algebra”.The students generally encounters obstacles in understanding the dynamic knowledge(folding and unfolding,etc.),while in “folding and unfolding ”,rural students’ performance is significantly higher than urban students.This Thesis is consisted of seven chapters.Chapter 1 is an introduction,including background,questions,significance and the core concept.Chapters 2 presents literature review,provides an overview of research on geometrical intuitive ability,and combines the relevant theories on geometrical thinking development and assessment,assessment model,mathematics literacy test and so on.Chapter 3 elaborates research design and methods,including research objectives and contents,methods,ideas and framework,testing tools development and so on.Chapter 4 explores the assessment indicators of the geometrical intuitive ability of primary school students,to construct operational definitions from the study the behaviors of geometrical intuitive ability,using factor analysis to explore the assessment indicators.Chapter 5 is the assessment model construction of the geometrical intuitive ability of primary school students,including the degree analysis of recognition about assessment indicators and confirmatory factor analysis,using factor analysis and expert ratings to construct the assessment model.Chapter 6 preliminarily testifies the assessment model of geometrical intuitive ability,including experts’ judgments,the development of test tools and using it to complete the verification.In addition,the characteristics of pupils’ geometrical intuitive ability are found.Chapter 7 is about discussion,conclusion and thoughts,that including discussion about the results,conclusion of the study,innovations of the study.Inspirations on curriculum construction,classroom teaching,and learning assessments,and finally outlooks are given.There are two innovations in this study: 1)The operational definition of primary school students’ geometrical intuitive ability is constructed and the assessment indicators of primary school students’ geometrical intuitive ability is analyzed for the first time 2)The assessment model for assessing primary school students’ geometric intuition ability is constructed and the test of geometric intuition ability is developed through systematic and scientific methods.After hard work and empirical research,these results(such as “study on constructing the assessment model of geometrical intuitive ability for primary school students ”,“ an awareness of the objectives of geometrical intuitive ability for the first three years of primary school mathematics”,etc.)have been published and reproduced on the key domestic educational journals.However,since the research such as the exploration of assessment indicators,the construction of assessment models and the development of test tools are just tentative explorations,there are still a lot of issues that need further in-depth thinking and exploration.For example,research can be conducted in other regions with larger samples,and verified repeatedly.Therefore,for future studies,it is better to conduct similar research in more sites,constantly improve the assessment indicators and the assessment model of the geometrical intuitive ability of primary school students.After empirical studies with bigger samples from more places,the assessment norm and standard of geometrical intuitive ability for primary school students can be established,which play a great role to promote geometrical intuitive ability’s evaluation,supervision and cultivation.