| Mathematical affect has a profound impact on learners’ mathematical thinking and behavior,and is related to learners’ mathematical engagement.Mathematical affect is an extremely important part of the goal of mathematics education.Mathematics teaching and learning must fully consider learners’ mathematical affect.As the monitoring and regulation of mathematical affect,mathematical meta-affect is a more explanatory perspective that helps to explore the internal mechanism of mathematical affect at the theoretical level,and is expected to have a substantial impact on mathematical affect education at the practical level,which is of great significance for mathematical curriculum and instruction theory research.From the perspective of the world,the research of mathematical meta-affect is in the ascendant.Currently,there is an urgent need to conduct basic research which on theoretical construction of the concept framework of mathematical meta-affect,and empirical exploration of mathematical meta-affect measurement and related factors.This study is just the starting point under this basic idea,aiming to propose and solve the following three research questions: Firstly,how to construct a theoretical framework that can be used to guide students’ mathematical meta-affect measurement? Secondly,how to develop an instrument with good reliability and validity for measuring students’ mathematical meta-affect?Thirdly,how to apply measurement instrument to explore the related factors of students’ mathematical meta-affect?In order to answer the above three research questions,the overall research design combining theoretical construction and empirical exploration was adopted.In terms of theoretical construction,the concept of "mathematical meta-affect" was taken as the research object,attempting to construct a conceptual framework that can be used to guide students’ mathematical meta-affect measurement.In terms of empirical exploration,first of all,the initially constructed theoretical framework of students’ mathematical meta-affect was empirically tested and revised.Second,the students’ mathematical meta-affect measurement instrument was developed based on the framework that has been tested and revised empirically,and its reliability and validity was tested.Finally,the students’ mathematical meta-affect measurement instrument was applied to preliminarily explore the related factors of students’ mathematical meta-affect.Specifically,the following research pathways and methods were used: First,with the help of relevant theoretical perspectives and research conclusions,the speculative research pathway was adopted to conduct normative argumentation,the conceptual framework of students’ mathematical meta-affect was initially constructed.Second,the variant of the exploratory sequential design of the mixed research pathway was adopted,the preliminary constructed theoretical framework of students’ mathematical meta-affect was tested and revised,and the measurement instrument of students’ mathematical meta-affect was developed and tested.Finally,the quantitative research pathway was adopted,the students’ mathematical meta-affect measurement instrument was applied to empirically test the related factors of students’ mathematical meta-affect expected by the theory(Gender,School Stage,Grade,Mathematical Academic Performance,Mathematical Classroom Culture,and Mathematical Teacher Support).The data collection methods involved include "classroom reflective writing + classroom video recording",telephone interview survey and electronic questionnaire survey.Data analysis methods included thematic analysis(hybrid coding including both deduction and induction with the help of NVivo11.0 software)and statistical analysis(descriptive analysis,independent sample t-test,Pearson correlation analysis,one-way ANOVA,dummy regression analysis,exploratory factor analysis,confirmatory factor analysis,reliability analysis,validity analysis,power analysis and effect size calculation with the help of SPSS24.0,R4.2.2,RStudio software and relevant R packages).Based on the above research design and methods,the main research conclusions obtained for the three research questions are as follows: Firstly,the POSE tetrahedron theoretical model of students’ mathematical meta-affect,which includes the four dimensions of "Process-ObjectSituation-Event",is a theoretical framework that can be used to guide students’ mathematical metaaffect measurement.The POSE tetrahedron theoretical model includes the Process(monitoring and regulation),the Object(self and others),the Situation(mainly mathematics test,task and class),and the Event(before,during and after the event)of students’ mathematical meta-affect.Each dimension is an aspect of the theoretical model,and the four dimensions constitute students’ mathematical meta-affect.Secondly,the "Secondary School Students’ Mathematical Meta-Affect Scale",which was developed based on the POSE tetrahedron theoretical model of students’ mathematical meta-affect,has good reliability and validity,and can be used as an instrument for the measurement of secondary school students’ mathematical meta-affect.Thirdly,the three theoretical expected correlation factors of students’ mathematical meta-affect,including Mathematical Academic Performance,Mathematical Classroom Culture,and Mathematical Teacher Support,have been empirically verified in secondary school students.Although there are significant differences in the level of mathematical meta-affect among secondary school students in different grades(stages),the research results do not support the hypothesis proposed in this study.The hypothesis of the theoretical expectation that "there is a correlation between students’ mathematical meta-affect and gender" has not been empirically verified in secondary school students.The main teaching implications based on research findings are as follows: Firstly,the implementation of mathematical affective goals in the current mathematics curriculum standards is based on students’ clear and correct understanding of mathematics and self.Mathematical metaaffect can help students have awareness and judgment of their own or mathematical partners’ mathematical affect,and then respond in the correct way and adjust when necessary.Cultivating students’ mathematical meta-affect is a necessary measure to implement the mathematical affective goals in mathematical curriculum standards.There is a positive correlation between students’ mathematical meta-affect and their mathematical academic performance.Effectively improving students’ level of mathematical meta-affect is not only the key to implementing mathematical affective goals,but also conducive to better achieving mathematical cognitive goals.To implement mathematical affective goals,it is necessary to start from the overall and developmental aspects of the entire basic education stage,and gradually increase reflective mathematical affective elements.Secondly,building a mathematics classroom culture that encourages experimentation,expression,discussion,and cooperation,allowing students to feel the support of mathematics teachers such as attention,questioning,and praise,can create opportunities for students to develop mathematical meta-affect.Thirdly,to help students develop mathematical meta-affect abilities,initial analysis of students’ mathematical meta-affective levels and types can be conducted based on measurement instrument,and observation points can be established based on the POSE tetrahedron theoretical model of students’ mathematical meta-affect.Through daily observation or with the help of mathematical classroom reflective writing,mathematical diary,etc.,the state and trait of students’ mathematical meta-affect can be deeply understood,and finally,through the infiltration of daily mathematics teaching ideas,the teaching of strategies in mathematics themed class meetings,mathematics after-school services,and other activities,targeted cultivation of students’ mathematical meta-affect abilities is achieved. |
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