The Case Study Of Improving Pre-service Teachers’ Mathematical Modelling Teaching Competence

Mathematical modeling(or,more broadly,"applications of mathematics")dates back to the very beginnings of mathematics.Since it was proposed as a separate concept,modeling itself and its learning and teaching have been studied for over forty decades.Positive effects of modeling teaching on students’ understanding and handling of realworld problems,development of general mathematical ability,and improvement of mathematical interest have been widely recognized in the process.Mathematical modeling has gradually been emphasized in the mathematics curriculum and textbooks worldwide,including China,where it has become an essential component of middle school daily classroom teaching routine.Teachers are a vital part of the current wave of change.Despite international attention has been paid recently on the research of teachers in modeling teaching and learning,few empirical studies exist on teachers in China,in addition,more attention is attached to the cultivation and evaluation of student’s modeling competence.Related teacher education courses or training programs are in their initial stages of development,with little evaluation of the corresponding training effect.Based on this research background,this study focuses on a teacher course entitled“Teaching and Learning of Mathematical Modeling in Middle Schools’ ’ conducted in a Normal University.The researcher carries out a case study on the enhancement of preservice teachers’ modeling teaching competence under the course intervention.The aim of this study is to explore effective ways to improve pre-service teachers’ mathematical modeling teaching competence.The study uses a case study approach and combines descriptive and explanatory methods to address two main research questions:(1)"how" pre-service teachers’ modeling teaching competence develops in this course,and(2)"why" such development occurred.The research analyzed data from quantitative questionnaire survey of all 53 pre-service teachers who participated in the course.Questionnaire 1 was used to test the modeling teaching competence before and after the course;Questionnaire 2 occurred at the end and was used to support in answering the research questions.Besides,the competence development process of 10 specific preservice teachers from 4 groups are qualitatively analyzed.The data are collected via classroom and after-class observations,follow-up interviews,and coursework materials.Building on the existing research at home and abroad,the researcher proposed a theoretical framework for teachers’ modeling teaching competence.Through comprehensive quantity and quality analysis,the study identifies positive changes in pre-service teachers’ competence after they participated in the course.Quantitative analysis shows significant improvement in their knowledge.The score rate of modeling teaching knowledge in Questionnaire 1 increased compared with the previous test,among which theoretical knowledge increased by 21.5%,task knowledge increased by5.9%,diagnostic and intervention knowledge increased by 9.2%,and the improvement of individual scores in these three types of knowledge was significant(p<.001).While qualitative analysis reveals the main changes brought about by the course were the acquisition of theoretical knowledge,the accumulation of teaching design experience,and greater recognition of possibility and necessity of modeling teaching in middle school.However,there is not much improvement in knowledge and skills of modeling tasks due to the limited exposure to tasks.It was also found that there were specific differences in the improvement of each dimension of competence among 10 individual cases,mainly in terms of perceptual control.Further analysis of the factors involved in the development of pre-service teachers’ competencies revealed that the commonality in the changes is attributable to key events in the course,such as task exchanges,collective reports,and lectures given by an experienced teacher.The heterogeneity of competence development is mainly influenced by the group partners and the origin background of the pre-service teachers.The researcher also examines their evaluation and reflection on the course from the perspectives of pre-service teachers and the lecturer,finding that improvements can be made by adding practical courses(or observing courses)and modeling tasks to better promote the improvement of preservice teachers’ modeling teaching competence.This teacher education course represents a novel attempt at present,and its significance and effects have been verified by this study.The study also explores the factors that promote or hinder the enhancement of pre-service teachers’ modeling teaching competence.The research results can provide valuable insights into promoting teacher education and broader teacher training in the field of modeling teaching.In the future,it is necessary to focus on teacher education courses and continuous teacher professional development projects,while carrying out simultaneous evaluation of teacher competence development in conjunction with corresponding training courses or projects.The lack of competence of teachers is still the biggest challenge in the implement of modeling teaching in China.Regional disparities and insufficient evaluation tools and methods are also standing in the way.Despite the existing obstacles,it remains feasible to widely implement mathematical modeling instruction in primary and secondary schools with the aim of developing student’s core competencies in this field.Achieving this goal requires the concerted efforts of multiple stakeholders,including mathematicians,mathematics teacher educators,pre-service and in-service teachers,working collaboratively towards a shared vision.