A Survey On The Understanding Level Of "High-View Mathematics Knowledge" By High School Mathematics Teachers

In recent years,with the continuous reform of education,the professional development level of teachers has attracted much attention.Scholars have begun to devote themselves to studying what stage the professional level of mathematics teachers is at and what stage it should be at.The ability of high school mathematics teachers to examine mathematics curriculum from a higher mathematical point of view is an important channel to promote the professional development of teachers' knowledge.That is,from the perspective of modern mathematics development,it can be used to examine if elementary mathematics meets the requirements to implement the Standards,and then to achieve the goal of understanding the textbooks deeply.Therefore,the paper uses questionnaire test,interview and case comparison to investigate 40 front-line senior high school mathematics teachers and the master students of mathematics education.It studies senior high school mathematics teachers' understanding level of "high-view mathematics knowledge" from the following two questions:(1)Starting from three dimensions of mathematical concept,mathematical proposition and mathematical problem solving,it investigates the current situation of senior high school mathematics teachers' understanding level of“mathematics knowledge under high viewpoints” through questionnaire test.The present situation of understanding level of mathematics knowledge under viewpoint;(2)Show a teaching case of infiltrating “mathematics knowledge under high viewpoints” in high school mathematics classroom teaching,and it will put forward suggestions on teachers' development.Among them,the classification of mathematics teachers' understanding level of "high-view mathematics knowledge" is based on CIPP teacher competence evaluation model,which is divided into operational understanding,initial conceptual understanding and exploratory understanding.Definitions are as follows:Operational understanding,It means that teachers know some facts,concepts and methods of mathematics and teaching,but they are limited to the textbook itself and can not explain clearly the origin of mathematical concepts,nature and so on.Initial conceptual understanding,It refers that teachers understand mathematical concepts,laws and so on.They can use senior high school mathematics methods to infer or explain reasonably,but they can't conduct deductive inference demonstration,and the understanding degree is not comprehensive enough.Exploratory understanding,On the basis of possessing initial conceptual understanding,we can use higher mathematical theory methods to solve the problems in senior high school mathematics textbooks and reveal the essence of the problems;on the other hand,we can deeply understand mathematics knowledge from multiple perspectivesand backgrounds,and understand mathematics in vertical and horizontal links.The results of the study show that:(1)On the understanding level of high school mathematics teachers to "high viewpoint" mathematics conceptual knowledge: the level of inquiry understanding covers 52.5%,the level of initial conceptual understanding covers4.17%,the operational understanding level covers 5.83%,and 37.5% of the teachers did not give the process of thinking,which is unable to judge the level of understanding;(2)On the understanding level of high school mathematics teachers to "high viewpoint" mathematics propositional knowledge: 36.67% are at the level of exploratory understanding,48.33% are at the level of initial conceptual understanding,8.33% are at the level of operational understanding,and 21.67% of the teachers can't be judged about their level of understanding.(3)In terms of the understanding level of “high-view” mathematical problem-solving knowledge,31.33% are at the level of exploratory understanding,the initial conceptual level of understanding accounts for 39.33%,the operational level of understanding accounts for 5.33%,and 26.67% of the teachers could not be judged about their understanding level.The results show that:(1)There are still teachers who ignore the importance of "understanding teaching",and there are obvious split and stratification phenomena in mathematics knowledge;(2)Teachers are overall lack of understanding of "high viewpoint knowledge",which will directly affect their mathematical literacy.Suggestions on the Mathematics Teachers:1.Teachers' own development suggestions:(1)While reducing the training of mathematical factual knowledge,strengthen the guidance and learning of mathematical conclusions;(2)Correctly locate the gap between their professional cognitive level and the requirements of the new curriculum standards,and pay attention to the transformation of knowledge from academic form to educational form.2.Teachers' classroom teaching suggestions:(1)Emphasizing understanding teaching;(2)Emphasizing inquiry teaching;(3)Emphasizing curriculum design teaching;(4)Emphasizing teaching evaluation;(5)Emphasizing teachers' development.