Study On The Investigation Of The Teaching And Learning Of Plane Vector Inner Product

As one of the important basic concepts in modern mathematics,plane vector has a clear physical background,and it is the bridge between algebra and geometry.Plane vector inner product is one of the significant content of plane vector,which is widely used,is also a hot spot of college entrance examination in recent years.The mathematics textbooks of the senior high school published in 2019 have significant changes in the content arrangement of the plane vector inner product.How to carry out the teaching and learning of plane vector inner product and its related content,and how to use the new textbooks,are urgent problems to be solved.The literature research method is adopted.Domestic and foreign works of literature related to plane vector inner product were collected through CNKI,VIP and Periodical Literatures Reprinted by China People's University.This paper sorts out,analyzes and reviews relevant domestic and foreign literature from multiple angles,such as learning influencing factors of plane vector inner product,solving strategies,and instructional design.Through literature research,it is found that most of the research on the teaching strategies of plane vector inner product remain at the theoretical level and lack empirical research.Questionnaire survey method and interview method are adopted.(1)The Plane Vector Inner Product Test Paper was compiled based on Bloom's cognitive process dimension.The Questionnaire on Non-cognitive Factors of Learning Plane Vector Inner Product was compiled from the non-cognitive factors(learning motivation,emotion,attitude,willpower,and personality)dimension.The respondents come from 4 middle schools in Neijiang City,Sichuan Province,with 338 students in grades 11 and 12.Excel2010 was used to process the collected and sorted data,and SPSS21.0 software was used to carry out descriptive statistics,normal distribution test,independent-sample t test,one-way ANOVA,and logistic.(1)The survey results of The Plane Vector Inner Product Test Paper show that: Firstly,senior high school students' high-level cognitive level of plane vector inner product learning is relatively low,and their "creation" level is the weakest,the overall score rate is only 16.22%;Secondly,students' memory of projection knowledge exists "rote learning";Finally,there is no significant difference between students' gender in each dimension of Bloom's cognitive level and academic performance.(2)The results of The Questionnaire on Non-cognitive Factors of Learning Plane Vector Inner Product are as follows: First,the level of non-cognitive factors of students is relatively low,with an average value of 3.2989(full score of 5),and a score rate of 65.98%;Second,the gender difference is obvious in non-cognitive factors.The level of non-cognitive factors of boys is higher than that of girls.The "learning motivation" and "personality" of boys are better than that of girls;Third,there are no significant differences in non-cognitive factors and each dimension between grades 11 and 12;Fourth,there are differences in non-cognitive factors among students from different schools;Fifth,the results show that some students have difficulties in understanding and applying the knowledge of plane vector inner product,and are resistant to mathematics learning;Sixth,overall non-cognitive factors have a greater impact on academic performance(accounting for 66.7% variation).The five dimensions of non-cognitive factors have the most significant impact on emotion(Beta=0.384),followed by attitude,willpower,personality,learning motivation(Beta=0.087),which have almost no impact on academic performance.(2)Interviews with 4 teachers and the conclusions are as follows:(1)The introduction of the new lesson is simple,and physical work is introduced into the new lesson.(2)The expert teachers(with the title of professor or associate professor)have a specific grasp of the teaching difficulties.The general teachers,especially the novice teachers,are more general about the difficulties.In terms of the breakthrough of the difficulties,they all pay attention to the students' practical operation,but the expert teachers pay more attention to the application of typical examples and the specific learning situation of the students;(3)It is believed that modern mathematics software such as The Geometer's Sketchpad is helpful to mathematics teaching,the main reason why they are not used frequently is that they are unfamiliar with software operation.Put forward the following teaching suggestions:(1)Study textbooks and use new textbooks creatively;(2)Pay attention to concept teaching and adopt reasonable teaching strategies;(3)Attach importance to the overall application value of plane vector inner product;(4)Appropriate attention should be paid to the development of students' high-level cognitive level;(5)To pay attention to the cultivation of non-cognitive factors of senior high school students,we can start from the aspects of improving learning interest,paying attention to the cultivation of achievement motivation,rationally designing problems,improving learning efficacy,helping students to correct their learning attitude,praising students' good psychological quality of perseverance,and paying attention to the cultivation of students' personality.(6)Diversified evaluation of student learning;(7)Pay attention to the cultivation of modern information technology ability.Based on APOS theory,this paper makes an instructional design for the plane vector inner product in the new textbook.