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A Study On The Mathematical Representational Ability Of Senior Students

Posted on:2024-06-06Degree:MasterType:Thesis
Country:ChinaCandidate:S S ZhaoFull Text:PDF
GTID:2557306917459734Subject:Education
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The description of mathematical objects can be multi-channel and multi-faceted.The declarative language of propositions,the representational language of graphs and the abstract symbolic language constitute the objective factors of multiple representations of mathematical objects.As one of the core competencies of mathematics,mathematical representation can help students better understand knowledge and facilitate problem solving.Mathematical representation is not only a part of mathematics teaching and learning,but also a teaching tool for understanding mathematics.Learning multiple representations in mathematics is an inescapable issue in mathematics teaching and learning.In this study,literature research,questionnaire and interview methods were used to implement the investigation study using the framework of Bao Jiansheng’s mathematical representational ability test.Based on the level of mathematical representational ability delineated by Bao Jiansheng,a test paper was developed using plane vectors to investigate the senior students in L city.Among them,the questionnaire investigated students’representational awareness,representational habits and representational metacognition,the test paper investigated students’ extrinsic representational ability,and the interview method analyzed students’ intrinsic representational psychology.The questionnaire revealed that:(1)in terms of representational awareness,62.59%of students think that representation can deepen their understanding of mathematical knowledge,while 28.74%of students still cannot transform real-life problems into mathematical problems;(2)in terms of representational habits,47.64%of students are accustomed to using multiple representations to solve problems;students use descriptive representations slightly more than narrative representations;(3)in terms of representational metacognition,34.25%of students are not able to represent the overall information in a topic and do not reflect on the process of solving a problem after completing the representation.The analysis of the test papers led to the following conclusions:(1)in general,the students’ mathematical representation level is 1.97,which is at the transition stage from Level 1 to Level 2 and close to Level 2;(2)the mathematical representation levels of the experimental class of physical and chemical students,the general class of physical and chemical students,the experimental class of politics and history,and the general class of politics and history were 2.29,1.96,2.08,and 1.66,in that order.From the class categories,the level of mathematical representational ability in the experimental class is higher than that in the general class;(3)there is a significant correlation between the questionnaire scores,students’ usual grades and mathematical representational ability,in general,the better the grades,the higher the level of mathematical representational ability,and vice versa;(4)the difference between students’ mathematical representational ability and gender is not significant.Interviews for individual questions in the test paper revealed that the main reasons for the representational impairment were:(1)students’ mastery of knowledge and the intrinsic connections between knowledge affect the mathematical representation;(2)students’different forms of coding knowledge lead to the inability to complete the conversion between representations;(3)the complexity of the problem situation affects whether students can correctly represent it;(4)the questions in the classroom exercises are more conventional,and I don’t know how to start when I encounter open-ended questions.Based on Tang Jianlan’s cognitive structure model,the students’ internal representation process was analyzed and teaching suggestions were given.
Keywords/Search Tags:Mathematical representation, Mathematical representation ability, Plane vectors
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