Investigation And Research On The Symbolic-graphic Combination Ability Of Mathematical Gifted Students In Senior High School

The idea of combining numbers and shapes has been used throughout the development of mathematics,and the idea of combining numbers and shapes is to establish a strong connection between the words and formulas used in the process of mathematical reasoning and the images produced in the learner's mind.In this study,we focus on gifted students in mathematics,based on high school mathematics curriculum standards,metacognitive theory,error classification and attribution theory,and other analytical frameworks to investigate the interplay between metacognition and problem solving by observing,analyzing,and reflecting on students' strategy selection,cognitive monitoring,and evaluation in the process of problem solving,so as to further explore the understanding and application of symbolic-graphic combination in the process of solving mathematical problems by gifted students.And further explore the interplay between metacognition and problem solving.In this study,through the preparation of a set of student test papers and metacognitive questionnaires related to the symbolic-graphic combination,we can understand the specific ability of high school mathematics gifted students to understand and use the symbolic-graphic combination.And the level of metacognition in the process of mathematical problems,and the correlation between the various factors of metacognition;the correlation between the various factors of metacognition and the level of ability to solve mathematical problems related to the symbolic-graphic combination.The study found that,firstly,the vast majority of gifted students in senior high school can accurately find suitable solutions to problems related to the symbolicgraphic combination,but when using the method of thinking about symbolic-graphic combination,students make more intellectual errors,mostly focusing on students' inability to accurately transform the three mathematical languages into each other,and inability to effectively perform subsequent representational transformations based on their own reasoning process.Secondly,in terms of metacognitive level,(1)The level of metacognition of gifted students in high school mathematics is relatively concentrated in solving mathematics problems,showing an intermediate level.Among them,the level of metacognitive knowledge "task" is relatively high,and metacognitive strategies capabilities(Including select strategies,timely detect results,and the ability to monitor and adjust)is relatively low.(2)Among the various factors of metacognition,there are six groups of factors that are related.Among them,the metacognitive knowledge "individual",that is,the students' clear understanding of their own strength is a key factor to promote the individual's cognitive ability and the achievement of learning achievements in solving mathematical problems related to the symbolic-graphic combination.(3)In metacognitive activities,boys have much higher metacognitive experience "cognition" and strategic "planning" abilities than girls.Thirdly,the "task" of metacognitive knowledge,the "cognition" and "emotion" of metacognitive experience,and the "regulation" of metacognitive strategies are all positively correlated with students' levels of symbolic-graphic combination.Based on the potential interaction between metacognitive factors,the higher the level of metacognition,the higher the ability of gifted students to use the thinking of symbolicgraphic combination.Finally,this research puts forward some teaching suggestions on mathematics education for gifted students based on the above research results.For example,"specialized" education for gifted students in mathematics means that gives students non-standard challenging questions or critical thinking questions,voice training or selfquestioning methods to train their metacognitive self-regulation through creative leaps.Guide students to enhance the use and belief of problem-solving strategies to build a complete body of thinking methods.