Research On The Influence Of Metacognition Of High School Students On Mathematical Modeling Ability

Mathematical modeling is the connection between mathematics and the real world.The newly revised general high school curriculum standard lists mathematics modeling as one of the core mathematics competencies,and puts forward higher requirements for learning mathematics application and modeling.However,mathematical modeling in daily teaching practice is limited to the literary application of modeling "coating".Faced with the gap between educational goals and practice in high school mathematics modeling,combined with the application of metacognitive theory in mathematical problem solving,the paper studies the influence of high school students'metacognition on mathematical modeling.The study used the high school students' mathematical metacognitive questionnaire scale,compiled mathematical modeling test questions and modeling evaluation indicators,and analyzed the relationship between metacognition and mathematical modeling.According to the modeling test results,high,medium and low level students were selected for interviews.In addition,the mathematical modeling feedback questionnaire was designed to investigate the metacognitive performance of the mathematical modeling of the students,and the metacognitive activity of the high school students' mathematical modeling process and the influence of metacognitive activities in the mathematical modeling process.Based on the research above,the following conclusions are drawn:(1)There is a significant positive correlation between metacognition and mathematical modeling.The results show that there is a significant positive correlation between metacognition and mathematical modeling results,and metacognitive monitoring is most closely related to mathematical modeling.The mathematical modeling process is the processing process of cognition and metacognition.The metacognitive monitoring mobilizes the modeler's self-awareness,and models the cognitive activity itself as the object of implementing metacognitive activities,planning,monitoring,adjusting,evaluation,reflection.(2)There is a significant difference in metacognition among high school students in the modeling process.The metacognitive differences in high school students'mathematical modeling are significant:the high-level students'modeling of modeling problems show effective metacognitive monitoring and processing activities,and real-time monitoring of the mathematical modeling process.Students with lower modeling ability can't consciously and independently monitor themselves or adopt metacognitive behaviors such as invalid monitoring when they encounter difficulties in the modeling process.Therefore,students who model low-level groups are more likely to be anxious,lack self-confidence,and solve problems when they encounter difficult obstacles in solving mathematical modeling problems.(3)High school students' mathematical modeling metacognitive monitoring ability is generally weakThe metacognition of high school students'mathematical modeling is not good,and the metacognitive monitoring of students in mathematical modeling is obviously insufficient.When students face the cognitive barriers of mathematical modeling,they lack the strategy of metacognitive monitoring and the ability to execute strategies.It is difficult to make effective monitoring and adjustment in time.Students generally lack the awareness of evaluation and reflection.Students have a weaker sense of returning to the reality test results,lack of reflective ability,and are not deeply concerned with the understanding of mathematical modeling.They neglect the two-way connection between mathematics and the real world.Combined with the above conclusions,the metacognitive strategies of mathematical modeling are proposed:mathematical modeling problem representation monitoring strategy,modeling strategy selection monitoring strategy and evaluation and reflection strategy,and based on metacognition,the teaching strategy for teacher modeling is proposed.