A Case Study Of The Cultivation Of Mathematically Outstanding Students’ Problem-Solving Ability Based On Thinking Aloud

After combining the requirements of curriculum standards for mathematical problem solving ability based on the relationship between vocal thinking,mathematics education and problem solving ability,in this thesis,the impact of the thinking aloud strategies of outstanding mathematical students on their mathematical problem-solving abilities is mainly investigated,the thinking aloud of outstanding mathematical students with different personalities and their mathematical problem-solving abilities are explored,and the suggestions are given.In this research,the case study and a pre/post test design are used to make descriptive analysis based on the observation of thinking aloud theory and the analysis of the two target behaviors of four participants,in which students’ metacognitive processes such as self-monitoring and selfadjustment,as well as problem-solving processes are included.Besides,the data analysis on students’ mathematics scores,classroom performance,thinking aloud summary scales,and problem-solving ability assessment forms is carried out.The analysis leads to the following conclusions are drawn: 1.The use of thinking aloud to solve problems can help students monitor and adjust themselves.The decline of variation coefficients for both groups can indicate the consistency of intervention and showing small improvements in the four components of understanding the plan,developing the plan,implementing the plan and checking the results;2.In accordance with the linear analysis on the two groups,the trend lines of increasing slopes and coefficients of determination indicated that the data values at the treatment stage were reliable and that the more introverted outstanding mathematical students present are more influenced by thinking aloud strategies,and their mathematics scores can be more positively influenced with the improvement of their problemsolving ability.The teaching suggestions proposed for teachers: such as 1.the guidance of students to explore how to establish mathematical models as well as strengthen their problem analysis ability and mathematical thinking;2.the application of the ways such as cooperative communication and so on to cultivate students’ oral expression ability,making students better carry out thinking aloud;3.the focus on the cultivation of divergent thinking among students in classroom teaching,helping stimulate students’ different knowledge and experience,as well as the emphasis of how to carry out self-guidance and self-questioning in solving mathematical problems.