Construction of Piano Performing Arts Talent Cultivation and Creative Thinking Based on the Constant Differential Error Approximation Method

IF 3.1 Q1 Mathematics
Xiao Yang, Yanyan Lu
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引用次数: 0

Abstract

Piano talent cultivation mostly focuses on repetitive training only, and lacks a clear cultivation program for theoretical knowledge and skill points. In this paper, we adopt the curriculum knowledge graph to extract the knowledge point subgraph of piano learning and provide an initialized knowledge graph structure for the learning path under the cultivation scheme. A multi-objective optimization model of the path containing constraints such as the difficulty and mastery of knowledge points is set, and the relevant parameters of the model are defined and calculated to establish a multi-optimization objective function. A solution method that uses constant differential error approximation is proposed as a means of approaching the Pareto optimal solution. To develop the LSPIA algorithm with reciprocal weights, the adjustment vectors are modified using a least squares asymptotic iterative approximation with minimum squares values. Following the discovery of the most suitable route, a teaching experiment was carried out. The results show that the posttest P-value of the total creative thinking score of the experimental and control classes is 0.022 less than 0.05, which indicates that there is a significant difference between the creative thinking of the students in the two classes in terms of affective characteristics. The experimental group achieved a mean score of 122.69 on the post-test, which was a significant improvement from the mean score on the pre-test. An innovative approach to cultivating piano playing talents involves optimizing learning paths.
基于常微分误差逼近法的钢琴演奏艺术人才培养与创新思维构建
钢琴人才培养大多只注重重复性训练,缺乏明确的理论知识和技能点的培养方案。本文采用课程知识图谱提取钢琴学习的知识点子图谱,为培养方案下的学习路径提供初始化的知识图谱结构。设定包含知识点难度和掌握程度等约束条件的路径多目标优化模型,定义并计算模型的相关参数,建立多优化目标函数。提出了一种利用常微分误差逼近的求解方法,作为接近帕累托最优解的一种手段。为了开发具有互惠权重的 LSPIA 算法,使用最小二乘法渐进迭代近似最小二乘法值来修改调整向量。在找到最合适的路径后,进行了教学实验。结果显示,实验班与对照班创造性思维总分的后测 P 值小于 0.05,均为 0.022,说明两班学生的创造性思维在情感特征方面存在显著差异。实验组在后测的平均分达到了 122.69 分,比前测的平均分有了明显的提高。培养钢琴演奏人才的创新方法包括优化学习路径。
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来源期刊
Applied Mathematics and Nonlinear Sciences
Applied Mathematics and Nonlinear Sciences Engineering-Engineering (miscellaneous)
CiteScore
2.90
自引率
25.80%
发文量
203
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