Xu Le, Liu Ru-De, Star Jon R, Wang Jia, Liu Ying, Zhen Rui
Institute of Developmental Psychology, Beijing Key Laboratory of Applied Experimental Psychology, Faculty of Psychology, Beijing Normal UniversityBeijing, China.
Graduate School of Education, Harvard UniversityCambridge, MA, United States.
Front Psychol. 2017 Aug 10;8:1368. doi: 10.3389/fpsyg.2017.01368. eCollection 2017.
Researchers interested in mathematical proficiency have recently begun to explore the development of strategic flexibility, where flexibility is defined as knowledge of multiple strategies for solving a problem and the ability to implement an innovative strategy for a given problem solving circumstance. However, anecdotal findings from this literature indicate that students do not consistently use an innovative strategy for solving a given problem, even when these same students demonstrate knowledge of innovative strategies. This distinction, sometimes framed in the psychological literature as competence vs. performance-has not been previously studied for flexibility. In order to explore the competence/performance distinction in flexibility, this study developed and validated measures for flexibility (e.g., competence, or knowledge of multiple strategies) and flexibility (e.g., performance, use of innovative strategies) for solving equations. The measures were administrated to a sample of 158 Chinese middle school students through a Tri-Phase Flexibility Assessment, in which the students were asked to solve each equation, generate additional strategies, and evaluate own multiple strategies. Confirmatory factor analysis supported a two-factor model of potential and practical flexibility. Satisfactory internal consistency was found for the measures. Additional validity evidence included the significant association with flexibility measured with the previous method. Potential flexibility and practical flexibility were found to be distinct but related. The theoretical and practical implications of the concepts and their measures of potential flexibility and practical flexibility are discussed.
对数学能力感兴趣的研究人员最近开始探索策略灵活性的发展，其中灵活性被定义为对解决问题的多种策略的了解以及在给定问题解决情境中实施创新策略的能力。然而，该文献中的轶事性发现表明，即使这些学生展示了创新策略的知识，他们也不会始终如一地使用创新策略来解决给定问题。这种区别，在心理学文献中有时被描述为能力与表现的区别，以前尚未针对灵活性进行过研究。为了探索灵活性方面的能力/表现区别，本研究开发并验证了用于解方程的灵活性（例如，能力，即对多种策略的了解）和灵活性（例如，表现，即使用创新策略）的测量方法。通过三阶段灵活性评估对158名中国中学生样本进行了这些测量，在评估中要求学生解每个方程、生成额外策略并评估自己的多种策略。验证性因素分析支持了潜在灵活性和实际灵活性的双因素模型。这些测量方法具有令人满意的内部一致性。额外的效度证据包括与先前方法测量的灵活性有显著关联。发现潜在灵活性和实际灵活性是不同但相关的。讨论了这些概念及其潜在灵活性和实际灵活性测量方法的理论和实践意义。
