【作者】 原露； 刘彦楼； 陈平； 辛涛；

【Author】 Lu Yuan;Yanlou Liu;Ping Chen;Tao Xin;Collaborative Innovation Centre of Assessment toward Basic Education Quality, Beijing Normal University;China Academy of Big Data for Education, Qufu Normal University;

【机构】 北京师范大学中国基础教育质量监测协同创新中心； 曲阜师范大学中国教育大数据研究院；

【摘要】 学习进阶是指学生对某个主题日益复杂的思考或理解方式的描述(NRC, 2007)。值得注意的是,学习进阶不仅可以从认知的角度描述学生的学习过程,而且可以架构学习研究和课堂教学实践的桥梁(Salinas,2009)。它的建立是一个从建立假设性学习进阶到验证假设的迭代过程。目前,已有一些关于学习进阶的验证方法,其中具有代表性的有Rasch模型和规则空间模型(RSM)的方法。由于前者主要用于测量学生能力,因此不能为学生提供细粒度的属性分析。虽然后者可以在认知诊断框架下测量细粒度的属性,但RSM有时无法获得正确的属性层级关系。针对上述两种方法的不足,本研究提出了一种新的基于认知诊断的学习进阶验证方法,即能够基于数据验证属性层级关系的层级诊断分类模型(HDCM)的方法。然后,以分数的加减运算为例,深入探讨了新方法在数学学习进阶中的应用。首先,基于专家评定法析取分数运算属性及其层级关系;随后,参考Klein等人(1981)的水平划分建构假设性的小学生分数运算学习进阶,用以描述分数运算发展过程;最后,收集817名五年级学生在56题的分数运算测验上的数据,采用层级诊断分类模型(HDCM)对数据进行分析并修正学习进阶假设。本研究的主要发现如下:(1)小学生分数运算包括5个属性:基本运算(A1)、约分(A2)、通分(A3)、带分数拆分(A4)和借位(A5);(2)确立的分数运算学习进阶包括4个水平:处于进阶水平1的学生只能掌握简单的同分母分数加减运算,水平2的学生能进行需要约分的同分母分数加减运算,水平3的学生能进行异分母分数加减运算及简单的带分数加减运算,水平4的学生能进行复杂的带分数加减运算。综合来看,本研究建构的小学生分数运算学习进阶确立了完整的小学生分数运算结构、刻画了分数运算发展的进程,不仅突破已有基于Rasch模型或RSM等学习进阶验证方法的局限,而且探索了基于带属性层级的参数化认知诊断模型的学习进阶的教学实践价值,对数学教育研究者、心理测量研究者以及一线教师具有借鉴意义。更多还原

【Abstract】 Learning progressions referred to descriptions of increasingly sophisticated ways of thinking about or understanding a topic(NRC, 2007). It is worth pointing out that learning progression can not only describe the learning process of a student from a cognitive perspective but also bridge learning research and classroom teaching practice(Salinas, 2009). Its establishment is an iterative process from the establishment of hypothetical learning progression to the verification of hypotheses.Up to now, some validating methods about learning progressions have been proposed and the representative ones include the method of Rasch model(Rasch, 1960, 1966 a, 1966 b) and the method of rule space model(RSM; Tatsuoka, 1983, 1995, 1996). Because the former method is mainly used to measure students’ abilities, it cannot provide fine-grained attribute analysis for students. Although the latter method can measure fine-grained attributes via the cognitive diagnosis framework, RSM sometimes fails to obtain the correct attribute hierarchical relationship. To overcome the shortcomings of the above two methods, this paper puts forward a new cognitive diagnosis-based verification method, i.e., the method of hierarchical diagnostic classification model(HDCM) which can verify the hierarchical relationship of attributes based on data. Then, the application of the new method in learning progressions of mathematics is thoroughly explored by taking the addition and subtraction of fractions as an example. First, the attributes of fractional operations and their hierarchical relationships were extracted using an expert assessment method. Following the level division of Klein et al.(1981), a hypothesized learning progression was constructed to describe the development of fractional operations. Next, the HDCM was used to analyze the test data on a 56-item fractional operation test collected from 817 fifth-grade students, followed by the revision of the learning progression hypothesis.Results showed that(1) the fractional operations involved five attributes: basic operation(A1), reduction of a fraction(A2), changing fractions to a common denominator(A3), split with mix number(A4), and borrowing(A5);(2) the constructed learning progression featured four levels: students at level 1 were only able to master simple addition and subtraction of fractions with the same denominator, students at level 2 could perform the addition and subtraction of fractions with the same denominator requiring reduction,students at level 3 were capable of performing addition and subtraction operations with different denominator fractions, as well as simple addition and subtraction operations with mixed numbers, and students at level 4 could perform complex addition and subtraction operations with mixed numbers. In conclusion, the constructed learning progression of fractional operations establishes a complete structure of fractional operations and characterizes the development of fractional operations. It not only breaks through the limitations of the existing methods of learning progression based on Rasch Model and rule space model, etc., but also explores the teaching practice value of learning progression based on the parameterized cognitive diagnosis model with attribute hierarchies, which can be a useful reference for mathematics education researchers, psychometric researchers and front-line teachers.更多还原