Xiao xue shu xue ke tang zhong jiao xue xing jie shi de shu xue feng fu xing ji yu xue sheng xue xi de guan xi: The mathematical richness of instructional explanation in primary mathematics classrooms and its relation to student learning.

本研究以"教学性解释"这一课堂会话形式为研究对象，调查小学数学课堂教学中教学性解释的数学丰富性特征和结构特征，以及它们与学生学习的关系。其中，数学丰富性是指课堂教学活动与数学内容的相关程度,以教学性解释中的学术词汇比例和教学性解释的概念水平为指标。本研究数据源于项目"课程改革的成效──教师课堂教学实践变化"（Ni, Li, Cai, & Hau, 2009），选取使用新课程教材的17名小学数学教师及其1013名学生作为研究样本。教学性解释来源于这17个班级的51节课录像（每个班级3节课录像，教学内容为"分数运算"）。同时，也对学生的认知学业表现（计算、简单问题解决和复杂问题解决）和数学学习的情感表现（学习兴趣、课堂参与、数学观、交流素养）进行了两次测查。研究一考察了教学性解释的结构特征。研究结果表明：小学数学课堂中教学性解释主要是教师进行引导，由学生来提供解释，教师的引导方式包括提问引导和回应性引导。就引导水平而言，教师将选择性引导、产品性引导、过程性引导和元过程引导这四种不同水平的引导方式相结合，其中高水平的引导方式（过程性引导和元过程引导）所占比例近四成，教师倾向于让学生表达观点和看法，提供解释，并且对自己的观点进行论述。研究二考察了教学性解释的数学丰富性特征。研究结果表明：教学性解释的学术词汇比例和概念水平可以作为数学丰富性的两个有效指标。小学数学课堂中教学性解释的丰富性水平较高：绝大部分教学性解释是数学解释，并且原理性解释是比例最高的数学解释。研究三考察了教学性解释的结构特征与丰富性特征与学生学习结果的关系。研究结果表明：教学性解释的丰富性对学生简单问题解决能力表现具有正向预测作用，但与学生计算能力表现呈负相关，同时，与学生复杂问题解决能力表现的关系更为复杂，受到学生原有的知识和技能水平的调节作用。教学性解释的丰富性与学生的数学兴趣、数学观和交流素养呈现负性相关。The main purpose of the present study was to investigate the mathematical richness and structural features of instructional explanation in 17 primary mathematics classrooms, and their relations to students’ cognitive and affective performance in learning mathematics. Mathematical richness in the present study refers to the extent to which classroom instruction is related to mathematics, or the extent of doing or talking mathematics in classroom instruction. The indicators of mathematical richness of instructional explanation included the ratio of academic words and conceptual level of instructional explanations.The data source of the study was from the project "Has curriculum reform made a difference? Looking for change in classroom practice" (Ni, Li, Cai, & Hau, 2009). The current study selected 17 primary mathematics classrooms and the 1013 students from the database. 477 episodes of instructional explanation were identified from the 51 videotaped lessons of the classrooms (3 lessons for each class). The content of all 51 lessons was about division with fractions. The identified episodes of instructional explanation were analyzed in terms of the indicators of mathematical richness. The students’ achievement data included two times of assessment on three aspects of cognitive performance (calculation, simple problem solving, complex problem solving) and four aspects of their indicated attitude towards mathematics and learning mathematics (interest in learning mathematics, classroom participation, views of mathematics, literacy about mathematical communication).Study One analyzed the structural features of instruction explanations in the 17 primary classrooms. The results indicated that teachers were used to guiding the students to provide explanations when constructing instructional explanation in the mathematics classrooms. Teachers’ elicitations consisted of questions and responsive elicitations. Four levels of elicitation were identified. They were choice elicitation, product elicitation, process elicitation and metaprocess elicitation. The higher levels of elicitations (process and metaprocess elicitation) accounted for a significant amount in the classrooms. The teachers tended to let students express their views, provide explanations and arguments of reasoning.Study Two investigated the mathematical richness of instructional explanations. The results showed that the ratio of academic words and conceptual level of instructional explanations could be valid and useful indicators of mathematical richness. The mathematical richness of instructional explanation was high for the observed classrooms in terms of the two indicators. Majority of the instructional explanations were mathematical and involved mathematical concepts and principles.Study Three examined whether the richness and structural features of instructional explanation were able to predict student learning outcomes in the cognitive and affective domain. The results indicated that the mathematical richness positively predicted students’ simple problem solving performance, but was negatively related to students’ computation performance. Furthermore, its relation to students’ complex problem solving performance was complicated, which was moderated by the students’ prior status in the knowledge and skills. Lastly, mathematical richness was negatively associated with students’ indicated interest in learning mathematics, view of mathematics and literacy about mathematical communication.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Detailed summary in vernacular field only.Detailed summary in vernacular field only.鄒君.Thesis (Ph.D.) Chinese University of Hong Kong, 2014.Includes bibliographical references (leaves 148-172).Abstracts also in Chinese.Zou Jun