Elementary, Secondary, and Informal Education: Using Student-generated Strategies in Instructional Interactions to Build Multiplicative Structures in Urban Schools

这个为期三年的项目的目标是在K-5年级的城市课堂上模拟儿童乘法推理的发展。该项目建议分析教学过程中的师生互动，以了解学生的成果(例如，策略、发明的符号、论点、主张和解释)如何用于集体构建复杂的数学知识，从而提高学生的成绩。该项目建议，通过在城市低收入学校的小学教室进行观察，来：(1)确定和分类有助于产生学生成果的师生互动以及导致重要的数学理解和实践的序列；以及(2)创建思维模型--一个可能的教学和学习行动的空间--可以帮助教师适应或复制有效的教学行动。所创建的模型将在研究的最后阶段与其他教师一起进行测试。本研究将使用两种类型的案例：学生个体思维发展的纵向案例和以师生互动顺序为重点的横向案例。第二个目标是了解儿童对乘法结构--包括分数、配给、比例、乘除--的推理是如何整合的。

The goal of this three-year project is to model the development of children's multiplicative reasoning in urban classrooms in grades K-5. The project proposes to analyze teacher-student interactions during instruction to understand how students' productions (e.g., strategies, invented notations, arguments, claims, and explanations) are used for collective construction of complex mathematical knowledge that can lead to enhanced student outcomes. The project proposes, through observation at elementary classrooms in urban, low-income schools, to: (1) identify and classify teacher-student interactions that help generate student productions and the sequence that lead to significant mathematical understandings and practices; and (2) create models of thinking - a space of possible teaching and learning actions - that can help teachers adapt or reproduce effective teaching actions. The models created will be tested with other teachers in the last phase of the study. The research will use two types of cases: longitudinal cases of the development of individual student's thinking, and cross-sectional cases in which the focus is the sequence of teacher-student interactions. A secondary goal is to understand how children's reasoning about the strand of multiplicative structures - including fractions, rations, proportions, and multiplication and division - become integrated.