Mapping Developmental Trajectories of Students' Conceptions of Integers.

由圣地亚哥州立大学的教师领导的项目“绘制学生整数概念的发展轨迹”，正在使用K-12学生和成人的访谈数据来描述负数概念和运算的共同理解和发展进展。 该项目的动机是广泛承认的发现，学生很难掌握关键概念和技能涉及的工作与整数。 两个问题框架和指导拟议的研究：* 什么是学生的整数和整数运算的概念？* 学生理解的可能发展轨迹是什么？研究人员正在通过对以下学生的结构化访谈来寻求这些问题的答案：在教授负数之前的小学生，课程包括明确教授整数的初中生，预计将在更高级的数学中使用整数先验知识的高中生，以及在工作中使用整数的成年人。除了提供一个以实验为基础的图片，学生获得越来越复杂的理解负数的方式，该项目正在制定有用的采访协议和一个可靠和有效的评估工具，用于描述学生在不同阶段的理解和技能，这样一个进步。 共同的学习进展的特点和评估工具将广泛有用的课程和测试开发人员和教师在K-12数学教室。

The project Mapping Developmental Trajectories of Students' Conceptions of Integers, led by faculty from San Diego State University, is using data from interviews with K-12 students and adults to describe common understandings and progressions of development for negative number concepts and operations. The project is motivated by the widely acknowledged finding that students have difficulty mastering key concepts and skills involved in work with integers. Two questions frame and guide the proposed research:* What are students' conceptions of integers and operations on integers?* What are possible developmental trajectories of students' understandings?The investigators are seeking answers to those questions through structured interviews with students in elementary grades prior to instruction about negative numbers, students in middle grades whose curriculum includes explicit instruction about integers, high school students who are expected to use prior knowledge about integers in more advanced mathematics, and adults who use integers in their work. In addition to providing an empirically-based picture of ways that students acquire increasingly sophisticated understandings about negative numbers, the project is producing useful interview protocols and a reliable and valid assessment instrument for describing the understanding and skill of students at various stages on such a progression. Both the characterization of common learning progressions and the assessment instruments will be broadly useful to curriculum and test developers and teachers in K-12 mathematics classrooms.