Long Term Effects of Conceptually-Based Instruction in Mathematics

这个项目将在三年的时间里记录基于概念的教学在小学数学中的效果。其主要目的是揭示早期概念理解的长期影响。教学的目的将是通过让学生参与到应用和问题情境中来支持他们学习计算和放置价值概念的努力。特别教学的一个目标是帮助学生通过使用数学符号作为工具--记录和分享数学思想和思考数学的工具--来熟练掌握以10为基数的书面符号。一年级学生的初始样本将包括接受概念丰富的教学的实验班和只接受常规教学的对照班。所有学生都将被跟踪到三年级。每年大约有一半的学生在学习目标概念时接受特殊指导。所有学生每年将接受三次专门设计的笔试，每次笔试后将立即单独面试一名学生。分析将集中在四个问题上：(1)基于概念的教学导致学生的思维过程和表现随时间的变化；(2)不同概念习得水平的学生在这些变化上的差异；(3)早于晚接受概念教学的学生在这些变化上的差异；(4)概念习得与成功成绩之间的关系。

This project will document the effects ofconceptually-based instruction in elementary school mathematics over a three year period. A primary aim is to uncover the long term effects of early conceptual understandings. Instruction will be designed to support students' efforts to acquire numeration and place value concepts by engaging them in application and problem situations. A goal of the special instruction is to help students become competent with the base-10 written notation by using mathematical symbols as tools--tools for recording and sharing mathematical ideas and tools for thinking about mathematics. The initial sample of first graders will include experimental classes that receive the conceptually -enriched instruction and control classes that receive only conventional instruction. All students will be followed through third grade. Each year about half the students will receive the special instruction while they are studying the target concepts. All students will receive specially designed written test three times each year and a subsample will be individually interviewed immediately after each written test. Analyses will focus on four issues: (1) changes over time in students' thought processes and performance as a result of conceptually-based instruction; (2) differences in these changes between students with differing levels of conceptual acquisitions; (3) differences in these changes between students who receive conceptually-based instruction earlier rather than later; and (4) relationships between conceptual acquisitions and successful performance.