Long Term Effects of Conceptually-Based Instruction in Mathematics

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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.