The effects of using "splitting" multiplicative structures on students' understanding of integer exponents /
The study was designed to examine students' rsity Microfilm Inc. understanding of integer exponents. Students in four sections of introductory algebra at a suburban community-college in southeast Texas participated in the study. Subjects took a pre-test and post-test on integer exponents, and r...
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1998.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=733029401&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | The study was designed to examine students' rsity Microfilm Inc. understanding of integer exponents. Students in four sections of introductory algebra at a suburban community-college in southeast Texas participated in the study. Subjects took a pre-test and post-test on integer exponents, and rated their self-confidence in their work. The experimental curriculum consisted of three projects that emphasized the isomorphism between the additive structure of exponents and the multiplicative structure of powers. Twelve students were interviewed prior to lessons on exponents and following the post-test. The initial interviews explored the research question: What models for multiplication (if any) do introductory algebra students employ? The follow-up interviews provided partial answers to the research question: What impact does a curriculum, based upon model of multiplication and the isomorphism between the additive structure of exponents and the multiplicative structure of powers, have on community-college students' understanding of integer exponents? The research focused on students: intuitive understanding of integer exponents, their ability to solve problems and conceptual problems, and their self-confidence in understanding problems involving integer exponents. It was found that introductory algebra students displayed inadequate multiplicative structures. Students used serendipitous strategies to solve multiplication problems, and exhibited non-conservation of operations and the "multiplication makes bigger, division makes smaller'' (MMBDMS) error. Students did not exhibit innate splitting multiplicative structures. Students had a deficient concept of reciprocal, used ambiguous language, and lacked understanding of the usefulness of exponents and the meaning of exponential growth. The experimental group exhibited limited improvement in recognition of the isomorphism between the additive structure of exponents and the multiplicative structure of powers. It slightly outperformed the control group in interpreting the zero exponent, in repudiating the error of interpreting negative exponents as the product of negative numbers, in solving combinatorics problems, and in scientific notation applications. Neither group performed particularly well, especially in the areas of applying forms on a number line. Their work was notable for the extensive number of errors. There was no difference in improvement of students' self-confidence in their ability to solve problems involving integer exponents. |
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| Item Description: | Vita. "Major Subject: Curriculum and Instruction". |
| Physical Description: | xvii, 255 leaves : illustrations ; 28 cm. |
| Bibliography: | Includes bibliographical references (leaves 213-221). |