Graduation Year

2010

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Secondary Education

Major Professor

Gladis Kersaint, Ph.D.

Keywords

Mathematics and Statistics, Technology, Knowledge of student thinking, Misconceptions

Abstract

Practical concepts, such as area and perimeter, have an important part in today's school mathematics curricula. Research indicates that students and preservice teachers (PSTs) struggle with and harbor misconceptions regarding these topics. Researchers suggest that alternative instructional methods be investigated that enhance PSTs' conceptual understanding and encourage deeper student thinking. To address this need, this study examined and described what and how PSTs learn as they engage in anchored instruction involving web-based microworlds designed for exploring area and perimeter. Its focus was to examine the influences of a modified teacher development experiment (TDE) upon 12 elementary PSTs' content knowledge (CK) and knowledge of student thinking (KoST) regarding principles, relationships, and misconceptions involving area and perimeter as they develop simultaneously in a problem-solving environment.

The learning of meaningful mathematics is a personal and independent activity, as one struggles to create and reason through their own mathematical realities and misconceptions. This study describes PSTs' reasonings, misconceptions, and difficulties as they grappled with new knowledge or reconciled new knowledge with prior understandings. Quantitative and qualitative research methods, including case-subject analysis, were used. Instructional sessions similar to Steffe's (1983) teaching episodes comprised this study's intervention. Results indicate that prior to intervention most of the PSTs possessed a procedural knowledge of area and perimeter and were bound by a dependency on formulas; their KoST pertaining area and perimeter was relatively underdeveloped. They seemed unaware of prevalent misconceptions students acquire while working with these concepts (specifically, units of measure and perceived relationships).

The PSTs displayed an ineffective use of drawings to support their responses. Their preoccupation with finding what they judged as "the answer" to various problem-solving situations hindered their ability to properly diagnose and address student thinking and limited their meaningful interaction with the microworlds (MWs). A majority of PSTs felt the MWs were a valuable learning tool for themselves but not for their future students. The planned intervention played a role in the PSTs becoming more perceptive of the difficult mathematics involved with area and perimeter and better equipped to anticipate and address those difficulties with future students.

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