Contemporary mathematics education reform has placed increased emphasis on K-12 mathematics curriculum. Reform-based curricula, often referred to as "Standards-based" due to philosophical alignment with the NCTM Process Standards, have generated controversy among families, educators, and researchers. The mathematics education research community has recognized a need to evaluate the impact of "Standards"-based instruction on K-12 students' mathematical development. The purpose of this dissertation study was to investigate the impact of one year of "Standards"-based instruction at the third grade level in a rural elementary school in the southern United States. Six fourth grade students participated as case studies for a period of eight weeks. Data consisted of field notes from classroom observations and transcripts of video-recorded problem-solving sessions outside of the participants' regular mathematics classroom. Data collection focused on samples of student written work, dialogue, and use of physical manipulatives within the classroom and during the problem-solving sessions. Results provided evidence that the participants continued to engage most strongly in the NCTM Process Standards of Communication, Representation, and Reasoning and Proof within the mathematics classroom and during external problem-solving sessions. Participants' use of written and physical representations provided valuable insight into the conceptual understandings and misunderstandings of elementary mathematics students not revealed through tasks focusing solely on computation and procedure. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]