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Author Lindaman, Brian J
Title Making sense of the infinite: A study comparing the effectiveness of two approaches to teaching infinite series in calculus
Descript 255 p
Note Source: Dissertation Abstracts International, Volume: 68-03, Section: A, page: 0920
Adviser: Susan Gay
Thesis (Ph.D.)--University of Kansas, 2007
The topic of infinite series poses significant difficulties for students in second-semester calculus. Existing research, while limited, does suggest students lack a conceptual understanding of series, but fails to provide significant insight into students' misunderstandings. Research on calculus reform projects of the past 15 years indicates non-traditional teaching strategies may improve students' conceptual understanding of topics in calculus
The purpose of this study was to explore students' understanding of infinite series, and to investigate the effects of reform-based instructional strategies on students' understanding of series. The setting was a large Midwest university and the participants were forty-eight undergraduate students. The participants were enrolled in a second-semester calculus course
The study was conducted in two phases. In the preliminary phase, a Series Understanding Instrument (SUI) was developed and this instrument was used to gather data on student understanding of series. Follow-up interviews were conducted which provided additional information. Results from the first phase were used in designing a unit of instruction on infinite series. The second phase of the study consisted of a three-week teaching experiment on infinite series. Instruction in one section of students serving as the experimental group utilized nontraditional classroom strategies and activities such as visualization, writing in class, and cooperative learning. Another section of students, taught with a traditional lecture-based approach, served as the control group. Three course assessments provided data on students' procedural understanding of series, and the SUI provided additional data on students' conceptual understanding of series
Students had varying levels of conceptual and procedural understanding of infinite series. ANOVA revealed that students in the experimental group demonstrated significantly greater procedural understanding than students in the control group on two out of three course assessments. There was no significant difference in conceptual understanding found between groups, as indicated by scores on the SUI. The experimental group demonstrated a greater understanding of convergence tests, determination of power series convergence criteria, and visualization of geometric series
School code: 0099
Host Item Dissertation Abstracts International 68-03A
Subject Education, Mathematics
Alt Author University of Kansas
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