Scholarship & Research
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Item Cognitive presence among mathematics teachers : an analysis of tasks and discussions in an asynchronous online graduate course(Montana State University - Bozeman, College of Letters & Science, 2008) Colt, Diana Lynn; Chairperson, Graduate Committee: Jennifer LuebeckHigher order learning, in terms of both process and outcome, is frequently cited as the goal of higher education (Garrison, Anderson, & Archer, 2000). However, the adoption of computer mediated communication in higher education has far outpaced our understanding of how this medium can best be used to promote higher order learning (Garrison, Anderson, & Archer, 2004). Researchers have examined quantitative components of computer mediated communication, but little work has been done to examine the cognitive aspects of online discussion. Those studies that do exist demonstrate inconsistent evidence of higher order learning in online discussions (Kanuka & Anderson, 1998; Littleton & Whitelock, 2005; McLoughlin & Luca, 2000; Meyer, 2003). Researchers conjecture that this could be due to the nature of the tasks that instructors implement for discussion purposes (Arnold & Ducate, 2006; Meyer, 2004; Murphy, 2004; Vonderwell, 2003). This study explored whether one component of instruction, the tasks assigned to students, had an effect on the level of cognitive presence that existed in the mathematical discussions of practicing mathematics teachers enrolled in an online graduate course. Through the method of content analysis, discussion transcripts were analyzed to look for evidence of higher-order learning based on the cognitive presence coding protocol developed by Garrison, Anderson, and Archer (2001). Seventeen students in a History of Mathematics course form the primary sample for this study. The results of the content analysis were triangulated with qualitative data from a questionnaire on student backgrounds and demographics and a post-course survey assessing student perceptions of their learning experiences. The researcher concluded that the MATH 500 course discussions did provide evidence of higher order learning in terms of cognitive presence. Task type, as defined in this study, was not directly related to the levels of cognitive presence achieved in the course. This finding does not negate the possibility of such a relationship, but in this study the effects of task type could not be isolated from other features of the course structure and assignments.Item The effects of a framework for procedural understanding on college algebra students' procedural skill and understanding(Montana State University - Bozeman, College of Letters & Science, 2006) Hasenbank, John Fredrick; Chairperson, Graduate Committee: Ted HodgsonThis dissertation examined the effectiveness of an instructional treatment consisting of lecture content, homework tasks, and quiz assessments built around a common Framework for Procedural Understanding. The study addressed concerns about increasing numbers of students enrolling in remedial mathematics courses because they did not develop sufficient understanding in previous courses. The Framework-oriented instruction was designed to help students develop deep and well-connected knowledge of procedures, which has been shown to facilitate recall and promote future learning. Data collection spanned the Fall 2005 semester at a western land-grant university. In the quasi-experimental design, instructors from six intact sections of college algebra were matched into pairs based on prior teaching experience, and the treatment condition was assigned to one member of each pair. Equivalence of treatment and control groups was established by comparing ACT / SAT scores for the 85% of students for whom those scores were available. Data collection consisted of classroom observations, homework samples, common hour exams scores, procedural understanding assessments, supplemental course evaluations, and a final interview with treatment instructors. Analysis of covariance was the primary statistical tool used to compare treatment and control group performances while controlling for attendance rates and pre-requisite mathematical knowledge. Treatment group students scored significantly higher than control group students on the procedural understanding assessments. Moreover, although treatment students were assigned 18% fewer drill questions than controls and 8% fewer problems overall, the gains in procedural understanding were realized without declines in procedural skill. The relationship between understanding and skill was also examined, and students with greater procedural understanding tended to score higher on the skills-oriented final exam regardless of which treatment condition was assigned to them. Finally, the interview with the treatment instructors provided insight into the implementation issues surrounding the treatment. They expressed concerns about time constraints and reported initial discomfort with, but eventual appreciation for, using the Framework for Procedural Understanding to guide instruction. The Framework-oriented treatment was found to be effective at helping students develop deeper procedural understanding without declines in procedural skill. Additional implications and recommendations for future research are also discussed.Item The use of computer algebra systems in a procedural algebra course to facilitate a framework for procedural understanding(Montana State University - Bozeman, College of Letters & Science, 2007) Harper, Jonathan Lee; Chairperson, Graduate Committee: Maurice BurkeThis dissertation study evaluated the implementation and effectiveness of an introductory algebra curriculum designed around a Framework for Procedural Understanding. A Computer Algebra System (CAS) was used as a tool to focus lessons on the Framework and help students gain a deeper, well-connected understanding of algebraic procedures. This research was conducted in response to the prevalence of remedial mathematics and addresses the need for students in remedial mathematics to have a successful learning experience. The curriculum was implemented in the Spring 2007 semester at a western land-grant university. In this quasi-experimental study, one section of introductory algebra was taught using the CAS/Framework curriculum. This treatment section was determined based on a pretest used to judge equivalency of groups. Data sources included procedural understanding assessments with follow-up student interviews, procedural skill exams, classroom observations, and a debriefing interview with the treatment instructor. Qualitative analysis of student and instructor interview transcripts was done to supplement independent observation reports to evaluate the implementation of the curriculum.