Browsing by Author "Mullins, Sara Brooke"
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- Examining the Relationship Between Students' Measurement Schemes for Fractions and Their Quantifications of AngularityMullins, Sara Brooke (Virginia Tech, 2020-06-26)In the basic understanding of measurement, students are expected to be able to subdivide a given whole into a unit and then change the position of that unit along the entire length of the whole. These basic operations of subdivision and change of position are related to the more formal operations of partitioning and iterating. In the context of fractions, partitioning and iterating play a fundamental role in understanding fractions as measures, where students are expected to partition a whole into an iterable unit. In the context of angle measurement, students are expected to measure angles as a fractional amount of a full rotation or a circle, by partitioning the circle into a unit angle and then iterating that unit angle to find the measure of the given angle. Despite this link between measurement, fractions, and angles, research suggests that there is a disconnect between students' concepts of measurement and geometry concepts, including angle and angle measurement. Therefore, one area of study that might help us understand this disconnection would be to investigate the relationship between students' concepts of measurement and their concepts of angle measurement. This current study documents sixth, seventh, and eighth grade students' measurement schemes for fractions and their quantifications of angularity, and then investigates the relationship between them. This research is guided by the following question: What is the relationship between middle school students' measurement schemes for fractions and their quantifications of angularity? Results indicate that the majority of students involved in this study do not possess a measurement concept of fractions nor a measurement concept of angularity. However, these results demonstrate that there is a relationship between students' measurement schemes for fractions and their quantifications of angularity. It is concluded that students who construct more sophisticated fraction schemes tend to construct more sophisticated quantifications of angularity.
- First mathematics course in college and graduating in engineering: Dispelling the myth that beginning in higher-level mathematics courses is always a good thingWilkins, Jesse L. M.; Bowen, Bradley D.; Mullins, Sara Brooke (ASEE, 2021-07-03)Background: Graduation rates in engineering programs continue to be a concern in higher education. Prior research has documented an association between students' experiences in first-year mathematics courses and graduation rates, but the influences of the mathematics courses completed and the grades earned are not fully understood. Purpose: The purpose of this study was to investigate the relationship among the first undergraduate mathematics course a student completes, the grade they earn in this course, and the likelihood of graduating with a degree in engineering within six years. Method: The study involved 1504 students from five consecutive cohorts of first-year students enrolled in an engineering degree program at a medium-sized Midwestern public university. Logistic regression was used to model the interrelationship between course and grade in predicting the relative likelihood of graduation for students enrolled in 16 different mathematics courses. Results: Overall, students who take Calculus I or a more advanced mathematics course as their first mathematic course and who are more successful in their first mathematics course are more likely to graduate with a degree in engineering. However, considering grade and course together, some groups of students who are more successful in lower-level mathematics courses are as likely to graduate as students who are less successful in upper-level mathematics courses. Conclusions: Evidence from this study helps to dispel the myth that beginning with higher-level mathematics courses is the optimal course-taking strategy when pursuing an engineering degree. Findings have implications for student advising, curriculum and instruction, high school course-taking, and broadening participation in engineering.