Barrett

Barrett, The Honors College at Arizona State University proudly showcases the work of undergraduate honors students by sharing this collection exclusively with the ASU community.

Barrett accepts high performing, academically engaged undergraduate students and works with them in collaboration with all of the other academic units at Arizona State University. All Barrett students complete a thesis or creative project which is an opportunity to explore an intellectual interest and produce an original piece of scholarly research. The thesis or creative project is supervised and defended in front of a faculty committee. Students are able to engage with professors who are nationally recognized in their fields and committed to working with honors students. Completing a Barrett thesis or creative project is an opportunity for undergraduate honors students to contribute to the ASU academic community in a meaningful way.

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The Mathematical Successes and Failures of Students in an Introductory Physics Course

Description
A working knowledge of mathematics is a vital requirement for introductory university physics courses. However, there is mounting evidence which shows that many incoming introductory physics students do not have the necessary mathematical ability to succeed in physics. The investigation reported in this thesis used preinstruction diagnostics and interviews to…

A working knowledge of mathematics is a vital requirement for introductory university physics courses. However, there is mounting evidence which shows that many incoming introductory physics students do not have the necessary mathematical ability to succeed in physics. The investigation reported in this thesis used preinstruction diagnostics and interviews to examine this problem in depth. It was found that in some cases, over 75% of students could not solve the most basic mathematics problems. We asked questions involving right triangles, vector addition, vector direction, systems of equations, and arithmetic, to give a few examples. The correct response rates were typically between 25% and 75%, which is worrying, because these problems are far simpler than the typical problem encountered in an introductory quantitative physics course. This thesis uncovered a few common problem solving strategies that were not particularly effective. When solving trigonometry problems, 13% of students wrote down the mnemonic "SOH CAH TOA," but a chi-squared test revealed that this was not a statistically significant factor in getting the correct answer, and was actually detrimental in certain situations. Also, about 50% of students used a tip-to-tail method to add vectors. But there is evidence to suggest that this method is not as effective as using components. There are also a number of problem solving strategies that successful students use to solve mathematics problems. Using the components of a vector increases student success when adding vectors and examining their direction. Preliminary evidence also suggests that repetitive trigonometry practice may be the best way to improve student performance on trigonometry problems. In addition, teaching students to use a wide variety of algebraic techniques like the distributive property may help them from getting stuck when working through problems. Finally, evidence suggests that checking work could eliminate up to a third of student errors.
ContributorsJones, Matthew Isaiah (Author) / Meltzer, David (Thesis director) / Peng, Xihong (Committee member) / Department of Physics (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
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Exploring the Origins of Physics Student Misconceptions in Mathematics

Description

Introductory physics is one of the most difficult course sequences one can take as an undergraduate, due in no small part to the prerequisite knowledge of mathematics. Over the past six years, David Meltzer and his research group have developed a diagnostic meant to test students’ abilities in core mathematical…

Introductory physics is one of the most difficult course sequences one can take as an undergraduate, due in no small part to the prerequisite knowledge of mathematics. Over the past six years, David Meltzer and his research group have developed a diagnostic meant to test students’ abilities in core mathematical concepts believed to be crucial foundations for learning physics. Concepts tested include the ability to solve systems of equations, work with trigonometric functions, manipulate fractions, and interpret information from graphs among others. With over 7000 students having taken the diagnostic, some patterns have begun to emerge, confirming work from other studies that suggest there is in fact a link between prerequisite math knowledge and success in an introductory physics course. However, most students take the diagnostic either in a classroom setting or online, so student responses are largely limited to being categorized as simply correct or incorrect. Even when students’ work is present it is impossible to assess their mindset when working through a problem without making inferences and logical leaps. In an attempt to better understand the nature of students’ misconceptions in mathematics I have conducted seven semi-formal interviews with introductory physics students just after they have completed the diagnostic where they walked me through their solutions and thought processes.
ContributorsByrd, John (Author) / Meltzer, David (Thesis director) / Covatto, Carl (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2022-05