Presentation Type
Oral/Paper Presentation
Abstract
In the infinite realm of mathematical research, understanding and communicating complex concepts require structured and logical approaches. However, a variety of research methods are employed in mathematical studies; these may differ in approach, historical context, and other important considerations which can contribute to confusion and a lack of effective communication. The genesis of this research began with personal confusion during my research on "Counting the Uncountable: Life in a World Without Numbers", setting the stage for the central challenge: How do mathematicians explain their research? To answer this issue, we analyzed a variety of mathematical research articles to highlight their similarities and unique qualities of each approach, demonstrating how different methods can complement and even build upon each other.
To the outside, mathematical research may seem straightforward; however, mathematicians actually use distinct methods to explain their research process, each serving different purposes and audiences. In my work, I explore some mathematical research approaches used by mathematicians by looking at different sources; these approaches include references and citations, historical context, IMRaD, direct experimentation, exploratory case studies, and mathematical models. Altogether, this research illustrates the importance of mathematicians as both researchers and educators, emphasizing the need for informed, clear, and effective communication of their findings. By using appropriate and diverse research methods, mathematicians can foster a community of learning and discovery, ultimately contributing to the advancement of the mathematical field.
Faculty Mentor
Dr. Gary Hall and Dr. Bethy Butler
Recommended Citation
Hall, Gary. Personal interview. 16 January 2025. Krusen, Kim. “A Historical Reconstruction of Our Number System.” Arithmetic Teacher, vol. 38, no. 7, 1991, pp. 46–48. Navarro, Jesus. "Analysis of Solutions to Writing Challenges." Corpus Project, 7 February 2025. Navarro, Jesus. “Counting the Uncountable: Life in a World Without Numbers.” Research Project, 11 November 2024. Nazan Mersin, et al. “Awareness of Preservice Mathematics Teachers About Prehistoric and Ancient Number Systems.” Malikussaleh Journal of Mathematics Learning, vol. 3, no. 2, 2020, pp. 57–61, https://doi.org/10.29103/mjml.v3i2.2904. Pagel, Mark, and Andrew Meade. “The Deep History of the Number Words.” Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, vol. 373, no. 1740, 2017, https://doi.org/10.1098/rstb.2016.0517. Romig, H. G. “Discussions: Early History of Division by Zero.” The American Mathematical Monthly, vol. 31, no. 8, 1924, pp. 387-389, https://doi.org/10.2307/2298825.
Analysis of Solutions to Research Methods: Navigating the Infinite Content of Mathematics
In the infinite realm of mathematical research, understanding and communicating complex concepts require structured and logical approaches. However, a variety of research methods are employed in mathematical studies; these may differ in approach, historical context, and other important considerations which can contribute to confusion and a lack of effective communication. The genesis of this research began with personal confusion during my research on "Counting the Uncountable: Life in a World Without Numbers", setting the stage for the central challenge: How do mathematicians explain their research? To answer this issue, we analyzed a variety of mathematical research articles to highlight their similarities and unique qualities of each approach, demonstrating how different methods can complement and even build upon each other.
To the outside, mathematical research may seem straightforward; however, mathematicians actually use distinct methods to explain their research process, each serving different purposes and audiences. In my work, I explore some mathematical research approaches used by mathematicians by looking at different sources; these approaches include references and citations, historical context, IMRaD, direct experimentation, exploratory case studies, and mathematical models. Altogether, this research illustrates the importance of mathematicians as both researchers and educators, emphasizing the need for informed, clear, and effective communication of their findings. By using appropriate and diverse research methods, mathematicians can foster a community of learning and discovery, ultimately contributing to the advancement of the mathematical field.
Comments
This presentation is just me articulating the research I've done for my University of Writing class into an oral presentation. It's called "Analysis of Solutions to Writing Challenges," and basically, I researched what methods do mathematicians use to present their research as my "writing challenge." That's why I cited the source as well. I also got inspiration from my other research project about the history of numbers which will be talked about more in the presentation for it contributes to my claim. Next, I will be using a PowerPoint presentation to provide visual aid for my audience (box quotes and math models), but it is not ready yet. I will contact Dr. Owens soon when it is ready and be on the lookout for proper due dates, etc. Lastly, I'd like to state a transparency statement about AI that I used for the Corpus project from University Writing. Statement:
"In the preparation of this paper, I utilized artificial intelligence tools, specifically Copilot, to assist with proofreading and constructing the work cited page. The AI was employed as a supplementary tool to enhance my research and writing process. All AI-generated content was critically evaluated, fact-checked, and substantially revised or rewritten by me. The analysis, arguments, and conclusions presented in this paper are my own original work, informed by my research and critical thinking. Any limitations or potential biases of the AI tool were taken into consideration during the writing process. This disclosure is made in the interest of academic integrity and transparency."