Journals and Conference Proceedings
https://digital.library.txstate.edu/handle/10877/136
Academic publications and conference proceedings from members of the university community.2022-11-30T05:00:51ZIt is Time to Think! Investigating the Impact of Reasoning Time in Precalculus
https://digital.library.txstate.edu/handle/10877/16338
It is Time to Think! Investigating the Impact of Reasoning Time in Precalculus
Buber, Zafer
<p>College-level mathematics courses have always been a gatekeeper for students. High attrition rates in these courses point out a very serious issue. Research has identified various factors contributing to these high attrition rates. To various studies, one of these factors has been observed to be fast-paced instruction in college-level mathematics courses. Also, the research underlines that students who are exposed to fast-paced instruction without conceptual understanding are more likely to drop out. This study focuses on the instructional time and precalculus achievement relationship. More specifically, we investigate how the private reasoning time provided explicitly impacts studentsâ€™ performance and achievement in college precalculus classes. This study aims to provide college students with more private reasoning time during the instruction and slow down the pace of the instruction. With this purpose in mind, we ask the following research questions:</p>
<ul>
<li>What is the impact of private reasoning time during the instruction on college studentsâ€™ precalculus achievement?</li>
<li>What is the optimal waiting time after students are given private reasoning time in precalculus classes?</li>
</ul>
<p>Students will be provided with a few explicit private reasoning time intervals from 30 sec to 1 min in precalculus classes. During these time intervals, students will be given some tasks designed to support their conceptual transitioning and some guiding questions that are supposed to help students reason about the mathematical concept. Each student is supposed to reason individually first. Then, around their individual thoughts, the instruction is supposed to go on.</p>
<p>Students will be provided with a few explicit private reasoning time intervals from 30 sec to 1 min in precalculus classes. During these time intervals, students will be given some tasks designed to support their conceptual transitioning and some guiding questions that are supposed to help students reason about the mathematical concept. Each student is supposed to reason individually first. Then, around their individual thoughts, the instruction is supposed to go on.</p>
<p>We will measure the impact of the planned intervention by using pre and post-design tools. Additionally, we will analyze semi-structured interviews with some students before and after the intervention to capture the change in their reasoning attitudes.</p>
<p>Due to the highly complex nature of teaching/learning activities, we are not sure to what degree increasing reasoning time might improve the learning of precalculus concepts. However, we conjecture that slowing down the precalculus instruction, together with guiding questions and appropriate tasks, will help students with having:</p>
<ul>
<li>more active learning opportunities</li>
<li>more interaction with the instructor</li>
<li>more instructors' noticing the students' struggles</li>
<li>more feedback from the instructor</li>
<li>less math anxiety</li>
<li>better achievement</li>
</ul>
<p>Based on the initial observations and the expected results, we hope that this study will improve the teaching/learning of precalculus, especially for the students who need more time to think during the instruction.</p>
2022-04-01T00:00:00ZDynamics of flocking models with two species
https://digital.library.txstate.edu/handle/10877/16286
Dynamics of flocking models with two species
Zhao, Qingjian; Shi, Shaoyun; Li, Wenlei
This article studies the flocking behavior of self-organized agents in two species. First, referring to the work of Olfati-Saber and the classical Cucker-Smale model, we establish a discrete system describing the flocking dynamic of the agents in two species. Second, by using the LaSalle's invariance principle, we show that the system with global interaction will achieve unconditional time-asymptotic flocking, and the system with local interaction has a time-asymptotic flocking under certain assumptions. Moreover, we investigate the local asymptotic stability of a class of flocking solutions. Finally, some numerical simulations and qualitative results are presented.
2021-12-30T00:00:00ZCurvature blow-up for the periodic CH-mCH-Novikov equation
https://digital.library.txstate.edu/handle/10877/16285
Curvature blow-up for the periodic CH-mCH-Novikov equation
Zhu, Min; Wang, Ying; Chen, Lei
We study the CH-mCH-Novikov equation with cubic nonlinearity, which is derived by an asymptotic method from the classical shallow water theory. This model can be related to three different important shallow water equations: CH equation, mCH equation and Novikov equation. We show the curvature blow-up of the CH-mCH-Novikov equation by the method of characteristics and conserved quantities to the Riccati-type differential inequality.
2021-12-27T00:00:00Zp-Laplacian equation with finitely many critical nonlinearities
https://digital.library.txstate.edu/handle/10877/16284
p-Laplacian equation with finitely many critical nonlinearities
Xia, Pengcheng; Su, Yu
This article concerns the ground state solution of the p-Laplacian equation with finitely many critical nonlinearities. By using the refined Sobolev inequality with Morrey norm and variational methods, we establish the existence of nonnegative ground state solution.
2021-12-24T00:00:00Z