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## Full-Text Articles in Education

Exploring Students’ Epistemological Understanding Of Atomic Structure Models, Claire V. Ward, Morgan Balabanoff

#### Exploring Students’ Epistemological Understanding Of Atomic Structure Models, Claire V. Ward, Morgan Balabanoff

*The Cardinal Edge*

Developing a robust understanding of atomic structure and the nature of matter is foundational across chemistry and STEM courses. The development of this concept is challenging because it relies on models to illustrate something not directly observable. Scientific models are important tools used to explain phenomena, particularly phenomena that are not directly observable. In general chemistry, students are typically asked to consider four different models: (1) the particle model, (2) the nuclear model, (3) the Bohr model, and (4) the Quantum model. Each depiction has its own advantages and limitations, where instructors introduce each model to explain specific parts of …

Collaboration In Mathematics Teacher Education: The What, How, And Why Of Mathematical Modeling, Aubrey Neihaus, Amy Bennett

#### Collaboration In Mathematics Teacher Education: The What, How, And Why Of Mathematical Modeling, Aubrey Neihaus, Amy Bennett

*The Advocate*

In this paper, we share our collaboration across the disciplines of mathematics and mathematics education to develop and implement a mathematical modeling task for prospective secondary mathematics teachers. Through this collaboration, we identified three key components of mathematical modeling: the *what*, *how*, and *why*. In this paper, we outline these components from the literature and how each framed our development and implementation of the Sprinkler Task in our mathematics content and mathematics methods courses for secondary teachers. These three components show that mathematical modeling is a particularly fruitful space for collaboration between the disciplines of mathematics and …

Using Differential Equations To Model Predator-Prey Relations As Part Of Scudem Modeling Challenge, Zachary Fralish, Bernard Tyson Iii, Anthony Stefan

#### Using Differential Equations To Model Predator-Prey Relations As Part Of Scudem Modeling Challenge, Zachary Fralish, Bernard Tyson Iii, Anthony Stefan

*Rose-Hulman Undergraduate Mathematics Journal*

Differential equation modeling challenges provide students with an opportunity to improve their mathematical capabilities, critical thinking skills, and communication abilities through researching and presenting on a differential equations model. This article functions to display an archetype summary of an undergraduate student team’s response to a provided prompt. Specifically, the provided mathematical model estimates how certain stimuli from a predator are accumulated to trigger a neural response in a prey. Furthermore, it tracks the propagation of the resultant action potential and the physical flight of the prey from the predator through the analysis of larval zebrafish as a model organism. This …

Teaching Differential Equations Without Computer Graphics Solutions Is A Crime, Beverly H. West

#### Teaching Differential Equations Without Computer Graphics Solutions Is A Crime, Beverly H. West

*CODEE Journal*

In the early 1980s computer graphics revolutionized the teaching of ordinary differential equations (ODEs). Yet the movement to teach and learn the qualitative methods that interactive graphics affords seems to have lost momentum. There still exist college courses, even at big universities, being taught without the immense power that computer graphics has brought to differential equations. The vast majority of ODEs that arise in mathematical models are nonlinear, and linearization only approximates solutions sufficiently near an equilibrium. Introductory courses need to include nonlinear DEs. Graphs of phase plane trajectories and time series solutions allow one to see and analyze the …

Calculus, Biology And Medicine: A Case Study In Quantitative Literacy For Science Students, Kim Rheinlander, Dorothy Wallace

#### Calculus, Biology And Medicine: A Case Study In Quantitative Literacy For Science Students, Kim Rheinlander, Dorothy Wallace

*Numeracy*

This paper describes a course designed to enhance the numeracy of biology and pre-medical students. The course introduces students with the background of one semester of calculus to systems of nonlinear ordinary differential equations as they appear in the mathematical biology literature. Evaluation of the course showed increased enjoyment and confidence in doing mathematics, and an increased appreciation of the utility of mathematics to science. Students who complete this course are better able to read the research literature in mathematical biology and carry out research problems of their own.