Coffee to Go! Modeling Thermoclines in Multivariable Calculus

While mathematical modeling is an integral process in applied mathematics, students rarely encounter genuine modeling opportunities in their calculus courses. Here we introduce a laboratory experience as a natural starting point for calculus students to investigate multivariable functions. A layered system of coffee and milk serves as a physical model for temperature gradients in lakes or the atmosphere, where temperature depends on both a temporal and spatial variable. Students create, observe, and collect temperature data of their own, graph the data, and develop mathematical models to fit the data. We require students to write a report about their findings. This article includes details about the class activity conducted in two different college settings and provides our assessment of student interaction with the lab, and how the lab informs student understanding of multivariable functions

Brine Shrimp Lab

Young brine shrimp movements within a petri dish are tracked by students. Students are challenged to determine and verify whether the brine shrimp move in a random walk. From this exercise students gain greater understanding of PDE models, diffusion and parameter estimation.https://digitalcommons.usu.edu/lemb/1001/thumbnail.jp

Coffee Thermocline Lab

A layered system of coffee and milk serves as a physical model for temperature gradients in lakes or the atmosphere, where temperature depends on both a temporal and spatial variable. Students create, observe, and collect temperature data of their own, graph the data, and develop mathematical models to fit the data.https://digitalcommons.usu.edu/lemb/1000/thumbnail.jp

The 13th Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics

Ngā mihi aroha ki ngā tangata katoa and warm greetings to you all. Welcome to Herenga Delta 2021, the Thirteenth Southern Hemisphere Conference on the Teaching and Learning of Undergraduate Mathematics and Statistics. It has been ten years since the Volcanic Delta Conference in Rotorua, and we are excited to have the Delta community return to Aotearoa New Zealand, if not in person, then by virtual means. Although the limits imposed by the pandemic mean that most of this year’s 2021 participants are unable to set foot in Tāmaki Makaurau Auckland, this has certainly not stopped interest in this event. Participants have been invited to draw on the concept of herenga, in Te Reo Māori usually a mooring place where people from afar come to share their knowledge and experiences. Although many of the participants are still some distance away, the submissions that have been sent in will continue to stimulate discussion on mathematics and statistics undergraduate education in the Delta tradition. The conference invited papers, abstracts and posters, working within the initial themes of Values and Variables. The range of submissions is diverse, and will provide participants with many opportunities to engage, discuss, and network with colleagues across the Delta community. The publications for this thirteenth Delta Conference include publications in the International Journal of Mathematical Education in Science and Technology, iJMEST, (available at https://www.tandfonline.com/journals/tmes20/collections/Herenga-Delta-2021), the Conference Proceedings, and the Programme (which has created some interesting challenges around time-zones), by the Local Organizing Committee. Papers in the iJMEST issue and the Proceedings were peer reviewed by at least two reviewers per paper. Of the ten submissions to the Proceedings, three were accepted. We are pleased to now be at the business end of the conference and hope that this event will carry on the special atmosphere of the many Deltas which have preceded this one. We hope that you will enjoy this conference, the virtual and social experiences that accompany it, and take the opportunity to contribute to further enhancing mathematics and statistics undergraduate education. Ngā manaakitanga, Phil Kane (The University of Auckland | Waipapa Taumata Rau) on behalf of the Local Organising Committ

Leaky Bucket Lab

Students test Torrecelli’s law and develop and compare their own alternative models to describe the dynamics of water draining from perforated containers. From this exercise students gain experience and perspective using a classic model as well as greater understanding of ODE compartment models, parameter estimation and fluid flows.https://digitalcommons.usu.edu/lemb/1004/thumbnail.jp

Mathematical Modeling Modules: Curriculum Material for Secondary Teacher Education

This NSF-funded project, the Mathematics of Doing, Understanding, Learning, and Educating for Secondary Schools (MODULE(S2)), supports collaborative development of mathematical modeling modules that were first piloted around the country in 2019–2020 and will be eventually made available widely. This report provides an overview of the structure of the material, highlights several modeling tasks, describes the use of simulations of practice in the curriculum materials, and summarizes activities conducted with piloting faculty

Mass Action in Two-Sex Population Models: Encounters, Mating Encounters and the Associated Numerical Correction

Ideal gas models are a paradigm used in Biology for the phenomenological modelling of encounters between individuals of different types. These models have been used to approximate encounter rates given densities, velocities and distance within which an encounter certainly occurs. When using mass action in two-sex populations, however, it is necessary to recognize the difference between encounters and mating encounters. While the former refers in general to the (possibly simultaneous) collisions between particles, the latter represents pair formation that will produce offspring. The classical formulation of the law of mass action does not account this difference. In this short paper, we present an alternative derivation of the law of mass action that uses dimensional reduction together with simulated data. This straightforward approach allows to correct the expression for the rate of mating encounters between individuals in a two-sex population with relative ease. In addition, variability in mating encounter rates (due to environmental stochasticity) is numerically explored through random fluctuations on the new mass action proportionality constant. The simulations show how the conditioned time to extinction in a population subject to a reproductive Allee effect is affected

The Development and Evaluation of a Program for Improving andAssessing the Teaching of Mathematics and Statistics

We report on a program intended to improve and assess teaching practices in our mathematics and statistics department, and on results from the program’s initial field tests. The structure of our program was influenced by current legal standards for “evaluation of personnel” that have been established through a string of litigations occurring over the past 25 years. Our program works as follows: an instructor employs two disjoint teams, formative and summative, which provide their respective recommendations and evaluations under the protection of a data curtain (teams are kept ignorant of each other’s activities), and all operations and logistics (including maintenance of the data curtain) are overseen by a third team. What we find notable is the measurably positive effect the process has on all involved, and the program’s ability to accommodate a variety of teaching styles and objectives. Our evidence suggests our program is comprehensive and notably constructive for participants