Welcoming students to the mathematics community: obstacles to “belonging”

This paper reflects on some of the obstacles which lead some students, particularly those from non-traditional academic backgrounds, to question whether they “belong” to the mathematics community.

Predicting COVID-19 Dynamics Using SEIR-PADC Model

There are a number of derivates of SIR type models developed in mathematics community with 5 to 8 ordinary differential equations to include detailed mechanisms. These models have included exposed, deceased, super-spreader, symptomatic and asymptomatic infected and hospitalized populations; but are mathematically complex and cumbersome. These methods rarely used actual clinical data in details and usually fitted with one or maximum two major clinical data. In this paper, we introduce SEIR-PADC model to include exposed, deceased, super-spreader and critical populations and divide infected population to symptomatic and asymptomatic. SEIR-PADC model is a set of 8 ordinary differential equations with 12 unknown coefficients. Along with, we used an optimization algorithm in MATLAB to find best fit coefficients to 5 set of COVID-19 data in Kuwait. Our focus is to track trends of COVID-19 in coming days. Initial conditions for 8 populations and initial guess values for 12 unknown coefficients are found in a way to best fit COVID-19 data. We used 136 days of COVID-19 data in Kuwait and obtained solutions to cumulative populations rather than daily population. Predictions for 5 different population of COVID-19 in Kuwait using SEIR-PADC model are promising and are discussed here.

Hegel and the mathematics community: a left-side history

Starting from a proof of the fundamental theorem of calculus accessible to K-12 students, we apply Hegel’s Science of Logic to Barrow’s theorem. This article may also be considered as an introduction to speculative philosophy, adequate for mathematics educators. We focus on the subsection Barrier and Ought, where Hegel twists Kant’s aphorism you can because you ought and obtains a precept of action aimed at infirming conservative political positions. We direct Hegel’s Ought to criticize the pedagogical conservatism of the twentieth century mathematics (M20) community and its consequences to mathematics education. From the development of the article we elicit the concept of speculative mathematics as a political agenda for mathematics education. Keywors: Fundamental theorem of calculus; Barrow’s theorem; Hegel’s Logic; Speculative philosophy; Mathematics community. Hegel e a comunidade matemática: uma história pela esquerda Resumo: A parir de uma demonstração do teorema fundamental do cálculo, acessível ao ensino médio, aplicamos a Ciência da Lógica de Hegel ao teorema de Barrow. O artigo também pode ser considerado como introdução à filosofia especulativa, adequada a educadores matemáticos. Focalizamos a subseção Barrier and Ought (Barreira e Dever), onde Hegel altera o aforismo kantiano podes porque deves e obtém um preceito para ação dirigido a abalar posições políticas conservadoras. Valemo-nos do Dever em Hegel para criticar o conservadorismo da comunidade de matemática do século vinte (M20) e suas consequências para a educação matemática. A partir do desenvolvimento do artigo, inferimos o conceito de matemática especulativa como agenda política para a educação matemática. Palavras-chave: Teorema fundamental do cálculo; Teorema de Barrow; Lógica de Hegel; Filosofia especulativa; Comunidade matemática

How Does a Mathematician Fit in? A Mixed-Methods Analysis of University Students’ Sense of Belonging in Mathematics

University mathematics has been described as a setting that has challenges in inviting everyone to be part of the mathematics community. Thus, university mathematics offers an important context for research on belonging. For this study, we utilised a mixed-methods approach to investigate the various ways mathematics students belong or do not belong to the mathematics community. Based on both quantitative and qualitative analyses, three student profiles were identified: Members of the Scientific Community, Members of the Social Community, and Non-Members. The first profile highlights students’ belonging to the scientific community, the second profile emphasises belonging to the social community of students, and in the third profile students’ responses reflected various ways of not belonging to the mathematics community. In addition, we elaborate on how university mathematics learning environments both promote and hinder students’ sense of belonging. Overall, the study broadens the understanding of the ways of belonging in the mathematics context and provides suggestions for teaching to address the issues of exclusion that are currently present in the culture of university mathematics.

From Rules That Expire to That Language Inspires

By focusing on the use of language that inspires, mathematics teachers can foster student agency and invite every student to be a member of the mathematics community.

Enjoy the pursuit, as Andrew Wiles did with Fermat’s Last Theorem

“Enjoy the pursuit, as Andrew Wiles did with Fermat’s Last Theorem” recounts the story of how mathematician Andrew Wiles was undaunted in the face of 350 years’ worth of mathematicians’ failed efforts at attempting to solve Fermat’s Last Theorem. He believed in his abilities and ultimately succeeded in providing a proof. Along the way, he satisfied a human longing to seek knowledge and energized the mathematics community. Mathematics students and enthusiasts are encouraged to remember to value the journey in mathematical and life pursuits, even when they struggle. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.