Inquiry Based Learning: A Teaching and Parenting Opportunity

In this paper, I discuss what appears to be a new perspective on inquiry based learning (IBL) by describing its parallels with parenting. IBL is a student-centered learning method involving collaborative work on carefully sequenced exercises, oral and written communication of solutions, and peer review. Students create their own knowledge and present their ideas, and the instructor acts as a facilitator. The parallels between IBL and parenting include a growth mindset, emphasizing process over outcome, learning from mistakes, learning how to get unstuck, and deconstructing tasks. IBL and parenting also involve similar social interactions, such as responding to difficult questions in the moment, being sensitive to body language, and active listening. I also discuss how both activities differ. By comparing IBL and parenting, instructors can understand both better; this can in turn make IBL seem like a natural type of instruction. Additionally, I describe opportunities for learning IBL that are particularly feasible for parents

On the Galois Group of the 2-Class Field Towers of Some Imaginary Quadratic Fields

Let $k$ be a number field, $p$ a prime, and $k^{nr,p}$ the maximal unramified $p$-extension of $k$. Golod and Shafarevich focused the study of $k^{nr,p}/k$ on $Gal(k^{nr,p}/k)$. Let $S$ be a set of primes of $k$ (infinite or finite), and $k_S$ the maximal $p$-extension of $k$ unramified outside $S$. Nigel Boston and C.R. Leedham-Green introduced a method that computes a presentation for $Gal(k_S/k)$ in certain cases. Taking $S=\{(1)\}$, Michael Bush used this method to compute possibilities for $Gal(k^{nr,2}/k)$ for the imaginary quadratic fields $k=\mathbb{Q}(\sqrt{-2379}),\mathbb{Q}(\sqrt{-445}),Q(\sqrt{-1015})$, and $\mathbb{Q}(\sqrt{-1595})$. In the case that $k=\mathbb{Q}(\sqrt{-2379})$, we illustrate a method that reduces the number of Bush's possibilities for $Gal(k^{nr,2}/k)$ from 8 to 4. In the last 3 cases, we are not able to use the method to isolate $Gal(k^{nr,2}/k)$. However, the results in the attempt reveal parallels between the possibilities for $Gal(k^{nr,p}/k)$ for each field. These patterns give rise to a class of group extensions that includes each of the 3 groups. We conjecture subgroup and quotient group properties of these extensions

Emotional Labor in Mathematics: Reflections on Mathematical Communities, Mentoring Structures, and EDGE

Terms such as "affective labor" and "emotional labor" pepper feminist critiques of the workplace. Though there are theoretical nuances between the two phrases, both kinds of labor involve the management of emotions; some acts associated with these constructs involve caring, listening, comforting, reassuring, and smiling. In this article I explore the different ways academic mathematicians are called to provide emotional labor in the discipline, thereby illuminating a rarely visible component of a mathematical life in the academy. Underlying this work is my contention that a conceptualization of labor involved in managing emotions is of value to the project of understanding the character, values, and boundaries of such a life. In order to investigate the various dimensions of emotional labor in the context of academic mathematics, I extend the basic framework of Morris and Feldman [33] and then apply this extended framework to the mathematical sciences. Other researchers have mainly focused on the negative effects of emotional labor on a laborer's physical, emotional, and mental health, and several examples in this article align with this framing. However, at the end of the article, I argue that mathematical communities and mentoring structures such as EDGE help diminish some of the negative aspects of emotional labor while also accentuating the positives.Comment: Revised version to appear in the upcoming volume A Celebration of EDGE, edited by Sarah Bryant, Amy Buchmann, Susan D'Agostino, Michelle Craddock Guinn, and Leona Harri