A Role for Affect in the Future of Mathematics Education (With Thoughts on Intelligence)

A Review of: 1. Alan Schoenfeld, Heather Fink, Alyssa Sayavedra, Anna Weltman, & Sandra Zuñiga-Ruiz’s (2023) Mathematics Teaching on Target, Routledge, 164pp. ISBN (HB): 978-1-0324-4167-2; 2. Alan Schoenfeld, Heather Fink, Sandra Zuñiga-Ruiz, Siqi Huang, Xinyu Wei, & Brantina Chirinda’s (2023) Helping Students Become Powerful Mathematics Thinkers, Routledge, 272pp. ISBN (HB): 978-1-0324-4168-9

“SHOULD WELLBEING BE THE SAME AS PERFECTION?” A CASE STUDY ON STUDENT WELLBEING IN HIGHER MATHEMATICS EDUCATION

Previous research has given the impression that reticent is our hunt for optimal teaching practices, educational goals, and nature of mathematical workings. In this regard, we have (seemingly) ended up with the following inquiries: What could the math classroom be for? and What has the math classroom been for? These two questions touch on the scary horns of two other charged philosophical dandruffs. Namely:“What are the aims of teaching mathematics?” and “What should be our objectives in learning it?” The term ‘positive education’ refers to an educational system engendering both the skills of positive wellbeing and traditional, academic achievement (Seligman et al., 2009). Many case studies—primarily in Australian schools—have been conducted. However, philosophical advancements in the wellbeing sciences indicate that wellbeing, as a construct, is context-dependent (Alexandrova, 2017). Conceptions of wellbeing may thus differ between social groups, geographies, and local cultures (Green et al., 2021; Jarden et al., 2021). In this thesis, I present a framework for understanding a novel construct in the mathematics education literature called mathematical wellbeing. This construct may be studied through a variety of lenses (public policy, sociology, mathematics, positive psychology, mathematics education, economics). I build on a few of these by investigating factors relevant to student mathematical wellbeing. I also offer ways to study this construct in a first-year, collegiate mathematics course

Radial Singular Solutions to Semilinear Partial Differential Equations

We show the existence of countably many non-degenerate continua of singular radial solutions to a p-subcritical, p-Laplacian Dirichlet problem on the unit ball in R^N. This result generalizes those for the 2-Laplacian to any value p and extends recent work on the p-Laplacian by considering solutions both radial and singular

Analysis on almost Abelian Lie groups: Groups, subgroups and quotients

The subject of investigation are real almost Abelian Lie groups with their Lie group theoretical aspects, such as the exponential map, faithful matrix representations, discrete and connected subgroups, quotients and automorphisms. The emphasis is put on explicit description of all technical details

Feeling \u27Good\u27 in the Math Classroom: Theoretical Perspectives on Mathematical Well-being

Twenty years ago, a study found that nearly 20% of adolescents in the U.S. experience an episode of clinical depression by the end of high school (Lewinsohn et al., 1993). On the global scale, this number ranges from 8 to 20% (Naicker et al., 2013) and once in college, it does not get better. This year alone, 47.3% of students at the University of Montana reported moderate to serious psychological stress [Kessler 6 Scale] and 38.2% reported feelings of hopeless most or all of the time. We are facing a very significant problem in the area of young adult well-being today. So what can we do about it? Positive psychology is the scientific study of what makes life worth living. It is an up-and-rising area of psychology that uses empirical methods to examine constructs like human flourishing, creativity, well-being, engagement, and happiness. A positive education refers to educational systems garnered to teach both the skills of well-being and traditional achievement. Many experiments (prominently in Australia) have measured success rates of integrating positivity into school settings. But recent studies now point to a possible hidden variable at play: one’s state of well-being could also be context dependent, as well as value dependent. Meaning a student’s subjective sense of well-being in the classroom may differ between individual subject disciplines as well as our own cultures and geography. Mathematics is a subject feared by many and enjoyed by fewer. It is viewed as a gatekeeping subject, and often reports high levels of low-engagement, anxiety, and negative emotions across all grade levels. While frameworks for understanding students’ context-dependent mathematical well-being have been proposed in the past, this area in mathematics education is still at its complete infancy. In addition to this, connections between ‘well-being’ from the positive psychologists, student well-being from the educational researchers, and subject-dependent well-being is not yet well understood. Using a known framework for teaching well-being and the latest framework for understanding (domain-specific) mathematical well-being, I propose embedding well-being practices to a subset of the University of Montana’s intro-level mathematics courses. As a first part to this project, a thorough literature review of well-being programs was conducted, and a model for positive, collegiate mathematics education was synthesized. In this process, the questions “Should a positive mathematics education exist?” and “Can a positive mathematics education exist?” were also approached using various theoretical lenses from areas of creativity research, positive psychology, and education. It is our hope that a successful integration of positivity into first-year math classes will allow UM a spot as one of the nation’s first universities attempting to concretely improve student well-being from one of the most unexpected places yet: a college-level math department