Revisioning the Classroom for Joyful Learning I

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Moderator: Kirsten Helmer, UMass Amherst

Thinking Out Loud: Catalyzing a Mathematist's Revolution Using the Commognitive Framework

Madeleine P. Chowdhury, Mesa Community College

My intention for my dissertation research was to influence and affect student attitudes toward mathematics and their calculus knowledge, particularly their thinking about, and understanding of, calculus concepts by motivating consistent discursive activity in and outside of our class. I imagined my students mathematizing and proud to call themselves mathematists—those who engage and revel in mathematical discourse. For my own pleasure, I imagined my most zealous student to be the catalyst of an imminent Mathematists' Revolution to impact and liberate their peers enrolled in the more traditional mathematics classes. The first purpose of my investigation was to engage students in mathematical discourse through a course-design grounded in four frameworks. We will look at the basic tenets of Sfard’s Commognitive Framework during our session. The second purpose was to assess the impact of the combination of two factors, Good and Ambitious Teaching, on a composite mathematics attitude comprising the dependent variables persistence, confidence, and enjoyment in mathematics.

We will engage in a brief discourse on the results for one focus question, RQ1, that has a direct, visible, and measurable effect on another RQ2: RQ1: To what extent does Good Teaching and Ambitious Teaching impact students’ attitudes toward mathematics, particularly persistence, confidence, and enjoyment in Calculus I?

RQ2: To what extent does participation in classroom discourse in Calculus I, as compared to traditional pedagogy, affect the understanding of the derivative concept in a Calculus I course? Sfard, a mathematics educational researcher stated, “A traditional mathematics classroom furnishes the most extreme example of communicational imbalance. Revolutions, on the other hand, are known to erupt where oppression is at its worst.”

Growing Together as Mathematicians in Discrete Math

Debra K. Borkovitz, Boston University

For the past several years the overarching goal of my Discrete Math classes has been, “To grow together as mathematicians,” with mathematician defined as anyone who engages with mathematics. For most semesters since the pandemic started, I’ve added, “To provide structure, connection, and joy in the midst of a global pandemic” as another overarching goal. Through teaching this and other courses, I’ve come to see math classes that have some curricular flexibility as ideal places for students to connect with each other and to experience a different way of being in community than many have seen in school. In this talk I’ll discuss aspects of the class structure including: alternative assessment; portfolios; personal goal setting and tracking; ways of structuring group work, including using random groups at portable whiteboards; peer editing; and the Joyful Finale. I’ll share some pictures from classes and some student feedback.

Ungrading Analysis

Jennifer Beichman, Smith College

Christopher Gole, Smith College

Real Analysis, the theoretical study of calculus, often carries an aura of make-or–break rite of passage for students of mathematics and statistics. At Smith College, we have taught this class using group-based Inquiry Based Learning for many years. This Fall 2022 semester, we experimented in making the course ungraded: based on individual goals they set with the instructor at the beginning of the semester, each student assesses at the end of the semester how they achieved these goals, and what grade they deserve for their effort. In a few cases the instructor may have to suggest an amendment to the proposed grade, which gets resolved by a short discussion. We have found that, while ungrading makes the class psychologically more accessible to students, they acquire the same skills as before. Moreover, this method makes the review of the assignments less stressful for the instructor and more constructive overall.