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Karaali, Gizem; Yih, Samuel – PRIMUS, 2020

When first learning how to write mathematical proofs, it is often easier for students to work with statements using the universal quantifier. Results that single out special cases might initially come across as more puzzling or even mysterious. In this article we explore three specific statements from abstract algebra that involve the number…

Descriptors: Mathematics Instruction, College Mathematics, Algebra, Numbers

Karaali, Gizem; Khadjavi, Lily S. – PRIMUS, 2019

We provide context and motivation for an instructor to use real-life examples in the calculus classroom. To this end we describe two specific project ideas, one related to the devastating impact of methylmercury fungicide in a grain seed supply and the other to a catastrophic methane leak. By using calculus in contexts that have social justice…

Descriptors: Calculus, Mathematics Instruction, Social Justice, Interdisciplinary Approach

Karaali, Gizem – PRIMUS, 2018

In recent years, I have cultivated an almost pathological resistance to grading. Here I explore the reasons why and describe how I eventually recovered. In particular, I propose that although grading, or more explicitly, effective assessment of student learning, is a challenging component of a mathematics instructor's job description, reflective…

Descriptors: Mathematics Teachers, Professional Identity, Grades (Scholastic), Grading

Karaali, Gizem – PRIMUS, 2015

Metacognition as a dimension of learning ranks highest in the revised Bloom's Taxonomy of cognitive tasks. In this paper we illustrate how it can be incorporated into a repeated exercise in the mathematics classroom, through a specific case study in the context of a liberal arts mathematics course. Through the semester, students were asked weekly…

Descriptors: Metacognition, Student Motivation, Self Concept, Mathematics Instruction

Karaali, Gizem – PRIMUS, 2011

In education theory, Bloom's taxonomy is a well-known paradigm to describe domains of learning and levels of competency. In this article I propose a calculus capstone project that is meant to utilize the sixth and arguably the highest level in the cognitive domain, according to Bloom et al.: evaluation. Although one may assume that mathematics is…

Descriptors: Classification, Cognitive Processes, Calculus, Mathematics Instruction