Archive for the preprints category

Techniques Grading

Standard post by ancoop on October 11, 2019
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To appear as: Cooper, Andrew A. (2020) Techniques Grading: Mastery Grading for Proofs Courses, PRIMUS
Abstract: Mastery grading is an approach to grading in which students are assigned term grades based on whether they meet certain enumerated objectives, rather than accumulating points. In this note, I describe my experiences using a mastery system, which I call techniques grading, which applies the insights behind the standards-based and specifications grading flavors of mastery grading to a proof-intensive course. In techniques grading, each objective assesses, in a binary (pass/fail) way, whether a student has mastered a specific proof technique.
I describe my implementation of this system in a transitions course and an undergraduate real analysis course. I discuss how the system works: how I developed the grading objectives, how individual assignments are assessed, and the collation of each student’s work into a final portfolio. I provide a theoretical assessment of techniques grading within the mastery grading framework, and some evidence from student surveys and my own impressions that the system meets its goals: improving the quality of student work; increasing student satisfaction; reducing grade-grubbing; and instilling mindfulness, good work practices, and pride.
Keywords: specifications grading, transitions, standards based grading, proofs, mastery grading


Incorporating Critical and Creative Thinking in a Transitions Course

Standard post by ancoop on August 19, 2018
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Date: 2018
Abstract: In this note, I discuss my experiences explicitly incorporating principles of critical and creative thinking in a transitions course which serves mathematics, mathematics education, and statistics majors. I describe several specific assignments and classroom tasks designed to enhance critical and creative thinking. I also discuss some evidence from survey instruments.
Keywords: critical thinking, creating thinking, transitions, proofs

Understanding Mathematical Induction by Writing Analogies

Standard post by ancoop on August 1, 2018
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published as: Cooper, A. (2019) Understanding Mathematical Induction by Writing Analogies, Prompt, 3(2).

Abstract: Mathematical induction has some notoriety as a difficult mathematical proof technique, especially for beginning students. In this note, I describe a writing assignment in which students are asked to develop, describe in detail, critique, defend, and finally extend their own analogies for mathematical induction. By putting the work of explanation into the students’ hands, this assignment requires them to engage in detail with the necessary parts of an inductive proof. Students select their subject for the analogy, allowing them to connect abstract mathematics to their lived experiences. The process of peer review helps students recognize and remedy several of the most common errors in writing an inductive proof. All of this takes place in the context of a creative assignment, outside the work of writing formal inductive proofs.



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