The broad goals of this writing assignment are two-fold: 1) To delve deeper into the inner workings of a chosen proof and explore fundamental motivation of the chosen result. 2) To enhance student learning in the area of academic writing in the discipline of mathematics.
By walking the students through a process of academic writing, we address the following DQP proficiencies: Specialized Knowledge, Applied and Collaborative Learning and Intellectual Skills – Use of Information Resources, Mathematics-Specific Intellectual and Practical Skills and Communicative Fluency.
Background and Context
This assignment has been used in a Mathematical Structures (introduction-to-proofs) course and has been modified slightly for use in a Modern Algebra I course in Spring 2016.Â The assignment was given near the beginning of the course in Fall 2015 and collected near the end of the course with parts.
Almost all of the students in Mathematical Structures are either Mathematics majors or minors. This includes about half majors and half minors. Almost all of the students in Modern Algebra will be Mathematics majors.
The assignment walks the students through a process of writing a research paper in mathematics from the selection of a topic all the way through drafting and editing. Students are given the freedom to choose a topic but papers were required to be formatted as if they were publishable mathematical research papers (which some may become).
This writing assignment or a modification of it, was used in each of a sequence of three courses as part of the Math Major at Georgia Southern University. These writing assignments together have a broader goal of developing and advancing the students’ skills in argumentation, analysis and synthesis skills through writing. The assignments were scaffolded to develop the writing skills throughout the process while at the same time, producing a polished final work. Writing skills are important for getting jobs but critical for advancement within any career so the overarching goals of these assignments are to prepare our students for advancement in their future careers.
Alignment and Scaffolding
The assignment should be integrated into the course and discussed throughout the course. Prior to assigning, the students should have been exposed to several proof techniques and basic proof-writing skills. There should also be an activity either before the assignment or during the assignment in which students are guided through the process of a literature search, preferably using MathSciNet.
This assignment was implemented in a sequence of courses within the mathematics major. The selection of topics and expectation of mathematical depth in the writing can be the determining factor in adapting this assignment for various levels. Through deepening the topics and expectations, this assignment can be built upon from one course to the next. For example, a second assignment (either later in the same course or in a subsequent course) could require that students select more advanced topics such as a proof of L Hospital’s rule in an Analysis course. The students may also be required to satisfy additional expectations, particularly in the areas of audience awareness and clarity of presentation.
Our response to the assignment has been quite good in general. The students, for the most part, turned in quality work. One of their favorite aspects was the freedom to select a topic. They performed surprisingly well on the peer review, providing numerous excellent comments to their peers.
One challenge that the students face is walking the fine line between citing others’ work and plagiarism. A strategy that we generally suggested was to copy theorem statements verbatim (with citation of course) while the rest should be original. There were still paragraphs copied from web sources but at least it seemed to help.
Revisions have been made on the timing and an outline component has been removed (since these papers should generally all follow the same outline).
An important aspect in the implementation is keeping the students motivated and making it clear why this (and any writing) assignment is important. We noticed that student performance and attitude was directly correlated to the motivation of the assignment and the emphasis on the importance of writing.
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