Collaborative Learning Through Formative Peer Review With Technology

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  • This article was downloaded by: [McMaster University]On: 08 December 2014, At: 05:57Publisher: Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954Registered office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH,UK

    PRIMUS: Problems, Resources,and Issues in MathematicsUndergraduate StudiesPublication details, including instructions forauthors and subscription information:http://www.tandfonline.com/loi/upri20

    Collaborative Learning ThroughFormative Peer Review WithTechnologyCarrie Diaz Eaton & Stephanie WadePublished online: 22 May 2014.

    To cite this article: Carrie Diaz Eaton & Stephanie Wade (2014) CollaborativeLearning Through Formative Peer Review With Technology, PRIMUS: Problems,Resources, and Issues in Mathematics Undergraduate Studies, 24:6, 529-543, DOI:10.1080/10511970.2014.881442

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  • PRIMUS, 24(6): 529543, 2014Copyright Taylor & Francis Group, LLCISSN: 1051-1970 print / 1935-4053 onlineDOI: 10.1080/10511970.2014.881442

    Collaborative Learning Through Formative PeerReview With Technology

    Carrie Diaz Eaton and Stephanie Wade

    Abstract: This paper describes a collaboration between a mathematician and a com-positionist who developed a sequence of collaborative writing assignments for calculus.This sequence of developmentally appropriate assignments presents peer review as acollaborative process that promotes reflection, deepens understanding, and improvesexposition. First, we distinguish writing-to-learn from writing-in-the-disciplines. Then,we review collaborative writing pedagogies and explain best practices for teaching peerreview. Finally, we present an implementation plan and examples of student work thatillustrate improved understanding of content and improved exposition.

    Keywords: Calculus, writing assignments, peer review, Google, LaTeX, collaboration.

    1. INTRODUCTION

    This paper describes a collaboration about collaboration. A mathematics pro-fessor and a composition professor devised a series of collaborative writingand peer review activities for a Calculus I and II course sequence. The math-ematics professor learned about composition research, which improved herability to teach writing. The composition professor learned about the disci-plinary conventions of writing in applied mathematics, which improved herunderstanding of writing across the curriculum. She also learned that distin-guishing between writing-to-learn and writing-in-the-disciplines helps facultystage assignments. The students gained deeper understanding of mathemat-ical content and improved ability to communicate mathematical concepts.We demonstrate how this project connects research in writing pedagogy andmathematics pedagogy. Then, we present the process and the results of ourcollaboration. We hope our work will motivate readers to pursue collaborative,transdisciplinary projects. Through collaboration and peer review, we improved

    Address correspondence to Carrie Diaz Eaton, Center for Biodiversity, Unity College,Unity, Maine 04988, USA. E-mail: ceaton@unity.edu

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  • 530 Eaton and Wade

    our understanding of our work, we improved this paper, and we improved ourstudents learning.

    2. WRITING-TO-LEARN VERSUS WRITING-IN-THE-DISCIPLINES

    Collaboration requires clear communication and precise definition of terms.For example, composition studies, a field that focuses on writing and rhetoric,distinguishes between writing-to-learn (WTL) and writing-in-the-disciplines(WID). Both WTL and WID are aspects of writing across the curriculum.WTL uses informal writing to promote student engagement and to facilitatelearning.WID teaches the conventions of disciplinary-specific genres [3]. WTLviews students errors and mistakes as part of the learning process and empha-sizes writing as a way to understand content. Examples of WTL activitiesinclude journals, informal writing, and online discussion boards or blogs [7].WID builds on WTL activities, with additional attention to the conventionsof disciplinary-specific genres. Typically, WTL activities are most appropri-ate for introductory classes, whereas WID assignments are more appropriatefor intermediate and advanced classes, after the students have at least a basicunderstanding of their discipline and of the genres expected in their discipline.Although WTL and WID are related in that the former can facilitate the latter,conflating the two is problematic, because each has different goals and requiresdifferent attention.

    Reva Kasmans 2006 article on peer review in mathematics demonstratesthe importance of distinguishing between WTL and WID [16]. Kasman doc-uments an assignment that presented fictional proofs for students to critique.Kasman intentionally created proofs with errors. She reports that findingand correcting these errors improved students understanding of content, butthat students writing did not improve [5, 10]. The activities described inKasmans study fall into the category of WTL. Helping students improvetheir writing in addition to their understanding of content requires several fur-ther considerations. Research indicates that as students continue to developtheir understanding of increasingly complex material, they will make mistakes,which may explain why the writing of the students in Kasmans study did notimprove [19, 20]. Furthermore, WID activities should explicitly introduce stu-dents to the genre expectations of disciplinary-specific writing, whereas theassignment in Kasmans study focused on content.

    Including both WTL and WID in mathematics classes may initially appeartoo time-consuming. Mathematics teachers need to cover content. Breakingwriting assignments into stages, teaching disciplinary-specific genre expecta-tions, and reading and responding to multiple student drafts all make furtherdemands on in-class and out-of-class time. Collaborative writing and peerreview address the problem of time because they present writing as a processwhile reducing the number of assignments faculty read, evaluate, and grade.

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  • Collaborative Learning Through Peer Review 531

    Collaborative writing and peer review allow students to measure their ownprogress, deepen their understanding of content, and improve exposition byproviding early feedback and examples of other student work.

    3. COLLABORATION AND PEER REVIEW FORUNDERGRADUATES

    Collaboration has had a place in writing classes for many years [5]. In the1970s, educators in the United States began to employ collaborative pedago-gies as a practical means of improving student learning, especially for studentswho resisted traditional pedagogies. These students, regardless of background,responded to peer assistance more so than faculty interventions.

    The history of collaboration is rooted in social constructivist theories oflearning [5]. Social constructivist theories posit education as a process ofmaking meaning with intellectual and affective dimensions. Collaborative ped-agogies align with social constructivist theories because they engage studentsin active participation, in group work, and in dialogue.1 Group writing ofassignments engages students in active participation and dialogue, so they gaina better understanding of concepts and genre conventions, which prepares themto meet WID expectations.

    Group work and group writing assignments are both examples of collabo-rative pedagogical techniques. Peer review is another collaborative pedagogicaltool that is both efficient and effective. Empirical studies demonstrate thebenefits of peer review over feedback from teaching assistants in scienceclasses [26] and the importance of teaching students to focus on con-tent [25]. Reflection on the peer review and composition process facilitatesmetacogni