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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    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 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 facilitatesmetacognition, which the Council of Writing Program Administrators definesas the ability to reflect on ones own thinking as well as on the individ-ual and cultural processes used to structure knowledge [8]. The skills ofmetacognition are important to writing because several studies correlate it withtransfer. In other words, when students are more aware of the way they thinkand act in one writing situation, they becomemore adept at thinking and writingin other situations [2, 9].

    Collaboration between faculty from different disciplines can reinforcetransfer. For example, in our collaboration, the composition professor learnedmore about writing in mathematics, so she could explicitly tell her studentshow to apply lessons from her class to other situations. The mathematics pro-fessor learned about how students learn to write, so she could more effectivelybuild upon what they learned in their first-year communication classes.

    1For a thorough theoretical rationale of the value of collaboration, see KennethBruffees 1984 article Collaborative learning and the conversation of mankind [5].

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    Unfortunately, many students and teachers have had negative experienceswith peer review and view it as ineffective. In order for peer review to be effec-tive, students need to understand why they are doing it, students need to knowhow to give good feedback, and students need incentive to take peer reviewseriously [13]. Although many colleges have writing specialists who could pro-vide resources and onsite support, below we will present a brief overview ofhow to introduce peer review and then we explain how collaborative writingtechnologies can facilitate successful peer review.

    4. IMPLEMENTING PEER REVIEW FOR COLLABORATIVELEARNING

    When introducing peer review for the first time, teachers will want to explainto students why they are doing it [13]. For example, a teacher might assign thisshort video about peer review created by MIT [21]. This video includes facultyand student voices to convey the three main benefits of peer review:

    1. Getting feedback aids revision.2. Seeing how classmates approached assignments aids revision.3. Giving feedback aids revision.

    These three reasons all emphasize how peer review aids revision. Thus, forstudents to effectively engage in peer review, they need to understand that writ-ing, even writing in mathematics, is a process that involves drafting, revising,and editing.

    Separating revision from editing is one step towards teaching studentshow to give good feedback. Revision involves choices about content; editinginvolves choices about language. Although editing is important, it is best tosave it for the very end of the writing process for two reasons. First, edit-ing the language of a section that might get cut out of the final draft wastestime, and second, focusing on correctness when drafting can create writersblock and prevent writers from attempting to represent complex ideas. If we areemploying writing as WTL, we need our students to focus on content first [28].

    We also want to address students possible inexperience with peer review.As Richard Chisholm writes:

    Experienced writers and experienced reviewers know that a solo draft is only adraft and that the purpose of peer review is to stimulate the writer to rethink theentire document [6].

    One way to teach inexperienced writers about the relationship betweenpeer review and revision is by asking students to begin peer review by setting

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    an agenda. What this means is that students tell each other where they wantfeedback and what, if anything, is off limits. Faculty who use a gradingrubric might direct students to refer to the rubric when they set their agenda.Setting the agenda not only provides students with some directions for peerreview, it also gets students reflecting on their own work, which contributes tometacognition2.

    Another way to emphasize content is to tell students to ask questions abouttheir peers papers. Questions help those who are giving feedback, by offeringa way to give feedback without direct criticism. They also help those who aregetting feedback by showing them that they have choices in terms of whatthey say and how they say it. Thus, these questions should address both formand content. For example: Why did you put this point in this paragraph? orWhat do you mean by regression? Whether using online collaboration toolsor working with print copies, students can include these questions as commentson each others papers.

    In addition to questions, students should be directed to write commentsat the end of each others papers. These comments should take the form ofsummary, praise, and constructive critique. The summary allows writers to seeif their main points are clear and ensures that the reviewers are reading care-fully. The praise helps writers see their strengths; it is surprising how oftenstudents note that peer review helped them develop confidence in their ownwriting. Finally, the constructive criticism allows writers to see where they needimprovement. Providing students with models of good peer review is anotherway to make peer review more effective. Chisholm provides such models onpages 16 and 17 of his paper [6].

    Although students may complete peer review in class or outside of class,it is still useful to devote some time in class for students to set their agendaand to discuss their work. Allowing the activity to be completed for homeworkallows students to work at various paces and accommodates slow readers whoneed more time to compose useful feedback.

    The final step in peer review is for students to compose a plan for revision.This takes the form of a paragraph or two or several bullet points about:

    what peer review helped them see about their work; the advice they will follow, the advice they will ignore, and why; what next steps they will take to revise.

    The plan for revision directs students to revise, facilitates their ownershipof their writing, and also contributes to metacognition.

    In addition, real-time collaborative writing technologies can facilitate col-laborative writing and peer review in and out of class. One popular example

    2Joel A. English [11] and L. Lennie Irvin [15] explain the connections betweenmetacognition, reflection, and computer-mediated writing.

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    is GoogleDocs: the suite of editors available within GoogleDrive, https://drive.google.com a cloud-based drive for housing files. GoogleDocs includessuch editors as GoogleSpreadsheet (which can run script for programming),GoogleDocument (word processing editor with a LATEX-based equation editor),and GooglePresentation. Students can work on every part of a project collabo-ratively, from computing figures on a spreadsheet, to writing the lab report, topresenting results to the class. The chat window available during the collabora-tion session allows for editing suggestions, e.g., Can you do some rephrasingto facilitate that section transition? without compromising the integrity of theworking document. Google also offers sharing and permissions options, sousers can set very specific controls over who has access to their document andhow much access they have. Individuals participating in group reports with fullediting privileges have access to detailed revision histories that are color codedby the account user. This revision history can be useful for both students andteachers when reflecting on group participation or on writing evolution. Peerreviewers can be added with editor or comment-only privileges.

    There are also free, web-based collaborative LATEX editors. WriteLATEX,https://www.writelatex.com/ is an example of such an editor that allows forsimultaneous cloud editing. Its split-screen design allows for the LATEX edi-tor to appear alongside the PDF document view, and files can be synced withDropbox for cloud-based access from anywhere. We chose to write the major-ity of this paper in GoogleDocs, using collaborative writing technology towrite about collaborative writing technology. After our first draft, we insertedour paper into LATEX for formatting reasons, then continued the collaborativewriting process in WriteLATEX. The advantages of writing collaboratively inLATEX for mathematical collaborations between math majors and math facultyare clear. However, GoogleDrive offers a suite of features accessible to fornon-math majors who may not need to learn LATEX to write collaboratively.

    5. CASE STUDY: COLLABORATION IN A MATHEMATICSSEQUENCE

    At Unity College, all mathematics courses are service courses. Our mathemat-ics courses serve many important objectives: content, technology skills, and,ultimately, the development of a fundamental language to support our sustain-ability science curriculum. As we strive to meet the needs of our students, wepay close attention to critical thinking and communication skills. While writingis an important feature of all mathematics courses at Unity College, the learningoutcomes of the applied calculus sequence include independently written fulllaboratory/research reports by the end of the second semester. Students workon labs in groups, which helps foster learning [17]. They then write the result-ing research reports in Calculus I as a group, and in Calculus II independently.To ease the transition between semesters, the same grading rubric is used [1];

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    however, in the second semester, the bar for an A is raised, which elevatespersonal responsibility and requires higher target mastery. Staging mathemat-ical writing over two semesters follows the recommendations of Kelly andLeDocqs study of writing in mathematics [18].

    Through collaborative writing, students in Calculus I work to create a finalproduct that represents the effort and knowledge base of the group. Throughthese group writing assignments, they practice the norms of the discipline,which deepens their knowledge of content and of genre conventions. In thisway, they practice WTL. When they are asked to transition to independentwriting in Calculus II, students lose the informal peer group that collaborativewriting provides and they are simultaneously asked to face more challengingdisciplinary-specific conventions. Some students have no trouble with this tran-sition. Other students struggle. Formal peer review allows instructors to providestudents with formative feedback in the early stages of writing as they makethis transition. In this way, students continue to practice WTL as a means ofimproving their ability to write according to disciplinary-specific conventions.

    Appendix A includes a worksheet that describes the peer review process.Through class discussion and review of the worksheet, we explain the threebenefits of peer review noted above: feedback, improved ability to critiqueones own work, and more familiarity with content and genre. Students wereasked to arrive to class with a draft of their report written. The teacher thenrandomly created pairs of peer reviewers (see the next section for variations).Next, the pairs set the agenda for each peer review and shared their papers.Students worked on the peer review for the remainder of class time and fin-ished it for homework for the next class. The peer review grade included botheffort in creating a reasonable first draft for review and effort and thoughtful-ness as a reviewer, which can be an additional source of motivation. Revisionsof the final draft were due the following week, and the revised product wasassessed using the standardized research report rubric developed by the UnityCollege Center for Biodiversity [1].

    Students in Calculus I who engage in a collaborative project and groupwriting were asked to reflect on their experience. The following are somequotations from these students.

    We have been working on another project for calculus, which I really enjoydoing. Its nice to work with peers on something that is applicable in our fields.I think that its beneficial to have somebody else explain the same thing butin a different way than someone. [Name omitted] has a really great way ofsimplifying everything and breaking things down so that I actually understandeverything that we are doing in our project. I really enjoy having her point ofview.

    The project that we have begun working on this week is very helpful too.Not only am I getting to figure it out myself and use a real-life type scenario,but I am also getting the opportunity to explain the process and everything to

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    someone else. This has helped me to really put what Im doing into words andmake sure both they and I have it down.

    We used Google docs to write it all up, and its [sic] so cool how you canliterally work on the project at the same exact time but be in two differentplaces! Her and I are planning on finishing up the rest of the paper this weekendand getting it in so we dont have to worry about it.

    The following are examples of improved exposition as a result of the peerreview process introduced in Calculus II. To give some context, in our particu-lar lab, we developed a program in GoogleSpreadsheet using script to calculatethe area under the graph of a positive function. A newer, MATLAB-based,version of this project is available in Appendix B.

    Draft title: Student Programming Project: Trapezoid Rule Project Peer comment: This is good as a description of the paper, but parts of it areunhelpful as the title. The title should describe what is going on in yourpaper.

    Final title: Calculating area using Trapezoid Rule Project in GoogleDocuments

    The following example is from the introduction of the same paper. Manystudents struggle with explaining why they are doing this exploration.

    Draft: Anti-derivatives are used in integration to find the equation for the inte-gral in question, but there are times in which anti-derivatives are unable to beused.

    Peer comment: This is confusing. Try re-wording. Final: Anti-derivatives are used in integration to find the equation for calcu-

    lating the area under the curve of the given function, but there are times inwhich anti-derivatives are unable to be used.

    The writer is still trying to clarify that anti-derivatives cannot always be cal-culated by hand, but still the exposition of this idea is much improved. Eventhe latter comment, while not particularly as thoughtful, forces the reviewedstudent to reflect on what he or she was trying to convey. In both cases,peer review helped the student solidify understanding of the link betweenusing numerical approximations derived using the equivalence of area toantiderivatives.

    Sometimes the peer review comments were a much needed early-intervention in the writing process, and therefore led to a much improvedstudent product. In one case, a student included the code and the functioncalls and output as an Appendix and only referred to it in the results section.However, the student had included no explanation for the code, no words thatsummarized the results.

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    Peer comment: What are your results?...You need to define your variables andoffer more explanation. Think of it as if you are writing this for an audiencethat has no idea what your project was to begin with.

    The peer reviewer also made a similar comment in the summary of review.In the interest of conciseness, the entire re-written Results section is notincluded, however, there was a much improved results section breaking downthe results in context to the problem at hand.

    6. ASSESSMENT, REFLECTION, AND REVISION

    Over time, we have made modifications to some of the activities describedabove. All of our students now have institutional Google Apps for Educationaccounts and are introduced to GoogleDrive in their freshman seminar course.Without this extra assistance, it was necessary to spend some class timeengaged in creating Google accounts and familiarizing them with the features,though some of this can be abated by using the plethora of tutorials avail-able on the web, see, for example, [23]. We now also have MATLAB availableso we do not use the GoogleSpreadsheet script. Although GoogleSpreadsheethas programming capability and collaborative ability, MATLAB is a much eas-ier programming tool to learn and also has more tutorials available online,see, for example, [4]. Since this was the students first introduction into pro-gramming, MATLAB also allowed students to explore programming morereadily. Although these seem like structural changes unrelated to writing, weacknowledge that writing mathematical ideas is in itself a challenge. Addingdifficult, unfamiliar tools or content mastery requirements to this challenge cansometimes interfere with the students ability to communicate it [14].

    In addition to staging levels of writing between courses, we have nowincorporated staged writing within each course. The first lab report in eachcourse is limited to the title, results, discussion, and references sections. In thenext lab, students finish the report. This allows students to develop fluency withaspects of the genre as they deepen their content knowledge, using writing tothink like mathematicians [27]. Peer review is part of both reports. In the sec-ond semester, students have two opportunities before advancing to the finalindependent project. During the first iteration of the course, only one peerreview per person was assigned, and some students were more helpful thanothers. Some students were disappointed by less-than-helpful or late feedback.Now each student is assigned two reports to peer review for each assign-ment. This increases the chance of helpful criticism and also gives studentsthe opportunity to elicit a diversity of opinions.

    Our collaboration has yielded several important lessons: Let students knowthat peer review is how academics craft effective writing in all disciplines. Usethe peer review handout provided in the Appendix and the MIT video, [21], to

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    reinforce this. Metacognition is important, so provide students with opportuni-ties to reflect on their learning [10, 24]. Let students tell their peers that they aredepending on them for their feedback. Peer pressure sometimes works betterthan instructor pressure. Use the collaborative technology first before assign-ing the task to students, so you will be prepared to vet their concerns. Eachtechnology has its own peculiarities. In addition, students may find a new tech-nological or pedagogical tool, like GoogleDrive or peer review, more tedious ifno one else employs it, so learn what your colleagues are doing and volunteerto teach others about your favorite tools.

    Most importantly, do not limit yourself to colleagues within your depart-ment; perhaps your peers in other departments are adapting these tools intheir first-year writing curriculum or in other courses. The writers of thispaper have benefited tremendously from collaboration and peer review. Theproblems we face in undergraduate education are complex and interdisci-plinary. By being more deliberate in our own learning processes and by sharingthis with our students, we explicitly illustrate the deep connections betweencollaboration, learning, and communication and we model transdisciplinaryproblem-solving.

    ACKNOWLEDGEMENTS

    We would like to acknowledge the work of the Unity College Center forBiodiversity faculty in creating the rubric used to grade biology researchreports [1]. We would also like to thank the Gretchen Schaefer, a friend andInstructional Technologist at Husson University and for her patience and helpwhile we learned and implemented new technology in our classes. We alsothank the organizers of this special issue and the MAA Contributed Sessionson Incorporating Writing and Editing into Mathematics Classes at Mathfest forencouraging this work to be submitted and fostering dialogue.

    APPENDICES

    APPENDIX A: PEER REVIEW HANDOUT

    Peer Review What have your past experience with peer review been like? Ifyou have never done it, what do you think you will like/dislike?

    What are the benefits of peer review?1.2.3.4.

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    Guidelines for successful peer review:

    1. Set the agenda with your partners. Tell your partners what sort of feedbackyou want and what sort of feedback you dont want. Listen to the type offeedback your partners want and dont want. Write this down. As you readtheir papers, address their concerns.

    2. As you read, address content and form. Use questions as a way to point outyour concerns.

    For example, if you find a section confusing, you might ask: What areyou trying to say here?

    For example, if the organization is unclear, you might ask: Why did youput the information or pictures in this order?

    You will write these questions in the margins of your partners paper(s).

    3. Look at most local issues of language in the last draft. You dont wantto wrestle with the language of a section that may get cut from the finalcopy. If the language interferes with your ability to understand your partnerspapers, let them know via questions.

    4. You should write at least three paragraphs of feedback.

    Start with summary. This will help your partners see if they conveyedtheir main points/achieved their purpose.

    Then, praise what is going well. Be specific. Finally, write about what needs improvement. Be specific, consider yourpartners agenda, and use questions to encourage critical thinking.

    5. After you give and receive feedback, review your own work and create aplan for revision. In your plan for revision, you will state the next steps youwill take to improve your paper. Note which of your peers comment youwill heed, which seem off base, and what new possibilities you see in yourown work.

    APPENDIX B: RESEARCH PROJECT

    Student Programming Project: Trapezoid Rule Project

    We have investigated integrals in two ways: by explicitly using antiderivativesand by approximation using sum of rectangles. For example, we can calculate

    101

    (3x2)dx = 3x1

    1101 = 3x1

    101 = (0.3) (3) = 2.7.

    This integral is easy to calculate since the antiderivative of its integrand,3/x, can be found exactly. But what if we want to allow the upper limit to beinfinity?

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    1

    (3x2)dx.

    Also some important functions do not have antiderivatives that are straight-forward to calculate. Consider this function, which is used in representingnormal distributions:

    p(x) = ex2/2/(2 ).

    We do not have the tools to calculate the explicit antiderivative for this function,so we must approximate any finite integral of p(x) numerically.

    We will use MATLAB to calculate integrals numerically with the trapezoidrule which we developed in class. The code can be found in the Bodine, Gross,and Lenhart book.

    1. Estimate using the trapezoid rule the area under the curve of

    f (x) = 3x2

    on the interval [1, 10] using 100 subintervals. You will have to modify func-tion in the f.m file in order to do this. Then run it and put in the appropriatevalues for a, b and n.

    2. Now calculate the approximate integrals for b = 100, 1000. Note: you mayhave to modify n in order to get good accuracy, so when you state yourresults, mention what n you used. You may want to think about what ngives you the same x as in #1.

    3. Calculate the exact value of the integrals in #2 using antiderivatives.Compare 13. What do you think is the value of

    1 (3x

    2)dx?4. Estimate using the trapezoid rule the area under the curve of

    p(x) = ex2/2

    2,

    over the interval [-1, 1] using an appropriate number of subintervals (youchoose n based on what gives you enough accuracy). Hint: ex is actuallyexp(x) in MATLAB, is pi, and the square root function is sqrt(x).

    5. Now calculate the same integral over [-2,2] for the same number ofsubintervals. Then try 10 times as many intervals.

    6. Repeat, but for [-5,5], then [-10,10]. Conjecture the exact value of thisintegral from (,).

    7. Write up a research report, with a title, results, and conclusions/discussion.Also discuss the accuracy of your results as well as comparing and contrast-ing results. Are the results what you expected or different? Include a copyof your modified function files as an appendix.

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    There will be three phases of research report: Phase I. Due Wednesday 2/27.You must upload your document to Canvas or submit a GoogleDoc URL (makesure you change settings to share by link).

    Phase II. You will be assigned two reports to read of peers and givefeedback. Please review by Monday 3/4.

    Phase III. Final drafts will be due, uploaded to Canvas by next Monday3/11.

    Follow the peer review guidelines from class.Your grade will be a combination of completion, effort in draft, peer review

    quality of comments you make for other people, and the writing quality, insight,and proper conclusions in the final version (all assessed by the Center forBiodiversity rubric at [1]).

    REFERENCES

    1. Baker, A., D. Potter, A. Remsburg, A. Arnett, E. Batchelder, E. Creaser,C. D. Eaton, E. Latty, and A. Phillippi. 2012. Center for Biodiversityresearch report rubric. Unity College, Unity, ME. http://goo.gl/SDzrq.Accessed 14 March 2013.

    2. Beaufort, A. 2007. College Writing and Beyond: A New Framework forUniversity Writing Instruction. Logan, UT: Utah State University Press.

    3. Beidleman, J., D. Jones, and P. Well. 1995. Increasing students conceptualunderstanding of mathematics through writing. PRIMUS. 5(4): 297316.

    4. Bodine, E. N. Tutorials for LATEX and MATLAB. https://sites.google.com/site/profbodine/tutorials. Accessed 29 May 2013.

    5. Bruffee, K. 1984. Collaborative learning and the conversation of mankind.College English. 46(7): 635652.

    6. Chisholm, R. 1991. Introducing students to peer review of writing. WACJournal. 3(1): 419.

    7. Cooper, A. 2012. Todays technologies enhance writing in mathematics.The Clearinghouse: A Journal of Educational Studies. 85(2): 8085.

    8. Council of Writing Program Administrators, National Association ofTeachers of English, National Writing Project. 2011. Framework for suc-cess in postsecondary writing. http://wpacouncil.org/files/framework-for-success-postsecondary-writing.pdf Accessed 13 September 2013.

    9. Douglas, D. and E. Wardle. 2007. Teaching about writing, rightingmisconceptions: (Re)Envisioning first-year composition as introduc-tion to writing Studies. College Composition and Communication. 58(4):552584.

    10. Driscoll, D. 2011. Connected, disconnected, or uncertain: Student atti-tudes about future writing contexts and perceptions of transfer fromfirst year writing to the disciplines. http://wac.colostate.edu/atd/articles/driscoll2011/index.cfm. Accessed 16 March 2013.

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    11. English, J. 1988. MOO-based metacognition: Incorporating online andoffline reflection into the writing process. Kairos. 3(1): http://kairos.technorhetoric.net/3.1/binder.html?features/english/intro.html. Accessed10 May 2013.

    12. Gere, A. R. 1987. Writing Groups: History, Theory, and Implications.Carbondale, IL: Southern Illinois University Press.

    13. Henry, L. 2011. Teaching intellectual teamwork in WAC courses throughpeer review. Currents in Teaching and Learning. 3(2): 414.

    14. Herrington, A. 1981. Writing to learn: Writing across the disciplines.College English. 43(4): 379387.

    15. Irvin, L. I. 2004. Reflection in the electronic writing classroom.Computers and Composition Online. http://www2.bgsu.edu/departments/english/cconline/irvin/Introduction.htm. Accessed 10 May 2013.

    16. Kasman, R. 2006. Critique that! Analytical writing assignments inadvanced mathematics courses. PRIMUS. 16(1): 115.

    17. Kast, D. 1993. Collaborative calculus. PRIMUS. 3(1): 5361.18. Kelly, S., E. DeLocq, and L. Rebecca. 2001. Incorporating writing in an

    integrated calculus, linear algebra, and differential equations sequence.PRIMUS. 11(1): 6787.

    19. Kroll, B. and J. Schafer. 1978. Error analysis and the teaching of compo-sition. College Composition and Communication. 29(3): 242248.

    20. Kutz, E. 1978. Between students language and academic discourse:Interlanguage as middle ground. College English. 48(4): 385396.

    21. Massachusetts Institute of Technology. No one writes alone: Peer review,a guide for students. http://mit.tv/zXCM6m. Accessed 14 March 2013.

    22. McLeod, S. 1987. Some thoughts about feelings: The affective domain andthe writing process. College Composition and Communication. 38(4).

    23. Michigan State University. Getting started with Google Docs. http://edutech.msu.edu/online/googledocs/googledocs.html. Accessed 24 May2013.

    24. National Research Council. 1999. How People Learn: Brain, Mind,Experience, and School. Washington, DC: National Academy Press.

    25. Patchan, M., D. Charney, C. Schunn. 2009. A validation study of stu-dentsend comments. The Journal of Writing Research. 1(2): 124152.

    26. Patchan, M., C. Schunn, R. Russell. 2011. Writing in natural sciences:Understanding the effects of different types of reviewers on the writingprocess. The Journal of Writing Research. 2(3): 365393.

    27. Poe, M., N. Lerner, and J. Craig. 2011. Learning to Communicate inScience and Engineering: Case Studies from MIT . Cambridge, MA: TheMIT Press.

    28. Sommers, N. 1982. Responding to student writing. College Compositionand Communication. 33(2): 148156.

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    BIOGRAPHICAL SKETCHES

    Carrie Diaz Eaton received her BA inMathematics andMA in InterdisciplinaryMathematics from the University of Maine and Ph.D. in Mathematics witha concentration in Mathematical Ecology and Evolutionary Theory fromUniversity of Tennessee. She then returned to Maine and is currently anAssociate Professor of Mathematics in the Center for Biodiversity at UnityCollege. Her goal as a teacher is to get students to see math in the world aroundthem and to use math as a tool to answer scientific questions. As her Twitterprofile @mathprofcarrie says, Carrie has an interest in evolution, ecology,social systems modeling, cloud technology, and becoming a better teacher.

    Stephanie Wade earned a BA in Psychology from Wesleyan University, a MAin English at the City College of New York, and a Ph.D. in English, with aconcentration on composition studies, at Stony Brook University, in New York.Currently, as Director of Writing and Assistant Professor of Writing at UnityCollege she teaches writing and humanities classes that aim to help studentssee the choices available to them as writers, thinkers, and citizens.

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    ABSTRACT1. INTRODUCTION2. WRITING-TO-LEARN VERSUS WRITING-IN-THE-DISCIPLINES3. COLLABORATION AND PEER REVIEW FOR UNDERGRADUATES4. IMPLEMENTING PEER REVIEW FOR COLLABORATIVE LEARNING5. CASE STUDY: COLLABORATION IN A MATHEMATICS SEQUENCE6. ASSESSMENT, REFLECTION, AND REVISIONACKNOWLEDGEMENTSAPPENDICESAPPENDIX B: RESEARCH PROJECTREFERENCESBIOGRAPHICAL SKETCHS