four-and-a-halfusefulmethods forassigningwritinginmathclasses · 2015. 7. 15. ·...

Four-and-a-half Useful Methodsfor assigning writing in Math Classes

Annalisa Crannell

January 2015

Four-and-a-half Useful Methods

1. Know why you’re assigning writing.

2. Focus.

3. Distinguish between feedback and evaluation.

4. Batch and Automate.

&12. Peer Assessment.

Annalisa Crannell | Franklin & Marshall College 2/29



And then let your students know why, too.



If these are your reasons . . .

Because I have nothing better to do on a week night than sit aroundgrading papers.

It will impress my dean.

Annalisa Crannell does it, and she’s totally awesome.

. . . then you might want to reconsider!



Slightly better possibilities:

To help students learn to do mathematics, as for example with

• homework or

• journals and process papers.

To help students learn to communicate mathematics, as for example with

• proofs or

• research papers.

Of course, the goal is usually some combination of these two approaches.



My Calculus Writing Projects: the rationale

Why write in a math class? For most of your life so far, the only kind ofwriting you’ve done in math classes has been on homeworks and tests,and for most of your life you’ve explained your work to people that knowmore mathematics than you do (that is, to your teachers). But soon, thiswill change.

Now that you are taking Calculus, you know far more mathematics thanthe average American has ever learned—indeed, you know moremathematics than most college graduates remember. . . . It becomesincreasingly important, therefore, that you can explain what you’re doingto others that might be interested: your parents, your boss, the media.



Shahriari Shariar’s assignment:Get students to read the research literature in his field and tell him whatit says. Oh, yeah, and introduce students to actual published research.

For this assignment, what you (the professor) do is

• photocopy the first page of papers you wish you had time to read,and

• dole those pages out to students.

Over the course of the semester, the students chose one paper, and thenread and write summaries of the main results and significance of thepapers they’ve chosen.




2. Focus.






Focus: Could shorter assignments give you the sameimpact?

For example, perhaps an abstract could do the work of an entire researchpaper.



Focus: Does it make sense to work on one thing at a time?• a thesis topic,

• a partial bibliography,

• a list of mathematicians with the same last names as they have(learning to use MathSciNet),

• a vocabulary list of relevant/confusing words,

• a rough draft of an introductory paragraph,

• an outline with a revised bibliography, and then finally

• the final paper.



Focus: Does it make sense to work on one skill at a time?

• correct punctuation of math sentences,

• switching from passive voice to the “mathematician’s we”,

• including figures in formal writing,

• correct citations and reference sections,

• transitions between paragraphs, and

• other?



Focus: What does a “good” paper look like?

Write a paper yourself and observe yourself.How long does it take?What parts of the paper are most important to you?Where are your students likely to get stuck?



Focus: What’s the difference between a “good” and “bad” paper?




2. Focus.






Compare math feedback & grading with the weird, foreign worldof the art critique, where feedback trumps grades.



Perhaps first drafts of proofs could be feedback, not grades:

You will have two chances to turn in each homework. The first week,homework will not earn a grade unless it is essentially perfect: in this case,it will receive a grade of ‘11’. If (I should say ‘when’) your homework isreturned without a grade, you have one week to revise it and turn it inagain. In this case, your homework will be graded on a 10 point scale,. . . .



Or you can provide feedback orally. In the old days, I used to use cassettetapes. Now I use “Audacity” to make MP3’s.




2. Focus.






Batch and AutomateUse electronic tools in TurnItIn.com or PDFpen to create “commentstamps” for comments you make frequently on a particular assignment.

Create a solution set that includes not only correct solutions, but alsocommon mistakes. (One of our adjuncts does this for her calculushomework and exams; students love it).

Create a “code sheet” of common mistakes. Our writing center providesone for standard writing correction marks (e.g., “ww” for “wrong word”).

Create a grading rubric. I hand these out to students before students turnin their assignments. Student use it while writing their papers, and itsignificantly speeds my grading.



Does this paper clearly (re)statethe problem to be solved?

Does it state the answer in acomplete sentence that stands onits own?

Does it state the physical formulasthat underlie the formulas?

Does it define all variables used,including units of measurement?

Is the mathematics correct?

grade NAME: out of

Checklist For Your Writing Project Directions: Please staple your paper and number the pages. Attach this page with a paper clip to the front of your writing assignment when you turn it in. Your instructor will use this list to grade your assignment, and will return it to you with comments. Keep a copy of your paper for your own reference. Please feel free to use this checklist as a guide for yourself while writing this assignment. Does this paper . . . 1. clearly (re)state the problem to be solved? 2. state the answer in a complete sentence which stands on its own? 3. clearly state the physical assumptions which underlie the formulas? 4. explain how the author derives each formula, or where the author found that formula? 5. aim those explanations at the appropriate audience? 6. clearly label diagrams, tables, graphs, or other visual representations of math (if these are indeed used)? 7. define all variables used? 8. give acknowledgment where it is due? In this paper, 9. are the spelling, grammar, and punctuation correct? 10. is the mathematics correct? 11. did the writer solve the question that was originally asked? Comments:




2. Focus.






Peer Assessment can be . . . a little . . . weak . . .

It works best when students don’t need to make value judgements or offeropinions.

Example of a bad exercise: Ask students to decide, “Does this paper havea strong thesis?”



Tamara Goeglein’s peer-review-of-thesis exercise:

• Read the paper over carefully and then turn the paper face down.

• On the back of the page, state the thesis of the paper.

• Turn the paper right side up, and then locate and circle thesentence that give the thesis.

• Put a star next to every sentence that provides evidence for orsupports the the thesis.

• Put an ‘X’ next to every sentence that contradicts or distracts fromthe thesis.



References

[1] Michelle Navarre Cleary, “The Wrong Way to Teach Grammar", TheAtlantic, February 25, 2014http://www.theatlantic.com/education/archive/2014/02/the-wrong-way-to-teach-grammar/284014/

[2] Marcus Cohen, Edward D. Gaughan, Arthur Knoebel, Douglas S.Kurtz, and David Pengelley, Student Research Projects in Calculus,MAA: Washington D.C. (1991).



[3] Annalisa Crannell, Gavin LaRose, Thomas Ratliff, and Elyn Rykken,Writing Projects for Mathematics Courses: Crushed Clowns, Cars,and Coffee to Go, MAA Classroom Resource Series, MAA:Washington D.C. (1998).

[4] Annalisa Crannell, “How to Grade 300 Math Essays and Survive toTell the Tale”, PRIMUS 4: 3 (1994) 193–204.

[5] Annalisa Crannell, “Assessing Expository Mathematics: GradingJournals, Essays, and Other Vagaries”, Assessment Practices inMathematics, MAA Notes 49 (1999) 113–115.

[6] Ralph Czerwinski, “A Writing Assignment in Abstract Algebra”,PRIMUS 4 no. 2 (1994) 117–124.



[7] Paul Halmos,“How to write mathematics”, Enseign. Math. 16(1970), 123–152.

[8] Nicholas J. Higham, Handbook of Writing for the MathematicalSciences, SIAM: Philadelphia PA (1994).

[9] S.K. Houston, C. R. Haines, A. Kitchen, et. al., Developing RatingScales for Undergraduate Mathematics Projects, University of Ulster,(1994).

[10] Steven G. Krantz, A Primer of Mathematical Writing, AMS:Providence, RI (1997).



[11] Stephen Maurer, “Advice for Undergraduates on Special Aspects ofWriting Mathematics”, PRIMUS, 1 (1990).

[12] John Meier and Thomas Rishel, Writing in the Teaching andLearning of Mathematics, MAA Notes Series 48, MAA: WashingtonD.C. (1998).

[13] Nancy Sommers, “Responding to Student Writing” Collegecomposition and Communication, 33 2 (1982) 148–156.

[14] N. E. Steenrod, P. R. Halmos, M. M. Schiffer, and J. A. Dieudonné,How to Write Mathematics, AMS: Providence RI (1973).



[15] Andrew Sterrett (ed.), Using Writing to Teach Mathematics, MAANotes Series 16, MAA: Washington D.C. (1998).

[16] Christopher Weld, “Listen to This! Utilizing Audio Recordings toImprove Instructor Feedback on Writing in Mathematics”, PRIMUS24, 513–528 (2014).

[17] R. Grant Woods, Calculus Mysteries and Thrillers, MAA ClassroomResource Series, MAA: Washington D.C. (1998).

[18] University of Michigan “Team Homework” site:http://instruct.math.lsa.umich.edu/support/teamhomework/




2. Focus.





four-and-a-halfusefulmethods forassigningwritinginmathclasses · 2015. 7. 15. ·...

Documents