tag:blogger.com,1999:blog-6421990566053383182.post3223860178033576909..comments2024-03-28T07:48:28.163-04:00Comments on The Big Mud Puddle: Correctness is a BooleanJon Purdyhttp://www.blogger.com/profile/08893015329760742645noreply@blogger.comBlogger2125tag:blogger.com,1999:blog-6421990566053383182.post-88685467594146144412011-10-08T13:21:19.924-04:002011-10-08T13:21:19.924-04:00@Joe:
Thanks for that quote! Programs, proofs, an...@Joe:<br /><br />Thanks for that quote! Programs, proofs, and essays are all closely related in my mind, and that interrelationship has been a wellspring of good analogies for my writing about software. It’s good to have some reassurance that I’m not completely crazy.Jon Purdyhttps://www.blogger.com/profile/08893015329760742645noreply@blogger.comtag:blogger.com,1999:blog-6421990566053383182.post-16529592228717928442011-10-06T22:12:24.734-04:002011-10-06T22:12:24.734-04:00Your analogy to proofs is actually not new:
From ...Your analogy to proofs is actually not new:<br /><br />From "The Art of Proof" by Matthias Beck & Ross Geoghegan:<br /><br />"On Grading Homework - The Red-Line Method <br /><br />It is essential that the student regularly hand in written work and get timely feedback. One method of grading that we have found successful lessens the time-burden on the instructor and puts the responsibility on the shoulders of the student. It works like this: <br /><br />Certain theorems in the book are assigned by the instructor: proofs are to be handed in. The instructor reads a proof until a (real) mistake is found—this might be a sentence that is false or a sentence that has no meaning. The instructor draws a red line under that sentence and returns the proof to the student at the next meeting. No words are written on the paper by the instructor: it is the student’s job to figure out why the red line was put there. Pasting as necessary so as not to have to rewrite the correct part—the part above the red line—the student then hands in a new version, and the process of redlining is repeated until the proof is right. <br /><br />The instructor will decide on the details of this method: how many rewrites to allow, and whether to give the same credit for a successful proof on the sixth attempt as on the first. Another issue that arises is how to handle students’ questions about red lines in office hours. Some instructors will want to explain to the students why the red line was drawn. Another approach, which we have found successful, is to have the student read the proof aloud, sentence by sentence. Almost always, when the student reaches the redlined sentence it becomes clear what the issue is. <br /><br />In all this we are not looking for perfection of expression—that will hopefully come with time. We start with the attitude that a proof is just an explanation of why something is true, and the student should come to understand that a confused explanation is no more acceptable in mathematics than in ordinary life. But the red line should be reserved for real mistakes of thought. To put this another way, the student needs to believe that writing correct mathematics is not an impossible task. We should be teaching rigor, but not rigor mortis. <br /><br />We sometimes say in class that we will read the proof as if it were a computer program: if the program does not run, there must be some first line where the trouble occurs. That is where the red line is."<br /><br />Comically (unless you've read this book and are giving it a stealthy homage), they draw the analogy the other way, as well. I think grading of computer programs for courses might be best done using this method, though programs have things like functions, making it difficult to know where to underline first.Joe Tannenbaumhttp://cs.binghamton.edu/~jtannen1noreply@blogger.com