tag:blogger.com,1999:blog-30611202.post5090468601678490597..comments2018-12-30T17:21:05.971-08:00Comments on Thales’ triangles: standards for analysisJoshua Bowmanhttps://plus.google.com/103262883740888913105noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-30611202.post-31039310003922184602014-08-20T06:43:27.950-07:002014-08-20T06:43:27.950-07:00The notes that include the weekly assignments also...The notes that include the weekly assignments also have "Big Picture" paragraphs interspersed (a feature I have kept from earlier versions of the class). So there are examples that model this kind of writing.<br /><br />I've found that when I suggest students provide a sketch of their proofs in their papers, they manage to draw out the key ideas. We'll see. :-) At first I'll be looking for self-awareness about what concepts and notation were new to them when they started solving the problem.<br /><br />If I were to use a (poorly constructed) biological metaphor, I would say "vocabulary and notation" form the skeleton of mathematical writing, "argumentation" is the muscle, and "exposition" is the skin. Then a "broad vision" would be the ligaments that bind bone to muscle.Joshua Bowmanhttps://www.blogger.com/profile/05825513382152813711noreply@blogger.comtag:blogger.com,1999:blog-30611202.post-12698553705669088912014-08-19T21:48:03.087-07:002014-08-19T21:48:03.087-07:00How much explicit instruction do you give them in ...How much explicit instruction do you give them in class for "Broad vision of the subject?"<br /><br />I am looking forward to diving into your next post.Bret Beneshhttp://symmetricblog.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-30611202.post-38912192564769840592014-08-18T14:00:47.170-07:002014-08-18T14:00:47.170-07:00Josh, as always I really appreciate your ideas and...Josh, as always I really appreciate your ideas and how much thought you've put into them. The comments have also been very thought-provoking. It's funny, because I am just now putting together some standards for my abstract algebra class. I was worried about how to break up the specific content into different standards, so I really appreciate your situation and your solution.Timhttps://www.blogger.com/profile/02168541630226144478noreply@blogger.comtag:blogger.com,1999:blog-30611202.post-59156990165674743482014-08-18T10:59:06.652-07:002014-08-18T10:59:06.652-07:00Bret: wait for tomorrow. I'm going to post my ...Bret: wait for tomorrow. I'm going to post my calculus standards, which will be more numerous and content-based.Joshua Bowmanhttps://www.blogger.com/profile/05825513382152813711noreply@blogger.comtag:blogger.com,1999:blog-30611202.post-15529186477079529122014-08-18T10:56:20.109-07:002014-08-18T10:56:20.109-07:00This looks really great. Funny, I am kind of goin...This looks really great. Funny, I am kind of going in the opposite direction this semester, with a whole lot of content-focused learning goals. For the record, I think that your way is the way I would prefer to do things (I do not think that my course---calculus---is the right place for me to start with this. Also, it is way too close to the semester for me to change things up).<br /><br />Bret Beneshhttp://symmetricblog.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-30611202.post-54421180779737671292014-08-18T10:38:31.077-07:002014-08-18T10:38:31.077-07:00Theron: Each week has 3 loosely-related problems a...Theron: Each week has 3 loosely-related problems assigned to different groups. Every student contributes to their group every week, but generally only to the problem they're working on. The end-of-week presentations give the groups a chance to share their problem and the solution they found with the other groups. Everyone is expected to understand the work that has been done; later problems often depend on conclusions from earlier ones, which the students are expected to recognize.<br /><br />I might have been unclear on the scaling of points for the final grade. An idealized picture would be one with four written papers and four exam problems. Then each of these would get a grade out of 4 points, yielding a total of 32 possible points, which would be added to the grades for standards 5–6 for a total out of 40. Since there are eleven papers instead of four, I will add up their total points and multiply by 4/11 to get a score out of 16. I don't know how many problems the exams will have, yet, but I'll use a similar scaling process to get another score out of 16. This will mitigate somewhat the scores required for various letter grades; a student could have a 3 on five of the papers and still get 38 points, if all the other grades are 4s.<br /><br />Each student will have four presentations. I expect them to improve over time, but I'll only count their highest presentation score in the final grade. If at the end of the semester there's a student who's unhappy with her presentation grade, then I'll give her a chance to "redo" one, but I think that's unlikely to happen.<br /><br />timfc: I think that last paragraph addresses some of your concerns, too. I've included in the syllabus the sentence, "I expect you to improve in each of these areas, and my criteria for success will become more exacting as the semester goes on." I could do a weighted system for the presentations, but the whole thing is complicated enough that I'd like to keep this part simple.<br /><br />The biggest challenge overall, I think, is going to be in gauging the early grades so that they're neither too strict nor too lax. I want the students to develop habits early on (like revising their papers and giving other groups constructive feedback) that will lead to growth. Much of this is about building a culture rather than being too focused on the grading system.<br /><br />Good questions. Thanks to you both!Joshua Bowmanhttps://www.blogger.com/profile/05825513382152813711noreply@blogger.comtag:blogger.com,1999:blog-30611202.post-85004442789990542592014-08-18T07:57:28.225-07:002014-08-18T07:57:28.225-07:00Thinking along the lines of Theron's comment.....Thinking along the lines of Theron's comment... at the beginning of the semester, students are likely to be not-very-good at the things that you want. <br /><br />Is it reasonable to either weight later material/presentations more heavily so that they'll have had a chance to develop their communication skills, or, offer, rather than a chance for a do-over, some notion of 'competency based grading' where by X week you need have demonstrated competency in the communication standards that you've outlined. Maybe have some gradations; proficient/advanced/jedi so that kids can see what's an C/B/A?<br /><br />I guess I'm okay with re-doing a presentation, but, I don't really like revisiting old content unless there's a pedagogical need to do so. timfcnoreply@blogger.comtag:blogger.com,1999:blog-30611202.post-62870250544560106062014-08-18T07:43:55.352-07:002014-08-18T07:43:55.352-07:00I like it. I think this has a good chance of encou...I like it. I think this has a good chance of encouraging the behaviors you want.<br /><br />I take it that every student does every assignment?<br /><br />How will you deal with the fact that students might write twenty-thirty proofs in a term, and thus have 20 different scores in the range of 0-16 for written assignments? Similarly, with n exams, where n > 1?<br /><br />And is there a way to handle the chance to "redo" a presentation that doesn't go well?Theron Hitchmanhttps://www.blogger.com/profile/07111353916174005765noreply@blogger.com