Reflections

Reflections are due Sunday evenings at 7:00 p.m.  Please  submit them to the Dropbox in our course file on the Middfiles server (middfiles  > Classes > Spring16 > MATH0302A > DROPBOX ).  I’ll put a new prompt here every week.

Due Sunday, February 21, 7:00 pm:  Read this blog post by my friend Professor Ben Bruan (U. of Kentucky).  Then write responses to the following questions:  1.  Have you had any “fixed mindset” moments during our class sessions so far?  If so, what  specific topic(s)  triggered that response?  2.  How hard would it be for you to adhere to  the “replacement phrase” policy in our class?

NOTE:  In the interest of full disclosure, I should note that (a) Ben Braun is the editor-in-chief of that blog, and I am one of the co-editors; and (b) I fell into the “fixed mindset” trap during graduate school, more often than I’d like to admit.  I share Ben’s sense that mathematicians at all levels ask The Secret Question of themselves.

Due Sunday, February 28, 7:00 pm: List two or three new concepts or definitions that you were introduced to this week. Pick one and explain what it means in language accessible to someone who has not taken this course. Be sure to use enough details and possibly examples.

Due Sunday, March 6, 7:00 pm:  What was not clear to you this week? List up to three ideas or problems that you think you don’t yet understand well. What do you think you need to do to improve your understanding?

NOTES:  Please give your file a name that includes your last name, perhaps of the form BremserMar6Refl.  Also put your full name at the top of the page. Also, feel free, in any reflection assignment, to add a message to me concerning any aspect of the course.

Due Sunday, March 13, 7:00 pm:  What was the most cognitively challenging class or homework problem this week? Would you describe the challenge as low (routine; applying known procedures), medium (involving some productive struggle), high (involving a lot of productive struggle), or extra high (all struggle, no product yet)?

NO Reflection due Sunday, March 20.

Due Sunday, April 10, 7:00 pm:  What mathematics did you learn in the process of doing the take-home exam?  Were there particular concepts that became more clear as you prepared your solutions?  Be specific.

Due Sunday, April 17, 7:00 pm: Has your experience doing math in a group changed since the start of the semester?  If so, how? Is there a relationship between communicating mathematics verbally and writing up homework solutions?

Due Sunday, April 24, 7:00 pm:  Describe, using nontechnical language, what it means for two groups to be isomorphic. (Assume your reader knows what groups are but has never seen the word “isomorphism.”) Then compare your description to the formal definition on Worksheet 10.  What details did you leave out? Do you think you captured the general idea?

Due Sunday, May 1, 7:00 pm:  Your most recent problem set began with a new theorem, and asked you to apply it in various situations.  Describe what you learned from that experience.

Due Sunday, May 8, 7:00 pm:  List the most important (in your view) eight or ten group theory definitions and theorems that you’ve learned this term.  Due Tuesday, May 10, at the start of class:  (I can’t ask you to type up this part!)  Arrange those definitions and theorems in a concept map.  Here’s one that we did in linear algebra last semester:  Math200ConceptMap2.  Movement goes from left to right (imagine arrows pointing right — I couldn’t get the software to do that for me); definitions are in boxes, and theorems are in ovals.  Feel free to use a different design, if you’d like.  An arrow from one concept to another means that the first is a prerequisite for the second.