MTH 350 Proof Portfolio guidelines

Purpose

The purpose of the Proof Portfolio in MTH 350 is twofold:

1. To isolate your best work on the hardest problems that you do in the course, and package it into a showcase for how much you have learned; and
2. To reflect on what you've learned in the area of mathematical problem solving and make that thinking visible.

The Proof Portfolio is not just another assignment; it's something you can carry with you once the course is over and show to employers, graduate schools, and others who might be interested in your problem-solving and learning skills.

What goes in the portfolio

On each of our six Problem Sets, there is at least one and usually more than one starred problem. The Portfolio will consist of the following:

NOTE: This was updated on 2021-03-26.

• A collection of six starred problems selected from the Problem Sets, that you consider to be your best work. You have free choice as to which problems are included, but you must include at least one starred problem from each of the six problem sets.
• Additionally, if you are attempting to earn a High Pass mark on the portfolio (see below), then you will choose two more starred problems from the Problem Sets and include those as well. These two additional problems may not be selected from the same problem set.
• The portfolio will also ask you to include some reflections on the work that you are including, especially regarding how you improved your work over time through the revision process and what you learned by doing so. Details on this added material will be given around week 9–10 of the semester. (NEW: See below for these reflection items.)

The entire package of your portfolio problems and the additional material will be submitted as a PDF on Blackboard, with a deadline of 11:59pm Eastern on Tuesday, April 27.

How to put your portfolio together

(UPDATED 2021-03-26) You have six Problem Sets to do throughout the semester, due roughly every two weeks. Each one has at least one starred problem on it, and you will be asked to do just one starred problem per Problem Set. This means that the basic six problems for your portfolio will simply be pulled from the work on problem sets you are already doing. If you are opting into earning a High Pass grade, you'll be choosing two more problems from this group to do. Again, those two additional problems must be picked from different sets.

You will be evaluated and get feedback on the six problems that come from your Problem Set work, in the normal course of getting a mark on those Problem Sets. If you are attempting a High Pass mark and are submitting additional problems, you may submit your work on those to me (Talbert) at any time through email, and I will evaluate them and give you constructive feedback and a mark of E, M, P, or X just like Problem Set problems; this mark does not count toward any grade, but is just for your information to get a sense of what you might need to improve on your work. There are no deadlines for completing those two additional problems other than the April 27 deadline.

How your portfolio will be evaluated

As mentioned in the syllabus, Portfolios are marked High Pass, Pass, or No Pass. The criteria for each mark are as follows:

(UPDATED 2021-03-26)

Mark	Criteria
High Pass	Eight problems are submitted, including one from each Problem Set and no more than two from any single Problem Set. Each of the eight problems meets the standard for a mark of M on Problem Sets, and additionally at least four of the problems meet the standard for a mark of E. Finally the additional reflection material is well written.
Pass	At least six problems are submitted, one from each Problem Set. Each problem submitted meets the standard for a mark of M on Problem Sets, and the additional reflection material is well written.
No Pass	The requirements for Pass are not met. For example: there are fewer than eight problems submitted; or the reflection material is incomplete or poorly written; or at least one of the problems submitted does not meet the requirements for a mark of M.

Specific criteria for the additional reflection material (what constitutes "well written") will be given when that material is announced later.

How do I know if my work is good enough to Pass, or earn High Pass? For the problems that you turned in as part of a Problem Set, you can look at the mark that the set earned: If you have earned a mark of M on a Problem Set, then every problem on that set is individually at least at "M" level; similarly if your entire Problem Set has earned an "E". However, if your Problem Set earned a mark of "M", it's possible that your starred problem is at "E" level; if you are considering including a starred problem from a set that earned "M" but you think the starred problem is better than an "M", let me know and I will evaluate it separately. As for the two additional problems, as mentioned above you can submit those at any time to get individual evaluation on those.

Reflection Items to include with your portfolio

NEW – ADDED 2021-04-06

Along with the problems you submit for your portfolio, include the following:

1. For each problem you submit, write a brief overview of about 100-200 words that explains why you picked that problem and chose to include it and what you learned in the process of solving it, either in terms of mathematics or in terms of your problem solving skills. For reference, this is what 200 words of text looks like. I won't be counting words here, but rather looking for substantive and authentic responses that show evidence of serious thought.
2. Then also submit one, longer-form reflection that addresses the question: How did you grow as a problem-solver by doing these problems, and where do you think you still have room for growth? You should aim for around 400 words on this one. Precise word count isn't that important; what matters is whether you're giving an authentic account of yourself that tells your story well.

Questions

Additions to this list might be made during the semester as they come up; watch this space for updates.

What if I didn't turn in one or more of the Problem Sets? If this is the case, you can still go back and do at least one and no more than two starred problems from each of the Problem Sets you did not submit. Just treat them like the two additional problems mentioned earlier; submit your work on them to me when you're ready to have it evaluated.

If I did a starred problem as part of a Problem Set submission, do I have to include it in the portfolio, or can I change my mind and do another one from that set instead for the Portfolio? To keep things simple and to encourage you to stick with a problem once you've chosen to do it, the answer here is no. In other words, once you do a starred problem as part of a Problem Set that you turn in, you are committed to that problem for the semester, and it needs to go in your portfolio. (UPDATED 2021-03-26) If you turned in a starred problem on a Problem Set but you no longer want to include it in your portfolio (because you're tired of working on it, are making no progress, etc.) then you are allowed to change your problem. If you do so, you will need to do the following: (1) let me know by email or Campuswire DM about the change (what problem are you dropping and what problem are you adding in its place) and (2) submit your work on the new problem ASAP by email, as if it were an additional problem being done for a High Pass mark, so I can give it an initial evaluation.

• If you change a problem: (1) the new problem must come from the same Problem Set as the old one, and (2) you are not allowed to change back, otherwise we might enter a cycle of switching back and forth that will make it impossible to evaluate your work.

• Changing problems is not recommended. This is because it shortens the amount of time you have for doing revisions of work. If you do a problem in Problem Set 3, then you have half the semester to revise and resubmit your work repeatedly until it meets the grading standard; but if you abandon it and switch to a new problem in week 12, then you have two weeks to do so. It's better to simply persist with a problem until you've cracked it.