I previously wrote about transitioning from Standards Based Grading (SBG) to Standards Based Feedback (SBF). Here is a first pass at the policies. These will hopefully address Andy Rundquist’s question about grading.

In a nutshell, a student’s grade is determined by (roughly) the number of standards met. Slightly more detail is given in the list below, and an excerpt from the first draft of my syllabus provides even more detail below it.

I would appreciate feedback, ideas, and critiques. This is a first draft, and there must be many improvements that can be made.

- Homework (in the form of proofs) will be assigned regularly, but it will only be submitted for written feedback—no grades.
- Students will also have frequent (weekly?) opportunities for peer feedback on their proofs.
- Since I need to assign a grade at the end of the semester, the students will need to reflect on how their homework has demonstrated understanding of the course standards. They will assemble well-written, correct homework in a portfolio that summarizes how they met the standards for the semester.
- The portfolio will also contain the student’s favorite three proofs for the semester. These should be correct and well-written. Ideally, the students will also have other reasons for including them—perhaps they worked really hard on the particular proofs, found them surprising, or found them particularly interesting.
- Also in the portfolio will be a cover sheet cataloging the homework assignments that correspond to each standard.
- The portfolio will contain a self-evaluation. We will take class time in the beginning of the semester to discuss what constitutes a good proof, and the syllabus (see below) details how the portfolio will be graded. The student will have to do an honest self-evaluation of the portfolio.
- At midsemester, students will need to submit a trial portfolio (thanks, Joss). This will be done for credit—students either get 100% on this assignment or 0%. The purpose for this is to give students a practice run at this unusual form of grading—I don’t want their first experience with it to be high-stakes.
- There will also be at least one traditional graded midterm (the students will decide how many) and a final.
- There will be at least one ungraded, feedback-only midterm.

*Syllabus Excerpt*

**Homework**

You will be given a selection of homework problems to do each night. You are encouraged to work with other people, but you must write up your own solutions.

There are three levels to handing in homework.

- Once per cycle, you can hand in three proofs for me to look at; these proofs should be considered drafts, not final papers. I will give you comments on what you did well and what you need to improve upon in your next draft. I will give you only feedback on how to improve; I will not give you a grade.
- There will frequently be an opportunity for peer feedback of the proofs in class. Your classmates will give you feedback on the quality of your proof, and you will do the same to their proofs.
- At two points in the semester, you will hand in proofs to be graded. See the grading section below.

Basically, I want you to have very good proofs by the time they are assigned a grade, and I am going to help you improve your homework (without any penalty) until then.

This homework should be mostly done in , if only for the very practical reason that you will be re-submitting drafts; instead of re-writing each draft by hand, you will be able to simply edit a computer file. You will put more time into creating the file at the beginning, but you will save time with each draft after that.

**Portfolio**

At the end of the semester, you should have a collection of completed homework problems. At the end of the semester, you will reflect on the problems you have done, organize your homework, and submit a selection of your completed homework assignments (called your “portfolio”) for a grade. At the end of the semester, you will literally create a physical portfolio of your best work.

Here is how you will select your portfolio:

- You will select all bits of homework that show evidence of the Course Topics (see the section above) and place them in the portfolio. You should have multiple proofs for those labelled “Core Topics;” you only need one proof to demonstrate evidence for the “Supporting Topics.”
- You will select your three Favorite Proofs and put them in the portfolio. These will be well-written according to the criteria discussed in class. Also, these may be proofs that you are particularly proud of.

There is a balancing act when deciding whether a proof goes into your portfolio. On one hand, you want to provide as much evidence for the Core Topics as possible (and some evidence for the Supporting Topics). Other the other hand, an incorrect or poorly-written proof is not counted as evidence and will weaken your portfolio. Part of your goal for the semester is to learn to determine what is a good proof and what is not, and use your judgment accordingly.

Here is how your portfolio will be graded.

A: All of your Favorite Proofs are well-written, complete, and concise. Well-written, complete, concise proofs are provided for all topics; many proofs demonstrate understanding of each core topics. There are no wrong or poorly-written proofs in the portfolio.

B: All of your Favorite Proofs are well-written, complete, and concise. Many well-written, complete, concise proofs are provided for all Core Topics. Most of the Supporting Topics are supported by well-written, complete, concise proofs. There is at most one wrong proof in the portfolio.

C: All of your Favorite Proofs are well-written, complete, and concise. At least a couple of well-written, complete, concise proofs are provided for all Core Topics. Many of the Supporting Topics are supported by well-written, complete, concise proofs. There are at most two wrong proofs in the portfolio.

I will use my judgement to decide for the grades AB, BC, CD, D, and F.

Finally, you will evaluate your portfolio and determine what grade you think you deserve according to the criteria above. Be honest and be specific in your justification.

Here is how you will organize your portfolio. The first page(s) will be a cover sheet with your name, your self-assigned grade (but no discussion of it), and a list of the topics for the course. You will see that you are going to number the proofs; you should write the number of each proof that provides evidence for each topic (a single proof might provide evidence for more than one topic).

After the cover page, include your three Favorite Proofs. Start numbering these with “1.”

Next, include proofs that demonstrate each of the Core Topics for the first Core Topic in the list in the syllabus. Continue numbering these proofs as needed. If one of your Favorite Proofs provides evidence for the first Core Topic, you do not need to include a second copy of it—your cover page will indicate that the proof is evidence for both. Then, do the same with the second Core Topic. Note that if a proof from the first Core Topic also demonstrates evidence for the second Core Topic, you do not need to include a second copy of it—your cover page will indicate that the proof is evidence for both.

Continue with the other Core Topics in the same manner. Then do the same for the Supporting Topics (in the order they are listed).

Finally, include your detailed self-assessment of the portfolio; be sure to include your self-grade on this sheet, too.

Tags: 343, Assessment for learning, Formative Assessment, Grading, Real Analysis, SBF, SBG

July 1, 2011 at 2:40 pm |

I’ll try to play the role of devil’s advocate to see if I can see how a student might poke holes in this:

weak arguments:

– I can’t get to work so this class sucks

– I worked hard on this, I think I should get some points for it

– now that I’ve got your feedback, I know just how to fix this, but I can’t do that until the end of the semester because I’m busy

stronger arguments:

– my friend so-and-so has a great proof for that one. I’ll just do what s/he did and then that standard is covered. I’m glad Prof. Benesh gave us his blessing about working together.

– I love this class. Nothing is for credit until the end.

I really like what you’ve got here. These were pretty lame attempts by me, almost all of which can be dealt with by getting the students on board with the philosophy at the beginning. How hard will that be?

I like the portfolio approach. It’s like a tenure file: give us evidence that you have met all the criteria we want to see. Thanks for letting us in on this draft process, Bret!

July 1, 2011 at 3:36 pm |

Hi Andy,

I really appreciate this. I agree that I really need to sell this to the class at the beginning of the semester, and I am not certain that will be easy. We shall see.

I will address all of your comments:

Andy: “I can’t get to work so this class sucks”

Bret: I have had good success getting my students to use in linear algebra and abstract algebra classes, so I am not too concerned about this. However, I am ready to make allowances in certain situations: students can hand-draw graphs, etc.

Andy: “I worked hard on this, I think I should get some points for it.”

Bret: This one scares me a bit, although I (perhaps naively) think that it will work out fine with my students. As you said, I just need to sell it at the beginning. Worst case scenario: tell them that they basically have received points for it, since it will be going in their portfolio.

Andy: “Now that I’ve got your feedback, I know just how to fix this, but I can’t do that until the end of the semester because I’m busy.”

Bret: This one scares me a lot—especially since this happened to me in my mini-experiment with this at the end of last semester (where students actually didn’t hand anything in, which is worse than what you suggested). I think that this might be able to be solved by nagging and Joss’s suggestion of having a mini-portfolio due at midterm.

Andy: “My friend so-and-so has a great proof for that one. I’ll just do what s/he did and then that standard is covered. I’m glad Prof. Benesh gave us his blessing about working together.”

Bret: This is also a distinct possibility. Combining this with using makes it even more dangerous, since copying is easier and somehow less objectionable for the students. If this is not too severe, I am not sure if I even have a problem with it, since I do not need every student to generate the ideas in this class. Moreover, keeping the exams will help keep the final semester grades be “right” (the students who understand the stuff well will get a bump up; those who don’t will get a bump down).

Andy: “I love this class. Nothing is for credit until the end.”

Bret: This is only a problem if they wait until the end to do all of the work.

I’ll add one other:

Bret-pretending-to-be-Andy: “I hate this course. I have to re-write my proofs (this isn’t English class!), and Bret never graded what we did. I am going to give him a bad teaching evaluation.”

Bret: This scares me a lot. I don’t have tenure, and I will have invested in a geothermal heat pump, fence, and possibly a new roof by the end of the summer. But I can’t let fear get in the way of becoming a better teacher, right? (Honestly—I think that I would be smarter if I tried this after tenure. I am not actually that worried about it, but it is in the back of my mind).

This was great, Andy. Let me know if you have more.

Bret

July 4, 2011 at 5:04 pm |

Bret I have some technical questions to help me put everything into better context.

1. How many students (approximately) will be taking this course?

2. Have the majority of these students taken a course with you previously?

3. Do you have any sort of A+ grade or does it top out at A?

4. What fraction of the grade is SBF and what fraction is made up from the exams?

As you know I think this idea has great potential and I’m very excited to see how it goes. Generating buy-in will be key!

July 5, 2011 at 10:10 pm |

Hi Joss,

Here are the answers:

1. How many students (approximately) will be taking this course? There are 17 in the first section, 8 in the second, so 17+8=25 total.

2. Have the majority of these students taken a course with you previously? Four of the 25 have taken a course with me already, although I know another eight students. Plus, this is a reasonably small school with social students, so many more have heard to expect weird things from me. Still, I agree that buy-in is key.

3. Do you have any sort of A+ grade or does it top out at A? The best grade is an A. There is no A+.

4. What fraction of the grade is SBF and what fraction is made up from the exams? I allow the students to determine the exact weights, but I give them ranges. I am planning to give the students the choice of letting SBF be anywhere from 60% to 80% of their final grade (the remainder coming from exams).

Thanks for the questions, Joss. Bret

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