Linear Algebra Grading Plan

I described my structure for my linear algebra class last week. This week, I will describe my grading system.

First, recall that this is typically a sophomore-level class (although 9 of my 16 students are first-years). It is typically the first mathematics course that a mathematics student takes after calculus II. The purpose is to learn about linear algebra—including abstract vector spaces—and gently introduce the students to proofs.

The grading system hinges on what I want the grades of A, B, and C to mean. My linear algebra class does not vary from my usual interpretation: To get a C, you must demonstrate conceptual understanding of the material. To get a B, you must demonstrate both conceptual understanding and computational proficiency. To get an A, you must additionally demonstrate an ability to learn independently.

Below, I describe the graded portions of the class, followed by a set of rules that determines the semester grade for each student. I reserve the right to raise a student’s grade from what this rubric says, but I will never lower it. The rest of this post is taken directly from my syllabus (modulo some formatting and possible editorial comments); I would appreciate any thoughts that you have on how to improve this.

Here we go; it may be helpful to see my structuring if you have questions about anything.

Presentations

Each time you present a Presentation Problem, I will make a note of it. It is better to correctly do a problem than to incorrectly do a problem, and it is better to correctly do a difficult problem than it is to do a relatively easy problem. Both the quality and quantity of the Presentations you give will be considered in determining your semester grade.

Part of the goal of this class is to help you hone your mathematical judgment. Because of this, I will limit the number of presentations that I confirm are correct (I will confirm 2 per day for the first three classes, 1 per day for the enxt three classes, and then 5 for the entirety of the remaining part of the semester). Please note that I will still do something during the semester to correct any misconceptions the class has—I just won’t necessarily do it immediately following the presentation unless the majority of the class wants to spend a Confirmation.

Giving a Presentation can never hurt your grade; the worst it can do is to fail to help your grade.

Daily Homework

You will be expected to submit you work for the Routine Problems and Presentation Problems at the end of each Monday and Friday during the first half of the semester. These will be graded on completion: as long as you make an honest effort at solving every Routine and Presentation Problem due that day, you will receive full credit. You are not expected to use \LaTeX for Daily Homework.

Since these are due at the end of the class, you may write on the homework with a marker (I will supply them, although I would appreciate it if any student brought his/her own). Your grade for Daily Homework will be based on the work you came to class with—the work in marker will not be graded.

Submitting Daily Homework can never hurt your grade; the worst it can do is to fail to help your grade.

Portfolio Homework

Each Monday and Friday during the first half of the semester, I will denote 1—2 of the Presentation Problems to be Portfolio Homework. This is homework that you are to write up nice solutions on \LaTeX.

Each problem will receive one of two grades: Complete or Resubmit. I will read your solution until I find an error. Once I find an error—it could be mathematical, grammatical, etc—I will mark it with Resubmit (or some suitable shorthand) and stop reading it. You can resubmit the same problem multiple times without penalty; if you eventually get a grade of Complete, you have been 100% successful on the problem, whether it was on your first attempt or your twenty-first.

You can only submit up to two Portfolio Homework problems per class day. This means that you should start working on them immediately—you do not want to have a lot of problems left to do during the last week of the semester, since you will not be able to submit all of them.

Submitting Portfolio Homework can never hurt your grade; the worst it can do is to fail to help your grade.

Mind Maps

You will be required to keep a “mind map” of all of the ideas described by the Chapter titles and Sub-Chapter titles in the table of contents of the course notes. Do this online using coggle.it, name it YOURNAME239MindMap, and share your work with me by using the “Share” button. You are to update this mind map weekly; I will check to make sure that it is up-to-date periodically, although I may not announce when I do so. (This is not in the syllabus: the whole point of the mind map is that I want students to start to intentionally make connections among the different topics..)

Quizzes
We will be having quizzes during the second half of the semester. Each question will be linked to a Learning Goal (and clearly labelled indicating which Goal it is attached to), and will be graded either as Acceptable (if there are no errors of any sort) or Not Acceptable (if an error exists).

You will need to get five problems correct for every Learning Goal to be considered to have successfully learned a particular Learning Goal. There will be a few Learning Goals (This is not in the syllabus: the topics are LU and QR factorization; the only time I am going to mention them at all in class is when I put them on the quiz. I will grade those quizzes, and perhaps answer some specific questions of students who come to office hours. But students really are expected to truly learn these topics on their own if they want an A.) that are not covered in class; these are only for students who are aiming to get an A in the class, and they are meant to be learned on your own.

Calculators will not be allowed on quizzes. You should also not need them.

Submitting a Quiz can never hurt your grade; the worst it can do is to fail to help your grade. Because of this, the course policy is that make-up quizzes will not be given; you should plan on “making up” the quiz by doing well on later quizzes.

Examinations
The quizzes largely take the place of most examinations. We will, however, have a final exam. There will be two components: We will have an in-class final exam on Thursday, May 15th at 8:00 am. The location is our usual classroom. Also, there will be a take-home portion of the final exam will be assigned in the last week of classes to be handed in at the final exam.

For students who wish to get an A for the semester, there will be a brief oral examination. You will receive the topic prior to the oral examination. This oral examination can only be done once you have at least 4 correct answers for each of the quiz Learning Goals (so this does not need to be done during Finals Week).

Project
You are encouraged, but not required to do a project for this course. These projects will be mini-research projects. Your job is to find a problem (I will provide some possible problems), try to solve the problem, create a poster for it, and be prepared to answer questions about the topic and poster. Toward the end of the semester, we will have a poster presentation session for the class. The poster presentation will likely occur on Scholarship and Creativity Day.

Department Colloquia

Part of being a mathematician is to listen to mathematics. Because of this, you will be expected to attend some number of the Mathematics Colloquium, which occurs most every other Thursday at 2:40 pm (if you have a scheduling conflict, please let me know).

Grading

Here is how your semester grade will be determined:

To get a C for the semester, you must:

  1. You successfully answered at least one Query
  2. You presented (perhaps unsuccessfully) at least a few times
  3. You received credit on Daily Homework on all but at most three attempts
  4. You have grades of Acceptable on all but at most two Portfolio Homework problems
  5. You were successful on all of the Quiz Learning Goals in the Conceptual Learning Goal section
  6. You maintained a mostly complete and mostly up-to-date mind map for the entire semester
  7. You got at least a CD on the final exam.

      To get a B for the semester, you must:

      1. You successfully answered at least two Queries
      2. You many successful presentations
      3. You received credit on Daily Homework on all but at most two attempts
      4. You have grades of Acceptable on all Portfolio Homework problems
      5. You were successful on all of the Quiz Learning Goals in the Conceptual Learning Goal and Computation Learning Goal sections
      6. You maintained a complete and up-to-date mind map for the entire semester
      7. You attend at least 1 Mathematics Colloquium this semester
      8. You got at least a BC on the final exam.

      To get a A for the semester, you must:

      1. You successfully answered at least two Queries
      2. You many successful presentations of difficult problems
      3. You received credit on Daily Homework on all but at most two attempts
      4. You have grades of Acceptable on all Portfolio Homework problems
      5. You were successful on all of the Quiz Learning Goals
      6. You maintained a complete and up-to-date mind map for the entire semester
      7. You successfully complete an oral examination
      8. You successfully complete a project
      9. You attend at least 2 Mathematics Colloquia this semester
      10. You got at least a $AB$ on the final exam.

      I will also make a judgment call about the grades of AB, BC, D, and F.

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7 Responses to “Linear Algebra Grading Plan”

  1. Joss Ives Says:

    How long do you think a typical student will spend on daily+portfolio homework each week?

    • bretbenesh Says:

      Hi Joss,

      Here is what I think an honest amount is, with what I think they _should_ be doing in parentheses::

      Daily Homework: 1.5 hours (3 hours) Portfolio Homework: 0.5 hours (3 hours)

      I need to have a talk with them about Portfolio Homework. Some people are putting in the reps; other people haven’t started. Bret

      On Sat, Mar 1, 2014 at 4:48 PM, Solvable by Radicals wrote:

      >

  2. jdydak Says:

    From your class structure post “This means that we need to average 16 problems per presentation day.” I am not sure how to interpret that. 3 minutes per problem on average?

    • bretbenesh Says:

      Hi,

      Sorry about not being clear. They students need to think about 16 problems per presentation day, although they only present 6 in class (which leads to a much more reasonable 8 or 9 minutes per presentation).

      So, of the 16, 6 are presented (6 of 16 are accounted for); the students watch solutions to another 6 problems on YouTube (12 of the 16 are accounted for); and roughly 4 problems are not discussed at all (16 of the 16 are accounted for).

      The 4 problems that are not discussed at all tend to be the easiest problems—usually computation problems that are similar to ones I already did in a video. Students are allowed to request a video on any of these if they are confused.

      Does this help clarify? We only discuss a small, carefully chosen subset (roughly 6 of 16) of the problems in class.
      Bret

  3. jdydak Says:

    Yes, thank you!

  4. Kate Owens (@katemath) Says:

    Hi Bret!

    I am envious that you are teaching Linear Algebra. That is one of my favorite courses! I noticed that you have a presentation requirement both in LinAlg and in your Problem Solving class. I have thought about, but not implemented, such a thing in my own courses. I can see a lot of reasons why this is a good thing to do. OTOH, I also remember dropping several courses as an undergrad exactly because of such a requirement — I was extremely shy and did not want to get up in front of people ever! While I’d agree this was probably ridiculous, especially given my current line of work, it does leave me with a good deal of empathy for students who would be uncomfortable in such a situation. Do you have any of those kinds of students? Do you have any alternate assignments for them? Or do you just encourage and coach them into getting over their fears?

  5. bretbenesh Says:

    Hi Kate!

    I am definitely loving linear algebra. This is my third time teaching it here, fourth overall.

    I also would have hated a course built on course presentations. Not because I was shy, but rather because I was just kind of a punk sometimes.

    Here is the funny thing: there is a good chance that the only reason I am teaching linear algebra this semester is because students didn’t want to present. I was originally slated to teach abstract algebra, but very few students signed up for my section (the other was full). Rumor has it that they did not like that I am a presentation-y teacher (there were issues aside from presentations, but the rumor was that my workload requirement was thought to be higher than the other instructor’s).

    The only issue I have come across are students who cannot present due to various medical issues. When this is the case, I always offer to make accommodations. My preferred accommodation is to present to just me in the office, although I have sometimes allowed for students to submit written work instead.

    It hasn’t come up, but—aside from a medical issue—I don’t think that I would grant many other exceptions. For one, I think that it is a valuable skills for anyone to be reasonably comfortable talking about technical ideas in front of an audience. I can sell this pretty easily at a liberal arts school. My other reason—which I usually explciitly tell the students—is that I want to teach the students to think critically about what is presented; I find that students do not do this when I lecture, but are better at doubting the results if another student does it.

    That said, I am not in love with the way I do presentations yet. I need to improve. If you (or anyone else) has any great ideas, let me know.
    Bret

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