# Specifications for Student Work in MTH 325

**This document contains all the details for what constitutes "successful" or "acceptable" work on each type of assignment in the course**. Use the table of contents in the upper-left to navigate to specific assignment types, and use this document to check your work for correctness before submitting it.

## Daily Prep

Daily Prep assignments are graded on the basis of **completeness and good-faith effort**. Correctness is not taken into account; but a good-faith effort to *try* to be correct must be evident.

| The work receives a mark of... | If it meets these criteria: |
| :----: | ---- |
| **Completed** | <ul><li>The assignment is submitted by the deadline, *and*</li><li>Every item on the response form has a response, *and*</li><li>There is at least one substantive question, comment, or comment reply on Perusall for either the text or a video</li></ul>
| **Not Completed** | One or more of the standards is not met: The assignment is late; or there is an item on the response form that is blank (even if by accident); or there is no substantive engagement with the reading and viewing on Perusall. |

## Content Skill Standards

There are three different ways to demonstrate skill on a Content Skill Standard: By working a problem on a quiz, by working a problem in an oral quiz in drop-in hours, and by working a problem recorded to a video.

Individual demonstrations of skill on a Content Skill Standard, regardless of the method, either meet the standards for success given below, or they do not. **The result of an individual attempt is not recorded on Blackboard; instead that information is given in the feedback on the item** (which is part of the PDF that you will submit on Blackboard, so it's "recorded" in that sense).

Demonstrations of skill on **written and oral quizzes** are graded on the basis of *completeness and correctness*.

| The demonstration is... | If it meets these criteria: |
| :----: | ---- |
| **Successful** | <ul><li>Each part of the problem has a good-faith attempt at a response, *and*</li><li>The response contains **no more than two simple errors**, and **no non-simple errors**, *and*</li><li>Unless specifically stated otherwise, the response must show all the significant steps used to arrive at the answers.</li></ul>
| **Not successful** | Not all the standards for "Successful" are met. |

:::info
**What is a "simple error"?** For MTH 325, a "simple" error is defined to be an error in logic, computation, or communication that *does not pertain to the learning target* and *does not oversimplify the problem*.

For example, suppose you are finding a minimum spanning tree for a weighted graph (Content Skill Standard G.7) and one of the edge weights is "12" but you accidentally copy it down as "2" in your work. As long as you go ahead and find the minimum spanning tree correctly with this incorrect information, the copy error is a "simple" error because it doesn't show evidence of any issues in your understanding of the standard, and replacing the 12 with a 2 doesn't make the problem any easier. On the other hand, if you "miscopied" *every* edge as having weight 2, then this is not "simple" because it makes the problem trivial -- it is no longer a legitimate source of information about your ability with the standard.

**Remember that only two simple errors are allowed on any Content Skill Standard problem.** Having three or more simple errors indicates that a retry is in order to apply more careful attention to the attempt. So **always double-check your work when possible**, and **proofread your solutions before submitting them**.
:::

**Video solutions** are graded similarly to written and oral quizzes, but there is an additional criterion for *technical quality* of the video:

| The demonstration is... | If it meets these criteria: |
| :----: | ---- |
| **Successful** | <ul><li>All the standards for "Successful" shown above are met, *and*</li><li>The video is less than 5 minutes in length, *and*</li><li>Your face, voice, and handwriting are simultaneously in the frame at all times, *and*</li><li>The handwriting is legible and both the video and audio are clear.</li></ul>
| **Not Successful** | Not all the standards for "Successful" are met. |

## Proof and Application problems

Proof and Application problems both involve writing and communication in addition to mathematical (and sometimes programming) work. A right answer is not enough on these; **the primary criteria for evaluation are the correctness of your *solution* and whether you communicate your ideas clearly and thoroughly**.

:::info
Note: **The audience for all Proof and Application problem solutions is your classmates** --- people who have the background mathematical knowledge that you have, but who have no familiarity with the problem you are working on. **Prof. Talbert is not the audience, and neither are you** --- so don't assume that the person reading the solution has a Ph.D. or has been studying the problem for a while.
:::

Proof and Application problems are marked either *Successful* or *Revise*. **To be marked *Successful*, a solution to a problem must fulfill all of the criteria below.** Notice these are formatted as a checklist; you should use this checklist before submitting your work to make sure it meets the specifications. **If you can check off each of these after an honest self-evaluation, you will save a lot of time and effort in revisions later.**

- [ ] All parts of the assignment have a good-faith effort at a complete and correct solution.
- [ ] The writing obeys fundamental rules of English grammar and syntax, including but not limited to: Correct spelling, use of complete sentences, agreement of subjects and verbs, and the correct use of punctuation.
- [ ] There are no errors in the mathematics in the solution. **See below for further details on errors.**
- [ ] The solution combines mathematics and writing to communicate effectively, and it is not simply one of these (math without words or vice versa).
- [ ] The solution presents its final results clearly and gives a thorough, complete, correct explanation that shows where the results came from and why they are correct.
- [ ] The writeup is typewritten and not hand-written.
- [ ] The writeup is formatted professionally: It uses correct mathematical notation, done using an equation editor; a clean and easy-to-read layout; and standard choices for font, page, and paragraph styles.
- [ ] The following additional criteria are in place for *Application problems that involve programming*:
- [ ] All programs are written in Python. No other languages are allowed for the final writeup (although you can prototype your solutions using whatever language you want).
- [ ] No syntax errors are thrown when the Python code is evaluated.
- [ ] All code is documented fully either as text explanations or as comments in the code. **The comments are considered part of the explanation needed for a Successful submission.**
- [ ] Usually, programming problems are evaluated by running them with a large set of test data. Any code you write, needs to produce correct results on all of the test data that are used.

Additional criteria for Successful submissions may be added to individual assignments as needed.

:::info
**Note on errors:** There are four basic kinds of errors that can happen in your mathematical work. These will often be referred to by name in the feedback you receive, so read carefully:

1. *Computational error*. This is when you simply make a mistake in computing something, like adding $5+3$ and getting $9$.
2. *Logical error*. This is when you draw incorrect conclusions from data. For example, if you are told that the statement "All math professors are over 40 years old" is false but conclude that *no* math professors are over 40, that's a logical error. (You can only conclude that *there exists* a math professor who isn't over 40.)
3. *Factual error*. This results from misstating definitions, theorems, or steps of an algorithm. For example, stating that the negation of "If A then B" is "If A, then not B" is a factual error. (It's "A and not B".)
4. *Semantic error*. This happens when you make a statement that is grammatically correct, but the statement itself has no meaning. The statement "[Colorless green ideas sleep furiously](https://www.wikidoc.org/index.php/Colorless_green_ideas_sleep_furiously)"[^1] is an example. So is the statement "The degree of this graph is 5" because there is no such thing as the "degree of a graph". Semantic errors often happen when applying a concept to the wrong kind of object (like using the word "degree" to describe a graph, when that term only applies to vertices in a graph).

Most errors are a combination of these, but make sure to proofread your work every time to rid your submissions of all of these.
:::

[^1]: https://www.wikidoc.org/index.php/Colorless_green_ideas_sleep_furiously

Please note that **when you submit work on a Proof or Application problem, you're expected to give a good-faith effort at a complete and correct solution.** If there are issues, you can always revise and resubmit. But **a submission will be marked "Revise" and returned to you without further comment if any of the following are found:**

- There are significant portions of the assignment not submitted, or the submissions are not good-faith efforts at a correct and complete solution;
- There are pervasive errors in basic English.
- In programming problems, if any of the code throws a syntax error. (You're expected to debug syntax errors prior to submission; just run the code and squash any bugs you find.)