Specifications for Student Work in MTH 312
About this document
Your work in MTH 312 is graded on the basis of the _professor's evaluation of your work relative to professional standards of acceptability, at a level appropriate for MTH 312. No points are used and no partial credit is awarded. Instead, each item of work you submit is evaluated using a simple rubric (either Pass/No Pass or EMRF, as described in the syllabus) that indicates whether or not it meets the standards for quality for that assignment. This document lays out the explicit details of those standards for each type of assssment. (For more information on the kinds of assessments in MTH 312 and information about how to revise work that does not meet specifications, please review the syllabus.)
Specifications for Course Management Assignments
Course Management assignments is a category that includes Course Awareness Quizzes, Preview Activities, and other assignments that may be given on a one-time basis. All of these are graded either Pass or No Pass. The criteria for earning Pass marks for each item are given below:
|Item||Criteria for Passing|
|Course Awareness Quiz||Attain a 100% score on the quiz (given three attempts and free access to collaborators and materials).|
|Preview Activity||Supply each question on the assignment with a response that shows a good-faith effort to be right, and submit the submission form no later than 1 hour before class.|
|Other||Specifications will be given with the assignment.|
Note that Preview Activities are only graded on completeness, effort, and timeliness. Mathematical correctness is optional.
The following are sufficient reasons to earn a No Pass on Preview Activities:
- The work is late.
- There is at least one item that is left blank.
- There is at least one item in which good-faith effort to be right is not shown. For example, responses of "I don't know", "I didn't understand the question", or "I need help" will result in a No Pass. If you have questions about an item, you are free to ask these prior to submission using office hours or the discussion board.
- There is at least one response that is clearly just a guess. For example, ending a response with a question mark (e.g. "Euclidean algorithm?") is a guess.
Errors and Grades
Four kinds of error and how they affect a grade
Assessments and Problem Sets, unlike course management tasks, are graded partially on mathematical correctness. Hence before we give the specifications, we need to be aware of the ways that work on these items can fail to be correct. There are generally speaking four kinds of error that can occur when doing significant work in mathematics:
- Computational error. This occurs when a mathematical computation (calculus, algebra, arithmetic, etc.) is incorrectly carried out, either by hand or on a computer. For example: Solving the equaton 3x = 9 to get x = 2 is a computational error.
- Logical error. A logical error occurs when a conclusion is drawn erroneously from a set of information. For example: Given the equation x^2 = 9 and concluding that x must be positive is a logical error (because x could equal 3, or it could equal -3). In algebra, if we factor x^2 - 25 into (x-5)(x+5) and then conclude that the graph of y = x^2 - 25 crosses the y-axis at y = 5 and y = -5, this is computationally correct (because the factorization is right) but logically incorrect (the conclusion drawn is wrong). Also included here are incorrect logical constructions, for example using an incorrect quantifier when setting up the induction hypothesis in an induction proof (e.g., "Now assume that for all positive integers k, the statement is true.")
- Syntax error. Syntax errors are failures in the grammar of a language. These can occur in two ways. First, they can occur as errors in English grammar, when the rules for language usage are not followed correctly, especially if the grammar and mechanics of a statement are so badly misused that it becomes difficult to parse what is being said. Second, syntax errors can occur as errors in the usage of mathematical notation, especially if the misuse of notation obscures the solution or introduces new errors. In mathematical notation, syntax errors can be caused by switching variables mid-solution (for example, solving 3t = 9 to get x = 3 is a syntax error); by misusing function notation, mismatching parentheses, and a host of other possibilities. And of course, syntax errors extend to computer code, for example if you use incorrect syntax for Python lists which causes incorrect output or an exception to be thrown.
- Semantic error. Semantic errors occur when the rules of the grammar of a language are followed but the resulting statements are nonsensical or meaningless. For example, the statement "Colorless green ideas sleep furiously" is correct English syntax but has no meaning, therefore it represents a semantic error. In mathematics, a similarly semantically erroneous statement would be "The following graph can be factored". This is a semantic error because we don't "factor" graphs; we factor polynomials and integers, but to say we are "factoring a graph" is meaningless. Another example would be "the graph is Eulerian because its degree is odd" because there is no such thing as the "degree of a graph". Semantic errors can also occur with symbols; for example, writing |x| = 6 (with absolute value signs on the left side) and then "solving" to get | | = 6/x is a semantic error because absolute value signs without something inside them are meaningless. (This is also partially a syntax error.)
All of these errors are equally bad, and each kind corrupts the solution of a problem to the same degree. However there are some errors that are bigger in magnitude than others (for example, a serious syntax error versus a minor syntax error).
The general rule is: Grades of E or M are awarded only if there are no signficant errors of any of the above kinds, and only if the number of minor errors of the above kinds is minimal. That is, a small number of minor errors can be tolerated as long as they do not cast doubt on your understanding of the concept, or cause the work to fail to meet the expectations of the assignment, or cause the work to be incomplete or poorly-communicated. However, large numbers of minor errors, or a single instance of a major error, will result in the work being marked "R" or lower.
Also, as stated in the rubric, a grade of "E" is awarded only if there are only a small number of trivial errors, that is, errors that don't really affect the solution (things like a few misspelled words, a minor sign error in a calculation that is later corrected, etc.)
As a corollary please note that it is possible to earn an E or M grade on an assignment even if you have a few errors in it. That is, "Passing" does not mean "perfect". A Passing grade (E or M) means that your work has demonstrated understanding of the concept, has met the expectations for the assignment, and it is complete and well-communicated.
The Standard Audience
For these items, we will often refer to the standard audience for MTH 312, which is defined to be:
The standard audience in MTH 312 consists of classmates in MTH 312 who are familiar with the mathematical ideas discussed in the class and have the appropriate background knowledge for the class, but who are unfamiliar with the particular problem whose solution you are presenting and therefore need to be persuaded that your solution is correct and your conclusions believable.
Note particularly that a solution to a problem is more than just a collection of computations that have a clearly-indicated answer. Solutions must be persusasive arguments that your answer is correct. More details on this follow.
Specifications for Assessments
Since each assessment will address a single specific learning target, the precise specifications for E, M, R, or F will be different. More information about specifications for the individual learning targets will be given in class. However the general rule above regarding the presence and severity of error will always still apply on each assessment.
Specifications for Problem Sets
Problem Sets ask for more than just clear understanding of basic concepts -- they ask you to apply basic knowledge to new situations, to solve problems, and to communicate your thoughts to the Standard Audience (see above).
A passing grade (E or M) will be given to work on Problem Sets if:
- All solutions show evidence of a good-faith effort to be right.
- All solutions are free of significant error.
- Minor error is either not present, or at worst occurs in small amounts.
- Each solution consists of a correct and clearly-indicated answer and a complete, clearly-communicated, and correct solution.
- The submission of work satisfies the formatting rules that are listed separately below.
- The solution must use clear and correct English. In particular, the following are considered syntax errors: misspelled words, incomplete sentences, subject-verb disagreements, and failure to use correct capitalization and punctuation rules. Excessive instances of these will downgrade the work.
- You are using Problem Sets to provide evidence you've mastered course content. Answers to problems by themselves, without solutions and explanations, are not sufficient evidence. So you need to make sure that above all, you are giving correct answers that are supported by complete, intelligible solutions.
- The solution must consist of more than just mathematical computations unless the context of the problem clearly indicates that computation alone is sufficient. For example, including a summary of what you are about to do in a solution at the very beginning of the solution is a simple and effective way of orienting and guiding the reader through a sequence of computations; providing only the computations is not persuasive because the reader has to do too much work.
- The solution should not omit any parts that would not be obvious to the standard audience that contribute to the solution. What counts as "obvious" is relative to the standard audience; see the definition of this term above. When in doubt, ask the professor.
- The solution should not include any information that is not relevant to the solution.
- You are expected to provide a complete solution to each problem, even if it has points where you are not totally certain you've done things right. It's entirely possible you can earn a "Passing" grade (that is, an E or M) on a Problem Set if you have complete, well-written solutions that have minor errors that lead to incorrect results; but if you submit correct results and nothing else then your grade will be R or F.
- Submissions that make no serious attempt on one or more of the problems will receive an automatic F, and no feedback will be given on any of the other work. That is, leaving off a problem or only giving a superficial effort on it will result in your entire submission being turned back to you without comment.
Here are the formatting rules that were mentioned above:
- You're expected to work out your Problem Set solutions separately on paper as a rough draft, and then you are to type up your final drafts using a computer. Typically just an ordinary word processor will suffice. If you need to use mathematical notation while you are writing up your solutions, then there are several options. MS Word and Google Docs both have equation editors built in that can handle simple notation (which is all you should need). If you want to try a more advanced solution, you can write up your solutions in $\LaTeX$, for example using the website Overleaf. You can be as fancy or as simple as you like, but the result needs to look good.
- The submission should be written in such a way that is professional and visually appealing. Things that interfere with this quality standard include bad font choices (in size or type), mistakes in mathematical notation, and poor or illogically laid out sections. One way to make your document look better without much work is to use headers and sections to break up the solutions into logical parts.
- The first part of your solution should be a header area in which the designation of the Problem Set is given (e.g., "Problem Set 3") and then your name.
- Each problem solution must be clearly indicated -- again, using a header or section label is a good idea.
- Once you have completed your work, it must be saved as a PDF document, using the name
LastNameis your last name and
Xis replaced by the Problem Set number. For example Chucky Chuckerson's work on Problem Set 6 would be titled
- To submit your work, simply save the PDF to your shared Dropbox folder. Since I have access to that folder, it is submitted just by putting it there. Do not submit by email and do not convert to another file format. The most sure-fire way to make sure your work is submitted on time is simply to create the file in your Dropbox folder and leave it there. Every time you save it, it will be backed up and synced both to your Dropbox account and to mine.
Once you save the work to your Dropbox folder, I will go in to your folder, grade it, and then leave comments in your Dropbox folder. The grade itself will be given on Blackboard.
Please note that later in the course, we may make some structural changes to your Dropbox folder if it becomes hard to find stuff in it.
Specifications for Blogging Assignments
You'll be doing some short writing assignments using the website Medium to respond to writing prompts and give your opinions. These will not usually involve mathematics but are rather intended to get you to share your thoughts on issues from your reading.
Here are the specifications for passing work on a blogging assignment:
- Your response should be between 200 and 300 words. Here are 300 words of dummy text to give you an idea of how long this is. Note that the word count will not be checked exactly, and if you want to go longer than 300 words you are most welcome (although, keep in mind blog posts are supposed to be brief and to the point). But responses that are clearly under 200 words will usually be marked "R" and possibly "F" depending on the rest of the post.
- Your response should contain substantive thoughts that are supported by sound arguments. Do not just spout off opinions without justification. Back up your thoughts with evidence and reason.
- Your response needs to be on-topic. Do not focus your response on items other than what you were asked to think about.
- Your response must be free of significant syntax and semantic errors as described in a previous section. Please make sure to proofread your work, or have someone else proofread it, before posting to check for errors.
Responses that follow these specifications will usually receive an "E" or "M" grade. Work that shows exceptional insights, truly excellent writing, and includes visual elements such as pictures or diagrams to help make its point will be considered for an "E" grade.
To get inspiration, you're encouraged to read the many excellent public posts on Medium. There you can get ideas for layout, including photos, and how to make your points well. (You may also find some truly bad stuff that teaches you what to avoid!) s