Specifications for Student Work in MTH 325
About this document
Your work in MTH 325 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 325. 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 325 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 Daily Homework. 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.|
|Daily Homework||Have your work available at the beginning of class, and supply each item with a response that shows a good-faith effort to be right.|
Note that Preview Activities and Daily Homework 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 and Daily Homework:
- 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. "Eulerian graphs?") is a guess.
- For Daily Homework, a No Pass is given if only answers are present without sufficient evidence of work.
Errors and Grades
Four kinds of error and how they affect a grade
Assessments and Miniprojects, 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 325, which is defined to be:
The standard audience in MTH 325 consists of classmates in MTH 325 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. Please check the card for each learning target on the Lessons and Learning Targets board (http://bit.ly/1n2R7VR or http://bit.ly/lessonslearningtargets, or go to Blackboard then "Lessons and Learning Targets" in the sidebar) for details.
However the general rule above regarding the presence and severity of error will always still apply on each assessment.
Specifications for Miniprojects
Miniprojects 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 miniprojects 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.
Additionally, here are specifications for what constitutes a "clearly communicated" solution:
- 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.
- 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. For example, in mathematical proofs, you should not include examples of how the theorem works; the proof should be persuasive enough to stand on its own without examples to support it.
Here are the formatting rules that were mentioned above:
- Miniproject writeups are to be done as Jupyter notebooks that contain Markdown, LaTeX, and code in appropriate proportions as needed. For example, if you are writing a proof, you will probably not be using code but will use a lot of Markdown and LaTeX. If you are doing a miniproject that involves writing code, then LaTeX probably won't be needed but obviousy code will, as will Markdown that explains what you are doing. Other kinds of miniprojects may contain equal amounts of all three.
- The first part of the Miniproject must be a Markdown cell that has the following:
- A level 1 (H1) header that indicates which miniproject you are doing, followed by
- A level 2 (H2) header that indicates your name and the date of submission.
- The Jupyter notebook should be written in such a way that is professional and visually appealing. Things that interfere with this quality standard include mistakes in Markdown code (for example, forgetting to close off an italicized block), 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 -- for example an H3 header (
###in Markdown) to separate sections with titles.
- When naming the document, use the name
LastNameis your last name and
Xis replaced by the miniproject number. For example Chucky Chuckerson's work on Miniproject 6 would be titled
- Please refer to the assignment itself for exact submission instructions.
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.
Additional specs for computer code
Unless otherwise stated, you are free to use computer code to do anything in a Miniproject. In fact some Miniprojects will require coding. If you write code, then the following additional specifications are in place:
- The code must not throw any exceptions. It is your responsibility to make sure there are no syntax errors in your code, if run inside the Jupyter notebook, before turning it in. Code that is submitted that does give syntax errors will not receive a passing grade (that is, it will get either R or F depending on the rest of the work).
- The code must produce the correct output. Often I will have a test set of inputs that I will use for grading, and the code must produce correct output on at least a large portion of these inputs. Getting correct output on a set of inputs that you provide is necessary but not sufficient for a passing grade. Also, please do not put test cases in your writeup.
Additionally, commenting your code is strongly encouraged since in case of errors, I can better judge whether you are understanding the concept. You can put comments in the code itself using Python commenting, or put all comments in a separate Markdown cell, whichever you prefer.