MTH 325 -- Specifications for Student Work (Winter 2016)

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:

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:

  1. 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.
  2. 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.")
  3. 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.
  4. 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:

  1. All solutions show evidence of a good-faith effort to be right.
  2. All solutions are free of significant error.
  3. Minor error is either not present, or at worst occurs in small amounts.
  4. Each solution consists of a correct and clearly-indicated answer and a complete, clearly-communicated, and correct solution.
  5. The submission of work satisfies the formatting rules that are listed separately below.

Additionally, here are specifications for what constitutes a "clearly communicated" solution:

Here are the formatting rules that were mentioned above:

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:

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.