Pre-Calculus

Math 115

A-level work

Excellent overall, no major weaknesses

1. A-level work demonstrates real achievement in grasping what mathematical thinking is, along with the clear development of the range of skills and abilities contained in the course learning objectives.

2. The work at the end of the course is, on the whole, clear precise, and well-reasoned, though there may be occasional lapses into weak reasoning.

3. Terms and notation are used effectively and accurately.

4. The work demonstrates a mind beginning to take charge of its own ideas, assumptions, inferences, and intellectual processes.

5. The A-level student usually analyzes issues clearly and precisely, usually formulates information clearly, usually distinguishes the relevant from the irrelevant, usually recognizes key questionable assumptions, usually clarifies key concepts effectively, typically uses language in keeping with educated usage, and shows a tendency to reason carefully from clearly stated premises.

6. A-level work displays excellent reasoning and problem-solving skills.

7. The A student's work is consistently at a high level of intellectual excellence.

B-level work

Demonstrates more strengths than weaknesses and is more consistent in high level performance than C-level work. It nevertheless has some distinctive weaknesses, though no major ones.

1. B-level work represents demonstrable achieving in grasping what mathematical thinking is, along with the clear demonstration of the range of skills and abilities contained in the course learning objectives.
2. The work at the end of the course is on the whole clear, precise, and well-reasoned, though with occasional lapses into weak reasoning.
3. Terms and notation are used effectively and accurately.
4. The work demonstrates a mind beginning to take charge of its own ideas, assumptions, inferences, and intellectual processes.
5. The B-level student often analyzes issues clearly and precisely, often formulates information clearly, usually distinguishes the relevant from the irrelevant, usually recognizes key questionable assumptions, usually clarifies key concepts effectively, typically uses language in keeping with educated usage, and shows a tendency to reason carefully from clearly stated premises.
6. B-level work displays good reasoning and problem-solving skills.

C-level work

Demonstrates more than a minimal level of skill, but it is also highly inconsistent with as many weaknesses as strengths.

1. C-level work illustrates some, but inconsistent, achievement in grasping what mathematical thinking is, along with an inconsistent demonstration of the range of skills and abilities contained in the course learning objectives.
2. The work at the end of the course shows some emerging mathematical thinking skills, but also pronounced weaknesses as well. Though some assignments are reasonably well done, others are poorly done; or at best are mediocre. There are more than occasional lapses into weak reasoning.
3. Terms and notation are sometimes used effectively, sometimes used inappropriately or ineffectively.
4. Only on occasion does C-level work display a mind taking charge of its own ideas, assumptions, inferences, and intellectual processes. Only occasionally does C-level work display display intellectual discipline and clarity.
5. The C-level student only occasionally analyzes issues clearly and precisely, formulates information clearly, distinguishes the relevant from the irrelevant, recognizes key questionable assumptions, clarifies key concepts, uses language in keeping with educated usage, reasons carefully from clearly stated premises, or recognizes important implications and consequences.
6. Sometimes the C-level student seems to be simply going through the motions of the assignment, carrying out the form without getting into the spirit of it.
7. On the whole, C-level work shows only modest and inconsistent reasoning and problem-solving skills, and sometimes displays weak reasoning and problem-solving skills.

D-level work

Demonstrates only a minimal level of understanding and skill.

1. D-level work shows only a minimal level of understanding of mathematical thinking, along with the development of some, but very little, of the range of skills and abilities listed in the course learning objectives.
2. The work at the end of the course on the whole shows only occasional mathematical thinking skills. Frequently, the work shows a pattern of illogical thinking and poor reasoning. Most assignments are poorly done, and there is little evidence that the student is reasoning through the assignment in a mathematical manner.
3. D-level work rarely shows any effort to take charge of ideas, assumptions, inferences, and intellectual processes.
4. In general, D-level work lacks discipline and clarity. The student rarely analyzes issues clearly and precisely, almost never formulates information clearly, rarely distinguishes the relevant from the irrelevant, almost never clarifies key concepts effectively, frequently fails to use language in keeping with educated usage, almost never reasons carefully from clearly stated premises, or recognizes important implications and consequences.
5. D-level work does not show good mathematical reasoning and problem-solving skills, and frequently displays poor reasoning and problem-solving skills.

F-level work

Demonstrates a consistent pattern of non-mathematical thinking

1. The student has not displayed any significant understanding of mathematical thinking, and has not demonstrated mastery of any of the skills and abilities listed in the course learning objectives.
2. The work at the end of the course is as vague, imprecise, and unreasoned as it was at the beginning of the course.
3. Little evidence that the student is genuinely engaged in the task of taking charge of his or her thinking; many assignments have been done without spending any significant effort on thinking his or her way through them, while others have not been done at all.
4. The student does not analyze issues clearly, does not formulate information clearly,  does not appear to distinguish between the relevant and the irrelevant, does not reason carefully from carefully stated premises, or trace implications and consequences.
5. The students work does not display discernable mathematical reasoning and problem-solving skills.

(adapted from "A miniature guide for those who teach on How to Improve Student Learning" by Dr. Richard Paul and Dr. Linda Elder)