I: Conceptual Understanding

Conceptual Understanding includes the ability to interpret the problem and select appropriate information to apply a strategy for solution. Evidence is communicated through making connections between the problem situation, relevant information, appropriate physical and mathematical concepts, and logical/reasonable responses.

5. (grade = A) Full Conceptual Understanding:

- The student uses all relevant information to solve the problem.
- The student uses all relevant physical concepts

- The student's answer is consistent with the question/problem.
- The student is able to translate the problem into appropriate mathematical language.

3 (grade= B-) Partial Conceptual Understanding:

- The student extracts the "essence" of the problem, but is unable to use this information to solve the problem.
- The student is only partially able to make connections between/among the concepts.
- The student's solution is not fully related to the question.
- The student understands one portion of the task, but not the complete task.

1 (Grade = D )Lack of Conceptual Understanding:

- The student's solution is inconsistent or unrelated to the question.
- The student translates the problem into inappropriate mathematical concepts.
- The student uses incorrect procedures without understanding the concepts related to the task.

Procedural Knowledge deals with the student's ability to demonstrate appropriate use of concepts. Evidence includes the verifying and justifying of a procedure using concrete models, or the modifying of procedures to deal with factors inherent in the problem.

5 (A) Full Use of Appropriate Procedures:

- The student uses principles efficiently while justifying the solution.
- The student uses appropriate mathematical terms and strategies.
- The student solves and verifies the problem.
- The student uses physical and mathematical principles and language precisely.

3 (B-) Partial Use of Appropriate Procedures:

- The student is not precise in using physical and mathematical terms, principles, or procedures.
- The student is unable to carry out a procedure completely.
- The process the student uses to verify the solution is incorrect.

1 Lacks Use of Appropriate Procedures

- The student uses unsuitable methods or simple manipulation of formulae and/or data in his/her attempted solution.
- The student fails to eliminate unsuitable methods or solutions.
- The student misuses principles or translates the problem into inappropriate procedures.
- The student fails to verify the solution.

Problem Solving requires the use of many skills, often in certain combinations, before the problem is solved. Students demonstrate problem solving strategies with clearly focused, good reasoning that leads to a successful resolution of the problem.

5 (A) Evidence of Thorough/Insightful Use of Skills/Strategies:

- The skills and strategies show some evidence of insightful thinking to explore the problem.
- The student's work is clear and focused.
- The skills/strategies are appropriate and demonstrate some insightful thinking.
- The student gives possible extensions or generalizations to the solution or the problem.

- The skills and strategies have some focus, but clarity is limited.
- The student applies a strategy which is only partially useful.
- The student's strategy is not fully executed.
- The student starts the problem appropriately, but changes to an incorrect focus.
- The student recognizes the pattern or relationship, but expands it incorrectly.

- The skills and strategies lack a central focus and the details are sketchy or not present.
- The procedures are not recorded (i.e., only the mathematical steps in the solution are present).
- Strategies are random.
- The student does not fully explore the problem, looking for concepts, patterns or relationships.
- The student fails to see alternative solutions that the problem requires.

In assessing the student's ability to communicate, particular attention should be paid to both the meanings he/she attaches to the concepts and procedures and also to his/her fluency in explaining, understanding, and evaluating the ideas expressed.

5 (A) Clear, Complete Communication:

- The student gives a complete response with clear, coherent, unambiguous, and elegant explanations.
- The student communicates his/her thinking effectively to the audience-
- The details fit and make sense.
- One step flows to the next and shows organization.
- The student presents strong supporting arguments.

3 (B-) Partial or Incomplete Communication:

- The student's explanation is unclear, inconsistent or not complete.
- The student uses terminology incorrectly or inconsistently.
- The student's visual aids (graphs, tables, diagrams, etc.) are inappropriate or not directly related.
- The student's explanation centers on the mechanics of his/her solution, not on his/her thinking.

- The student's explanation is not understandable or not present.
- The student either does not use or misuses appropriate physical and/or mathematical terminology .
- The student does not use essential visual aids to enhance or clarify the explanation.
- The student's explanation lacks focus.

Source: Oregon Department of Education Modified by S.M. Lea