| Novice |
- There is no solution, or the solution has no relationship to the task.
- Inappropriate concepts are applied and/or procedures are used.
- The solution addresses none of the mathematical components presented in the task.
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- No evidence of a strategy or procedure, or uses a strategy that does not help solve the problem.
- No evidence of mathematical reasoning.
- There were so many errors in mathematical procedures that the problem could not be resolved.
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- There is no explanation of the solution, the explanation cannot be understood or it is unrelated to the problem.
- There is no use or inappropriate use of mathematical representations (e.g. figures, diagrams, graphs, tables, etc.).
- There is no use, or mostly inappropriate use, of mathematical terminology and notation.
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| Apprentice |
- The solution is not complete indicating that parts of the problem are not understood.
- The solution addresses some, but not all of the mathematical components presented in the task.
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- Uses a strategy that is partially useful, leading some way toward a solution, but not to a full solution of the problem.
- Some evidence of mathematical reasoning.
- Could not completely carry out mathematical procedures.
- Some parts may be correct, but a correct answer is not achieved.
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- There is an incomplete explanation, it may not be clearly presented.
- There is some use of appropriate mathematical representation.
- There is some use of mathematical terminology and notation appropriate of the problem.
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| Practitioner |
- The solution shows that the student has a broad understanding of the problem and the major concepts necessary for its solution.
- The solution addresses all of the components presented in the task.
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- Uses a strategy that leads to a solution of the problem.
- Uses effective mathematical reasoning.
- Mathematical procedures used.
- All parts are correct and a correct answer is achieved.
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- There is a clear explanation.
- There is appropriate use of accurate mathematical representation.
- There is effective use of mathematical terminology and notation.
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| Expert |
- The solution shows a deep understanding of the problem including the ability to identify the appropriate mathematical concepts and the information necessary for its solution.
- The solution completely addresses all mathematical components presented in the task.
- The solution puts to use the underlying mathematical concepts upon which the task is designed.
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- Uses a very efficient and sophisticated strategy leading directly to a solution.
- Employs refined and complex reasoning
- Applies procedures accurately to correctly solve the problem and verify the results.
- Verifies solution and/or evaluates the reasonableness of the solution.
- Makes mathematically relevant observations and/or connections.
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- There is a clear, effective explanation detailing how the problem is solved. All of the steps are included so that the reader does not need to infer how and why decisions were made.
- Mathematical representation is actively used as a means of communicating ideas related to the solution of the problem.
- There is precise and appropriate use of mathematical terminology and notation.
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