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No strategy is chosen, or a strategy is chosen that will not lead to a solution. Little or no evidence of engagement in the task is present.
A partially correct strategy is chosen, or a correct strategy for only solving part of the task is chosen. Evidence of drawing on some relevant previous knowledge is present, showing some relevant engagement in the task.
A correct strategy is chosen based on the mathematical situation in the task. Planning or monitoring of strategy is evident. Evidence of solidifying prior knowledge and applying it to the problem-solving situation is present. Note: The Practitioner must achieve a correct answer.
An efficient strategy is chosen and progress towards a solution is evaluated. Adjustments in strategy, if necessary, are made along the way, and/or alternative strategies are considered. Evidence of analyzing the situation in mathematical terms and extending prior knowledge is present. Note: The Expert must achieve a correct answer.
Reasoning and Proof
Arguments are made with no mathematical basis. No correct reasoning nor justification for reasoning is present.
Arguments are made with some mathematical basis. Some correct reasoning or justification for reasoning is present.
Arguments are constructed with adequate mathematical basis. A systematic approach and/or justification of correct reasoning is present.
Deductive arguments are used to justify decisions and may result in formal proofs. Evidence is used to justify and support decisions made and conclusions reached.
No awareness of audience or purpose is communicated. No formal mathematical terms or symbolic notations are evident.
Some awareness of audience or purpose is communicated. Some communication of an approach is evident through verbal/ written accounts and explanations. An attempt is made to use formal math language. One formal math term or symbolic notation is evident.
A sense of audience or purpose is communicated. Communication of an approach is evident through a methodical, organized, coherent, sequenced and labeled response. Formal math language is used to share and clarify ideas. At least two formal math terms or symbolic notations are evident, in any combination.
A sense of audience and purpose is communicated. Communication at the Practitioner level is achieved, and communication of argument is supported by mathematical properties. Formal math language and symbolic notation is used to consolidate math thinking and to communicate ideas. At least one of the math terms or symbolic notations is beyond grade level.
No connections are made or connections are mathematically or contextually irrelevant.
A mathematical connection is attempted but is partially incorrect or lacks contextual relevance
A mathematical connection is made. Proper contexts are identified that link both the mathematics and the situation in the task. Some examples may include one or more of the following: • clarification of the mathematical or situational context of the task • exploration of mathematical phenomenon in the context of the broader topic in which the task is situated • noting patterns, structures and regularities
Mathematical connections are used to extend the solution to other mathematics or to a deeper understanding of the mathematics in the task. Some examples may include one or more of the following: • testing and accepting or rejecting of a hypothesis or conjecture • explanation of phenomenon • generalizing and extending the solution to other cases
No attempt is made to construct a mathematical representation.
An attempt is made to construct a mathematical representation to record and communicate problem solving but is not accurate.
An appropriate and accurate mathematical representation is constructed and refined to solve problems or portray solutions.
An appropriate mathematical representation(s) is constructed to analyze relationships, extend thinking and clarify or interpret phenomenon.