Student #1’s work according to the following category:
Reasoning & Proof
Overall Achievement Level
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 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.
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 of an approach is evident through a methodical, organize, coherent, sequenced and labeled response. Communication of an 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 two formal math terms or symbolic notations is beyond grade level.