4 Points: COMPLETE RESPONSE
correct numerical answer,
rigorous evidence gathered and presented in a logical order, justifying all steps, demonstrating clarity of thinking, and full understanding of the mathematics,
completed “4 part check,”
formulas, relationship, or theorem stated, AND
clearly labeled diagram/graph is used, when appropriate, to clarify communication
3 Points: SUBSTANTIAL RESPONSE (Demonstrates mastery)
Student made any one of the following errors:
correct numerical answer, but there is a shortcoming in providing mathematically powerful communication
OR
the evidence is all there, but it was not presented in a logical order
OR
the communication is good, but a computation or transcription error was made. The incorrect answer still makes sense in the context of the problem, and is within an order of magnitude of the correct answer (However, note that a missing “check” is a 2 point response).
OR
did not fully simplify an expression or fraction, or provided an inappropriate number of decimal places
OR
a portion of the “four parts” of a check is missing
OR
provided a decimal approximation without providing an exact answer (1.4142, but not root 2). For some problems, this error will be a “Developing Response.”
Note: Many students will get a “3” on review problems from previous chapters.
2 Points: DEVELOPING RESPONSE
some evidence of how the problem could be completed is shown, but reponse gets off-track
OR
the student provides guess-and-check when a more elegant method is available
OR
two of the errors in “Substantial Response” above
Note: It appears that with minor feedback, this student would be able to provide a complete response.
1 Point: MINIMAL RESPONSE
appears to have been exposed to the concept, and an attempt is made at solving the problem using the correct justification, but does not show evidence of being able to carry it through. This student needs reteaching and more practice before mastery.
OR
a correct numerical response is given with minimal communication or justification
OR
“fudged” a check to make an incorrect response appear to be correct