Here is a question from the June 2014 New York State Algebra I Common Core Regents Exam as it was included in its page of annotated items, together with one of its sample responses.

I will claim that this answer is worth more than 2 credits.

This question was testing the knowledge that in any function, no domain element (first coordinate) maye be paired with more than one range element (2nd coordinate).

The student here demonstrated that (s)he knew this, and demonstrated it by visually connecting each domain element with its correct range element. I recognize that the explanation was not given in sentence form, but the justification is there nonetheless. This answer should be worth full credit.

Here is a second sample response to the same question, followed by its sample score.

In this second sample response, the student earned more credit, apparently due to the fact that (s)he used a complete sentence to demonstrate that (s)he did not know the fact that was being tested.

The alleged rationale for this question is given here

This question asks the student to determine whether a function could be presented by four given ordered pairs given the domain and range of the function. “Domain” refers to the set of input values, while “range” refers to the set of corresponding output values. Additionally, the student must determine whether exactly one output is assigned to each input. As indicated in the rubric, a correct response will state “yes”, with a correct justification given supporting the student’s reasoning. The justification can be presented in either written form or mathematical form which could include creating a graph of the function. The determining factor in demonstrating a thorough understanding is using mathematically sound justifications for the response.

This is quoted directly from the annotated file as referred to above. All these can be found here.

This absolutely befuddles me. New York State is apparently taking the stance that incorrect work with verbal support is better than correct work. I find it even more amazing that their score for the second response above presupposes that the student knew the definition but misapplied it. On what basis can they make that claim? There is no information within the student's response that supports that claim. It is merely giving the student the proverbial "benefit of doubt". I guess we better not give that benefit to someone who knows what they are doing!

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