You have to take a point off. "Root of an equation" is synonymous with "solution of an equation" and is vocabulary that students must learn and that teachers should emphasize.
An equation in one variable has one solution. I agree that it is difficult for students to learn to distinguish between a graph of y = ax^2 + bx + c and a root (or solution) of 0 = ax^2 + bx + c. The former is two-dimensional while the latter is one-dimensional. However, it is an important distinction that they ought to master.
Someone mentioned " Roots of a parabola", but there is no such thing. There is(are) the "root(s) of an equation". Again, what is confusing but must be mastered is that the "root(s) of an equation" are the x-intercepts of the related parabola. In a related example, if the student is asked for an x-intercept of a graph, and if the student gives the coordinates of the x-intercept, a point should be deducted.
The unfair thing is the way the questions have the points allotted. 2-, 3-, and 4-point questions are the problem requiring a deduction of 1/2, 1/3, and 1/4 respectively of the total points that a question is worth when there is only a small error.
Years ago when this type of allotting points on high stakes tests first started, I often wrote about the unfairness to the students. A kid who makes five careless errors, loses five points. When the longer questions were worth 10 pts, and the whole exam was worth 100, it made sense. If the only errors were the five careless mistakes, the student's grade was 95%. Now the 5 pts. are actually more than that because the total number of possible points is less than 100.
The old Regents Rating Guide, which I mentioned in a previous posting to this listserv, distinguished between a careless error (deduct 10% of the value of the question) and a conceptual error (deduct 30% to 50% of the value of the question). I hope my memory is intact on that latter point.
So if a Part II question had a few parts, and one part was worth three points, and since fractional point deductions were not allowed, 10% of 3 and 30% of 3 would both give a -1 deduction.
Even on the AP Calc exam in the free response questions, a student loses a point the first time a careless error is made in one part of the question but not repeatedly in other parts of the same question for subsequent boo-boos. (I haven't been to an AP Calc marking workshop in several years so please correct me if this info is no longer accurate.)
On Jun 15, 2012, at 9:04 AM, Katherine Cook wrote:
> We understand what is technically mathematically correct, but the issue is, is it worth taking 33% of the credit off on this question because of that concept on an Algebra 1 exam? > > From: firstname.lastname@example.org [mailto:email@example.com] On Behalf Of Kathleen Curtis > Sent: Friday, June 15, 2012 8:49 AM > To: firstname.lastname@example.org > Subject: RE: #34 Algebra Regents > > Because there is no y in the equation they are asked to solve, the answers should not be in ordered pairs. > We were grumpy about a similar question a few years ago, but there is no y in the quadratic equation. So mathematically the answer should not be an ordered pair. > SED is consistent on their answer from years past. > > Sincerely, > Kathy C > From: email@example.com [firstname.lastname@example.org] on behalf of Katherine Cook [email@example.com] > Sent: Friday, June 15, 2012 8:30 AM > To: firstname.lastname@example.org > Subject: #34 Algebra Regents > > We are about to call SED 518-474-5900 about the rubric on #34. The rubric says to take one point off if they list the roots as an ordered pair. We disagree. Roots of a parabola are the x-intercepts. Why can?t they be written as an ordered pair? Especially since the question requires students to do the graph. > What are other people?s thoughts on this? > > Thanks, > Katie Cook > Fayetteville-Manlius CSD > Manlius, NY 13104 > (315) 692-1951 > > > This email message and any attachments may contain confidential information. If you are not the intended recipient, you are prohibited from using the information in any way, including but not limited to disclosure of, copying, forwarding or acting in reliance on the contents. If you have received this email by error, please immediately notify me by return email and delete it from your email system. Thank you.