New York State asked high school students to find the inverse function of a non-invertible function. 32. If $f(x) = x^2 - 6$ find $f^{-1}(x)$. Youch. Teachers across the state yelled and screamed, but most importantly called the testing hotline (I never got through, all busy). What was the response?

They backed down. But tried to weasel out and claim they had not made an error. Here is the language in their clarification memo:

“Because of variations in the use of $f^{-1}$ notation throughout New York State, a revised rubric for Question 32 has been provided. Please rescore all students’ responses to Question 32….” And then they allow $\pm\sqrt{x+6}$ or $\sqrt{x+6}$ or $-\sqrt{x+6}$ or “An explanation stating that the original function is not one-to-one and therefore there is no inverse”

Surrender? No. They ascribe their error to “variations in notation.” Actually, even if they were right, they have some explaining. How could the test-makers not be aware of “variations in notation”? Also, notice how there is an asymmetric justification burden on a kid claiming (correctly) that the inverse does not exist.

Before we got that memo, what response did they give teachers?

Tuesday late afternoon (report is by a math teacher from the Association of NY State Mathematics Teachers listserve): I called the state today about question #32.  I told the woman that by definition, for a function to be invertible it must be 1-1.  Her response was that every function has an inverse, it just that every inverse is not necessarily a function.  She said that the inverse could just be a relation.  I told her that she was wrong and then quoted her a definition that says that a function is invertible if and only if it for every input there is exactly one corresponding output value.  I then said that it was only invertible only if we restrict the domain to all value greater than or equal to zero, or all values less than or equal to zero.  It the domain is restricted in this way, the student shouldn’t write positive or negative.  She said that they can receive full credit if they only stated the positive solution, given that they explained that they restricted the domain to make it 1-1.  I asked her why did I have to expect so much from the kids when a bunch of adults who made the exam, didn’t make that distinction?  She told me that i wasn’t going to win the argument.  This error  is more apparent given that the question uses function notation.

Wednesday morning (report from another teacher on the list): I just got off the phone with a person from State Ed (who refused to give his name).  … After much discussion, I pretty much got him to agree that the inverse should be a function.  When I insisted that the answer should be correct with +sqrt, – sqrt as well as both, he finally said “use your professional judgement!”  I then said- why don’t they admit the question was flawed and issue a correction statement so we are all grading the question the same way?  His response was we will look into it.

Then Wednesday late morning they started telling teachers that they were working on a memo, which finally came at 1:48 PM.

June 23, 2011 am30 11:29 am 11:29 am

I also called the board of regents about question #16, where they asked which choice was equivelant to the expression given. It was the one where you were supposed to rationalize the denominator and had two equivelant answers (choice 3, rationalized correctly and choice 1, rationalized incorrectly but still equivelant!) I told the woman that it was unfair to the students to have two equivelant choices. If students were unsure of their answers and then saw that the calculator returned the same number for two of the choices, then obviously knock out those two choices because since there can only be once correct answer – or so they thought. I told her that they should disqualify that question.

Well the woman I spoke to agreed with me that it was unfair to put students in that position and told me to write that on the evaluation sheet. When I asked if anything would change, she said probably not :)
I just don’t get it…

June 23, 2011 pm30 3:55 pm 3:55 pm

I think the Regents should go — NYS is just so bad at making these tests. If a student has obviously mastered the material, then the test should be made clear-cut (not easy) but clear-cut and straightforward to get a 97-100 range. Anyone agree? NYS throws not needed information and trick questions that sometimes are even incorrect which I do not think is fair at all — especially for a regents.

This also, takes away time during the regents. This means students had less time to work on other questions and thought long and hard about this incorrect question instead. This regents should be not counted and they should administer one in August for those who want to re-take.

Agree?

June 24, 2011 pm30 7:45 pm 7:45 pm

I most definitely agree. I know some people want the state to do away with regents altogether. However as a teacher, I do find that having a regent at the end of the year focuses the students. I just wish the test was more straight forward and just tested their mathematic abilities.

By the way, does anyone know where I can find stats about the passing rates for these regents? is this information available to the public?

3. June 23, 2011 pm30 4:21 pm 4:21 pm

Even more of a burden is placed on the student because they are likely to assume that there MUST BE an inverse or else they wouldn’t ask the question. Or at the very least end the question with “… or explain why the inverse doesn’t exist.”

June 24, 2011 am30 2:15 am 2:15 am

Question 29 on the Geometry Regents asks them to write the negation of the true statement, “The medians of a triangle are concurrent.” and to give the truth value of the negation.

Many students wrote, “The medians of a triangle are not congruent.” False. Our school called the state and they gave that full credit, 2 points.

If your school did not give full credit for this, I would go back and change the scores.

5. June 24, 2011 am30 10:09 am 10:09 am

I don’t teach in New York, and for that matter, not at all anymore…. and this is just ONE MORE REASON I am so glad I don’t! This is appalling and exactly why way more thought needs to be given to all this merit pay discussion.

However, be thankful that you at least get to see these questions and make such comments. In Georgia, we are not allowed to look at our End of Course Tests, much less discuss them with students! There is certainly no hot-line to call!

Hopefully this gets resolved in the best interest of the students!

June 24, 2011 am30 11:21 am 11:21 am

Does anyone think they will disqualify any of the questions and regrade the regents?
Or change the curve so more students pass?

June 27, 2011 am30 8:05 am 8:05 am

Wow, I am really glad I found this blog. Saturday, I was informed that my child, who is a consistent A- student, failed this exam. We were quite surprised because many of her friends, who are also good students,also failed the exam. I am in agreement with the sentiments here. I truly hope they do something about the exam!

June 28, 2011 pm30 6:55 pm 6:55 pm

My situation is much like Tammy’s. My son’s 4th marking period grade (all I can currently access) was a 97, but he received a 60 on the Regents. How will parents know if NY state makes adjustments or throws out the test? With August regents for Trigonometry not available in our district (Syracuse city), what recourse do students have?

June 29, 2011 pm30 4:21 pm 4:21 pm

A Rush-Henrietta teacher photocopied a regents field test for this algebra 2 trig exam and gave it to a tutor who then used it with her students. The questions on this field test were used on the June 2011 algebra 2 trig regents test. NYSED is aware that this test was compromised and is refusing to invalidate it. At the very least, a new test should be offered in August of 2011

July 6, 2011 am31 8:34 am 8:34 am

What are we to tell our students entering 12th grade who have just failed the alg2/trig regents. By the time they can retake it again, which is June 2012 since the state is not offering it in August or january, these students will already be enrolled in college. By then the regents grade is a mute point although their chances of getting in to certain NY state colleges without advanced regents diplimas will be lowered. So.. do I look a student straight in the face and say “don’t bother.”

July 8, 2011 am31 1:29 am 1:29 am

call the board of regents to complain