A Second New York Math Teacher: Regents Exam Was “One of the Best” (??)

On June 24, 2015, I posted an email that a New York State algebra teacher wrote to parents regarding the Regents algebra exam. In short, the teacher wrote that the exam “did a serious disservice to your child,” and he/she included several examples of test questions that he/she judged to be problematic.

On July 1, 2015, a reader who identified him-/herself as also being a New York State math teacher wrote a comment to the first teacher’s email on another blog where my post had been reblogged. The second teacher judged the exam to be fine and concluded that the problem was with the first teacher, not the test questions the first teacher highlighted. The second teacher concludes his/her comment with, “In summary, teachers who can’t teach should not be allowed to complain about Common Core.”

I forwarded the first teacher the comment written by the second teacher and asked the first teacher if he/she would like to respond.

The answer was yes.

In this post, I first reproduce the algebra teacher’s original email. Following that, I provide the second, dissenting teacher’s response. And, finally, I post the original teacher’s response to the second, dissenting teacher.

Also, those interested in viewing the Regents Algebra I exam are able to access the exam by clicking here.

Let’s get started.

Here is the first teacher’s original email, a communication to the parents of her/his algebra students:

Dear Algebra Parents, 

The results from this year’s Common Core Algebra exam are now available and have been posted on the high school gymnasium doors. They are listed by student ID number and have no names attached to them. The list includes all students who took the exam, whether they were middle school students or high school students.  

I’ve been teaching math for 13 years now. Every one of those years I have taught some version of Algebra, whether it was “Math A”, “Integrated Algebra”, “Common Core Algebra”, or whatever other form it has shown up in. After grading this exam, speaking to colleagues who teach math in other school districts, and reflecting upon the exam itself, I have come to the conclusion that this was the toughest Algebra exam I have ever seen.

With that in mind, please know that all 31 middle school students who took the exam received a passing score. No matter what grade your son or daughter received, every student should be congratulated on the effort they put into the class this year. 

Although everyone passed, many of you will not be happy with the grade that your son or daughter received on the exam (and neither will they). While I usually try to keep the politics of this job out of my communications, I cannot, in good conscience, ignore the two-fold tragedy that unfolded on this exam. As a parent, you deserve to know the truth.

I mentioned how challenging this exam was, but I want you to hear why I feel this way.

Let’s start with question #24, which was a multiple choice problem. 30/31 of my students missed this problem. Why? Because it was a compound inequality question, which is neither in our curriculum nor is it found anywhere in the modules. As a matter of fact, this is a topic that was previously taught in Trigonometry.

Or how about #28, the open response question that required students to subtract two trinomials, then multiply by a fractional monomial? While that may sound like Greek to some of you, what it means is that there were several steps involved, and any slight miscalculation on any step would result in a one-point deduction on a problem that was only worth two points in total. 

Additionally, the only 6-point problem on the test was a graph that used an equation so ridiculous that it didn’t even fit well on a graphing calculator. The list of examples like this goes on and on.

Additionally, students were met with the toughest curve I’ve ever seen on a Regents exam as well. Typically you think of a curve as something that will add a few points onto every student’s exam to account for the difficulty level of that exam. All Regents exams have some version of a curve or another, and while this curve did help the lower-performing students, it also HURT the highest-performing students. For example, a student that knew 94% of the exam received a grade of 93. A student that knew 86% of the exam received an 84. When you look at the class as a whole, only two students met the “85 or above” that they were striving for all year long.

As if that isn’t alarming enough, let’s look at the difference between a grade of a 70 and a grade of a 75. You may look at those two and think that they are just five points apart, right? Well the way the scale works, a student who knew just 47% of the material got a grade of a 70, while a student who knew 71% of the material got a 75. Therefore, a student who got the 75 may have actually gotten almost 25% more of the exam correct than the student who got the 70! This creates one of the worst bell curves I have ever seen. 

Now let’s put that into perspective. The old-style (Integrated) Algebra exam was also given this year to a small subgroup of students. None of the middle school students were eligible to take this exam. However, were I to apply the curve that was assigned to that exam (which was a MUCH easier exam), a student who knew 78% of the exam would be given a grade of an 85. All in all, over half of the class would have gotten an 85 or above had that scale been used instead!

Let me sum up what the last three paragraphs really say: the exam did a serious disservice to your child and will be reflected in their grade. It’s not a fair representation of what students knew, what they did all year, or what they were capable of. There is nothing that your son or daughter could have done to have been better prepared for this exam. Words cannot describe what an injustice this truly is to your child.

So instead of just sitting back and accepting it for what it is, I’d like to offer you the best that I have. I’m willing, I’m ready, and I will be running review sessions free of charge this summer prior to the August administration of the Common Core Algebra Regents. This will be open to any student who wishes to retake the exam. We will take a look at every question that students missed on their individual test and talk about why they missed them, in addition to reviewing topics from the school year. We will also take a look at some of the wording that showed up on the exam for the first time that likely threw off many students. It’s the least I can do for students that worked so hard during the year. They should not be penalized for the state’s ridiculous examination.

I know that this has been an extremely long email, but I hope you understand the importance of what I had to say and that you can be proud of your son or daughter no matter what grade they received. Although I had promised that this would be my last email to you, expect one more with information about tutoring and the date of the August administration of the Regents. Thank you for listening.

Sincerely, 

NMS Math Teacher

Now, here is the second teacher’s response, written as a blog comment on July 1, 2015:

As a New York State High School teacher of mathematics, I am appalled at the  inaccuracy of much of what this particular teacher says.

#24 – Students are not expected to solve the compound inequality.  They are simply asked to calculate an average over an interval.  The question basically says that if the cost of an event is $750, how many students must attend if the average cost per person is to be between $0.50 and $1.00.  The “compound  inequality” is simply the range of students.  This type of inequality has been presented many times over the course of the year in nearly all the modules, including the 6 point graph question.  

#28 – The teacher forgot to mention to the parents that the big, scary fraction was 1/2.  I think most kids, especially those equipped with a calculator that can provide answers in fractional form, could handle this.  

#37 “The graph” – Any good instructor always shows their students how to use the tools at hand.  Yes, the equation was messy, but the students, by law, must have a graphing calculator.  One of the first things we teach our students is that when an interval (i.e. compound inequality) is given (in this case 0 < x < 150) you enter that domain as the bounds of the graph in the graphing window (usually called xMin and xMax).  Then they can use the ZFit function on the calculator which sets the range (y-values) for the given domain (x-values).  My guess is that this instructor is not aware of this function and probably had his/her students graphing everything in a standard -10 < x < 10 window, which is odd since the modules are littered with examples of these “messy” functions.

Now, I have only been teaching for 22 years, but in my limited experience, I have found this exam to be one of the best that New York State has administered. It was challenging, fair, and expected a high level of rigor.

Having said that, what all of us MUST BE CONCERNED ABOUT is the ABSOLUTELY  ABSURD curve the state dictated regarding this exam.  According to New York, the  following is a true statement:

35 = 65 

You see, sum of the points on this exam was 86, but ONLY 30 POINTS WERE NEEDED TO PASS (i.e earn a grade 65).  Now, I realize everyone hates percents, but go on your calculator and do 30 / 86 * 100 and you will see that by scoring 35% correct, you earned a 65%.

So, I really disagree with this teacher on their point about, “every student should be congratulated on the effort they put into the class”, and “students were met with the toughest curve I’ve ever seen on a Regents exam”.  If your child passed this exam with anything less than an 80  (which, incidentally was actually 80% correct of the exam), they probably don’t know any algebra at all and will definitely struggle through geometry and algebra,  Don’t congratulate them, but instead make them learn the algebra they were supposed to.

In summary, teachers who can’t teach should not be allowed to complain about Common Core.

And, finally, the first teacher’s rebuttal to the second teacher’s comment:

The original letter that you read was meant for an audience of parents, not mathematicians.  Full mathematical justification for the examples I gave them was not necessary to get across the message I was trying to send.  Since the “teacher” missed (or chose to ignore) the point on several portions of the email, please allow me to expand on my previous message.

#24:   

The problem can be found directly at this link: https://roundtheinkwell.files.wordpress.com/2015/06/image2.jpg

My first gut instinct looking at the problem is to first find the average cost, and then to make sure that the average is between the two acceptable numbers given (2.75 and 3.25). The average can be found by using the expression (750 + 2.25p)/p. Since this needs to be sandwiched in-between the acceptable numbers, that then creates the inequality 2.75 <  (750 + 2.25p)/p < 3.25.  That is a compound inequality with a variable in the denominator (which is the real sticking point here).  The type of compound inequality that the “teacher” claims can be found throughout the modules (and in problem #37) does exist as a range of values, however, he/she ignores the fact that students are GIVEN that range of values in those problems, not asked to solve for them!  Could a student have broken this down and done it in two separate steps, looking at the “at or above 2.75” first and then, as a separate problem, “at or below 3.25?” Sure, but that’s exactly how you solve a compound inequality!   Even if a student were able to come up with an average between $.50 and $1.00, as the “teacher” claims, they would still be left with the compound inequality .50 < 750/p < 1.00, which still needs to be solved and still has a fraction in the denominator. For reference to previous inequality questions of a much easier (and appropriate) caliber, see the Jan 2015 exam, questions #7 and 13. 

#28:  I never said the fraction was tough.  The whole point of that paragraph, had this “teacher” bothered to read it, is that there are way too many steps involved (and portions of standards being assessed) for this to be considered a two-point question, in my opinion.  A student needed to A) subtract two trinomials, B) multiply by a monomial (that also happens to have a fraction) and C) put the answer into standard form.  If you look at previous exams, say for example January 2015, question #28 (ironically enough), just subtracting the two trinomials was worth the exact same number of points.  The same could be said about the June 2014 exam, problem #3.

#37:  At least we can agree on the first sentence; knowledge of how to use the graphing calculator is integral to success on this exam!  I’m not sure why the “teacher” assumes that I wasn’t aware of the functions on the calculator, however, I can assure you that we, as a class, have needed to use “zoom fit” on many, many occasions throughout the school year.  That being said, you still needed to create an appropriate scale for both the x-axis and the y-axis, where the x-values needed to cover at minimum of 151 numbers to show the full path of the football, and yet the y-values only needed to go up to 25.  Even if you use zoom-fit and change the scale of your graph, the majority of the points you will try to graph are still not whole-number values, so you’re still left to estimate (as best as possible) where to plot those values.  I never said that this was impossible, however, the majority of the questions like this throughout the modules used “nicer” equations that typically follow the numbers found in gravity/motion problems that students will see when they get to physics (ie. using -9.8 or -16 as leading coefficients, and working with trinomials to boot).  See Module 4, Mid-Module Assessment, question #3 for a perfect example of this.

As for the “teacher’s” sarcastic opinion on the exam as a whole, I respectfully disagree entirely (which was why I wrote my letter to begin with).  It was TOO challenging, TOO rigorous, and NOT fair to the students.  I guess we will have to agree to disagree on that one.  Additionally, since you have never been in my classroom, and you are not a parent of any of these students, you have no standing to judge how much effort these students put into the course.  I have at least 31 sets of parents that I’m sure would dispute your claim.

Finally, to your point about me not being able to teach…I’d like to see the statewide results from this Regents exam and put my students scores up against everyone else that took the exam before jumping to any conclusions.  If that doesn’t satisfy you, let’s take a look at two years ago, which was the last true group of students that took the Integrated Algebra Regents exam (the old standards prior to the common core).  That year, my class had a 96% MASTERY rate (85 or above), and the only student who did not achieve mastery got an 84.  Either I lucked out and everyone in that class was a genius, or I might know a thing or two about teaching.

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Schneider is a southern Louisiana native, career teacher, trained researcher, and author of the ed reform whistle blower, A Chronicle of Echoes: Who’s Who In the Implosion of American Public Education.

She also has a second book, Common Core Dilemma: Who Owns Our Schools?, newly published on June 12, 2015.