*One of the commenters here takes me to task for my description of this as a PEMDAS problem. OK, that's fair; the part at the end is clearly about decimals converted into fractions. The first four... what do you call those, "operands"?... really don't need parentheses because the last one is "1." I was thinking that @rratto was just subbing numbers in, and that if the last operands was, say, "2" it would change the answer depending on whether you followed PEMDAS or not.*

*So, maybe a bad assumption on my part. However...*

*There's just no way this teacher should have been removed from his classroom for tweeting this if it's not an actual problem on the test. And I do think there is a "gotcha" quality to the question, although that's obviously a matter of opinion.*

One of the friends of this blog is teacher/blogger @rratto; he's reposted and retweeted me more times than I could count, which I very much appreciate. So this is hardly an unbiased opinion on my part; nevertheless, the story he is telling at his blog is shocking and disturbing:

Go to the blog and read the rest; it's incredible. @rratto is accused by a stranger on Twitter of posting test questions -

It all began Wednesday evening with the following “tweets”;

My initial tweet was an editorial comment based on a Common Core standard (which includes a similar example in the standard), and included a generic example that can be found in many practice workbooks. As you can see Allison Sitts, aka, IthacaGorges took exception to my message and accused me of posting an actual test question. I followed up with a response stating that it was not an actual test question. At this point I thought little of Allison, I didn’t remember conversing with her before and just assumed the conversation was over. Well it wasn’t!The next morning ( Thursday) I administered part 2 of the New York State Math Common Core Math assessments to my class. Immediately following this exam, ( It was literally minutes after collecting the test books.) My principal was standing at my classroom doorway , with a very distraught and serious look on her face, and says, “I need you to come outside now.”I say, “OK, I’ll be right there.”She then says, ” I need you right now. “

**an action that is easily verifiable**. The state should have been able to confirm whether his tweeted problem was the one from the test book immediately. They could also have easily given permission to the superintendent to look at the test book and see if the problem @rratto had posted matched his tweet.

__Obviously, it does not.__

I'm not a math teacher, but even I recognize @rratto's example as a classic "order of operations" problem. You have to know PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (left-to-right) - as the order of operations in order to solve the problem. This is a great example of how an item can be constructed to "trick" a test-taker into giving a wrong answer, even if she grasps the concept. Adding parentheses to the first two multiplication operations would easily clarify the problem, but they are excluded here, increasing the chance of a wrong answer.

Psychometricians at testing companies must love PEMDAS problems: I'll bet their inclusion into a test almost guarantees that a certain percentage of test takers get the item wrong, which gives that nice normal distribution test-makers crave. But they don't necessarily tell us much about a child's ability to complete math problems: they may only tell us how well a child can be fooled.

You may agree or disagree with me or @rratto, but we both have every right to broach the issue.

**He and I and every other educator have the right, as American teachers, to use our First Amendment protections to publicly question the validity of state-mandated tests**.

**This was an act of intimidation**. NY Education Commissioner John King has proved himself to be a bully and a hypocrite. Regents Chancellor Merryl Tisch has proved herself to be indifferent to the suffering of children under this testing regime. Governor Andrew Cuomo has proved himself to be uninterested in the opinions of teachers and contemptuous of their professionalism.

But these people do not like to be challenged by those on the ground who actually work with our nation's kids every day. So the very minute someone stands up and points out the insanity of this system, he is descended upon like a pack of wolves. Why?

**Because they do not have an answer to their critics that can justify what they are doing.**

__@rratto is a hero and a true educator__. He has done a great service for his students and their families by questioning the authorities who are imposing their will on our public schools. He is following a great American tradition of healthy skepticism for our "leaders," and I am proud to serve with him as part of America's teaching corps.

We teachers are the last defenders of critical thinking this country has left. Purge us at your peril; right George?

Word.They spend billions of dollars every year lobbying -- lobbying to get what they want. Well, we know what they want -- they want MORE for themselves and less for everybody else. But I'll tell you what they don't want.They DON'T want a population of citizens capable of critical thinking.They don't want well-informed, well-educated people capable of critical thinking. They're not interested in that, that doesn't help them. That's against their interests. That's right. They don't want people who are smart enough to sit around the kitchen table and figure out how badly they're getting ****** by system that threw them overboard 30 ******' years ago. They don't want that.You know what they want? They want OBEDIENT WORKERS. OBEDIENT WORKERS. People who are just smart enough to run the machines and do the paperwork, and just dumb enough to passively accept all these increasingly ******** jobs with the lower pay, the longer hours, the reduced benefits, the end of overtime, and the vanishing pension that disappears the minute you go to collect it.

## 5 comments:

According to the math specialist at my school (who would never dream of filing a false complaint against another teacher), the distractor answers chosen by students on tests reveal just as much information as correct answers. In the beginning... before politicians co-opted the test data and the DOE (the horse that outclasses it's rider), the wrong answers that tempted the children would have been pored over by educators to determine implications for future instruction.

I wonder where the NY teachers' union will stand in all this, now that one union member has bypassed them to file a complaint against another, and been 'outed' by top admins for her trouble??? No matter what happens, this forum is the pivotal player and the only one with potential to bring about authentic reforms in education.

PS I forget to say that I visited rratto's blog and he looks like a lively, interesting math teacher. I can see why his students would love math.

It doesn't appear this question has anything to do with order of operations. It's 65.427 expressed as a product of powers of 10; the question basically is asking "do you understand how decimals work?"

We also don't know if the original question had consistent use of parentheses or if some were elided for a shorter tweet.

If the question wanted to be tricky, you would reverse the order or switch them up, but this is pretty clearly a good question IMHO. A person who understands the underlying concepts can read off the answer without any calculations; a person who doesn't is going to be confused and bewildered.

If it wasn't clear, it's this paragraph that's completely off-base:

I'm not a math teacher, but even I recognize @rratto's example as a classic "order of operations" problem. You have to know PEMDAS - Parentheses, Exponents, Multiplication, Division, Addition, Subtraction (left-to-right) - as the order of operations in order to solve the problem. This is a great example of how an item can be constructed to "trick" a test-taker into giving a wrong answer, even if she grasps the concept. Adding parentheses to the first two multiplication operations would easily clarify the problem, but they are excluded here, increasing the chance of a wrong answer.PEDMAS has nothing to do with this question, and looking at the question again, it might be more confusing if parentheses were added to 10 & 1 (10*1? 1*1? that would make no sense). It's likely the question appeared exactly like that; it's fine as-is.

Look at the comment posted "Mrs. King's music students said...

According to the math specialist at my school (who would never dream of filing a false complaint against another teacher), the distractor answers chosen by students on tests reveal just as much information as correct answers."

I agree: you can learn an awful lot about how a student thinks even when they get this question wrong. BUT WE DON'T GET TO SEE OUR STUDENTS ANSWERS!!!! WE DON'T EVEN GET TO SEE THE QUESTIONS! How can I help the student if I don't know if it was PEMDAS, or the fraction piece, or addition, or if they thought 2(1/100)means the same as 2 1/100 that made them get it wrong. Stop telling me that bubble tests help me help students!

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