## My Dilemma

I had an experience last week that has me in a professional dilemma, and I’m looking for your input. My dilemma may be emotionally charged to you; it is to me, but I assure you that I want to seek a positive outcome for everyone involved (the student, teacher, parent, and me) in this critical conversation. Bear with me.

My dilemma: **What is our responsibility when a teacher delivers a lesson with outcomes that are detrimental to the development of students? How do we have those conversations in a way that leads to positive growth for all involved (and isn’t reduced to the teacher feeling attacked)?**

## Backstory

H is a soon-to-be 14 year old girl who started high school on Tuesday. She is the daughter of a friend. Although she once identified as “bad at math,” she now identifies as a strong math student because she gets right answers and earns A’s in math class. Her standardized test scores are good, not great. She is a responsible student and follows rules. She does not have a history of questioning authority.

While at my friend’s house, I found a sticky note with this problem written on it. It was from H’s first day in Algebra 1 class.

As a math educator, I recognized this type of problem, and I was immediately curious about why her teacher was asking her to find the value of this numerical expression. Why was this problem chosen? What was the intended outcome from the teacher perspective? Was it to assess math skills of incoming students? Was it to promote dialogue and discussion about precision and how math strives to avoid ambiguity (and that this expression lacked the necessary grouping symbols to make it’s value clear)? What was the value of this problem to the teacher? And why was that value so great that the teacher chose it to be the first problem to launch not just the school year, but all of high school math? Might the “Four of 4s” problem been a better choice?

I completed the problem on my own, and I got 10. I did it again, and got 10. I did it a third time and tried to find out how she got 7 and was able to see how she did that. Then I noticed that there was an erased answer underneath the written work. She had gotten 10 too.

I was aware that H’s teacher, an educator I never met, deserved the benefit of the doubt. I had to know more. I wanted to hear H talk through not only her thinking, but also hear her take on what was going on in the lesson.

H and I chatted. She explained how she got 10 and defended every choice she made using PEMDAS as a device to structure her decisions.

Me: Why did you erase 10 and write 7 down as the answer?

H: Because the teacher said the right answer was 7.

Me: What did other students get for answers?

H: Most of us got 10.

Me: Did anyone else get 7?

H: One student got 7.

Me: So what happened next?

H: Well, the teacher said all but one of us were wrong, and that our math skills were weak, and that this was going to be a difficult year for us because this is a middle school problem and we didn’t know how to do it.

Me: Wait. Your teacher said those words?

H: Pretty much. She told us we were all wrong and the answer was 7 and that we didn’t know math.

Me: Did the teacher share student work to show different ways of approaching the problem.

H: No.

Me: And what’s your takeaway from the lesson? What did you walk away knowing or feeling?

H: I felt bad when I got it wrong. I usually get answers right in math. (Long pause.) I hope I don’t have to learn another type of math so I can get my grades right and pass tests.

At this point, my emotional and reactionary self was saying: “This is really bothersome. This is a negative math teaching outcome on so many levels for H and possibly her other classmates. This problem could be a pedagogic choice that is a harbinger of other pedagogic choices to come. It distorts what math is and what it means to learn math and do math. It centers the authority onto the teacher and takes all intellectual power away from students. And it eroded H’s confidence as a math student. And she might not be the only student to feel this way.”

And I also knew that I didn’t know the teacher’s side. I trust H. She’s an honest, face-value kid. She doesn’t want to disappoint adults or disparage them. But she’s also only one perspective (and an adolescent one at that). I wanted to hear the teacher’s perspective.

But how the hell is that conversation going to go? I don’t know this teacher. And to send an email inquiring about her intent behind the lesson didn’t seem like a good idea. I am just some random math dude to this teacher and have a hunch sending such an email would make the teacher defensive. I know I would’ve been when I was teaching in the classroom.

What do I do? Do I have the parent (my friend) request a meeting? And do I go with? Is that any less threatening? Do I coach H on how she might bring up with something like “Couldn’t it also be 10 depending on how we interpret the structure of the expression?” in class? (I asked H. Nope. H isn’t that kind of kid. To question a teacher’s authority is disrespectful.) What should the parent say? What approach would you take if you were a parent, especially if you were a non-math-educator?

So that’s the backstory of my dilemma. Do I have an obligation to speak up? Do I owe it to the teacher? H? The other students? **How do we make difficult conversations like this with teachers (colleagues and non-colleagues) productive?** What would you do if you were me? I’m wide open to feedback about how best to have this critical conversation.

## A Quick Add-on From the Twitter Community

Over the Labor Day weekend, I posted a poll on Twitter. You can find the Tweet and productive conversation that ensued here. Here are the results of the poll:

It validated some of my thinking about how the problem might be useful for discussion about the need to eliminate ambiguity and attend to precision in the math class. It’s actually a really amazing problem for that reason alone. Look at those results! The debate is clearly rich.

Most (math) folks, regardless of the answer, agreed that the problem wasn’t a good math problem unless the goal was to talk about the need for structure to make math clearly understood.

It’s a juicy problem. To be clear, I don’t want to sound like I’m adding to the pile of “Viral Math.” This dilemma isn’t about the math. It’s about the discussion that needs to happen and how best to make that happen.

What do you notice that I may not about this potential critical conversation? What would you do if you were in my shoes? Or the parent’s shoes?

Thanks for helping us get better together. Thank you for letting me take a risk by sharing this dilemma with you.

Interesting dilemma with many points to consider. My specialization is therapeutic communication in healthcare and education. I too am a professor. I imagine you already brainstormed with H regarding her approach to solving the math problem indicating there are many roads to Rome. BTW full disclosure here – I have limited math skills, have a Ph.D and use statistics to analyze data, but am definitely not a lover of math.

What to do? Suggest this: after class some day soon, H asks to speak to her teacher, indicating she has a different approach and a different answer for him/her to consider. H will be friendly, smiling, and mention she has a sincere interest in math and learning more. She also says she used a different approach, came up with a different answer, and would like to share her approach/answer. H will not press the teacher for an immediate response nor put them on the spot, but give them some space, thank them for listening and reviewing her approach and then exit. I understand that teachers are receiving more verbal assaults these days. This is a softer approach but one which may allow this teacher to grow interpersonally and professionally. The benefit – H has gathered her resolve, softly “confronted” the teacher, and remained respectful. This approach MAY enable this teacher to re-think everything, keep their composure, and possibly come to a softer, more thoughtful approach to teaching. The bigger win is for H – to not be afraid of talking/crossing someone in authority. Thanks for reading all this!

Hi Jan! I appreciate your thoughtfulness and helping to further the discussion!

Hi Chase,

There are two separate issues here. The most important is the one you raise about building self-esteem in students (in this case, the negative sense of that issue). I am of the persuasion that there is nothing more important in life and no greater duty as a teacher than building self-esteem. My counsel on that part of the issue would be to delay any response to the teacher (with the possible exception of pointing out the misunderstanding) until more information is collected to decide whether this is an aberration or something of greater consequence. But delicately point out to H (without undermining any cause she might have to believe her teacher is worth paying attention to) that this was a very tricky problem and her approach was easily understandable and should be no cause for disappointment. I’d point out to her that even among your tweets (presumably they were mathematicians alerted to the fact that something was tricky here, more people answered 10 than got the right answer.

The outcome the math part of the dilemma hinges on sequence: addition and subtraction normally, according to protocol, await the resolution of multiplication and division. But in this case the parenthetical expression (5-3) raises the exception. Parentheses should be treated as a unit and resolved before proceeding to the balance of the problem. Only then should the standard protocol be followed before adding the 6 and 1. Seven is the correct answer but I’m in agreement that this is questionable as an initial approach early in a new semester.

I commend your raising this issue and your very delicate handling of this dual problem.

Thanks for taking the time to read and reply, Ken! I appreciate the insights.