Problem Solving Classroom

Tips from a Master Teacher (This is a work in progress.)

A Dream Letter

by Mark Illingworth
A Dream Letter

Over the years I got many letters from students thanking me for one aspect their education that they liked. My most frequent letter by far had to do with students appreciating my teaching them to think. That’s why I’m here taking the time to share it with you. (By the way, I chose the graphic above because I like how ludicrous it is to think of a student writing a hand-written letter instead of an e-mail, let alone using a fountain pen.)

The letter below is not real. It’s more of an amalgamation of all the letters I received. It’s the dream letter that you might hope to receive one day, although it’s more likely that you’ll receive these things in shorter letters, conversations, and from your own observations of your students’ growth and successes.


Ms. Pringle:

Surprise! I wanted to let you know that I switched from political science to mechanical engineering. Why? You, of course.

Thank you—both for making me love mathematical challenges and for making me good at it. I was even more surprised than you probably are by my change, but I found that as much as I was fascinated by the intricacies and foibles of politics, when I thought about it over the summer, I realized I was more pulled by the power of math to analyze complex phenomena.

I remember loving puzzles when I was in first grade with Mr. Kane. I couldn’t get enough of them, and if I went home stumped, I’d spend hours trying to solve something until my mom had to drag me away for dinner. Somehow, I lost that over the years. I’m not sure what it was. Maybe partly that teachers stopped giving me challenges. That and the grades. I got good at the game of memorizing whatever technique it was so that I could spit it out reliably on quizzes so I could get my A. I love those A’s. By the time I got to high school, I was obsessed with the all-so-important GPA. Difficult was a threat and not fun, anymore.

You changed this by pushing me out of my comfortable nest and making me fly. At first I hated you for it. I couldn’t just memorize things anymore; I actually had to think. I worried a lot about my GPA. If I couldn’t solve one of your more difficult challenges—designed to develop my higher order thinking skills as you put it—I panicked that it was going to reduce my class rank. (By the way, I’ve used my analysis skills to come to the conclusion that class rank is a statistically ridiculous and worthless concept. I hope you guys are doing something about it.) Thanks so much for your cleverly designed grading scheme that emphasized what I could figure out instead of what I couldn’t figure out. I really liked your trapeze analogy. You’re right that the most difficult things should not be assessed in a right-wrong way with no safety net. I wish you could have convinced other teachers to do this because it makes so much sense and it encourages rather than discourages students willing to take risks.

So, now in my second year I am in a lab class in which I am supposed to think cooperatively with other students to analyze things like compressors, combustion engines, wind tunnel experiments, and even the university’s steam-generating plant. This is where I am so appreciative of all the ways you asked me to really think both analytically and creatively. I’m with some really smart teammates, but when it comes to problem solving, they can’t think their way out of paper bag. Also, they give up so easily. That’s another thing you taught me—perseverance.

I still remember that first month how I would feel so stupid when I couldn’t get something right away. I was used to just following a lesson and then doing the pages in a book, so when there’d be a problem so difficult that I’d go home not knowing the answer yet, I was terrified. Thanks for coaching me—well, the whole class—through that and getting me to point where I saw this as part of the process. I eventually got to the point where if something was so challenging that I had no idea (at first) how to solve it, I got that same sense of excitement that I used to feel in Mr. Kane’s class. So, thank you for helping me find that again.

Oh, and I loved all the puzzles and challenges that you posted on your site. I think the puzzles are where I first started liking challenges again. At first I tried to solve as many of these as I could just to beat out Kevin Allen and Elena Diaz. Remember them? I eventually I stopped seeing it as a competition and instead just liked tickling my brain. It didn’t take long before I realized that your challenges within the actual math lessons were learning were just puzzles. That was a game changer for me. Your classroom was like a candy store.

I hope you’re doing well and that you’re still doing all of this stuff. To be honest, I’ve gone to your site a few times over the last year just to try some of the puzzles you post. I liked “Hallway Door”, even though it took me two days to figure out. I know you probably get some flack from administration because if I remember right, they believed a lot (as ridiculous as it was) in every teacher doing the same thing the same way. I hope you’re resisting the pressure to stop innovating. I guess I wrote to tell you how much you influenced me to be a confident, flexible thinker so you would be reminded how important your mission is to the students you teach.

One of these days when I’m home, I’ll drop by for a visit. There are so many other things I have to share.

Take care,

Victoria Hallett

p.s. I have to confess that as much as we complained about your jokes, some of them were actually pretty good. Note that I said “some” of them.

Article Topics

In a Nutshell


It will become clear to you that your students are thankful for your teaching them to think.


Your policies and procedures tell your students how much you care about and support their overall growth.


Students secretly even like some of your jokes.

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