Feedback from Former Students
The City of Oberlin, surrounded by corn fields, is a college town of about 8000 residents in rural northern Ohio. Oberlin High School serves about 300 students in grades 9-12. 51% of the students are on the free lunch program. The student-teacher ratio of 15:1 is lower than the Ohio state level of 18:1. Minority enrollment is 54% of the student body, which is nearly twice the Ohio state average of 29%. 4% are Asian, 7% Hispanic, 26% Black, 46% White, and 17% of two or more races. There are several foreign exchange students each year. Students are from the town and the surrounding rural townships; they thus span a wide socio-economic spectrum. Students who may have hardly ever been outside of Lorain County may be sitting in class next to a pair of students arguing over the best Metro route from the Louvre to the Eiffel Tower. The students view themselves as a tribe—indeed, they used to be the Oberlin Indians and are now the Phoenix. They are fiercely protective of each other when, for instance, they are at out-of-town sports events.
As a reality check on my own fond memories of working with students and Stella, I put up a message on Facebook a year or so ago, knowing that many former students were Facebook friends of mine and hoping that I would hear from at least some of them.
I put up a request on Facebook for feedback on students’ Stella experiences. Here is a more-or-less random sample of what I got back.
Molly: "Stella made the SAT's easy. In fact, Stella got me into law school!"
Sebastian: “What I remember about Stella's Stunners is that they brought a sense of mystery and excitement about problem solving. The way you used them took math away from the drab, lifeless context we were used to, and into a feeling of real-world challenge. They helped to engage more ‘right-brained’ students (like myself) in a subject that we had previously written off.”
Amanda: “Oh my, it’s so long ago but all I can remember is how you made me love math. The Stella Stunners just made it easier.”
Julie: “Stella helped contribute to my anxiety! Math stressed me out! To this day, I get anxious about it. Add in Stella and yikes! I never seemed to get her! Had to rely on my mathematician friends to explain!”
Mark P: “I loved to try them. They were great lateral thinking exercises. They were impossibly hard but fun. They were the problems that I remember enjoying from math even though they were so hard. I liked them on their own... like I enjoyed Chemistry... Do you list them with concept hints for example if you learn these concepts this will help solve this problem? I don't remember. They were extra and optional so there was no pressure to do them.”
Monica: “They really irritated me because it was always one little thing that I was missing when trying to solve them. They irritated my dad even more because I'd always take them home for his help.”
Chris, a hard-working high school student and now a pro football player and sometime trainer to me: “Now, with regards to the Stella's, that you had discussed with me a couple times during our workouts, they made Math, which I have ALWAYS dreaded, very fun. It was a great change from the typical $y = mx + b$ type Math that I was never really interested in. For a person like me, I wish there were a class solely based around Stella's. I'd have taken it immediately.”
Sara: ”I loved working the stunners when my older sister brought them home. They seemed easy and were fun. When I was actually in your class (14 turning 15) they were suddenly a lot more difficult and no fun. This anecdote probably says more about the onset of adolescence than math learning.”
Nick: “I remembered doing math problems that were more of a challenging puzzle and fun than a monotonous stream of repetition that begins to feel like a broken record 3 problems in [I'm looking at you arithmetic *scowl*.... f**king 100 problems in a row that all feel like the same thing over and over and over..er..er..er...fzzzzt...er...].
Anonymous: “When I was 19 and 20 my younger, home schooled, brother would come over and want to play video games with me. He lived with my mother, who wasn't very gifted with math, and he wasn't doing well with math and kept getting frustrated by it. I was inspired by the problems from your class that were more fun than boring and would tell him he could only play my GameCube after he'd done the problems I laid out for him, which were directly inspired by YOU. At first he'd go and play directly after doing the problems, then after a while he'd want to do more problems than I'd given him. Now he has no trouble with math or creative problem solving and seems to enjoy it.
Cindy: “I really enjoyed the challenge of Stella's Stunners. It also gave us a chance to learn to work together. I think that the problem solving skills Stella's Stunners taught me have helped me in my job as an engineer. Thanks Mr. Crawford and Stella!”
Brian: “In my case these problems really sparked an appreciation for problem solving. These problems could not immediately be put into neat little formulaic boxes. Solving them required some creativity and outside the box thinking. That mental approach, and awareness, really helped me get through college and continue on in my work. I think for some, problems tend to create a roadblock they keep slamming into head on, but once your approach and creativity is practiced, you quickly begin to look for ways around, over, or under, the roadblock. Thanks for the Stella experience!”
Kurt: “Can't wait to introduce my son to Stella.”
Deb: “Stella helped me think around corners!”
Jerry: I'm a better person for having known Stella. She challenged my thinking Mr. C.”
Anon: “Btw, I have loved them and they were a big part in helping me learn to love math and recognizing my potential. Maybe that was you... anyhow. Stella too lol. I usually never figured them out as a high schooler... but after you showed us it wasn’t as hard as it looked, it helped learn to think outside the box in everyday life as an adult and not be afraid to tackle something, even if it’s big and monstrous looking. Just break it into smaller parts till you figure it out. Thank you for that... math has become my favorite thing now.
Kelly: “I absolutely LOVED Stella! I actually enjoyed (and scored well on) the logic section of the LSAT because of my Stella practice. 😉”
Amy: Stella's Stunners really taught me not just to solve problems, but how to slow down and clearly communicate how I was getting to my solutions. I think your advice to "explain it in words as you would to someone who only knows basic algebra" served me well throughout the time I was getting my engineering degree, and now in my career as a scientist. Although I'm still far better with numbers than words, it is my ability to explain the how and why, not just a final answer with lots of figures and equations, that has helped me to succeed.
Kevin: I'm absolutely sure Stella's Stunners have been part of the development of my overall problem-solving strategy. Stella's Stunners are story problems, and really, so is every interesting problem... ever. I remember spending days on some of them in high school. These days, I think that's a short amount of time to spend, doing math. As I've worked as a neuroscientist and software engineer it's been expected that teams would take weeks arguing over how to do the math, and convincing everyone that the math does what we think it does.
Stella taught me some of these lessons:
- Draw a picture!
- Try out a small example
- Make sure everyone's talking about the same problem
- 0 = 0 (Don't worry: some of your equations are really saying the same thing. Go back to your picture.)
- Write a program.
- Write down the logic formally. (You'll find all your assumptions when you explain it to someone.)
- Is everything on and are all the wires plugged in? (This isn't from Stella but it's worth it.)
Kelly: You had a way... of helping me see the problem wasn't as big as it looked on paper. To break it down. I actually look at all my problems like that to this day! I don't look at the whole huge issue I break it down and then deal with it.
Billy: Stella's stunners... made it fun to push myself to learn more. As the father now of two – one in college and one a junior in high school – and as someone who works in the education space I see daily how hard that is to do.
Peter H: “As your former colleague and (some time ago) problem solving researcher, Stella influenced my teaching. I developed a yet unquenched thirst for non-routine problems and continue to enjoy tempting my grad students with problems. I've recommended Stella to many math teachers over the years. And the grandkids are getting old enough to do the dance with Stella.”
Here’s a comment from a parent. “One of the great things about Stella's Stunners is that there are no right ways to solve the problems; they allow students with different strategies for problem-solving to be equally productive. One year we had two daughters in the same high school mathematics class doing Stella's Stunners. There was one plane geometric problem that I remember them both solving. One daughter had (and still has) a bent for theoretical analysis, and she solved the problem using geometric theory. The other daughter was (and still is) a practical, hands-on person, and she solved the problem by constructing geometrical figures on paper, cutting them out, and weighing them. They both arrived at the same answer; they were both pleased with themselves at having solved the problem; and they both were amused at the glee their parents took at seeing two entirely different ways of thinking at work productively on the same problem.”
Phyllis: I don’t remember the particular occasion that Dad described, but it certainly rings true. I’m the theoretical one of the pair. Now I’m an environmental scientist, and Edie is a therapist. I give you credit for the real-life math confidence that helped me solve the problem laid out in the attached paper [a tract in a scientific journal]. Basically, there was a famous equation (at least, famous to those studying contaminated sediments) that didn’t work for a whole set of chemicals. I found the flaw in the math and fixed it, so now it works universally. It was just like a Stella’s Stunner. Thanks!
So what can we take away from reading these comments? One, for almost all of these self-selected respondents, Stellas were an enjoyable experience for students; they relished the mental challenge. Two, Stellas thus provided a value-added experience to their mathematics studies that went beyond their more customary lessons. And three, they knew that Stellas taught them something about how to think, how to learn, and how to persist.
Final riff: Doing textbook exercises is riding a bike with training wheels. Doing Stellas, the training wheels are gone. So we wobble, we’re scared, we veer left and right, we go in circles, we fall down and get back on the bike or wait and try again later, and by and by we become competent riders, enjoying our rides and reaching our destinations.