Problem Solving
I was a math teacher for 32 years. I taught every math subject under the sun, first in high school for 10 years, then eighth grade for 11 years, and then finally spending the final 11 years of my career teaching an elective course called 7th Grade Math Problem Solving. Now, what Math Problem Solving consisted of was a question for the ages. No one seemed to know. The teacher who was teaching it while I was teaching eighth grade hated the idea of a nebulous, free-form course that had no formal textbook or ordered set of standards. She was as uncreative a teacher as I’ve ever met. I don’t think it’s a coincidence that she left teaching to become an administrator shortly afterward. I, on the other hand, despised being tied to specific texts and schedules.
A little background is required, here. At the beginning of my career, teachers had the power to select their own textbooks, by school system. Every seven years, just as Vulcans return to their home planet to mate, textbook companies would come courting, to try to bribe us teachers to vote to adopt their textbook. I guess you could call it Textbook Pon Farr. In a large school system with thousands of students, this adoption would be extremely lucrative for the book company. And when they courted us, they meant business, literally. Teachers would be treated to meals at the best restaurants in the area, and companies would try to sway us with promotional items, sample textbooks, and other gifts. One time, we teachers and a guest were treated to a private showing of Star Wars The Force Awakens, complete with free popcorn and snacks! Clearly, this system is ridiculous and corrupt, and just before I took on the problem solving course, the power to vote for a preferred textbook was taken from teachers completely. An administrator and his hand-picked committee made the decision for us, and in this particular instance, a very poor and unpopular decision was made. A problem-based curriculum was chosen, which would have been great, except for one thing; it was scripted.
When I say the textbook was scripted, that is precisely what I mean. It was in the format, say this, do that example, ask this question, assign these problems. And we were required to attend inservices where the teachers who piloted the program insisted that every page must be followed to the letter, or it would have no validity. We had some really creative, experienced teachers at that time, and I would stack their homemade lessons against the scripted curriculum any day of the week. They were told they could not vary from the book, even when their activities were similar. There was a mass exodus soon after, as they fled the system. If I’d had the experience and the years in, I would have followed them. As it was, I had the opportunity to jump ship and teach the soon-to-be-abandoned problem solving course. And jump I did.
One of the first things we established about the problem solving course was that it was to supplement the regular curriculum, remediating kids who had done poorly and enriching the kids who’d done well. It was a semester course, and at my suggestion, we put struggling students in the first semester so that I would have them for a full semester preceding the big test, ISTEP+, which was given in the spring. Higher-performing students would be scheduled in the second semester, so they could also benefit from the course, but their need wasn’t as critical as the struggling students. This process seemed to work well, as we saw a rise in scores soon after. It may have been a coincidence, and there is absolutely no way to make a case for the effect of this course. I just like to think it was.
I was free to use whatever materials I chose, and I was careful to support my choices with the state standards we were required to teach. I still laugh about those state standards, because they are so poorly written. In 2014, Indiana moved away from Common Core State Standards because of a misinterpretation of their origin. Tea Party Republicans viewed them as a federal takeover. And in 2014, then-Governor Mike Pence signed legislation making Indiana the first state to walk away from the national rollout of CCSS. We reverted back to the 2000 academic standards that we had been using before the advent of CCSS. When we finally adopted new standards written by Hoosiers for Hoosiers, they were about 80% Common Core, but paraphrased. So, by the time I was writing lessons to match the standards, we were using the Cliff’s Notes version of Common Core. But I wasn’t complaining, because one standard stood out over all others. I present to you, Indiana Math Standard 7.C.6:
Use proportional relationships to solve ratio and percent problems with multiple operations (e.g. simple interest, tax, markups, markdowns, gratuities, conversions within and across measurement systems, and percent increase and decrease).
At that time, we were required to write the standard we were teaching on our whiteboards, and I printed a copy off, posted it, and never took it down. It kind of covers a lot, doesn’t it? Other standards say stuff like “Add integers.” This one, though, could keep you busy for five months!
And busy we were. At the time of this writing, it’s the week of Thanksgiving, and I always had a lesson prepared that covered 7.C.6. Regular textbooks often had sections on unit pricing. You know what excited kids about those units? Absolutely nothing. Here’s how I handled it. I stopped at the local grocery chain, Martin’s Supermarkets, on Monday morning when the new flyers came out, and asked a manager if I could take 150 of them to use in the classroom. Now, what manager is going to say no to that? Free advertising directly into the hands of 150 students’ families, right? Win-win. I broke the students up into groups of four with an odd group of three if necessary and gave them a budget to buy communal food for a week. NO ALCOHOL! What, did you think I was a n00b? It was always the first thing they asked.
Martin’s sales always have a variety of unit pricing: 5/$5, 2/$4, etc. We’d start off easy on those. But then something like this would come up and the kids would choke.
Suddenly, kids were in a panic. They couldn’t make it come out even. Ah, to heck with it, I’ll just buy three! And I’d point out, what if you just needed two? Are you going to waste that money? They usually thought better of it and played along. The unit price rounded to $1.67. The second one you bought would also cost $1.67, and the third one you bought would be $1.66, and the kids accepted that, as they should. I warned them, however, that it didn’t always work like that.
I’m a storyteller, you see. And there are very few things for which I don’t have a story readily available, and unit pricing is right in my wheelhouse. I worked at Meijer as a cashier when I was in college, back in the distant past of 1985. That’s right, the year Back to the Future came out. And we had just gotten those newfangled scanners. Before that, we had to ring everything up manually. Now, the problem with the computers was that they didn’t care about your rounding rules. I still remember a customer complaint when cans of Starkist tuna were 3/$1. Those were the days, right? And one day, a particular customer bought one can of tuna. It scanned $0.34. The customer complained. I agreed, one can of tuna at 3/$1 should have come out at $0.33. So, just for the sake of curiosity, I scanned it again. The second time, it scanned at $0.33, as it did on the third time. After I canceled the second two scans, I called the customer service manager, who actually got mad at me for questioning it. I said that the customer questioned it first, but that was unpersuasive. He yelled at me some more. Honestly, I don’t think he wasn’t cut out for customer service. He explained that the computers were programmed to do it that way because the company was losing that valuable penny on single can purchases, and if you sell 50,000 cans of tuna chainwide, that starts to add up to real money. How much money? By now, you see, the kids were hooked. They started whipping their calculators out and figuring it out for themselves. And this is what we call teaching.
I miss teaching this lesson, and I would have been doing it this week had I not retired.
