Help me develop topics for a high school course on problem solving.

May 12, 2009 2:29 PM

Help me develop topics for a high school course on problem solving.

I am a high school teacher (previously) with hopes of creating a problem-solving course. I've not found good materials online for a course like the one I am conceiving, nor have I taken one of this sort (except for a small-group excercise I participated in in 5th grade), but here's what I have in mind:

1) Break students into groups of 4 or 5 students of mixed ability (my school has a fairly broad range of students, but they are mostly centered at a bit below grade-level expectations).

2) Assign a problem that is fairly specific though also fairly open ended.

3) Then, my role as teacher is to guide the groups over the course of, say, 2 to 3 weeks toward a creative, collaborative and somewhat viable answer by asking students to refine and challenge their own group work. Meanwhile, I will provide materials (mainly related readings) that guide students to these viable answers.

4) Ultimately, students will present their findings/solutions to a panel (probably a group of teachers and students, though maybe invited experts).

5) Move on to next problem...

I've wanted to post this question for a while, but didn't quite have my head wrapped around a good sample topic, but now that I think I have one, let me show you what I mean:

Problem: Devise a one-time, one-way communique to be transmitted to an extraterrestrial intelligence.

I would then pass out markers and paper and ask students to put together their message, which would probably consist of a paragraph written in English saying, "Hi. We're from Earth and we would love to meet you. When you get here we'll take you to McDonalds. Love, Earthlings."

We would then critique our messages and begin the formal study of the problem and look at related readings:

--Aliens won't understand our writing (readings on hieroglyphics, the Rosetta Stone and/or cryptography)
--How has this problem been approached before? (Pioneer, Voyager, Arecibo)
--Problems associated with previous attempts (like this)

In other words, assign a tough problem that requires creative solutions to which a constructivist, pursuit-based approach is manageable for the teacher. With the alien message example above, I could provide lots of support materials and be a gadfly to students while letting students invent their own solutions.

What I don't want are things like the you-are-stuck-on-an-island-with-these-20-things-now-rank-them-in-order-of-importance-and-we'll-see how-well-you-did-against-a-predefined-correct-answer sort. And I want the project to have lots of paths and dead ends (which I think the alien message does). Another idea I was considering was a nuclear war scenario in which groups are given, say, $2000 to stock a bomb shelter--what do you buy?--but I'm afraid I would have trouble finding useful resources for my gadfly-ing, and I don't feel like the answer is open ended enough (you know: "water, food, guns, two-way radio, etc.").

I am also interested in a problem-solving framework that we would study at the beginning of the term and use throughout, though there are some AskMes on similar topics, but what I really want here is your good idea of a problem and links to a bunch of related readings that would provide the basis for student inquiry, like the example above.

posted by etc. to education (16 comments total)

what about:
1. cracking the mayan writing system. there is plenty of stuff on that, including a pbs nova episode. where do you begin in attempting to decipher an unknown langauge? you could start with how do we translate this german phrase? then go to arabic phrase? then chinese phrase? then mayan phrase? then incan rope knot writing - which is still un-deciphered

2. planning a first attempt at the south pole. again tons of resources. plus, with this one, the logic is a bit backwards. scott brought everything, including the kitchen sink and hundreds of men. amundson brought barely anything and only eight men. scott dies, amundson is the first man to the pole. a great book on this subject is the last place on earth by roland huntford

3. planning the lewis and clark expedition. just read undaunted courage by stephen ambrose - great book, very readable - and he discusses in depth exactly how they planned and approached the entire trip

just a couple of thoughts off the top of my head
posted by Flood at 3:46 PM on May 12

A great book on problem solving is Gerry Weinberg's Are Your Lights On?

His emphasis is on first defining the problem, then solving it.
posted by metaseeker at 4:18 PM on May 12

Can I suggest that you please, please not assign group work? It invariably means that students who are further ahead or have a better understanding of the topic are bored, students who understand the topic less don't learn as much, students who think they are smarter belittle the ones whom they think are stupider, students who think of themselves as stupider feel even worse about themselves and drop out of the exercise, quieter students get crowded out, and students who care most about their grades end up doing most or all of the work. It's a terrible system, and it doesn't result in kids learning more or socializing better or ending up with a greater understanding of the topic at hand.

If you are insistent on group work, for whatever reason, please make sure that each student in the group is clearly assigned part of the question and that each student is graded only on work that he or she personally completed and not penalized for work neglected by other group members. Group grading exacerbates all of the problems I outlined above.
posted by decathecting at 4:29 PM on May 12

This sounds a lot like Future Problem Solving, at least as it was back when I was in school (mid-ninties). It looks the program still exists although I had heard rumours over the years that it had changed somewhat, so might be a good place for you to look for ideas and resources?

FWIW my team were the 1992 NZ Senior Champions, and I still use the ideas and ways of thinking I learnt back then in my now-life as a research scientist (currently a PhD student). It was definitely worthwhile and I wholeheartedly support your efforts to set up something along these lines in your classroom.
posted by shelleycat at 4:30 PM on May 12

Wow, what an adverse reaction from decathecting! I 100% endorse the group work concept. It is an essential skill we don't get to practice enough in school. You do have a responsibility as a teacher to find out what is going on in each group, but beyond that..

I suggest anything related to planning, urban design, architecture or construction. Something like deciding where bus shelters in their neighborhood should be and how they should look. Something that is creative and open ended. Then as they move through each stage of the design you can identify the new challenges that arise and pursue them as well.

A quick google search shows there are plenty of resource out there about the design process.
posted by meinvt at 4:59 PM on May 12

While I can't vouch empirically for this statement, not being a teacher, it seems that this would benefit from a use of simple engineering materials. Something "real."
posted by LSK at 5:10 PM on May 12

I love this idea, it will require a lot of extra attention on your part to make sure everyone participates. A couple of ideas come to mind

1) lending my support to meinvt's urban planning idea, I am reminded of a project I did in 7th grade. Designing a city, naming it, coming up with a history, tourism literature, and an essential element that makes the city desireable (mine was a mag-lev train system). The most fun is requiring a model to be constructed, and of course there are presentations and displays at the end of the program.

2) Different types of marketing games may fall into categories like this. Maybe designing and marketing a new type of board game? A lot of different skills go into board game design . . .
posted by Think_Long at 5:10 PM on May 12

I did an activity in Middle School where we had to design a new building for the campus. It worked well because it had a lot of parts: what does the school most need a building for, where to put it, how big to make it, floorplan, individual room layouts, etc... Each student can be responsible for a room and they can all work together on the big picture parts. The project ends with a presentation of the whole design and justifications. This activity also works well because it requires reasoning about something the students know well: school.

Also, design a storage system for nuclear waste that will last 10,000+ years. How will you communicate to future humans that the contents are highly dangerous. There has been a lot written on this topic.
posted by zachlipton at 5:54 PM on May 12

The problem with the alien message idea is that there is no feedback. Since you don't have any actual aliens to talk to, you have no way to judge the solutions. A major component of problem solving is being able to see what works and what doesn't; being able to reexamine your assumptions and modify your solution; learning how to be objective in your analysis, instead of getting emotionally invested in your decisions and turning a blind eye to failures. Coming up with a solution that looks good on paper is only half the picture.

For problems that can be experimentally tested, you might want to look into the kind of stuff they do in physics classes--building mousetrap cars, catapults, etc. Or maybe a computer science problem, like inventing a sorting algorithm, or compressing English text.
posted by equalpants at 6:24 PM on May 12

I also want to vote for doing something as real as possible. If it's something they actually might care about the answer to, they'll try a lot harder.

For example, at my high school there were several lunch periods and you were segmented into one period at the beginning of each quarter. Regardless of your lunch period, everyone knew that if you weren't in the first half of the lunch line for your period that all the decent stuff would be gone and you'd have about 5 minutes to eat the crap you did get. Everyone also had their favorite strategy for trying to make sure they were in the first half of the line. It's a tougher problem than it seems at first glance, with a lot of classic problem solving ideas.
* creative problem framing - Do you solve the problem of getting there faster, or do you solve the problem of needing to be in the first half to get what you want?
* game theory - Given the fact that variables change (which classroom you're in before lunch, if you have a teacher that holds you during that period, size/aggression of lunch period), is there a strategy that is likely to work every quarter?
* information security - Does the fact that your strategy will be made public effect it's usefulness?

I realize that's quite a digression from the send-a-message-to-aliens kind of problem, but I was trying to come up with an example of a problem that might pass the I'm-16-and-too-cool-for-this filter.

If that doesn't tickle your fancy, you could try having them solve famous mysteries (from both points of view).
* Who built the Georgia Guidestones?
* Who was DB Cooper?

These aren't quite as good because they don't actually get anything for having the best solution, but at least it's stuff that actually happened.


Another crazy idea that just occurred to me is to turn the entire class into an Alternate Reality Game with problems built in. The ARG is all about slowly pulling people in to the point where they're working hard to solve problems that under any other circumstance they would see as contrived and pointless. Just look at how many people tried to solve all the LonelyGirl15 stuff even after it was obviously a show. Some possible premises:
* You got permission to have a student participate in your class over video. Maybe he/she's in another country. Maybe he/she's one of those kids that can't ever go outside. Things happen. This is a really sketchy idea that I don't actually endorse, but it's the first thing that came to mind.
* Be really boring for the first few days, then have a 'vandalism event' at your school. Some people break in and spray paint something on the lockers / football field. Is it a code? What's with that goo on the ground? Maybe the math/science teachers can help? Maybe you find a URL in the code and it leads somewhere. A mystery man provides clues from time to time, but always in code. Security footage is missing.

Stories are fun and they always have problems. That's the nature of stories. Just tell the story of the problem you want to solve.

I'll admit this would take some serious effort, but I'm pretty sure if you pulled it off you would be the coolest high school teacher of all time.

OK, done with my crazy ideas. Good luck!
posted by systematic at 6:28 PM on May 12

Group work is an important skill. I'm not sure that throwing some students together and expecting them to "work together" will necessarily help teach that skill to a lot of students. I know it's not a perfect world, and I know that you'll probably end up with a group exercise, and I'm pretty sure it will be a good thing -- but I just wanted to add the thought that group exercises should probably be carefully monitored, guided, and constructed to make them work.

If the OP is a teacher, he or she probably has some training in this - but it seemed worth mentioning. Decathecting offers a worthwhile perspective, in any case.

- never learned to work well in groups while in school
posted by amtho at 7:06 PM on May 12

A few thoughts-
- Start small, so students have successful experiences to build on. Outward Bound-type courses start with group problem solving exercises like these. Or just 'build a tower with soda straws & toilet paper' kind of exercises.
- Brian teasers are good warm-ups that can be fun for all types of students.
- Like others have said, for a 'big problem', make it real. Problems don't have to be technical either, which can also broaden the appeal to other types of learners. How to organize a team is a problem. A person good at doing that can become president!
- Of course, the real goal isn't to solve the problem, but to learn about and use effective problem-solving tools. The more tools in the toolbox, the better prepared you are for then next problem.
posted by TDIpod at 7:16 PM on May 12

I remember participating in OM all throughout middle and high school. Unfortunately where and when I grew up, US First wasn't an option. Professionally, I've had the privilege of being able to work with teams on US First projects. The great thing about both competitions is that they require and focus diverse skills for success. Book smarts only got a team so far - you needed both that kid and the kid who was a pro in shop.

Poblem solving on paper is fun for analytical minds, but for some who might have a harder time focusing their minds on a task, physical construction can sometimes warrant many of its own elements of problem solving. Everyone gets the oportunity to not only participate in something which usually covers a strength, but they get to learn skills from eachother.

Things to think about:
What works projects could be student implemented at the school? Irigation projects to prevent damage to athletic fields (mathematics, civil engineering, natural sciences, general contracting), Planning and constructing nature trails (biology/botany, geology, fitness, general contracting), Improving school lunches on a budget (Health, nutrition, culinary arts, accounting, cost analysis, forecasting).
Think about some fun shows for inspiration: Junkyard wars (welding, machining, engineering) and Robot Wars (electronics, mathematics, engineering).

Make sure that there are constantly small problem solving tasks for students to do: build a tower out of straws, toothpicks, and a cup filled with shaving cream; list off different methods for crossing a body of water that don't involve a boat; etc... just keep their brains flowinging.

Last but not least, understand while this is nigh impossible, even the funny answers one might start to concoct to address each question take a person in the right direction towards being able to solve such a question.
posted by Nanukthedog at 8:08 PM on May 12

I'd like to apologize. I'm pretty sure my answer to your post about problem solving was zapped. I'm not sure if you saw it. I wanted you to know that I wasn't just trying to be a smartass; I had a longer response, and deleted it in favor of one that I thought was clever, but also meaningful through irony.

I wanted to take a moment to elaborate, if you'll bear with me. I was always either the smartest kid in class, or the one who (falsely) thought himself to be the smartest kid in class. Either way, I don't think it was fair to 100% of the students in any group into which I was placed. I always felt it was unfair to me -- that I was dragged down by underachieving students, that I was placing my grade at risk by their lack of attention. It may well have been the case that it was more unfair to the students who didn't think they were the smartest -- I am sure I came off as supercilious and even hostile. My response to your post suggests I have not entirely outgrown this.

In my time as a student, I thought that assigning groups was a sign of lazy teaching technique -- that the teacher was handing out roles not for group collaboration, but for certain students to teach certain other students. This may well have been false.

One point remains true, however: even if you are teaching honors classes, the groups that you assign will be nowhere near as homogeneous as the groups into which adults self-select. The overachievers will, largely, end up working with other overachievers. The underachievers will be installing sprinkler systems or flipping burgers. Of course there are counterexamples and overlap, but the frustration of this technique, so popular in my high school, led to my leaving school at 16 to become a college freshman. This may or may not have been an ideal choice.

So: just, please, be really careful when you're assigning groups. Not everyone is as misanthropic as I, and maybe, were I to have stayed in high school, I would have recognized value where I previously found none.
posted by quarantine at 11:27 PM on May 12

Lots of good ideas that I can do the legwork on. Shelleycat's mention of Future Problem Solving is a mindtrip to me, as I now recall that was the program I was in as a 4th-grader (I think I said 5th above, but remmeber better now). I never imagined that program existed beyond mid-1980s Nebraska where I experienced it, but that is exactly the kind of thing I had in mind.

I'll come back when I have a few more moments to add more thoughts, but in the meantime please rest assured that I am a semi-competent teacher and can handle the assignment of groups effectively. I have a lot of experience in the domain. Also, for the uninitiated, group work is THE WAY THINGS ARE DONE these days. It is the norm, it is expected and, done right, confers a great deal of benefits. Lazy teaching can take many forms--all of which are criminal--but group work is not inherently a lazy technique.

Hope we don't derail the conversation in this direction.
posted by etc. at 5:47 AM on May 13

I don't have any specific problem-solving ideas, but I want to suggest that you include some brainstorming practice in your initial class meetings. I have some very basic notes that I use for one of my [college-level] classes if you're interested. It's surprising how little my college kids know about how to come up with ideas.

And speaking as someone who gets your kids in class in a few years, THANK YOU! I love your idea and good luck with it.
posted by SuperSquirrel at 10:38 AM on May 13