One of the most talked-about skills in education is the skill of problem-solving.
But, as this list of acronyms indicates, educators are almost baffled as to how to actually teach problem-solving.
Instead of teaching the authentic process, we sometimes fall onto the trap of using only test-taking strategies to mimic what critically think adults actually do when presented with a question or problem. I had certainly fallen into this trap my first year of teaching.
The science and math departments at KIPP Academy recognized this, thank goodness, and so we came together to align how we teach and reinforce problem-solving across our content areas as well as across our grade levels.
At first, we began with just placing all or our problem solving strategies on the table so that soon, all the strategies bled into one another and started to look like alphabet soup. Our 6th grade math teacher, however, pushed back and said*… “We don’t solve problems like this, so why do we teach our kids to? They hate going through all these steps and complain about it.” He went on to say, “I think about problem-solving as layers. At the most basic, problem solving is understanding the question and then thinking about it. That’s it. The next layer is the one that includes strategies.”
A light bulb went off in my head. “I get it! The first layer is like buckets. One bucket holds all the strategies for identifying the problem, like underlining important words and defining them, and the questions/brainstorming/pondering bucket has strategies like researching, or making connections.”
“Right, and each layer is like a transparency, one on top of the other.”
“But what are those buckets? Or layers?”
“I don’t know, but just talking about it won’t help. I’d like to do an actual problem together, as a team, and see how we actually figure it out. I wish we could video tape it or something, to see what we do.”
“Well, what’s a good problem that we can use?”, another teacher piped in.
“I have some sample problems right here.”
“What about, ‘Why do glasses have the shape they do?’”
“Do you mean reading glasses? Or drinking glasses?” someone asked.
“Drinking glasses.”
“That was important,” I said, “because I was totally thinking reading glasses.”
“Do we actually have transparencies? And markers?”
“Yeah, I do,” the sixth grade science teacher said. One minute later we had transparencies and expo markers on the table.
“Here, you get it, right?”
“I think I do,” I said. “I’ll go ahead and write what we do. I think that we’ve all agreed that the first step is ‘Identify the question’, right? Remember how we had to clarify whether or not it was drinking glasses or reading glasses?” I wrote “Identify the Question” on one transparency.
“And if you were a child,” the seventh grade math teacher commented, “you’d also have to translate ‘glasses’ into cups. My kids call all glasses, ‘cups.’”
“Right, so a strategy to identify the question would be to define the vocabulary.” I wrote “Vocabulary” in another color and on another transparency to visually make a second layer.
At this point, everyone started jumping in. “I would start by drawing a picture of all the different glasses I can think of. Some with stems, some without, some that are large, some that are small” said the seventh grade science teacher.
“Great, then I would ask, why are there some similarities, and why are there some differences? For example, why are all glasses round?”
“Well, that helps you drink from any part, right? You don’t have to worry about putting a corner in your mouth.”
“And why are glasses a certain size? I mean, why is its circumference a certain size”
“It has to do with efficiency. If it’s too small, then you can’t pour anything into them.”
“I was thinking more that it can’t be too large, otherwise you can’t pick it up…”
Our discussion went on as we kept on proposing new questions and new answers. We talked about how we were using strategies like visualizing objects in our mind, and asking clarifying questions. We talked about how it was important that throughout this whole process, we were checking for reasonableness. Did our ideas make sense? We built off of each other’s thoughts and went off on different tangents, but we always returned to the question of, “Why do glasses have the shape they do?”
Finally, as we were exhausting our different options, I suggested that the best way to present our answer would be through an infographic. I quickly sketched out my idea and explained, “Let’s draw a picture of a glass, or make a model, and then identify each part of that glass and explain the different variations that are possible for that part and why each variation was necessary. In other words, let’s apply what we had discussed and learned to some product to communicate our results!”
We agreed as a faculty that this would be an excellent idea.
“So wait, what do we call the second step to problem-solving? We’ve been questioning, pondering, brainstorming…”
“What about brainstorming?”
“I don’t like that, because we’re doing more than brainstorming.”
“I think we’ll just have to call it ponder.”
“I agree.”
“And what about that last step. It’s not coming up with an answer, and we don’t want students to get there too quickly.” (Students sometimes have the bad habit of choosing an answer first, and then retroactively justifying their answers instead of the other way around.)
“Let’s just keep the word, apply.”
“I agree. It leaves open the option to use multiple ways to share the answer, whether it’s through an infographic, model, or book report.”
“Awesome.”
“Cool.”
And, there you have it, the three steps to problem solving:
- Identify the Question
- Ponder
- Apply
I learned a lot from this experience.
First, I was completely impressed by how collaboration could really bring out the best. As a joint math and science faculty, we are more tightly knit together as a professional learning community because of this experience, and we’ll be using the same language to support our students as they develop their own problem solving skills.
Second, we’re aligning our work so that our students, too, can have the authentic experience we had problem-solving. This experience has inspired me to allow my students the time and skills to really work together to tackle problems. Not only will they learn content more deeply and authentically, they’ll be engaging in the exact kind of authentic work adults do when they are faced with a problem.
Finally, I like how this new framework gives students the flexibility to choose strategies that work for them. My team teachers and I did not all use the same strategies on this problem, but that was great because we were able to put our strengths and contributions together to make something truly valuable. In the same way, I’ll teach my students the different strategies they can “try out”, but then give them the choice to choose strategies that work the best for them. Never again will I give my students an problem solving strategy that they have to follow. Instead, as long as they show that they’ve gone through the three steps above, they’ll be golden.
My Infographic Sketch (not complete, but hopefully you get the idea) (= :
*All quotes have been reconstructed from memory. I tried to be as close to the spirit of our conversation as I could, but I also know how fickle our memory is, so all mistakes / misinterpretations are my own.
Deborah Chang
Deborah,
Thanks for posting. First of all, I was a little appalled by the title of your post, but quickly learned to appreciate that you mean “death to cutesy frameworks that are only really useful to answering word problems that seldom resemble the real world.” Amen to that. But STRATEGIES, at least as I understand the term, are super important and need to be taught explicitly, then called out when students are using them. I use Rafe’s framework for solving problems (of any kind): 1. Understand the question. 2. Gather relevant data (adults usually do this so naturally they don’t realize it.) 3. Choose a strategy/Make a plan 4. Use your plan to solve the problem, or, if you aren’t yet able, go back to a previous step (1,2, or 3.) 5. Look back: Did you answer the question? Does your answer make sense? 6. I like to add a sixth step: Can you generalize from your answer to this question? What are the implications?
In terms of strategies, unless you teach kids how to guess and check, it’s tough to help them become better at it. Other strategies include choosing an operation, writing an algebraic equation, drawing a picture, looking for a pattern, and many more. If I had to describe, using my framework, what you all did to solve the glasses problem, I would say you primarily used “find a pattern”, as you tried to boil down all possible shapes of glasses into the features common to all glasses before intuiting why these glasses had to have these elements in order to function as glasses.
Also, thanks for sharing