My brother and I crouched in the dark, damp earth. I scraped with a stick until a bright glint of white caught my eye. Carefully, I pried at the sharp edges with gritty fingers. A grin spread across my face as I looked closer and noticed the delicate designs covering the smooth shard.
Clink! It hit the growing pile of objects that stood out like a floral suitcase on a carousel of black ones. There were parts of metal hinges and nails, but most intriguing to me were the shards of painted china.
How did they end up on this mountain hillside? We could only guess.
As a kid, I felt like I had absolutely found treasure on that camping trip. And as an adult, I still get amped up when I find a hidden gem.
I’ve got a hidden gem for teaching problem solving to share that I can’t believe I didn’t find sooner.
But first, let’s be real for a second:
Problem Solving Expectations Are Off the Hook
You were probably a smart kid like I was. Do you remember when you could just skim for the two numbers in a word problem and then either add or subtract, depending on the theme of that side of the worksheet? Not anymore!
I’m pretty sure I was in denial the first time I read the standard saying my 2nd graders need to solve problems with “unknowns in all positions.”
The thought of giving kids an equation with a blank spot anywhere BUT at the end made my stomach churn.
The good news is, it doesn’t have to be that way.
The Secret is in the Schema
Do you remember our old pal Piaget from educational psychology in college? He put forward the idea of schemas which are like frameworks for organizing information in our brains.
For example, you’ve probably built up a decent schema about animals over the years. You know there are categories such as mammals, reptiles, birds, etc. and you can list basic traits and examples of these kinds of animals.
So when you encounter an animal at the zoo that you’ve never seen before, you probably would say something like, “well, it’s got to be some kind of antelope.”
That’s because you noticed this animals has four legs with hooves, short bristly fur, a slender body, and two pointy antlers.
When you reached back into your animal schema and compared the traits of this unfamiliar animal with the animals you already know about, you came to the reasonable conclusions that it was similar to an antelope.
Schema plays a big role in problem solving, too.
How to Build a Word Problem Schema
Have you seen the cube-shaped shelves at Ikea? I definitely don’t know the Scandinavian term for them but I do love an organized shelf! It’s a good way to imagine a solid word problem schema.
Picture a 3×4 set of these shelves. There is one problem type for each of the 12 compartments.
12 different problem types!?!?
I know, I know…but your kids are probably already familiar with at least a couple of them and some of them are pretty similar to each other so…you’ve totally got this!
When kids are aware of and have practiced each problem type, then when they encounter a new word problem, they can compare to the types they already know about and get a good idea of how it could be solved.
The secret gem I referred to earlier is a chart of the problem types and how they’re related that I originally found here.
I’ve translated it into a more kid friendly version AND a mini book which you can get for free!
So what do you do with the chart?
- Use it to make sure you’re giving students practice with each problem type. (Confession: before finding this chart I wasn’t even aware of some of these problem types)
- Spend time to focusing on the tricky problem types like comparing
- Show students how to use pictures, number lines, bar diagrams, and equations to model the problem types. Identify which strategies work the best for each problem type.
- Give students word problems with the numbers blanked out. This lets them focus on identifying the problem type FIRST rather than scanning for two numbers to pop into an equation. When they truly understand the problem they’re much more likely to get the right answer!