Even students who are quick with math facts can get stuck when it comes to problem solving.
As soon as a concept is translated to a word problem, or a simple mathematical sentence contains an unknown, they’re stumped.
That’s because problem solving requires us to consciously choose the strategies most appropriate for the problem at hand. And not all students have this metacognitive ability.
But you can teach these strategies for problem solving. You just need to know what they are.
We’ve compiled them here divided into four categories:
- Strategies for understanding a problem
- Strategies for solving the problem
- Strategies for working out
- Strategies for checking the solution
Get to know these strategies and then model them explicitly to your students. Next time they dive into a rich problem, they’ll be filling up their working out paper faster than ever!
Strategies for understanding a problem
Before students can solve a problem, they need to know what it’s asking them. This is often the first hurdle with word problems that don’t specify a particular mathematical operation.
Encourage your students to:
Read and reread the question
They say they’ve read it, but have they really? Sometimes students will skip ahead as soon as they’ve noticed one familiar piece of information or give up trying to understand it if the problem doesn’t make sense at first glance.
Teach students to interpret a question by using self-monitoring strategies such as:
- Rereading a question more slowly if it doesn’t make sense the first time
- Asking for help
- Highlighting or underlining important pieces of information.
Identify important and extraneous information
John is collecting money for his friend Ari’s birthday. He starts with $5 of his own, then Marcus gives him another $5. How much does he have now?
As adults looking at the above problem, we can instantly look past the names and the birthday scenario to see a simple addition problem. Students, however, can struggle to determine what’s relevant in the information that’s been given to them.
Teach students to sort and sift the information in a problem to find what’s relevant. A good way to do this is to have them swap out pieces of information to see if the solution changes. If changing names, items or scenarios has no impact on the end result, they’ll realize that it doesn’t need to be a point of focus while solving the problem.
This is a math intervention strategy that can make problem solving easier for all students, regardless of ability.
Compare different word problems of the same type and construct a formula, or mathematical sentence stem, that applies to them all. For example, a simple subtraction problems could be expressed as:
[Number/Quantity A] with [Number/Quantity B] removed becomes [end result].
This is the underlying procedure or schema students are being asked to use. Once they have a list of schema for different mathematical operations (addition, multiplication and so on), they can take turns to apply them to an unfamiliar word problem and see which one fits.
Strategies for solving the problem
Struggling students often believe math is something you either do automatically or don’t do at all. But that’s not true. Help your students understand that they have a choice of problem-solving strategies to use, and if one doesn’t work, they can try another.
Here are four common strategies students can use for problem solving.
Visualizing an abstract problem often makes it easier to solve. Students could draw a picture or simply draw tally marks on a piece of working out paper.
Encourage visualization by modeling it on the whiteboard and providing graphic organizers that have space for students to draw before they write down the final number.
Guess and check
Show students how to make an educated guess and then plug this answer back into the original problem. If it doesn’t work, they can adjust their initial guess higher or lower accordingly.
Find a pattern
To find patterns, show students how to extract and list all the relevant facts in a problem so they can be easily compared. If they find a pattern, they’ll be able to locate the missing piece of information.
Working backward is useful if students are tasked with finding an unknown number in a problem or mathematical sentence. For example, if the problem is 8 + x = 12, students can find x by:
- Starting with 12
- Taking the 8 from the 12
- Being left with 4
- Checking that 4 works when used instead of x
Strategies for working out
Now students have understood the problem and formulated a strategy, it’s time to put it into practice. But if they just launch in and do it, they might make it harder for themselves. Show them how to work through a problem effectively by:
Documenting working out
Model the process of writing down every step you take to complete a math problem and provide working out paper when students are solving a problem. This will allow students to keep track of their thoughts and pick up errors before they reach a final solution.
Check along the way
Checking work as you go is another crucial self-monitoring strategy for math learners. Model it to them with think aloud questions such as:
- Does that last step look right?
- Does this follow on from the step I took before?
- Have I done any ‘smaller’ sums within the bigger problem that need checking?
Strategies for checking the solution
Students often make the mistake of thinking that speed is everything in math — so they’ll rush to get an answer down and move on without checking.
But checking is important too. It allows them to pinpoint areas of difficulty as they come up, and it enables them to tackle more complex problems that require multiple checks before arriving at a final answer.
Here are some checking strategies you can promote:
Check with a partner
Comparing answers with a peer leads is a more reflective process than just receiving a tick from the teacher. If students have two different answers, encourage them to talk about how they arrived at them and compare working out methods. They’ll figure out exactly where they went wrong, and what they got right.
Reread the problem with your solution
Most of the time, students will be able to tell whether or not their answer is correct by putting it back into the initial problem. If it doesn’t work or it just ‘looks wrong’, it’s time to go back and fix it up.
Show students how to backtrack through their working out to find the exact point where they made a mistake. Emphasize that they can’t do this if they haven’t written down everything in the first place — so a single answer with no working out isn’t as impressive as they might think!
Need more help developing problem solving skills?
Read up on how to set a problem solving and reasoning activity or explore Mathseeds and Mathletics, our award winning online math programs. They’ve got over 900 teacher tested problem solving activities between them!