How My Students Really Became Excellent Problem Solvers

Growing up, I was pretty good at math except for problem-solving.  When I think about it, we were just sort of expected to be able to solve problems if we knew the math.  We weren't actually taught how to solve them.  Thank goodness that has changed!

Problem-solving is an essential part of mathematics education, and it is a skill that can be developed and nurtured at an early age. In the Ontario math curriculum for the primary grades, problem-solving is a significant focus, with students expected to develop problem-solving strategies and apply them to a range of mathematical situations.

Because I didn't think I was good at problem-solving, I made it a priority to learn how to teach it.  In fact, most of my math programming focused on solving problems.  And my students really became excellent problem solvers!

This was my approach to teaching problem-solving:

Emphasize problem-solving strategies: Teach students a variety of problem-solving strategies, such as using manipulatives, drawing pictures, acting out problems, and making a list or a chart. Encourage students to explain their thinking and reasoning behind the strategies they use.  This takes the emphasis off getting the right answer and focuses more on the process of solving the problem.  

We had daily problem-solving sessions regardless of the strand we were doing.  Students used their math journals to record answers and then we would share their strategies.  I would put that strategy on the board and we would discuss how it might work.  Participating improved as students were exposed to different strategies and they developed confidence in their skills.  

Use open-end problems:  Open-end problem solving is a skill that helps students think creatively and critically.  It also focuses more on the process rather than the answer.  If a student comes up with just one possibility, and they usually do, it is a success!

Sample problems included:

• There are 5 apples in the bag.  Some are red and some are green.  How many could be red and how many could be green?
• I have 3 coins in my pocket.  They add up to 25 cents.  What coins could I have?
• how many ways can you make "10"?

Solve a simpler problem first.  Although this is a common "strategy" to solve problems, it is also a good way to teach.  When reading or hearing a problem with big numbers in it, some students tend to feel overwhelmed and "go blank" Use the same words but change the numbers to those that are less threatening.  Students will feel safer using smaller numbers and, once they have their confidence back, can go on to solve the more difficult ones.  The students must have experience with the different wording of problems so that they are not confused when presented with them.

Use visual aids: Visual aids such as diagrams, pictures, and graphs can help students understand and solve problems more easily. Use visual aids to illustrate problem-solving strategies and to show the relationship between numbers and quantities.  I had a problem-solving strategy "board" in my classroom and would encourage students to check it out if there were having difficulty.

Provide practice opportunities: Practice is key to developing problem-solving skills. Provide students with a variety of problems to solve and encourage them to work in pairs or small groups. Monitor their progress and provide feedback and guidance as needed.

When teaching a new or different type of problem, I would often put students in carefully selected groups usually with a strong student, a struggling one, and then two average students.  This worked for new situations when the stronger student could guide the others.  

Sometimes I would group by ability.  I would give them chart paper and markers and set them off.  The struggling students were less intimated by stronger students this way and those who normally sat and did nothing became leaders.  When we shared, we saw a wider variety of strategies, such as very basic and some highly skilled.  Everyone felt proud of their work and eager to share.  There was no judging of strategies - we just looked at how they worked and celebrated the "differentness" of them.  Regardless of the groupings, having students work together to solve a problem is a valuable experience.

Foster a positive attitude towards problem-solving: Encourage students to take risks and try different problem-solving strategies, even if they are unsure of the answer. Celebrate their successes and encourage them to learn from their mistakes.  If the teacher seems excited to teach it (even if you don't feel it), the students will be excited to learn it.  I would start off a lesson with "Guess what?  We are going to do our favourite thing today and that is to SOLVE PROBLEMS!  Yay!"  It worked!

One thing I did NOT do was teach students to look for keywords.  This is fine if you are using a standard problem such as:  "There were 5 birds in the pond and 5 birds in the tree.  How many birds were there altogether?"  But how about this one?  "There were 10 birds.  Some flew away.  Now there are 5.  How many birds flew away?"  Students are more likely to add 10 + 5 to get 15.  

Here are some sample problems I used in Grade 1:

6 birds are in a tree. 4 more come.

How many birds are in the tree now?

10 birds are in a tree. 7 fly away.

How many birds are left in the tree?

8 birds are in a tree. Some fly away. Now there are 5 birds left. How many birds flew away?

There are some red birds in a tree. 6 bluebirds come. Now there are 9 birds in the tree. How many red birds are there?

There are 8 birds in a tree. Some are red. Some are blue. How many birds are red and how many are blue?

There are 4 red birds in a tree. There are 2 more blue birds than

red birds. How many bluebirds are there?

There are 6 red birds in a tree. There are 3 fewer bluebirds than redbirds. How many bluebirds are there?

How to Assess Word Problems:  Students should have a rubric to help ensure that they are showing their work including a number sentence, pictures, and a word answer.  I have created a simple rubric for this purpose along with a recording sheet and a student self-assessment in our Problem-Solving Assessment package for Grade 1 although it could also be used up to Grade 3.  Click on the image to have a look!

 

Problem-solving is an important skill for students to acquire.  Focus on strategies, not the answers.  They will come.  Students need experience with a variety of problem types, specific teaching of strategies, and a positive classroom environment where they feel safe to share.  Open-ended problems encourage higher-order thinking skills while visual aids help remind students of strategies and how they work.  Solving a simpler problem is an excellent strategy to build student confidence. Check out our Problem-Solving Assessment package for an easy-to-use rubric, class recording sheet, and student self-assessment.