As math educators, one challenge we face is guiding our elementary students to become “patient problem-solvers” rather than “impatient answer-pluckers.” If a student doesn’t develop confidence in math class during their early years in school, it can be easy for them to feel like they can’t be creative, engaged learners – instead, they can get focused on just finding the right answer to every problem. That focus can become a barrier to truly understanding concepts and thriving in math class.

For example, story problems offer students a way to explore how math applies to all kinds of real-life situations outside of the classroom – and that can get them really interested in math! But when students get into the habit of operating like “answer-pluckers” in math class, they don’t see a story problem as a chance to explore how math works; they just start trying to pluck out the solution. That’s why I developed a strategy that encourages my students to approach story problems – and all math learning – as patient problem-solvers. 

By putting my students in charge of building and solving story problems together, I encourage them to bring their full, creative selves to math class – and to see themselves as math people. Here’s my five-step process:

1. Use a slow reveal to introduce the lesson

My first step is to choose a few pictures to launch math class. To generate some interest and energy, I won’t start with the picture that’s directly connected to our math learning, and I’ll make the conversation feel open-ended. For example, if I show pictures of people with pets, I start by asking, “What do you notice? What do you wonder?” and then shift to questions like, “What’s your favorite color for a cat or a dog?” Sometimes I’ll ask questions to get their minds moving toward math, but nothing too direct, because I want to introduce our lesson with a slow reveal, and I want the ideas to come from my students. 

Let’s say we’re going to work on adding and subtracting. I won’t ask, “How many cats and dogs are in these pictures?” But I might ask, “If you could have any number of pets, how many pets would you have?” That gets students engaged, and it gently encourages them to take on a math mindframe without the teacher directing their thinking. 

Next, I show them the picture I built my lesson on. I tell them the facts, but I make it sound like a story: “This is Jenny, and she has eight cats and five dogs.” I’ll ask, “What do you notice and wonder about Jenny and her pets?” As soon as students start looking for things to notice and wonder about, they start seeing quantities and differences – especially because we used those previous pictures to shift into a math mindframe. Students naturally volunteer math-related observations like, “All the dogs are on the floor. Four are sitting up, but that one is lying down.” This sets the stage for our next step: collaboratively building math problems to work on.

2. Chart student questions to co-create the lesson

I always have a core math question in mind that I want students to engage with, but I also want them to be co-creators and owners of their learning. So I encourage them to ask questions that will lead to practicing the math skills we need to uncover, and I write their questions on a chart. As educators, we know sometimes students will ask exactly the questions we hoped for, but sometimes they won’t! So if you ask your class, “What do you wonder?” and students don’t come up with addition or subtraction questions, that’s OK. In those moments, I’ll follow up with guiding questions like, “What questions could we ask?” and “What question do you think I’m going to ask?”. As students generate ideas, they’ll come up with math questions I can record on the chart, like “How many pets are inside and how many are outside?” Or I’ll say, “This is my question for the chart: ‘How many more cats does Jenny have than dogs?’” and ask students to build on that. 

Then, I encourage students to go deeper in thinking about math, beyond what’s in front of them. I’ll say, “What questions would change the picture?” Students will share ideas like, “What if Jenny came home from school and each cat had three kittens?” This encourages students to take ownership of the lesson – and it shows them that they can use math imaginatively, not just to solve problems on a page. Lastly, I always add a large question mark at the end for any questions that may come to students later, when they start solving problems. The possibilities are often endless! This sets us up for what I call “Easy Differentiation” (more on this below in step 4).

3. Choose student questions for skills practice

When we have enough questions, I’ll say, “These are all great, but I need to choose one, because we want to look at our work together and compare our strategies. Let’s start with this one.” I usually have students solve the first question on their own, but you could have them work in groups. They share their answers with the class and I learn which aspects of adding and subtracting we need to review. We discuss those, and that helps me choose our next question. 

I love how this process builds in formative assessment because that allows me to zoom in on the math skills my students need to work on. But I also love how organic and fun this process feels for my students. The problems they come up with are exactly the same as the word problems I could give them. But because they generated each problem as part of our story, they’re not focused on getting the answer right – they’re just excited about calculating how many surprise kittens Jenny has. In my experience, it usually takes about three tries doing this with students before they really get good at thinking of their own questions – so if you are trying to implement this strategy, be patient and give yourself grace as you hone your craft.

4. Use student questions to provide differentiation for readiness

Each time I share this process with a first-year educator, I hear, “How do you build in differentiation?” That’s exactly what I would have asked, too! It can feel overwhelming for a new teacher to plan differentiation strategies for every student. I recommend my approach because it promotes student engagement AND teacher sustainability. When a student is finishing each question early, we go back to our chart and pick a more complicated question or create a bigger challenge. This differentiation strategy takes the student deeper into the content instead of pulling them away from it. I call it “Cheap Differentiation” because the students are doing the hard work, not the teacher. 

This makes lesson planning more manageable, and it renews student investment, too, because kids enjoy being invited to find a new question on the chart. Often, students are more motivated to solve problems which they or a friend thought of than the one that I’ve chosen. It doesn’t feel like “busy work” when a fellow student came up with it! Instead, I’ll hear them tell their classmate, “Hey, look, I answered your question about how many dogs could fit on the couch. I even drew a picture, do you want to see it?” Now both students are talking in an enthusiastic way about math, and it feels completely natural to them. Their teacher didn’t prompt them – they’re just making math language their own.

5. Invite students to be examiners, not explainers

When students are ready to come together and review problems, I recommend selecting a student’s work to share and discuss – but don’t let that student talk about their work! This might feel counterintuitive at first, but it promotes great engagement: Instead of passively listening to one student explain their work, the whole group gets to examine the work like detectives. Invite the class to think about these questions:

• Does the work make sense to you? What do you agree with?
• What connections do you make to your own work?
• Can you get inside ______’s head and figure out what they were thinking?
• Do you have any questions for ________?

When we do this on a regular basis, students learn to expect that their work may be shown and they won’t be able to explain away incomplete or messy work. That encourages them to invest in making their work more organized, complete, and precise – because they have an authentic audience with which to share their ideas. As students become more confident about having their work discussed, I add in the question “What might you suggest to this student to help them make their work even better?” By building a classroom culture that empowers students to support one another with compliments and suggestions, we can encourage all our students to take on a growth mindset and a continuous improvement trajectory.

I think that’s the core of why it’s so valuable for students to become patient problem-solvers: It empowers students to be active owners and users of math, not passive recipients of it. When I share this strategy with fellow educators and their classes, it’s so powerful to see the impact. Students who usually walk into each math class without much enthusiasm start getting so interested in building our story problems and figuring out solutions. After a while, students don’t just want to pluck out the right answers by the time class ends – they want to understand and enjoy how math works. There’s no better way for a math class to conclude.