Teaching Problem-Solving

Posted by Richard Kingham on March 09, 2022

Problem-solving is the most important skill that students learn in the classroom. It is the meat and potatoes of mathematics, whether the problems perplex the Stephen Hawkings of the world or first graders learning basic arithmetic. Strong problem-solving abilities will serve students in every profession and aspect of life. In this light, the teacher’s mission hinges on a single question: How can instruction develop all students into keen problem-solvers, regardless of mathematical aptitude or expressed interests?  
Let’s Get Meta

Teaching problem-solving is itself an act of problem-solving. Teachers encounter a jumble of student attitudes, skills, and behaviors when attempting to ingrain problem-solving into their approach to math. Some common challenges include students waiting for answers instead of trying to solve problems themselves, learning gaps, math-induced anxiety, misunderstanding of how problems are set up, and gaps in vocabulary and reading comprehension. Teachers need to untangle and identify these issues and then plan carefully in order to overcome them.

As with everything else in the classroom, structure is critical. At STEMscopes Math, we like the three-act method: engage and perplex; seek information and solutions; and reveal, discuss, and extend. 

Act I: Engage and Perplex

One of the first lessons creative writing students learn is the importance of capturing your reader’s attention from the get-go. The opening line from Franz Kafka’s Metamorphosis“As Gregor Samsa awoke one morning from uneasy dreams he found himself transformed in his bed into a gigantic insect”—pushes you headlong into the story. It is unusual for someone to wake up as a bug, and you just gotta know why it’s happening to this Gregor guy. The same principle of captivating your audience applies to math instruction. 

Each STEMscope Math lesson (which we call scopes) includes a hook, which consists of two parts: the pre-explore hook and the post-explore hook. The pre-explore hook includes an activity or engaging piece of content (such as a video, a discussion of students’ observations, or an opportunity to record questions from the whole classroom) that motivates students and defines the purpose of learning the new skill. The hook ultimately nurtures curiosity—a trait found in every great thinker who is compelled to solve difficult problems. 

Act II: Seek Information and Solutions

Curiosity generates questions, and questions encourage students to seek information and solutions. Act II is all about questions. Once students start asking questions on their own, teachers know they’re on the right track. The “explore” component in STEMscopes Math is largely dedicated to this purpose. In this section, students hone new math skills through several activities, including collecting data that will help them solve problems. 

Explore teaches students a vital part of problem solving: research. Research is a necessary skill for any long-term project: whether they’re solving problems in quantum physics or building a table, they will need to engage in research.

Act III: Reveal, Discuss, and Extend

The third and final act consists of students sharing, discussing, and extending their work. Act III depends heavily on students’ efforts during Act II. The better their research and preparation, the more every student will benefit from this last phase. 

In STEMscopes Math, the post-explore hook (the second half of the hook activity mentioned above) is a great tool for structuring Act III in your classroom. The post-explore hook is found in every STEMscopes Math lesson and acts as the second half of the hook. Here, students discuss their solutions and problem-solving methodology with the class. This is an excellent time for teachers to provide constructive feedback on student work. 

One struggle many teachers face is that students are unwilling to grapple with problems. Too often, they want teachers to give them the answers. The interactive, hands-on content in the pre-explore and post-explore hooks helps draw students into the problem-solving process and encourages productive struggle by making math less abstract and more approachable and connected to students’ daily experiences. 


Problem-solving is work—slow, hard, and frustrating work—even for the most advanced mathematician. It takes discipline and patience, so when we teach problem-solving to students, we are not simply equipping them with a set of tools. Rather, we are instilling in students positive habits and a way of facing the myriad challenges they will encounter in the world. 

Topics: math, "STEM", k12 education

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