Balancing Instructional Strategies in the Math Classroom

December 2023

When you read inquiry-based instruction or direct explicit instruction, what feelings come to mind? Are they positive? Negative? Neutral? It often feels like an “either-or” debate, doesn’t it? Many educators like yourself feel caught in the middle. If your school emphasizes inquiry-based instruction in mathematics, you may feel insubordinate if you use some direct explicit instruction. And if your school emphasizes direct explicit instruction, you may feel like you are being noncompliant if you use some inquiry-based instruction. However, there is a time and place for both methods of instruction, and our job as educators should be to use appropriate strategies at appropriate times.

There is often a misunderstanding about what these two strategies look like in the mathematics classroom. Some perceive inquiry-based instruction as completely hands-off; the educator presents the problem and then expects students to figure everything out independently. This simply is not true. Educators must be actively involved, monitoring how students approach the problem, providing scaffolding instruction as needed, and then selecting, sequencing, and sharing student work so that all students develop an understanding of the concepts. Some perceive direct explicit instruction as the educator doing all the thinking and the students merely mimicking what the educator has done. This is not true if this strategy is employed correctly. The instruction can build off existing student knowledge and provide the opportunity to formalize student thinking and develop precise vocabulary.

The question should be “When do I use each?” rather than “Which one should I use?” Inquiry-based instruction should be used most of the time as students begin to understand the concepts they are studying. Their curiosity is sparked, and they can begin to see the reason of learning the content, often increasing their desire to learn the material. Inquiry-based instruction centers on and is driven by students’ thinking as they develop a deeper understanding. Direct explicit instruction can then be used to formalize that understanding and provide precise mathematical vocabulary and language. It can provide an opportunity for students to consolidate their thinking. We should also acknowledge that there are some skills or ideas that students need to be told, for example, what numerals are called, explanations of mathematical symbols, and standard mathematical vocabulary.  

Historically, and likely in many settings today, direct explicit instruction has been over-emphasized and overused, while inquiry-based instruction has been underutilized. As a result, many adults confess that they disliked learning mathematics and don’t feel comfortable in their mathematical abilities. If we are genuinely interested in meeting the needs of all our students, we must continually work to increase the amount of inquiry-based instruction while still using direct explicit instruction when and where appropriate.

As we approach some time away from our regular schedules and routines with our students at the end of the month, I hope each of you can find some time to rest, relax, and rejuvenate before resuming the vital work we do in better meeting the needs of each of our students.

Kevin Dykema
NCTM President
@kdykema