5 Key Steps to Creating a More Productive Classroom

Every teacher has days where there’s a hum of energy during math class. Students are excitedly discussing their ideas about how to solve problems. Some kids draw to better explain their thinking. Others work with manipulatives to explore a novel approach. A few students are huddled together as they consider and discard various solution paths. Your students are learning, and they are having fun. Not every day will be like this, but what can you do to ensure that most days math class is a time when students eagerly take on new challenges, confident that they can do math.

Although there are many ways to make sure you bring your A game to the math classroom, I think the following five steps are key to ensuring that your students become capable mathematicians.

Step 1: Believe all students can learn.

Too many students believe that they just aren’t good at math, and therefore they think working hard in math class isn’t worth the effort since they aren’t math people. There is no such thing as a math person, no math gene that some kids have, and others don’t. Every student can do math given the time and right instruction, even those children who may have heard (from parents, teachers, classmates) that they’re bad at math.

When you believe students can do math, they believe it too. They may struggle, but that’s okay. Math can be hard. Every student—even those who seem to whiz through every assignment— struggles. As long as the struggle remains productive, students can master the material you are teaching. Their belief that with effort, they can learn prepares students to succeed not only in math class but life in general.

Not every student will pursue advanced math, but every student deserves the opportunity to become a competent, confident mathematician.

Step 2: Create a safe, student-centered classroom.

You may remember your math class as a place where you hoped the teacher didn’t call on you for fear you might not know the correct answer. It can be hard to make mistakes in front of your classmates. But progress in math, as with so many areas, is often driven by making mistakes. Think about theoretical mathematicians who may work for years on the same problem without ever finding a workable solution. They know that with each theory they test, even when it is not correct, they get closer to finding an answer.

Students must feel that they can take risks, try new approaches, and share their thinking. In math class, the real learning takes place not in quickly finding answers, but in understanding the math behind the problem. Students need a supportive environment to explore (on their own or together) new ideas, make observations, and posit solutions so they can make sense of math. To grow as mathematicians, they need to know that they can suggest novel approaches, even ones that seem off track, and make mistakes. It’s simply part of the learning process.

And I would encourage you to show your students that you make mistakes too. No one, not even the teacher, knows everything.

Step 3: Ask questions.

If I had a magic wand, I would make sure that every teacher in every math class at every grade level asked more questions. Too many students think when the teacher asks a question it means they’ve made an error and out comes the eraser. However, asking questions should be seen as a normal part of math class. Mathematicians ask lots of questions, of themselves and of their colleagues. It’s a way to better understand their own and others’ thinking.

We need to ask questions so students can share their ideas and listen to and learn from classmates’ perspectives. There are different types of questions you can ask depending upon the learning purpose of your inquiry. The important thing is that questions help students explain their ideas, consider different perspectives, and consolidate their understanding. Ultimately effective questioning leads to deeper learning.

Furthermore, asking questions helps you assess your students’ understanding and progress. Where do they need additional instruction? What misconceptions do they have? Are they ready to move forward?  Do they need more challenging or less complex problems?

Step 4: Give students time and space to think.

Too often we move kids from reading a word problem or learning about a new concept directly to symbolic language. But when students don’t have time to use visuals or manipulatives or explain concepts in their own words, they never explore the math behind the equation. To truly make sense of math, students need to spend time in what I refer to as the “math sandbox.” Just as kids use buckets and shovels to build sand creations, they need the opportunity to use drawings, ten frames, counters, and other mathematical representations to explore the math behind the concept. It’s while exploring in the math sandbox where they select and discard tools and strategies, that they deepen their understanding and start to own their learning.

Step 5: Be a life-long learner.

Even after more than three decades as a mathematician, I look forward to learning new ways to teach math more effectively. I regularly check in with other math content creators, I attend conferences, I read cutting-edge research papers, and I visit classrooms across the nation. There are so many exciting ideas in the math sphere, and I’m eager to learn how I might apply the best of these to improving the work I do for ORIGO.

So, take advantage of the great learning opportunities available. Review the research, lesson, and assessment notes provided with your curriculum. Join a group of teachers from around the country on Facebook. Read a math blog, perhaps this one regularly. Attend a webinar. Take a class. Read a book. Listen to a podcast. Just make sure you tap into the great thinking from math thought leaders, education companies, and other teachers. I think you’ll find that not only do you improve your practice, you’ll also continually renew your enthusiasm for teaching math.