Getting Students to That 'Aha!' Moment in the Math Classroom

This post is part of the Into the Classroom blog series, in which educators share their successful teaching strategies and practices.

As a teacher, you may feel pressure at times—to get through a curriculum, for instance, and to have students perform well on assessments. When you first introduce a topic, it can be difficult to take the time to allow students to really make sense of the math in the hopes that you will spend less time later reviewing topics due to their lack of understanding. 

As a coach, I am fortunate to be in a variety of classrooms to support teachers and student learning. The best days are when teachers tell me that a previously unengaged student was engaged in a lesson for the first time and was “actually doing the math.” That aha moment on a child’s face when connections are made is unmistakable.

Change is difficult. Think of personal changes you have tried to make, such as living a healthy lifestyle. If just the desire to do well was the answer, we would all eat healthy, exercise, and be at our ideal weight. We all have habits and practices we need to change and obstacles to overcome to improve our health. The same idea applies in classrooms and how we teach.

As educators, we should be striving for meaningful improvement in our instruction and students’ learning. This requires being mindful of changes we need to make to allow each of our students to become engaged in the mathematic concepts we present.

How do we teach at a deeper level so students can really understand concepts, then apply their understanding and skills to solve problems? One way is to allow and actually expect students to think about contextual problems. Even when we provide tasks that have a wide range of accessibility, we all too often jump in to “help” them by providing clues or rules and even telling them what to do next at the first sign of a struggle. Students learn to just wait for this to happen instead of engaging in a productive struggle. 

Here’s Your Challenge

I challenge readers to think about, and maybe track, how many tips, acronyms, and rules we give to kids to get them to perform steps to find an answer. This can be an eye-opening and even a painful awakening. Have a fellow colleague track these practices or film or audio record your lesson. When I did this, I went with the voice recording first. This way, only I would know how many times I did the work for my students or led them to a solution. After all, no one needs to know the 1,000-calorie indulgence you had in a moment of weakness. 

I, like all good educators, wanted my students to really be engaged in their learning, so I knew I needed to make a change. Being aware of my reliance on procedures when students struggled made me mindful of the need to increase my own understanding of concepts. As I dug into the concepts that my students struggled with most and personally learned the how and why behind those concepts, connecting multiple ways to represent and model the mathematics, I was able to better choose good tasks and questioning strategies to lead the lessons. 

Moving forward, I made a conscious effort to not provide the tips and tricks to my students. Increasing my own understanding of a concept allowed me to ask questions about the concept when students went down that familiar path. For example, rather than relying on common denominators as the single method for comparing fractions, I asked questions about fractions with common numerators and benchmarks, and encouraged students to create models. In return, my students became engaged, and even the most reluctant learned that I was not going to swoop in and provide answers. I started to see that look on their faces and hear, “Ooh, I get it!” There is nothing more rewarding than that aha moment when students make connections and actually apply the mathematics. 

Awareness of what we are actually doing is the key to making positive changes. It is like watching your movements in a mirror while working out. What is in your mind’s eye does not always match what you see in the mirror.

My Final Tips
  • Make a commitment. Long-term improvement in instruction takes time and effort.
  • Voice record, use video, or have a peer keep track of tips, tricks, and hints you give while teaching.
  • Set realistic goals.
  • Dig into the math to make sure you personally have a deep understanding of key concepts. This is crucial to picking good tasks and planning questions you will ask to elicit thinking and promote discourse.
  • Reflect on lessons and take notes on student thinking to help you form better questions.  
  • Be patient, stay the course, and enjoy watching students make sense of concepts.

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Learn more about HMH’s Into Math program for K—8 students and Into AGA program for grades 9—12.