Teaching conceptually means stepping back. This was incredibly hard for me. By nature, I want to help, hence why I (and you) became an educator. My first few years of teaching involved me rambling in the front of the room. While I was loving every second of my math lessons, I was doing all of the work.
Taking Away the “Think” Component
My early lessons were like the first page of every lesson in a textbook. These mostly involved students inputting numbers into blank spaces with step-by-step instructions provided. I was thinking for them. There was no productive struggle involved. I thought I was doing everything right. I had great standardized test scores, and I felt as though my students left me every year knowing the standards. However, they weren’t problem solvers, and they lacked math grit.
Through time, I learned that I shouldn’t be doing all of the talking and thinking. In fact, I realized that I should be doing about 30% of the talking and that timing was everything. You need to give your students time to grapple with the task at hand. I like to do this step of the process in groups. Typically you’ll see each group member contemplate the question and then someone finally starts the conversation. It might be quiet at first. It’s okay. Don’t panic. Eventually ideas are tossed around and then the group dynamic starts to grow. This collaboration is important for developing accountable talk. Students are defending and explaining math concepts. They are living the math instead of listening to it.
Here is an example of a task I presented to my students. To kick off our studies on classifying triangles by angles and sides, I gave each group a bag of triangles. They were asked to complete the first row of the chart. I did not explain what each header meant. That was their job to figure out. After some time, I filled in the first row with students’ ideas. If the students did not mention key ideas, such as equilateral triangles always have intersecting lines, then that was my time to intervene and model.
When To Step In
If a group is struggling you need to assist. Give them a hint or ask a question that will spark an idea. What you say or don’t say will affect the group, so be careful not to give away too much information. You don’t want your students to hit high frustrations level daily, but you’re taking away the productive struggle if every time they need help you come running. This process will take time for you and your students to master. The key is careful observations. I walk around all the time during math, watching facial expressions and listening to group discussions. I let the students dictate my level of interaction. When I sense that my students need help, I give them a scaffolding clue. The productive struggle doesn’t have to cease immediately. They need a lifeline to help them advance to the next step, and that next step should never be the answer itself.
You know what they need
We’re trying to build the problem solvers of tomorrow, students that work smarter, not harder. Children that truly conceptualize math. Take it day by day and modify accordingly.
My line of Power Problems are designed to target conceptual understanding of standards thru productive struggle. They are available for grades 3rd-6th.