How do students come to know that persevering in mathematics has merit? I believe it is with the help of a great teacher. Teachers can listen to students and help them to understand that their mathematical thinking is powerful. Teachers facilitate the learning of students, justifying their mathematics in appropriate ways and gear lessons to the level of their mathematical maturity. It is important for students to know they are expected to explain how and why they have arrived at a math problem’s solution. All of this takes perseverance by students, even though this may mean enduring being “productively stuck.”
I recently received a letter from a North Carolina first grader. She wrote to me because she had been working on an AIMS math task based on finding puzzle solutions using tangrams. When doing the task, she ran into a roadblock. She was “productively stuck.” She was presented with the outline of a shape and was asked to fill it with five pieces of a seven-piece tangram puzzle. She could only find a solution for the shape that used four pieces from the tangram puzzle but did find that five puzzle pieces could fill the shape if she could use two sets of tangram puzzles.
This first grader persevered to find a possible solution to the problem. She wanted us at AIMS to know about the dilemma she had faced and how she had found a solution for it. I was puzzled how the situation could have come about in the first place. I looked at the AIMS task, “Sea Shapes”. The crab claw outline the student questioned did list that five tangram puzzle pieces were needed to fill it. Turns out her teacher had an older version of the task that originally went out to print originally which contained a mistake. I made sure I sent the corrected version to the teacher right away.
This student was “productively stuck,” but persevered. She found a solution and justified her mathematical thinking. Her teacher facilitated her in the process and invited her to work until she came up with a solution. She went farther than what her teacher may have imagined and ended up sending a question to the AIMS Center for Math and Science Education. This is exactly how we hope that students will always persevere!