There is a big difference between getting the right answer and explaining how you got the right answer. Just ask renowned math educator Marilyn Burns, the founder of Math Solutions and creator of Math Reasoning Inventory (MRI). MRI is a formative assessment tool which helps teachers assess students’ numerical reasoning and understanding of math principles through conversations.
Like Marilyn Burns did when she laid the groundwork for MRI, many math teachers are having conversations with their students to hear how students ended up with any given answer. A recent Education Week article explores the old adage in the math classroom of “I can't help you if I can't see what you did.” As the author explains, when requiring students to show their work, it may be taking away from a child’s mathematical thinking and weakening his or her problem solving skills. But when students explain their answer, they are sharing their mathematical thinking in a thoughtful and thorough way, while also contributing their opinions on incorrect responses.
I think this method is critical to confirming student comprehension. If the goal is understanding, and a student cannot explain their thought process and fully communicate how they got the answer, then they have not truly mastered the task at hand. It's easy to get stuck memorizing algorithms and processes.
As the Common Core Standards for Mathematical Practice say, “Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.”
Teachers: Do you have any strategies in getting your students to explain their answers?