Learning More About The Mindsets And Behaviors That Make Us Successful Mathematicians Is Key To Growing Young Mathematicians.
Unfortunately for many adults, the way we went about being successful in our elementary and middle school math classes was to try to fly under the radar, do exactly as the teacher said, never challenge anything, try to guess what the teacher wanted us to answer to a particular question, regurgitate exactly what we learned the day prior, and mimic the way our teacher solved a problem by mirroring his or her work. This is the opposite of what a child needs to believe about what it means to "do math" or to "be a mathematician” and a classroom culture built on these ways of interacting — such as through regurgitation, mimic, and copying — creates a maladaptive concept of a student’s role in a mathematics course.
In our classrooms, students learn quickly— as that is our expectation — to think of their role in interacting with mathematics as very active.
Students understand their role is to “construct understanding” of the math concept in the lesson and that this is best accomplished by asking questions, making observations, discussing errors, and challenging themselves. Math is treated as a serious topic, and accountable thinking, logic, good questions, analysis, the challenging of assumptions, persistent attention, wondering, encouraging one another, using precise mathematical language, justifying thinking, and making a strong argument are revered and encouraged. Mathematics is not something that one just “absorbs.” It is not something one just does. It is not something you just “get” because the teacher spoke aloud. Mathematics is something you interact with, wonder about, grapple with, discuss, and come to understand deeply. Making sense is the goal, and deep understanding comes from high expectations, the right learning community, and strong teaching.