You play a vital role in the development of
mathematical habits by conveying to your students a mindset that fosters productive struggle and emphasizes the possible value of wrong answers.
Students immersed in classroom experiences that let them engage in learning mathematics concepts through problem solving, making and using abstractions, and developing and applying mathematical theories have greater opportunities for developing
mathematical habits of mind.
Student mathematicians
develop mathematical habits of mind - problem solving, reasoning, flexibility, justifying, modeling, resilience, and perseverance throughout collaborative learning in partner and small group activities.
As a result the participants will produce a book (available in print and digital formats) of worked examples that model
effective mathematical habits of mind.
Since the early nineties, researchers have agreed that students need to focus on the related mathematical practices or mathematical processes (National Council of Teachers of Mathematics, 2000),
mathematical habits of mind (Cuoco, Goldenberg, & Mark, 2010; Mark, Cuoco, Goldenberg, & Sword, 2010), and more recently, the eight Standards for Mathematical Practice (SMPs; Common Core State Standards [CCSS] Initiative, 2010).
According to Levasseur and Cuoco (PDF, 80KB), it's
the mathematical habits of mind, or modes of thought, that enable us to reason about the world from a quantitative and spatial perspective, and to reason about math content that empowers us to use our mathematical knowledge and skills to make sense of and solve problems.
The more you engage your students in learning and doing mathematics, the greater the likelihood of their developing
the mathematical habits of mind of a productive mathematical thinker — and becoming experienced problem solvers who know what to do when they don't know what to do.
They practice perseverance and automatically employ
the mathematical habits of mind of a productive problem solver in their quest for a problem solution.