I Students explore mathematical ideas in ways that help them develop depth of understanding. Students learn mathematics when they understand it deeply and are able to use it effectively. To achieve mathematical understanding, students should be actively engaged in doing meaningful mathematics, discussing mathematical ideas, and applying mathematics in interesting and thought provoking situations. Students should have coherent and comprehensive curricula that foster mathematical development over time. It is important to engage students in tasks designed to challenge them in multiple ways.
Projects are excellent vehicles for involving students in exploration of mathematical concepts.
Activities that build upon prior knowledge and provide opportunities to solve problems that become progressively deeper, broader, and more sophisticated help students achieve more advanced levels of proficiency. Mathematical tasks and experiences generate active discourse, promote the development of conjectures, and lead to an understanding of the necessity for mathematical proofs. Mathematics presented as an integrated whole leads to the development of other mathematical ideas, makes meaningful connections to areas both within and outside mathematics, and permits depth of study. Teachers are a key factor in what mathematics students learn and how well they learn it. Therefore, it is important that teachers have the tools and support necessary to actively engage students in cognitively demanding and worthwhile tasks that reflect sound and significant mathematics.