The mathematics program provides a student-centered, hands-on, constructivist environment for all students to explore, invent, discuss, and debate the meaning of math. Subject matter is treated as an integrated whole rather than as a collection of isolated concepts and procedures that are each to be taught and tested individually. Building a sequence of experiences in a gradually enlarging spiral, teachers use problem-solving approaches to develop students' thinking and understanding.
In a spiraled, integrated curriculum, major strands are revisited each year and explored in greater depth. This approach takes advantage of gifted students' ability to use and understand mathematics deeply and their ability to approach problems from multiple perspectives. The four major content strands in the Nueva mathematics program are Data and Probability, Geometry and Measurement, Numerical Relationships and Operations, and Algebra and Functions. These strands are adapted from the state's Common Core State Standards for Mathematics.
An integrated curriculum also provides more opportunities for investigations and problems that offer experiences that engage all students and by which gifted students can extend beyond what they might do in a traditional math class. Through direct investigative experiences, communication and collaboration, and questions and discussions, students build content knowledge in the four mathematics strands listed above.
The program design strives to develop a strong sense of mathematical empowerment in students by
- providing a safe and engaging environment for inquiry and exploration.
- teaching students to use a variety of tools to problem-solve, reason, and communicate their ideas.
- valuing multiple problem-solving approaches, solution methods, and thinking strategies.
- valuing proficiency and fluency in basic math skills, including computation.
- creating and fostering a deep sense of numeracy—as mathematician John Allen Paulos puts it, "Viewing and questioning the world with a mathematical lens."
- discovering mathematical connections in the world and among mathematics fields.
- integrating mathematics within mathematical strands as well as across disciplines.
- constructing and discerning meaningful connections between the curriculum and opportunities such as Math Club, contests, and field trips.
- fostering interchanges between students and mathematicians through mentoring and real-world interdisciplinary projects.
- building mathematical capacity throughout the school's extended learning community.
- developing a deep understanding of and appreciation for the intrinsic beauty of mathematics.
Because gifted students are capable of reflecting not only on what they learn but also on how they learn it, a mathematics program for gifted students can and should make process goals explicit to students. At Nueva, mathematical processes are recognized and valued as much as mastery of other mathematical skills and facts.