Which of the following best describes mathematical proficiency?

Mathematical proficiency is best described as a combination of various interconnected components that foster a comprehensive understanding of mathematics. Adaptive reasoning, which involves the ability to think logically about the relationships between concepts and flexibly apply mathematical knowledge in unfamiliar situations, ensures that students can connect ideas and reason through problems. Procedural fluency refers to the skill in carrying out mathematical procedures accurately and efficiently. These two components, along with others like conceptual understanding and strategic competence, support a well-rounded grasp of mathematics.

In contrast, focusing solely on conceptual understanding ignores the importance of procedural skills and reasoning abilities, which are critical for solving complex mathematical problems. Rote memorization limits learning to just memorizing facts or procedures without understanding the underlying concepts, which can hinder deeper learning and application. Additionally, restricting proficiency to basic arithmetic fails to encompass the broader skills involved in higher-level mathematics, which are essential for a complete mathematical education. Thus, the choice that highlights both adaptive reasoning and procedural fluency accurately captures the multifaceted nature of mathematical proficiency.