Final answer:
Sally uses cognitive schemas when applying formulas in geometry. Experts recommend understanding concepts over memorizing equations for deeper learning and better problem-solving skills. Building this conceptual understanding can form lasting neural connections for mathematical proficiency.
Step-by-step explanation:
When Sally uses a formula in her high school geometry course to calculate an aspect of a geometric figure, such as its area, she is making use of what psychologists call cognitive schemas.
These schemas are mental structures that help individuals organize and interpret information. By applying these formulas, Sally is engaging in the process of equation hunting, which can be seen as relying on memorized algorithms to solve problems. However, experts suggest that deep learning occurs when students focus on understanding the core concepts behind equations, allowing them to generate these formulas from a foundational comprehension rather than mere memorization.
When students work on figuring for themselves and engage in collaborative group activities, they develop a systemic way of knowing. This means they gain knowledge by learning the system of symbols, their relationships, and the rules for operating within this system. Such an understanding can also lead to the development of mental agility and the ability to make estimations, which can be valuable skills, particularly when exact numbers are not available.
Ultimately, while memorization of formulas may provide a short-term solution to solving mathematical problems, it's the struggle and effort of understanding the mathematical concepts that form the neural connections necessary for long-term mathematical proficiency.