Conceptual understanding refers to a deep and integrated grasp of related ideas. It is the ability to take what is learned in class and apply it across domains. Students with conceptual understanding know more than isolated facts and methods, they understand why a mathematical idea is important and the kinds of contexts in which it is useful. They have organized their knowledge into a coherent whole, which enables them to learn new ideas by connecting those ideas to what they already know. Conceptual understanding also supports retention because facts and methods learned with understanding are connected, they are easier to remember and use, and they can be reconstructed when forgotten.
Conceptual understanding is particularly important in mathematics because it involves making sense of the main ideas of mathematics. Students with conceptual understanding of mathematics can apply and adapt prior knowledge to new tasks, making math applicable beyond solving just a single math problem. It is achieved through project-based learning and exploratory units, where students are given the chance to experience exploratory learning. Conceptual understanding unfolds over time, across years and a lifetime, and is a strand of achieving mathematical proficiency that involves making sense of the main ideas of mathematics.
In summary, conceptual understanding is a deep and integrated grasp of related ideas that goes beyond isolated facts and methods. It is particularly important in mathematics and can be achieved through exploratory learning and project-based learning.
