Jean Piaget viewed intellectual growth as a process of adaptation (adjustment) to the world. This happens through Assimilation, which is using an existing schema to deal with a new object or situation. Accommodation which happens when the existing schema (knowledge) does not work, and needs to be changed to deal with a new object or situation.
When a student is faced with new math concepts like algebra that require the student to think about hypothetical situations in order to solve the problem, the student will have to create a new scheme in order to process the algebraic problems that include variables, letter symbolism, formulas, and functions that have never been used before by the student. None of the previous math schemes that the student has developed would accommodate the new concepts that they need to learn and utilize from this point on in their educational career, and therefore the old schemes' inadequacies force the development of a brand new scheme specifically designed to handle more complicated mathematical concepts.
Piaget's theories on assimilation and accommodation are important when trying to understand how humans perceive the world. Assimilation and accommodation are both important for child development, and Piaget theorizes that they are both occurring at the same time. These theories are beneficial to teachers, students, parents, and anyone who wants to understand how humans perceive reality.