Which concept is least likely to be supported by manipulatives?

Manipulatives are physical objects that provide hands-on experiences for students to learn various mathematical concepts. They are particularly effective in helping students grasp concrete ideas before moving to more abstract thinking. In this regard, advanced theoretical mathematics typically involves more abstract concepts that don't translate well to physical representations.

When students are learning about fractions, addition, or geometric shapes, manipulatives can provide a concrete way to visualize and understand these topics. For instance, blocks or pie charts can be used for fractions, counters for addition, and models for geometric shapes, making these concepts more accessible and tangible for learners.

However, advanced theoretical mathematics, which often includes topics like calculus, complex numbers, or abstract algebra, typically requires a level of abstract reasoning that goes beyond what manipulatives can illustrate. Therefore, while manipulatives are valuable for foundational concepts and early learning, they are less applicable for advanced theoretical topics that involve higher-order thinking and abstract reasoning.