Exploring Students' Ownership of Their Conceptual Level Thinking about Sandwich Theorem, Rolle's Theorem and Mean Value Theorem in Calculus
The present study explores students' conceptual knowledge of the sandwich theorem, Rolle's theorem, and the mean value theorem. Focusing on the computational aspect of one of these theorems only showcases the theorem's application, which is a small portion of the mathematical background that is connected with that specific theorem. However, at a conceptual level, our study investigates students' ability to apply conceptual understanding and critical thinking to novel problems about these theorems. First-semester calculus students encountered certain theorems while we investigated their critical thinking by collecting their work and responses to conceptual and computational problems via group and individual assignments. During the analysis process, we conducted one-on-one interviews to explore participants' knowledge and understanding of the theorems. When students encountered computational problems in groups, many students showed fluent understanding of the application of certain theorems and were able to communicate that comprehension in their work. However, when given an individual assessment that suggested a possible alternative approach to a problem and asked students to critique that approach ,only a few were able to identify the mathematical error with their unique interpretation. The mathematical ideas that students build on their own, and the distinction between their procedural and conceptual knowledge is highlighted in the study via the constructs of mathematization and context familiarity.