TITLE
A NONLINEAR APPROACH TO TEACHING THE MEAN VALUE THEOREMS
PART II: NEW THEOREMS AND GRAPHICAL REPRESENTATIONS
AUTHOR(S)
Valentina Todorova-Lazarova*, Penka Ivanova, Radostin Lefterov
ABSTRACT
This paper presents a nonlinear approach to teaching the Mean Value Theorems (MVTs), which are recognized as crucial for mastering calculus. Students experience significant struggles in understanding the proofs and applications of MVTs due to traditional linear teaching methods. A nonlinear teaching methodology is proposed to address this issue, emphasizing interconnected understanding among MVTs and fostering conceptual clarity and critical thinking. Graphical representations are utilized, and new theorems are explored, leading to engagement in collaborative and interactive learning environments. New proofs are introduced, establishing relations among various MVTs, including Cauchy’s Mean Value Theorem involving three functions. It is demonstrated that this approach significantly improves students' comprehension and ability to apply MVTs to complex problems. Practical implications suggest that diverse teaching strategies should be incorporated by educators to facilitate deeper learning. This research provides a novel framework for understanding MVTs, emphasizing their relevance and application in calculus.
DOI
http://www.doi.org/10.70456/QHFT3045
DOWNLOAD
https://unitechsp.tugab.bg/images/2024/11-MI/s15_p83_v3.pdf
How to cite this article:
Valentina Todorova-Lazarova*, Penka Ivanova, Radostin Lefterov, A NONLINEAR APPROACH TO TEACHING THE MEAN VALUE THEOREMS
PART II: NEW THEOREMS AND GRAPHICAL REPRESENTATIONS, UNITECH – SELECTED PAPERS - 2024