Holistic Teaching and Holistic Learning, Exemplified Through One Example from Linear Algebra

Abstract

Here we discuss ways to teach and learn holistically. The holistic method encourages student curiosity and respects student input fully, however qualified. A teacher’s holistic approach leads to open discussions and deep learning in class. Using the students’ innate desire to understand drives the course of such a class. The teacher’s role is to guide and adjust the course as the subject matter, experience, and—in mathematics courses—as the algebraic, geometric and logic rules of mathematics dictate. Holistic Teaching respects and adheres to the ‘necessity principle’ of learning and it applies the ‘holistic management principle’ that is successfully used for many other complex systems to achieve a comprehensive teaching and learning experience for both teachers and students. Teaching holistically is exemplified by one extended in-class study of how to measure angles in $\mathbb {R}^n$ from first principles of both Geometry and Linear Algebra .