As an art tutor, my approach to conducting classes revolves around providing a comprehensive and personalized learning experience that encompasses the development of artistic fundamentals, exploration of various art mediums, and a deep dive into art history. Here is an in-depth analysis of how I would structure my classes:

Assessment and Analysis:
At the beginning of each student's journey, I would conduct a thorough assessment to gauge their current level of artistic proficiency. This evaluation would involve analyzing their technical skills, understanding of art concepts, and knowledge of art history. By understanding their strengths, weaknesses, and goals, I can tailor the lessons to suit their specific needs.

Fundamentals of Art:
Building a strong foundation is crucial for any artist. I would focus on teaching the fundamental principles of art, including composition, perspective, color theory, form, light and shadow, and anatomy. Through a combination of theory, practical exercises, and constructive feedback, I would guide students in mastering these essential skills.

Academic Methods:
Drawing inspiration from European academic institutions, I would incorporate academic methods of painting into the curriculum. This would involve studying classical techniques, such as the use of underpainting, glazing, and chiaroscuro. Students would learn to create realistic and expressive artworks by applying these time-tested methods.

Exploration of Art Mediums:
To encourage creative exploration, I would introduce students to a wide range of art mediums beyond painting, including drawing, sketching, mixed media, and sculpture. By experimenting with different materials and techniques, students can discover their preferences and develop a diverse skill set.

Art History:
Understanding the historical context and artistic movements is essential for any artist. I would integrate art history into the lessons, exploring various periods, artists, and styles. This exploration would provide students with a deeper appreciation for art, inspire their own artistic development, and help them develop a unique artistic voice.

Breakdown of Lessons (Focused on Fundamentals of Art):

a. Lesson 1: Introduction to Composition and Design

Understanding the rule of thirds and other composition techniques
Analyzing artworks to identify effective composition choices
Applying composition principles in practical exercises
b. Lesson 2: Exploring Perspective

Learning the basics of one-point, two-point, and three-point perspective
Creating simple geometric forms in perspective
Applying perspective principles to draw more complex scenes
c. Lesson 3: Color Theory and Application

Understanding the color wheel and color harmonies
Exploring the effects of color temperature, value, and saturation
Applying color theory in exercises and studies
d. Lesson 4: Form, Light, and Shadow

Studying the principles of light and shadow, including cast shadows and form shadows
Applying shading techniques to create three-dimensional forms
Observing and rendering the effects of light on different surfaces
e. Lesson 5: Anatomy Basics

Introduction to human anatomy and Proportions
Studying skeletal structure, muscles, and major body landmarks
Applying anatomical knowledge to figure-drawing exercises
Throughout the lessons, I would provide demonstrations, hands-on exercises, individual guidance, and regular critiques to help students progress and refine their skills. The aim is to create a supportive and inspiring learning environment where students can develop their artistic abilities, gain a deeper understanding of art, and ultimately express their unique creative vision.