Instrumental tuition has predominantly been conceptualized in terms of a master-apprentice model that facilitates the transmission of skills, knowledge and cultural intellect through teaching and learning. Research suggests the one-to-one tuition model needs to evolve and adapt to meet the demands of the 21st century musician. Within the jazz/improvisation lesson, the learning and teaching of improvisory ability is a complex activity where developing improvisers hone motor-specific skills, audiative ability, imaginative and creative impulses that connect and respond to strategic individual and collaborative catalysts. Observing the negotiation of learning and teaching in three lessons in improvisation between expert practitioner-educators and their students, this study reveals a cognitive apprenticeship model that can provide a framework for teachers to develop students' cognitive and meta-cognitive abilities, and understandings of expert practice. Case studies of three teacher-practitioners and their advanced students explore the "in the moment" teacher--student interactions and teaching techniques that expert improviser-educators utilize in developing mastery and expertise in their students. Teaching to an advanced improvisation student is a dynamic, fluid and reflexive interplay of pedagogical applications of modelling, scaffolding, coaching, and reflective processes. The holistic imparting of knowledge can be understood as a cognitive apprenticeship. Careful guidance by a teacher/mentor can offer the student an immersive environment that brings thinking, action and reflection to the forefront of learning. Implications are identified for more effective, collaborative and inventive ways of assisting learning and inculcating deeper understandings of factual, conceptual and problem-solving concepts that draw students into a culture of expert practice.