The learning of jazz improvisation is often treated as the incorporation of stylistic vocabulary and development of technical dexterity. Although this methodology is effective, considering other aspects of jazz improvisation can make the learning process a more holistic and less technical endeavour. My experience teaching improvisation has led me to formulate a method based on the cognitive process of improvisation conceptualized as a multi-dimensional model consisting of five improvisational cognitive skills: performance of material; creation of material; continuation of ideas; structural awareness of the improvised material; and temporal awareness of the improvised events. This model indicates that, during improvised performance, the player shifts the focus from one cognitive skill to another; this ability to establish links between skills is what I define as "improvisational intelligence." The proposed method develops this linking ability through exercises complementary to the more common methods of jazz improvisation. In this article I present the multi-dimensional model for improvisational cognition drawing from the existing literature. After breaking down the five cognitive aspects of the model and explaining how they work together, I provide exercises for each cognitive aspect in isolation and in conjunction. This method can be taught to high school and undergraduate jazz students and, with some modifications, to non-jazz musicians seeking to develop improvisation skills.