Multimodal analysis of classroom music interactions, using the model of the "Space of Music Dialogue" in video analysis of students' music improvisation, was useful to inform teachers of students' collaborative achievements in music invention. Research has affirmed that students' cognitive thinking skills were promoted by improvisation. Students purposefully selected from many modes such as movement, gaze and spatial relations as domains of learning. The students, for example, rearranged these modes to promote musical arrangements and a growing sensitivity to visual and rhythmic perception. Students selected and rearranged modes to solve problems. Over time, students realised cognitive relations of modes in music, for example, through a deeper understanding of the elements of music: pitch, rhythm, dynamics, structure, phrasing. Only some students reached the realm of transmodal redesign, made possible as students became familiar with the music mode, and the conceptual elements of music. Choices in problem solving in the arts, through multiple choices in multimodal redesign, granted all students the ability to build their self-esteem through transformational redesign. New challenges allowed students to develop conceptual understanding. Students succeeded at problem solving in music, and the model assisted in the analysis of events including improvisation.