Recent developments about cognitions underlying mathematical learning are beginning to suggest that the activation and appropriate use of prior knowledge by students is, to a large measure, controlled by the quality of organisation of that knowledge. Thus, teaching needs to support the construction of well-connected mathematical knowledge. An important assumption here is that teachers need to construct a repertoire of subject-matter knowledge that is rich and well connected before they can help their students build similar mathematical knowledge. Thus, mathematics knowledge building is an important issue in teacher preparation programs. This paper reports on a study about the knowledge state of a pre-service teacher who planned to use computers in the teaching of linear functions. The results of the study indicate the existence of gaps in the student teacher's subject-matter knowledge. Significantly, there was also a lack of important connections between his understanding of linear functions and the instructional use of a computer software. Knowledge gaps and implications for classroom students' acquisition of mathematical schemas and mathematics teacher education programs are examined and discussed. (Contains 2 tables and 1 figure.)