An investigation of students' knowledge after a traditional advanced high-school course in electromagnetism shows deficiencies of their knowledge in three major areas: (1) the structure of knowledge--e.g., realizing the importance of central ideas, such as Maxwell's equations (expressed qualitatively); (2) conceptual understanding--e.g., understanding the relationships between the electric field and its sources; and (3) application of central relationships in problem solving. To remedy these deficiencies we propose an instructional model which integrates problem solving, conceptual understanding and the construction of the knowledge structure. The central activity of the students is a gradual construction of a hierarchical concept map organized around Maxwell's equations as central ideas of the domain. The students construct the map in five stages: (1) SOLVE--they solve a set of problems that highlight the central ideas in the domain; (2) REFLECT--they reflect on the conceptual basis of their solutions; (3) CONCEPTUALIZE--they perform activities that deal with relevant conceptual difficulties; (4) APPLY--they carry out complex applications; (5) LINK--they link their activities to the evolving concept map. This integrative model (experimental treatment) was compared to an isolated treatment of drill and practice or treatment of conceptual difficulties without linkage to the proposed knowledge structure. The comparison shows that students in the experimental treatment performed better than the other students on measures of recall, conceptual knowledge and problem solving. Students in the experimental treatment were also able to transfer and extract central ideas in a domain different than physics.