For over a decade, a declarative approach to problem solving based on the use of abstract data types (ADTs) has been taught to high-school students as part of the logic programming instructional unit. We conducted a study aimed at assessing students' problem-solving processes when utilizing ADTs. The findings indicated that students' strategies that diverged from the conceptual model often cause the students to develop incorrect programs. Specifically, students have difficulties in establishing correct mapping between the problem and its abstract model - the corresponding ADT, and in establishing proper connectivity between layers of abstraction related to different stages of the problem-solving processes (e.g., between distinct programming modules). These difficulties are apparently associated with general difficulties that novices encounter when learning programming, and with the cognitive load encountered when dealing with high levels of abstraction. With the intention to reduce student difficulties, we suggest using an instructional approach designed to gradually educate the students toward attaining proficiency as ``problem solvers'' through the use of integrative knowledge and autonomous problem-solving techniques. This approach should be further evaluated regarding its feasibility and applicability to reducing students' difficulties in dealing with abstraction processes.