This study compared the influence of two instructional models--explicit instruction and problem-based instruction--on the procedural and conceptual understanding attained by prospective elementary teachers from a unit on place value in different number bases. In the explicit instruction the instructor included intuitive conceptual explanations. In the problem-based instruction students worked on tasks intended to elicit the students' discovery of these same conceptual understandings. Students worked in groups and then explained their insights and approaches to the whole class. The essential difference in the instructional models was who was responsible for providing explanations: the teacher or the students.

The students answered procedural and conceptual questions on an immediate post-test and on a delayed post-test, and wrote a written reflection on place value. The differences in scores on the post-tests and written reflection were not attributable to the differences in instructional model, even after using math SAT scores as a covariate. A mild interaction was observed between treatment and math SAT score on the conceptual portion of the delayed post-test, in which students with lower math SAT scores who were in the problem-based group did somewhat better than those with lower math SAT scores in the explicit instruction group.

Seven students were interviewed to learn more about their understanding, attitudes, and persistence in problem solving. The interview analysis suggested that students' differences in understanding, attitudes, and persistence were due to their prior (pre-study) experience rather than to differences in instructional model for the study unit. The students from the problem-based group, however, were more likely to identify working in groups as a helpful learning strategy than those from the explicit instruction group.