To Teach or Not to Teach the Conceptual Structure of Mathematics? Teachers Undervalue the Potential of Principle-Oriented Explanations

Publication date: Available online 22 March 2019Source: Contemporary Educational PsychologyAuthor(s): Andreas Lachner, Mona Weinhuber, Matthias NücklesAbstractPrinciple-oriented explanations have demonstrated to foster students’ mathematical understanding, as they integrate conceptual and procedural information to make the solution process tangible to novice students. Teachers, however, often omit conceptual information when explaining procedures. In two experimental studies, we tested the hypothesis that teachers’ tendency to omit conceptual information may have occurred, as teachers generally devalued the potential of principle-oriented explanations. In Study 1, we randomly provided two cohorts of secondary students (N = 129) with principle-oriented versus procedure-oriented explanations on four mathematical topics. Afterwards, students answered a knowledge test. We replicated previous findings that students with principle-oriented explanations outperformed students with procedure-oriented explanations on the knowledge test (application test, transfer test). In Study 2, we gave mathematics teachers (N = 69) these explanations as judgment materials. Teachers randomly rated a balanced set of four explanations of Study 1 which varied in their procedure- versus principle-orientation. We found no significant differences between teachers’ judgments of principle- versus procedure-oriented explanations. Content analyses of the justifications revealed that teachers were more ...

Source: Contemporary Educational Psychology - March 23, 2019 Category: Child Development Source Type: research