Combining exploratory learning with structured practice educational technologies to foster both conceptual and procedural fractions knowledge

Abstract

Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often, conceptual knowledge by means of exploratory tasks. However, both types of knowledge are needed for complete domain knowledge that persists over time and supports subsequent learning. We investigated in two quasi-experimental studies whether a combination of an exploratory learning environment, providing exploratory tasks, and an intelligent tutoring system, providing structured tasks, fosters procedural and conceptual knowledge more than the intelligent tutoring system alone. Participants were 121 students from the UK (aged 8–10 years old) and 151 students from Germany (aged 10–12 years old) who were studying equivalent fractions. Results confirmed that students learning with a combination of exploratory and structured tasks gained more conceptual knowledge and equal procedural knowledge compared to students learning with structured tasks only. This supports the use of different but complementary educational technologies, interleaving exploratory and structured tasks, to achieve a “combination effect” that fosters robust fractions knowledge.