“Look at Me and Do Likewise”: Learning mathematical procedures through explicit instruction
Read the full dissertation (in Hebrew).
Learning mathematical procedures, such as long division, is a central challenge in mathematics education; however, it remains unclear how different instructional approaches affect the acquisition of procedural knowledge.
The present study examined how explicit instruction affects the acquisition of procedural knowledge. To isolate procedural knowledge acquisition from the influence of prior knowledge, mathematical meaning, and familiar solution strategies, we developed an artificial mathematical procedure designed to preserve the core characteristics of a mathematical procedure while minimizing the influence of prior knowledge and potential confounding variables. The study included 89 adult learners, who were randomly assigned to either an explicit instruction group (n = 45) or a traditional instruction group (n = 44). Both groups learned the same procedure and were assessed immediately after learning and again one week later.
The findings demonstrated a consistent advantage for explicit instruction. Participants in the explicit instruction group correctly performed more procedures, showed better retention of the acquired knowledge over time, and demonstrated greater self-monitoring ability, as reflected in their detection and correction of errors. In addition, they reported greater enjoyment of the learning process and higher motivation to continue learning, and the dropout rate was lower in this group. Taken together, the findings suggest that the advantage of explicit instruction extends beyond improved performance alone. They raise the possibility that procedural knowledge acquisition is a multidimensional process involving cognitive, metacognitive, behavioral, and affective dimensions. Potential mechanisms underlying this advantage were examined through a theoretical analysis of the components of explicit instruction implemented in the present study. These findings provide a foundation for future research examining the relative contribution of these mechanisms to the acquisition of procedural knowledge.