Helping Students Know ‘Further’ – Increasing the Flexibility of Students’ Knowledge Using Symbolic Invention Tasks

Invention as Preparation for Learning (IPL) is a teaching strategy in which students attempt to develop novel solutions prior to receiving instruction (Schwartz & Taylor, 2004). This method was previously shown to prepare students to learn independently from future learning opportunities that build upon the materials learned in class. We began unpacking the IPL process by identifying its components and evaluating the contribution of generative reasoning (in the form of symbolic invention) on top of comparative reasoning (in the form of ranking alternatives). An in-vivo study in 6 middle-school classes with 105 students found that generative reasoning is an essential component of IPL. Furthermore, we found that students who attempted to invent symbolic models during the IPL process (generative reasoning) were able to invent new strategies during the post-test. At the same time, students who completed the IPL process without designing symbolic methods were in need for worked-out examples in order to solve new-strategy problems in the post-test. We propose a mechanism that explains how invention leads to the observed increased flexibility in students’ knowledge.