Effects of elaborating on typical errors when learning fractions

• Applicant: Professorin Dr. Katharina Loibl
• Subject Area: General and Domain-Specific Teaching and Learning
• Term: from 2015 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 273274104

Learning approaches with problem-solving activities prior to explicit instruction by the teacher, allow students to explore and discover mathematical concepts and their connections actively (Aebli, 1976; Freudenthal, 1976). When students attempt to solve problems targeting yet unknown concepts, they generate solution ideas that are usually erroneous or incomplete and do not match the canonical (i.e., correct) solution (Vosniadou & Verschaffel, 2004). However, these student ideas can form the basis for acquiring canonical knowledge during subsequent instruction. Multiple studies have shown the effectiveness of problem-solving prior to instruction approaches on the acquisition of conceptual knowledge (e.g., Kapur, 2010). Nevertheless the underlying learning mechanisms remain unclear. Literature on conceptual change (e.g., Vosniadou & Verschaffel, 2004) as well as the findings of own studies on problem-solving prior to instruction (Loibl & Rummel, 2014a) indicate that elaborating on typical errors and comparing these erroneous solutions to the canonical solution may be crucial for learning in these settings. It seems reasonable to argue that elaborating on typical errors becomes even more important in learning domains (e.g., fractions) with epistemological barriers, because learning in a domain with epistemological barriers requires conceptual changes (e.g. Prediger, 2008). Against this background the main research question of this project is: how does fostering elaboration on typical errors during explicit instruction impact learning fractions? After a problem-solving activity that introduces fractions, students work on tasks that a) do not include typical errors, b) include typical errors, but do not explicit require students to elaborate on them, and c) that include typical errors and explicitly ask students to elaborate on these errors by comparing and contrasting them to the canonical solution. In addition to testing for differences between conditions in the learning outcomes, the impact of the epistemological barriers will be investigated by analyzing students' solution ideas. The analysis of students' solutions provides information about the occurrence of epistemological barriers. It further allows studying the relationship between epistemological barriers and learning in the different conditions.

• DFG Programme: Research Grants