Supports for preservice teachers’ metacognitive monitoring and explanations of fraction comparisons

Abstract The ability to provide clear and comprehensive instructional explanations on mathematical concepts is key to supporting student learning in the classroom. This is especially important when teaching content that students most often struggle with. A large body of literature has established the challenges that elementary students face with developing fraction magnitude concepts. More recent work points to the struggles that both pre- and in-service teachers have with fraction magnitude. Though much work exists on interventions for students in supporting their fraction understanding, there is a dearth of literature on how to support teachers’ provisions of high quality explanations. We designed and evaluated the effectiveness of three instructional supports on elementary pre-service teachers’ (PSTs) revision and improvements of their explanations of fraction concepts. We also examined their metacognitive monitoring and calibration skills as they relate to the revision process. Elementary PSTs were instructed to identify the larger of two fractions and then explain and justify their choice. They had an opportunity to revise after examining different instructional supports depending on their condition. We found that PSTs who were provided with instructional supports that provided a correct and complete exemplar of a fraction magnitude comparison showed greater improvements in their explanations than those who studied example explanations that displayed common misconceptions and errors. Correct and complete exemplars also supported greater detection and correction of errors and omissions in their explanations than those provided with a list of steps focused on structural aspects of the explanation. Hedges’ g effect sizes ranged from medium to large ( g = 0.64 to 0.95) for the three comparison tasks. Most PSTs also showed limitations in calibration, indicating over-confidence in the degree of completeness of their explanations at both time points. These findings can inform instructional materials design for pre-service teacher mathematics content courses as they learn how to monitor their own thinking and explain fraction comparisons to students.