The effects of feedback during exploratory mathematics problem solving: Prior knowledge matters.

Abstract

Providing exploratory activities prior to explicit instruction can facilitate learning. However, the level of guidance provided during the exploration has largely gone unstudied. In this study, we examined the effects of 1 form of guidance, feedback, during exploratory mathematics problem solving for children with varying levels of prior domain knowledge. In 2 experiments, 2nd- and 3rd-grade children solved 12 novel mathematical equivalence problems and then received brief conceptual instruction. After solving each problem, they received (a) no feedback, (b) outcome feedback, or (c) strategy feedback. In both experiments, prior knowledge moderated the impact of feedback on children's learning. Children with little prior knowledge of correct solution strategies benefited from feedback during exploration, but children with some prior knowledge of a correct solution strategy benefited more from exploring without feedback. These results suggest that theories of learning need to incorporate the role of prior knowledge and that providing feedback may not always be optimal.

Positioning organisational culture in knowledge management research

“…In problem solving, prior knowledge about related strategies enhances the efficiency of problem exploration, according to Fyfe et al (2012). Another group of researchers forge a link between employees' levels and the types of knowledge required.…”

Benefits of “concreteness fading” for children's mathematics understanding

“…We designed the transfer items to be more structurally complex than the instruction items. We based this on previous studies of math equivalence that had used transfer tests with similar-aged children (e.g., Alibali, 1999;Fyfe, Rittle-Johnson, & DeCaro, 2012;Matthews & Rittle-Johnson, 2009;Perry, 1991). Problems differed from instructional problems in terms of addends on the left side (e.g., three instead of two), the position of the blank (a þ b þ c ¼ __ þ c), and the presence/absence of a repeated addend (a þ b þ c ¼ d þ __).…”

Transitional feedback schedules during computer-based problem-solving practice

“…However, with additional developing knowledge of the domain, feedback delivered immediately after every problem solving step could become disruptive to learning because students are required to mentally process new (and extraneous) information rather than continuing to the next step. Learners in more advanced stages of learning may have already developed problem-solving schemas; thus, presenting immediate feedback after each problem solving step could unnecessarily disrupt their problem-solving process, creating extraneous processing demands and hindering learning (Fyfe, Rittle-Johnson, & DeCaro, 2012;Kalyuga, 2007;Kelley & McLaughlin, 2012;Kester & Kirschner, 2009). This study found no significant difference between the TFS-P and SFS conditions, indicating that in the examined engineering problem solving instruction, the feedback after each problem step did not significantly disrupt learning for the novice students.…”