Effects of Verification and Directive Feedback With the Opportunity to Revise on Fraction Arithmetic Performance

• In Event: The Importance of Mathematical Competencies: When and for Whom Do They Matter?

Abstract

1. Objectives
The purpose of this study is to investigate the impact of feedback and the opportunity to revise on preservice teachers’ (PSTs) fraction arithmetic performance and their perceptions of feedback and revision.
2. Theoretical Framework
Fractions present teaching and learning challenges (Lamon, 2007; Newton, 2008), especially fraction division for both pre- and in-service teachers (National Mathematics Advisory Panel, 2008; Sahin et al., 2020). Although interventions have improved fraction concepts knowledge (Barbieri et al., 2020), work on improving fraction arithmetic knowledge is scarce. Designing and evaluating effective instructional techniques that improve fraction arithmetic skills is crucial. This study extends previous work (Attali & Powers, 2010; Attali & Stone, 2016) by examining effects of feedback with revision opportunities on PSTs’ fraction arithmetic skills, addressing the need to support PSTs’ in enhancing their mathematics content knowledge for effective teaching. Moreover, this approach may encourage future teachers to provide similar learning opportunities to their students.
3. Methods
Participants included (N=70) PSTs enrolled in two mathematics courses (Table 1 for demographics). In a pretest-intervention-posttest design, PSTs were randomly assigned to one of the three experimental conditions: directive feedback (i.e., PSTs were explicitly told what error they made) with revision opportunities (DF+R); verification feedback (i.e., PSTs were told correctness of an answer but not the specific error) with revision opportunities (VF+R); and verification feedback with no revision opportunities (VF).
4. Materials
Participants first took a pretest on fraction arithmetic (Figure 1 for sample items). They were then given feedback on their responses. Feedback type depended on condition. In two of the three conditions (DF+R and VF+R), PSTs were given the chance to revise their incorrect responses. Finally, all three conditions took an isomorphic posttest followed by a survey measuring their perceptions of and experiences with revisions and feedback in prior classes (Figure 2 for sample items), as well as a demographics survey.
5. Results
First, we found that there was significant growth between pre- and posttest when comparing all three conditions (See Tables 2 & 3). However, significant growth only emerged when we compared those who received verification feedback versus those who received directive feedback, but not for the comparison between those who received revision opportunities and those who did not (see Table 3). Interestingly, directive feedback showed significant improvements, whereas the two corrective feedback conditions showed declines from pre- to posttest.
Survey responses revealed PSTs commonly experienced revision opportunities and feedback in English classes. Most PSTs reported that they would revise for better grades and to improve their skills. PSTs had a positive perception of revision and feedback (Table 4) and 81% of PSTs revised when given the chance in the study. These findings suggest that PSTs welcome feedback with the opportunity to revise.
6. Significance
Preliminary findings suggest that directive feedback significantly improves fraction arithmetic performance compared to verification feedback alone or with revision. PSTs also had positive perceptions of revisions and feedback, revising even without obvious benefits. These findings provide a promising foundation for incorporating feedback and revisions into mathematics instruction.

Authors

• Sarah Clerjuste, University of Delaware

• Christina Areizaga Barbieri, University of Delaware

• Amanda Jansen, University of Delaware