Conference Poster
Citation
Ngo, V., Perez, L., Closser, A. H., & Ottmar, E. (October, 2021). The effects of operand position and superfluous brackets on student performance in math problem-solving. Poster presented at the 43rd Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA). p. 67.
Project Overview
Students frequently demonstrate a left-to-right solving tendency when working with arithmetic expressions, which can lead to systematic errors when expressions require attention to order of operations. Drawing on perceptual learning theory, this study examined whether subtle changes in mathematical notation—specifically operand position and the inclusion of superfluous brackets—influence student performance during math problem-solving.
The goal of this work was to understand how visual and structural cues in notation can support or hinder students’ reasoning and accuracy.
The goal of this work was to understand how visual and structural cues in notation can support or hinder students’ reasoning and accuracy.
Research Questions
- Does the position of a higher-order operand impact student performance, as measured by mastery speed and response time?
- Does the presence of superfluous brackets affect student performance?
- Do the effects of superfluous brackets differ depending on the position of the higher-order operand?
My Role
- Contributed to study design grounded in perceptual learning theory
- Supported analysis of student performance data from an online learning platform
- Assisted with interpretation of results and development of instructional implications
- Co-authored and presented the accepted conference poster
Study Context
- Conducted within ASSISTments, an online tutoring system for K–12 mathematics
- Problems were delivered through the Skill Builder Activity, which requires students to demonstrate mastery by correctly answering multiple consecutive items
- The study leveraged platform-generated performance data, including mastery speed and response time
Methods
Participants
- 88 fifth- to eighth-grade students
Design
- All students completed a three-item baseline assessment
- Students were then randomly assigned to one of six experimental conditions, varying by:
- Operand position (left, center, right)
- Presence or absence of superfluous brackets
Outcome Measures
- Mastery speed (time to reach mastery criteria)
- Response time on math problems
Analytical Approach
- Two 3 × 2 ANCOVAs predicting mastery speed and response time
- Controlled for student grade and gender
- Planned interaction analyses between operand position and bracket presence
Preliminary Findings
- No significant main effects of operand position or superfluous brackets were detected in the preliminary sample
- Because no main effects emerged, interaction effects were not tested at this stage
- Full interaction analyses were planned for the final sample
Why This Matters
Although preliminary results did not reveal statistically significant effects, this study contributes to the learning sciences literature by:
- Isolating specific perceptual features of mathematical notation in a controlled experimental design
- Advancing understanding of how notation structure influences student cognition
- Informing the design of instructional materials and educational technologies that better support mathematical reasoning
This work highlights the importance of examining how math is visually presented, not just what content is taught.
Skills Demonstrated
- Experimental design in education research
- Application of perceptual learning theory
- Quantitative analysis of learning platform data
- Research collaboration and academic dissemination
- Translating theory into instructional design implications