Study 1 results

The present study examined whether and how congruent perceptual cues (spacing and color) affected students’ performance on order-of-operations problems and considered potential moderators. 

The analysis included 482 middle-school students randomly assigned to one of three conditions: spacing (e.g., 4×3 + 5 + 7), color (e.g., 4 × 3 + 5 + 7), or no cues.  

We found that neither spacing nor color cues significantly impacted problem-solving performance in students. While we hypothesized that the cues would improve accuracy and efficiency, further studies are needed.

However, student attributes influenced outcomes—students with greater perception of equivalence were helped by spacing (see Figure 1), and lower-achieving students benefited from color cues. Math-anxious students performed worse overall but not due to the cues.

What does this mean for the classroom?

Findings indicate the role that perceptual processing plays in math learning and the challenges that students with math anxiety face. While color cues alone did not benefit performance, our follow-up study showed that with training, certain perceptual cues benefited problem-solving, suggesting that instruction is key to their success in the classroom.

Study 2 results

This study examined the effects of two perceptual cues (i.e., symbol spacing and font color) embedded in instructional activities on 688 sixth-grade students’ performance, learning, and retention in the context of order-of-operations problems through a multi-session online intervention.  

Our study found there was a significant learning effect from training, with greater median accuracy from pretest to immediate and delayed posttests. Participants learned better under training with perceptual cues compared to no cues (NSNC). The best conditions were:

• Congruent Spacing, Neutral Color (CSNC) → 10 + 4×8 − 3

• Congruent Spacing, Incongruent Color (CSIC) → 10 + 4×8 − 3

• Congruent Spacing, Congruent Color (CSCC) → 10 + 4×8 − 3

• Incongruent Spacing, Congruent Color (ISCC) → 10 + 4×8 − 3

Students with lower math anxiety learned more from CSCC cues, and CSNC cues had a prolonged learning effect.