Understanding the influence of perceptual cues is critical for educators.
Perceptual groupings are consistent across languages and cultures and thus may offer a scaffolding pathway that does not depend on students’ backgrounds.
Leveraging perceptual cues in instruction and problem-solving helps students notice important systematic structures of math notation that afford efficient strategies and lead to long-term learning by changing the way students perceive, encode, and interpret math information.
We aim to understand how middle school students’ mathematics learning could be improved by using perceptual scaffolding (e.g., color and spacing of problem features) while solving math problems. Specifically, we are examining the individual effects of cues in mathematical notation on sixth-grade students’ performance on order-of-operations problems. We are examining the following conditions:
congruent spacing (e.g. 1 + 12×3 - 6, where numbers involved in higher-order operations are grouped more closely together),
congruent color (e.g. 1 + 12 × 3 - 6, where numbers involved in higher-order operations are colored),
incongruent spacing (e.g. 1 + 12 × 3-6, where numbers involved in lower-order operations are grouped more closely together),
incongruent color (e.g. 1 + 12 × 3 - 6, where numbers involved in lower-order operations are colored),
and no perceptual cues (e.g. 1 + 12 × 3 - 6).
To address the aims of this project, we will conduct two experimental studies:
Study 1 will focus on the effects of congruent cues on math learning.
Research activities occured between October 2023 and May 2024.
Study 2 will focus on the effects of both congruent and incongruent cues on math learning.
Research activities will occur between August 2024 and February 2025.
800 6th graders and their 6th grade teachers were invited to participate in this study. This study was implemented from October 2023 to May 2024.
Participating teachers assigned a link to and supervise students while they completed a 45-minute online session. The session had sections as follows:
First, students were asked to complete an assessment of their prior order-of-operations knowledge and perceptual processing skills.
Then, students were randomly assigned to one of the three conditions to solve a set of 16 order-of-operations problems, in either a congruent spacing, congruent color, or no perceptual cues condition.
Finally, students took a posttest of 12 order-of-operations problems without any perceptual cues, and a questionnaire regarding their feelings about math.
We will recruit 15 teachers and approximately 1200 sixth-grade students from 12 middle schools.
Similar to Study 1, students will solve order-of-operations problems in an online platform under their teachers' supervision. Study 2 will be conducted on 4 school days across the span of approximately 8 weeks. Every 2 weeks, teachers will receive instructions for the next session.
Session 1. Students will be asked to complete an assessment of their prior order-of-operations knowledge, metacognitive monitoring and confidence, perceptual processing skills, math anxiety, and math value.
Session 2. Students will be randomly assigned to one of nine conditions and will solve a series of 21 problems specific to their condition. Each condition will have a specific spacing setting (Congruent spacing, Incongruent spacing, or Neutral spacing) and color setting (Congruent color, Incongruent color, or Neutral color). Students will receive immediate post-problem feedback and worked examples.
Session 3. First, students will complete a series of 9 problems, again specific to their condition, with immediate post-problem feedback and worked examples. Then, students will complete a mirrored posttest of 10 order-of-operations problems without any perceptual cues. Students will also answer questions about their metacognitive monitoring and confidence.
Session 4. Students will complete a delayed posttest, which will include a 10-item problem set akin to Session 3 posttest, as well as an assessment of metacognitive monitoring and confidence and perceptual processing skills.