PROJECT Overview
background
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.
project goals
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 will occur between October 2023 and February 2024.Study 2 will focus on the effects of both congruent and incongruent cues on math learning.
Research activities will occur between October 2024 and February 2025.
Study 1
Participants
6th graders and their 6th grade teachers will be invited to participate in this study. We will target a minimum sample of 600 students.
Study 1 Design and procedure
Participating teachers will assign a link to and supervise students while they complete a 45-minute online session. The session will have sections as follows:
First, students will be asked to complete an assessment of their prior order-of-operations knowledge and perceptual processing skills.
Then, students will be randomly assigned 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 will take a posttest of 12 order-of-operations problems without any perceptual cues, and a questionnaire regarding their feelings about math.
Study 2
Participants
We will recruit 15 teachers and approximately 1200 sixth-grade students from 12 middle schools.
Study 2 Design and procedure
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 a month:
Session 1. Students will be asked to complete an assessment of their prior order-of-operations knowledge, math anxiety, and perceptual processing skills. Then, students will be randomly assigned to one of nine conditions and will solve a series of 16 problems without feedback, specific to their condition. Each condition would have a specific spacing setting (Congruent spacing, Incongruent spacing, Neutral spacing) and color setting (Congruent color, Incongruent color, Neutral color).
Session 2. Students will complete a series of 30 problems, again specific to their condition, with immediate post-problem feedback.
Two-week break
Session 3. First, students will complete a series of 30 problems, again specific to their condition, with immediate post-problem feedback. Then, students will complete a mirrored posttest of 12 order-of-operations problems without any perceptual cues.
Two-week break
Session 4. Students will complete a delayed posttest, which will be a problem set akin to the problems solved in the posttest in Session 3.