Math should be a gateway to academic, professional, and personal opportunities in K-12 education, higher education, and beyond. However, national statistics in the U.S. reveal a concerning reality: only a fraction of students demonstrate proficiency in math by eighth grade. So what’s happening? Many students in the U.S. often solve problems by performing calculations from left to right. This strategy commonly emerges in early elementary school as students are exposed to rote arithmetic practice (e.g., 2 + 3 = __ ). This becomes a rigid routine that falters in the face of different problem representations (e.g., many students will solve 3 + 2 = __ + 4 by filling in the blank with 5) and prevents students from using efficient problem-solving strategies. More concerningly, this strategy may reflect students’ mis- or lack of understanding about fundamental mathematical principles such as equivalence and inverse operations. These early concepts lay the groundwork for later math comprehension and are pivotal for students’ success as they progress beyond arithmetic, or they may potentially hit a roadblock as they reach eighth grade.

**Now I See It: Supporting Flexible Problem Solving in Mathematics through Perceptual Scaffolding in ASSISTments**

With the project, “Now I See It: Supporting Flexible Problem Solving in Mathematics through Perceptual Scaffolding in ASSISTments,” we aim to curtail elementary students’ rigid problem-solving strategies and promote their understanding of equivalence and inverse operations by designing instructional support and practice for students in ASSISTments, one of the five digital learning platforms funded by SEERNet. We will leverage ASSISTments’ problem builder to design worked examples and content-based practice problems then use the E-TRIALS research platform to deploy two online experiments for 2nd-4th grade students during the 2024-2025 school year.

So how can we help students be more flexible and efficient problem solvers *and* grasp the underlying math concepts in those problems? People often focus on finding patterns and groups to make sense of what they see. Noticing perceptual cues in the world around us is ubiquitous and so are the principles that we use to find patterns. For example, multiple cultures recognize the same groups of stars as constellations based on the stars’ magnitudes, brightness, and spatial proximity to one another. As we process information, we tend to look for such patterns and groups in order to interpret information efficiently and make quick decisions. And over time, we get better at noticing the aesthetic cues that give us important information, known as *perceptual learning*.

Whereas prior research has shown that viewing perceptual cues changes how we solve math problems, this project will indicate whether perceptual scaffolding can be used to *teach* students to attend to important pieces of information in math problems that map onto foundational concepts. We will design, implement, and assess perceptual scaffolding that redirects students’ attention towards critical information within worked examples to promote flexible problem solving and mapping connections to the underlying math concepts. Specifically, we will change how the worked examples are presented to highlight problem structures that are relevant to equivalence and inverse operations.

*Left*: Worked example on equivalence using the principle of common visual regions. *Right*: Worked example on inverse operations using the principle of similarity.

The project is funded through August 2025. During that time, we plan to conduct two large-scale online experiments in ASSISTments with elementary students to examine how perceptual scaffolding affects immediate and distal outcomes related to math learning. The project should yield immediate implications for teachers and content developers by indicating whether and how perceptual scaffolding on these two content areas should be used in ASSISTments for student practice. If we find increases in students’ performance, learning, and retention, this approach would demonstrate how features of digital learning platforms can draw on students’ natural resources (i.e., their visual perceptual processing system) to feasibly implement theory-driven perceptual scaffolding. If successful, leveraging perceptual scaffolding in digital learning platforms may be one avenue to help students grasp foundational math concepts and prepare them for later topics.

Learn more about this study in this short video.