Cognitive Development in Mathematics
My research investigates how people learn and think about mathematical ideas.
I ask broad questions like: Why are fractions so hard to understand for so many students? How do different visual models like number lines, pizza models, or gestures influence students' thinking in math? How can instruction most effectively leverage children's prior knowledge and informal math experiences to help them learn new ideas?
Why Fractions?
Fractions are one of the most important domains of K-12 mathematics, but they are challenging for many people! Many students struggle to cohesively integrate multiple aspects of a fraction’s meaning (e.g., ¼ is one part out of a four-part whole and ¼ is a ratio or multiplicative relation between 1 and 4), and multiple visual representations (e.g., 1/4 is the same as 2/8, 0.25, 25%, a point ¼ of the way from 0 to 1, etc.).
Interdisciplinary Approach
I am an interdisciplinary researcher. I draw heavily from information-processing theories of cognitive science, and I also recognize that mathematical thinking is constructed and develops in specific contexts and communities. I aim to unite psychology’s emphasis on statistical modeling and causal inference with math education’s deep attention to student thinking.
Recent and Ongoing Projects
Informal Fraction Knowledge in 1st Grade
In my postdoctoral research, I worked with Dr. Nancy Jordan (Delaware) and Dr. Nora Newcombe (Temple) on their NSF-funded grant to investigate foundations of fraction learning in first graders. We are currently developing playful learning tools to build fraction skills.
Read our recent article here.
Using Analogy to Build Fraction Understanding
In experimental studies, I tested alternative lessons to teach 2nd-3rd graders about fraction magnitude. Teaching children to use an analogy to whole number estimation (e.g., 3 : 10 :: 3/10 : 1) was at least as effective as an alternative lesson using partitioning on number lines.
Read our recent article here.
Which Fraction Skills Support Algebra?
In correlational and longitudinal studies, I am investigating which aspects of fraction knowledge are related to various aspects of algebra knowledge in 7th-9th grade students. This 5-year project is funded by a $2.5 million NSF grant in collaboration with Drs. Ana Stevens, Percival Matthews, and Martha Alibali at UW-Madison.
Learn more about the grant here.
Recent Publications and Preprints
Viegut, A. A., Resnick, I., Miller-Cotto, D., Newcombe, N. S., & Jordan, N. C. (2023). Tracking informal fraction knowledge and its correlates across first grade. Developmental Psychology, 59(10), 1739–1756. https://doi.org/10.1037/dev0001581
Link to Accepted Manuscript Preprint: https://psyarxiv.com/dbj83/
Viegut, A. A., & Matthews, P. G. (2023). Building fraction magnitude knowledge with number lines: Partitioning versus analogy. Developmental Psychology, 59(10), 1757. https://doi.org/10.1037/dev0001616
Link to Accepted Manuscript Preprint: https://osf.io/azkh7
Viegut, A. A., Stephens, A. C., & Matthews, P. G. (in press). Unpacking the connections between fractions and algebra: The importance of fraction schemes and units coordination. Investigations in Mathematics Learning.
Link to Preprint: https://osf.io/preprints/psyarxiv/xzep4
Infographics and Public-Facing Summaries of My Research
EarlyFractions_Infographic_Summer2023.pdfFamilyUpdate_LoL_Newsletter_toShare.pdf