In one arm of my graduate studies, I have been exploring how people mentally represent negative integers. There are potentially two ways to represent a negative integer such as -4. One approach is to imagine the positive number "4" and then apply a rule to account for the negative sign. The other approach is to represent the integer holistically, perhaps by visualizing it on a mental number line.

Each type of mental representation leaves distinct behavioral "traces," such as reaction times during symbolic number comparisons. In multiple studies, I examined the behaviors of both adults and children during these tasks. Our results indicate that there are indeed multiple ways to represent integers, and that people may represent integers in different ways depending on the task at hand.

In future work, I plan to (1) explore factors that influence how people represent integers, including task characteristics and instructional experiences, and (2) strategically manipulate task features during symbolic magnitude comparisons to induce specific representations of negative integers.

• Vest, N. A., & Alibali, M. W. (2024). Is zero more than nothing? Relations between concepts of zero and integer understanding. paper
• Vest, N. A., & Alibali, M. W. (2023, June). Conceptions of zero and the semantic congruence effect: Evidence from children and adults. MCLS. slides
• Vest, N. A., & Alibali, M. W. (2021, July). The mental representation of integers. Proceedings of CogSci. paper

In my graduate studies, I investigated students' explicit and implicit concepts of zero, the potential of number line activities to foster sophisticated understandings of zero, and whether these concepts predict performance on problems involving the additive inverse principle (X + -X = 0).

Many children viewed zero as "nothing" (null conception), while some saw it as the symmetry point between positive and negative integers. Children in higher grades were more likely to express a symmetry conception. Those with a symmetry conception showed greater understanding of the additive inverse principle and better integer arithmetic skills.

We also explored whether a brief lesson on zero as the symmetry point could shift conceptions and enhance additive inverse understanding — but the brief lesson did not significantly change conceptions or additive inverse knowledge. In future research, I will develop more extensive assessments and test more substantial interventions.

• Vest, N. A., & Alibali, M. W. (2024). Is zero more than nothing? Relations between concepts of zero and integer understanding. paper
• Vest, N. A., & Alibali, M. W. (2023, June). Conceptions of zero and the semantic congruence effect. MCLS. slides
• Vest, N. A., Weaver, H. J., & Alibali, M. W. (2022). Zero in on this: Children are exposed to various concepts of zero prior to age six. Proceedings of CogSci. paper

Three competing accounts of how people represent negative numbers have been proposed in the literature: the componential, extension, and reflection accounts. This project tests how these accounts hold up across adolescence by embedding cognitive research tasks within Atlas, Innovamat's digital learning platform, drawing on data from 708 students in Grades 7–10 across six secondary schools in Spain.

Contrary to preregistered predictions, we found no evidence of a grade-related shift in mixed-sign distance effects. Instead, students showed substantial and stable individual variability, with behavioral patterns consistent with all three theoretical accounts present at every grade level. At the group level, performance was most consistent with the extension account, and arithmetic performance improved primarily for extended-range integer operations. Individual differences in integer representation were not associated with arithmetic performance.

Together, these findings suggest that representational heterogeneity, rather than a uniform progression toward a single mature representation, characterizes adolescent integer cognition.

• Vest, N. A., Colomer, M., & Closser, A. (2026). Negative number representations and arithmetic across secondary grades: Evidence from a digital learning platform. Revise & resubmit, Contemporary Educational Psychology.

Mathematics is essentially the science of patterns. Children are constantly recognizing and encoding patterns in their environment. Importantly, children's ability to recognize shape patterns is related to their numerical knowledge. Part of my research focuses on approaches to teaching patterning skills to young children.

In one study, I investigated whether an instructor's gestures could help children identify pattern units and improve performance in patterning tasks. The inclusion of gestures by the experimenter did not significantly affect children's learning outcomes compared to speech alone. However, children's spontaneous mimicry of the experimenter's speech was positively associated with better posttest performance.

In another study, I examined whether providing perceptual support — such as drawing a line under the pattern unit — would help children recognize pattern units more effectively. I am currently preparing a manuscript with these results.

• Vest, N. A., Anthony, L. E., Callery, K., et al. (2024, June). Does focusing on the unit of change help children extend and abstract shape and number patterns? MCLS. slides
• Vest, N. A., Anthony, L. E., Becerra, C., et al. (2024, March). Learning to extend shape and number patterns. CDS. poster
• Vest, N. A., Fagan, S. E., & Fyfe, E. R. (2022). The role of gesture and mimicry for children's pattern learning. Cognitive Development. paper

I have worked with an interdisciplinary team of psychologists, computer scientists, and educators to study how to enhance algebra learning through the integration of key concepts and problem-solving procedures. Our team used a software-based intelligent tutoring system (ITS) that provides detailed, targeted guidance adapting to students' errors, strategies, and developing algebra knowledge.

In one study, students completed a pretest, a computer-based lesson, worked examples with explanations, and a posttest. We found that expressing concepts when explaining worked examples helped activate and strengthen conceptual knowledge, particularly for learners with low prior knowledge.

In earlier work, I spearheaded a project exploring gesture and algebra learning, finding that students whose gestures aligned with a computer-animated pedagogical avatar scored higher than those who did not.

• Vest, N. A., Silla, E. M., Bartel, A. N., et al. (2022). Self-explanation of worked examples integrated in an ITS enhances problem solving in algebra. Proceedings of CogSci. paper
• Vest, N. A., Silla, E. M., Bartel, A. N., et al. (2021). Learning from worked examples: Conceptually rich explanations predict conceptual gains. SRCD. poster
• Vest, N. A., Fyfe, E. R., Nathan, M. J., & Alibali, M. W. (2020). Learning from an avatar video instructor: The role of gesture mimicry. Gesture. paper

Students often struggle with linear functions that have negative slopes, yet the task conditions under which this difficulty arises have remained unclear. This project examined how slope direction (positive vs. negative), representational format (graphs vs. tables), and response format (equation generation vs. multiple choice) jointly influence performance and metacognitive judgments during a function translation task, across 351 U.S. undergraduates solving 20 linear translation problems.

Negative-slope problems yielded lower accuracy than positive-slope problems, but this disadvantage emerged only for tables and not for graphs, and it did not vary by response format. Error analyses showed that slope-sign reversals were the error type most systematically associated with decreasing functions. The absence of a response-format effect suggests the difficulty does not primarily reflect symbolic production demands.

Graphical representations appear to attenuate the negative-slope disadvantage not simply by being easier, but by making direction perceptually salient — supporting accurate encoding and error detection. Students' confidence and difficulty judgments mirrored this pattern, indicating well-calibrated awareness of the task conditions that amplified performance costs.

• Task-dependent difficulty with negative slope in linear functions. Submitted to Journal of Numerical Cognition, March 2026.

I co-lead a multi-site quasi-experimental study examining the implementation and impact of Google Gemini for Education within Miami-Dade County Public Schools (MDCPS), in partnership with Google.org. The study follows teachers, students, and school leaders across participating high schools, combining propensity-score-matched achievement comparisons with classroom observation, survey, and AI usage-log data.

The project examines how AI self-efficacy, professional development, and school leadership shape adoption, and whether consistent use of Gemini for Education is associated with gains in math and ELA achievement and in student engagement — while paying particular attention to students with IEPs and other subgroups whose usage patterns and outcomes may differ.

• Multi-site quasi-experimental study underway with Google.org and Miami-Dade County Public Schools; baseline and mid-year data collection in progress.

As PI on the AIMS EduData Initiative, a Gates Foundation-funded grant in partnership with Digital Promise and EdLight, I lead a project testing whether longitudinal patterns in students' misconception types improve prediction of end-of-year math outcomes beyond static cognitive indicators and behavioral engagement metrics.

Using EdLight's longitudinal, AI-annotated corpus of handwritten middle-school math work, we engineer features capturing error-type slopes, conceptual-versus-procedural error accumulation, and profile volatility over time, then compare their predictive value against static aggregate error rates and behavioral engagement indicators through nested predictive models. A central goal of the project is equity: subgroup calibration and fairness analyses will assess whether trajectory-based signals identify risk earlier without introducing differential bias for English learners, students with IEPs, or racial and ethnic groups.

• Feature engineering underway (2026); nested predictive modeling and subgroup fairness analyses planned through early 2027.