**We use concepts and tools from developmental psychology, cognitive science, and cognitive neuroscience to understand how humans acquire, use and teach numerical and mathematical concepts. Our work touches on a wide range of topics, including how mathematical thinking interfaces with attention, memory, networks, emotional processes, genetics, education, among other topics. Research in our lab thus intersects with disparate fields ranging from cognitive neuroscience to developmental psychology to the emerging field of educational neuroscience.**

### BrainSTEM

While we have learned a great deal about the psychological factors that predict success in STEM fields, much less is known about how years of exposure to STEM thinking alters the integration of cognitive, neural and affective functioning. By leveraging recent developments in modeling changes in the integration of different brain systems (e.g., functional connectivity and representational similarity analysis), we will uncover the specific mechanisms by which learning to think scientifically alters how humans think in general. This understanding can be not only descriptive with respect to how and why scientific thinking may differ from other kinds of thinking; it can also be prescriptive: What specific mechanisms might we tap to elicit the right blend of scientific and non-scientific thinking that engenders an informed, responsible citizenry?

In BrainSTEM, the central goal is to understand how learning STEM thinking alters the integration of cognitive, neural and emotional functioning. By focusing on college-level learning, we capture the time frame where students first begin to enjoy substantial control over their own academic trajectories and when respective levels of STEM experience begin to vary dramatically between individuals. By contrasting fMRI analysis of college-level seniors with and without substantial STEM exposure at the collegiate level, we may be able to identify differences in neurocognitive integration within individuals as a function of this exposure.

### Math Anxiety

Mathematical skills in children have been shown to be the strongest single predictor of their later overall academic achievement, predicting outcomes at the individual level, including lower earning potential and probability of mortgage default. At the national level, improving math skills is related to GDP. According to trends in PISA scores, math achievement is on the decline, which creates not just an individual problem, but a rising social issue.

Previous work has identified five main factors that predict mathematical performance: basic numerical skills, spatial processing, verbal processing, executive functioning, and attitudes/anxieties about mathematics. This study aims to explore these factors in greater detail: Are some factors more predictive than others? Do some factors contribute in the same manner as another factor? In this way, we can begin to untangle the complex structures by which various cognitive and psychological factors contribute to the understanding of the foundational building blocks that allow humans to perform mathematical tasks – a fundamental ability in modern society. Measuring factors behind mathematical success can have immediate implications for designing interventions and curricula aimed at ensuring mathematical success from an early age.

### Symbol Processing

Humans use a variety of symbols every day, such as letters (e.g. A, B, C…) and numerals (e.g. 1,2,3…). Understanding how we learn these symbols is critical to developing the best way of teaching these symbols which are foundational to common tasks (such as reading and math). Notably, in most cases, letters and numbers are abstract shapes (i.e. the shapes do not convey their meaning). Results from this work will be used in developing educational programs which optimize learning efficiency and retention.

In this research, we investigate how humans learn to attach meaning (e.g. magnitude information, ordinal information, arithmetic operations, etc.) to abstract symbols. This includes human ability to learn abstract novel symbols (i.e. symbols which do not have any inherent meaning), which allows us to determine the learning process without the confounds from previous experience with the symbols. We also utilize known symbols in different training paradigms to evaluate the learning process with symbols that do have prior meaning and can be used in more advanced contexts (e.g., doing arithmetic with numbers or ordering the alphabet, etc.). In addition, we will assess how different factors (e.g. the training paradigm used, academic related anxieties such as math or reading anxiety, working memory ability, etc.) influence this learning process.

### Time Pressure

Time-pressure is a common component of math assessments on both standardized and classroom exams. On the one hand, timed testing may index and encourage development of math fluency (rapid and fluent math calculation), a valuable skill in its own right that also reduces cognitive load in the service of learning new, more complex math concepts. On the other hand, opponents of timed-testing point to the irrelevance of expedient calculation for many types of mathematics, and timed-testing tends to compromise performance most in underrepresented groups, including those with disabilities. However, the impact that time-pressure has on the way individuals feel about mathematics – including math anxiety – remains unknown.

The current project aims to provide a comprehensive picture of how time-pressure impacts the way both adults (college students) and children think and feel about mathematics. In this three part study, we aim to find the answers to three major questions:

- Does math time-pressure cause in-the-moment math anxiety?
- Does time-pressure impact math learning, future resilience to time-pressure, and trait-level math anxiety?
- Does math time-pressure modulate the reciprocal relations between math anxiety and ability in children?

### Social Networks

Math anxiety represents a significant obstacle for those who wish to succeed in mathematics, as increased MA is associated with decrements in math performance. Math anxiety is related to avoidance of math, both in avoidance of math problems and avoidance of math classes and careers. Social cues, awareness of others’ expectations, and affective signals of others may contribute to the experience of math anxiety, and previous work indicates that these interpersonal cues are a component in the spread of math anxious beliefs and behaviors, such that math anxiety may be “contagious” across individuals.

Social networks provide rich information about the social ties that exist between individuals, and how these individuals are affected by the behavior of others in their network. Information and behaviors can ripple through a social network, exerting influence across direct connections between individuals, but also across three degrees of separation within a network. How does misinformation about math attitudes, the role of math, and improvement spread throughout a network? Though there are a myriad of factors that may contribute to the “contagion” of math anxiety across a social network, in the present research, we are interested in examining how social connections to others may be related to math anxiety, academic choices, and academic achievement.