# research Projects & Grants

In a nutshell, we LOVE learning and thinking about how people learn and think about math (very meta, we know!). How does mathematics knowledge develop over time? Why are so many people so afraid of math while others are so in love with it? Why do some people view math like a puzzle or game while others view them as confusing procedural rules and algorithms? Where do people who are "bad" at math get stuck? What are mathematical and contextual predictors of mathematics learning and achievement? What does good mathematics teaching look like? Why is teaching math so hard? What skills (other than math knowledge) are required to successfully teach and understand mathematics? These are just a few of the questions I try to answer in my research.

My research aims to develop and evaluate classroom interventions that improve mathematics teaching and learning. My research is highly interdisciplinary and focuses on the intersections of educational, cognitive, and developmental psychology. My work is focused on the development, design, and testing of innovative classroom interventions and technologies that embed cognitive and educational principles of learning into everyday practice. I also use classroom observations, longitudinal data, and multi-level modeling to examine how mathematics and social-emotional learning (SEL) interventions in schools can enhance students’ opportunities to learn. Ultimately, I am interested in understanding how cognitive and non-cognitive pathways combine to produce learning and growth for all children in K-12 classrooms (and beyond!)

## Some of my Funded Research Projects

Over the past five years, my work has been supported by over $7.5 million in research funding from the Institute of Education Sciences, National Science Foundation, Spencer Foundation, Hewlett Foundation, and the American Educational Research Association.

My work explores the ways that instructional interventions that integrate perceptual learning, gesture, and embodied cognition can improve student learning and engagement in mathematics. Many leading curricular programs in mathematics and science have often used more traditional algorithms and static representations to teach algebraic notation; however, there is some reason to think that students may better recognize the construction of algebraic notation if they dynamically transform expressions using manipulation of physical objects. In theory, perceptual training may help build students understanding of algebraic concepts by internalizing the appropriate way of visualizing and gesturing patterns in algebraic structure. Symbols are presented as literal (sometimes virtual) objects, which children can touch and move, and which respond in natural, object like ways (constrained by mathematical law). This novel, dynamic program allows students to explore patterns and properties of mathematics by rearranging, splitting, and manipulating numbers and expressions. To date, much of my work has focused on building and designing several instantiations of the approach and coordinating across multiple representations for flexible use in classrooms by both teachers and students. Working with an iterative design cycle has allowed me to evaluate what components of the intervention work best in applied classroom settings and has provided me great feedback about how to adapt the program to better fit the needs of teachers and students. My quantitative work provides evidence of the program’s efficacy and offers new and innovative insight into thinking about how we learn abstract concepts.

## NSF CAREER GRANT (RETTL)

Through a 5 year NSF CAREER Grant through RETTL, I will examine ways that Teacher Orchestration and Perceptual Learning can help provide insights about students mathematical strategies and understandings.

## GRASPABLE MATH

About 9 years ago, my colleague David Landy and I designed an initial prototype for a dynamic math notation that was based on theory and research in cognitive science and perceptual learning. What started as an initial idea has turned into a widely used dynamic algebra notation tool called Graspable Math. With the support by iES, we have developed several different initiations of this tool and my research has explored its impact on learning and the ways that we can use the data from students problem solving to understanding perceptual and mathematical mechanisms of learning.

Graspable Math (IES) -I co-developed Graspable Math , an interactive web-based tool that allows you to manipulate and solve mathematical expressions and equations. My empirical work uses data collected from the GM technology to answer important theoretical questions about student interactions, problem solving, and mathematics teaching and learning.

Graspable Math Activities (IES/SBIR) - With Graspable Math Activities, teachers can assign algebra tasks to your students and see live feedback of their step-by-step work. It is powered by Graspable Math, a digital algebra notation that provides a powerful and flexible way to work with algebra in the digital space. The phase I and II SBIR grants were focused on developing the product and examining its initial promise in classrooms. My lab and WPI lead the initial user-centered design research.

From Here to There! (IES-CASL)- Algebra can be a fun and engaging game! (really, it can!). FH2T is a game-based application and intervention that I co-developed (and have tested) that embeds perceptual learning and cognitive science principles into mathematical puzzles. From Here to There (FH2T) allows students to explore patterns and properties of arithmetic and symbolic algebra by rearranging, splitting, and manipulating numbers and expressions to reach a specified goal. We know that playing it relates to improved mathematical understanding but we don't yet know WHY or HOW....A large scale RCT study with 4,000 7th grade students was conducted in Fall 2020 to compare the efficacy of From Here to There! to other math technologies. While a team of external evaluators are conducting the impact analyses, my lab is currently analyzing the data from this study to understand mechanisms of learning.

## Wearable Learning Cloud Platform

Wearable Learning Cloud Platform (NSF-Cyberlearning) - I have worked with my colleague Ivon Arroyo on the Wearables for Learning Project. The Wearables for Learning project is investigating mathematics learning in elementary and middle school via authentic games that children play in the classroom and the playground, which are full of rich mathematical properties. We integrate technology with relay races, and scavenger hunts that target the development of number sense, measurement and geometry, and overlap technology to authentic children’s games that capitalize on this infrastructure to learn mathematics and excite kids about learning math. With an EAGER award and a recent NSF award from the National Science Foundation, we will investigate middle schooler’s development of computational thinking as children create math games themselves, defining the behavior of wearables as finite-state-machines. This research explores how learning with physical-technology compares to learning with classic/passive-technology and how problem-posing adds inquiry-based approaches and ownership into the game, as well as motivational/affective impact on perceptions of mathematics and the drive to learn.

You can learn more about this project and tool by visiting wearablelearning.org

## Automated Classroom Observation Using Machine Learning

Teachers Are the Learners: (NSF- Cyberlearning)- I am Co-PI on a project exploring how machine learning and computer vision can be harnessed to characterize automatically the interpersonal dynamics between students and teachers from videos of school classrooms, and how machine perception can deliver new training experiences for both pre- and in-service teachers. The project is an interdisciplinary collaboration that spans multi-modal machine learning, data visualization, classroom observation, and teacher training. This project brings me back to my roots in classroom observation and social and emotional learning.

Towards Computer-Assisted Coding of Classroom Observations: A Computer Vision Approach to Measuring Positive Climate (Spencer Foundation)- We explored how machine learning and computer vision algorithms can be used to characterize automatically the teacher-student and student-student interactions from classroom observation videos. Partially automating the process of classroom observation could facilitate finer grained and more efficient feedback on teachers' classroom interactions, which could provide teachers with improved professional development feedback and researchers with a more powerful lens with which to measure the impact of educational interventions. As first steps, the researchers are investigating how automatically extractable features such as the facial expression of each participant (teacher, student), as well as auditory features of speech, can be analyzed by recurrent neural networks to predict positive climate and negative climate of the Classroom Assessment Scoring System (CLASS). Later work will consider how to identify which participants are interacting with whom at each moment in time based on their audiovisual profiles, as well as how to combine machine-coded with human-coded CLASS scores to improve accuracy. This study harnesses a dataset of hundreds of CLASS-coded videos of toddler classrooms collected and annotated by the Center for the Advanced Study of Teaching and Learning at the University of Virginia.,