## About

57

Publications

27,444

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440

Citations

Introduction

I am an assistant professor of psychology and learning sciences at WPI. My research is highly interdisciplinary and focuses on the intersections of educational, cognitive, and developmental psychology and aims to develop and evaluate classroom interventions and technology that improve mathematics teaching and learning. Ultimately, I am interested in understanding how cognitive and non-cognitive pathways combine to produce learning and growth in mathematics.

**Skills and Expertise**

Additional affiliations

July 2015 - present

August 2014 - August 2015

August 2011 - August 2014

Education

August 2007 - May 2011

August 2001 - May 2005

## Publications

Publications (57)

Online educational games have been widely used to support students’ mathematics learning.
However, their effects largely depend on student-related factors, the most prominent
being their behavioral characteristics as they play the games. In this study, we applied a set
of learning analytics methods (k-means clustering, data visualization) to clicks...

This preliminary study examined whether distinct student profiles (N = 760) emerged based on their behavioral patterns in an online algebraic learning game. We applied k-means clustering analysis to clickstream data collected in the game and then examined how students' behavioral patterns varied across the clusters using data visualization. The res...

This emerging technology report introduces the WearableLearning (WL) platform as a tool to exercise computational thinking and STEM learning for 5-12th grade students through mobile technology-augmented active game play and game creation. Freely available at WearableLearning.org, it allows students and teachers to play, create, debug, and manage mu...

This study investigated the effects of 1) proximal grouping of numbers, 2) problem-solving goals to make 100, and 3) prior knowledge on students’ initial solution strategies in an interactive online mathematics game. In this game, students transformed an initial expression into a perceptually different but mathematically equivalent goal state. We r...

Worked examples are effective learning tools for algebraic equation‐solving. However, they are typically presented in a static concise format which only displays the major derivation steps in one static image. The current work explores how worked examples that vary in their extensiveness (i.e., detail) and degree of dynamic presentation (i.e., stat...

We examined the influences of pre-solving pause time, algebraic knowledge, mathematics self-efficacy, and mathematics anxiety on middle-schoolers' strategy efficiency in an algebra learning game. We measured strategy efficiency using (a) the number of steps taken to complete a problem, (b) the proportion of problems completed on the initial attempt...

We apply an advanced data visualization technique, Sankey diagram, to explore how middle-school students (N = 343) solved problems in a game-based algebraic notation tool. The results indicate that there is a large variation in the types of students' strategies to solve the problems, with some approaches being more efficient than others. The findin...

In this work we present a multi-modal machine learning-based system, which we call ACORN, to analyze videos of school classrooms for the Positive Climate (PC) and Negative Climate (NC) dimensions of the CLASS observation protocol that is widely used in educational research. ACORN uses convolutional neural networks to analyze spectral audio features...

Smith, H., Closser, A. H., Ottmar, E., & Arroyo, I. (2020). Developing mathematics knowledge and computational thinking through game play and design: A professional development program. Contemporary Issues in Technology and Teacher Education, 20(4).
Abstract. The Game Play and Design Framework is a project-based instructional method to engage teac...

The current study explores the effects of physical spacing within mathematical expressions on student performance. A total of 2,152 students in 5th-12th grade were randomly assigned to one of four conditions within an online problem set, with terms in algebraic expressions spaced 1) neutrally, with no spaces in the expression, 2) congruent with the...

A rising epistemological paradigm in the cognitive sciences-embodied cognition-has been stimulating innovative approaches, among educational researchers, to the design and analysis of STEM teaching and learning. The paradigm promotes theorizations of cognitive activity as grounded, or even constituted, in goal-oriented multimodal sensorimotor pheno...

In this work we present a multi-modal machine learning-based system, which we call ACORN, to analyze videos of school classrooms for the Positive Climate (PC) and Negative Climate (NC) dimensions of the CLASS observation protocol that is widely used in educational research. ACORN uses convolutional neural networks to analyze spectral audio features...

This study investigates relations between cognitive, interpersonal, and intrapersonal opportunities, noncognitive outcomes, and student achievement in 1,096 students from 20 high schools (10 Deeper Learning [DL] network, 10 control) who participated in the Study of DL (SDL). DL is an umbrella term used to encompass the cognitive, interpersonal, and...

This paper examines whether using From Here to There! (FH2T:E), a dynamic game-based mathematics learning technology relates to improved early algebraic understanding. We use student log files within FH2T to explore the possible benefits of student behaviors and gamification on learning gains. Using in app measures of student interactions (mouse cl...

Embodied cognition is growing in theoretical importance and as a driving set of design principles for curriculum activities and technology innovations for mathematics education. The central aim of the EMIC (Embodied Mathematical Imagination and Cognition) Working Group is to attract engaged and inspired colleagues into a growing community of discou...

Games as a means of education have been starting to become more of an everyday reality. Not only are games used in classrooms, but they are used in industry to train soldiers, medical staff, and even surgeons. This paper focuses on physically active (i.e. embodied) multiplayer games as a means of education; not only by having students play, but als...

Our research uses game creation and play to explore methods for computational thinking assessment and practice in mathematics classrooms. We present the first iteration of this research that aims to evaluate the feasibility of using game creation with high school students. Students designed math-related games, modified the game to incorporate techn...

Motivations for This Working Group Recent empirical, theoretical and methodological developments in embodied cognition and gesture studies provide a solid and generative foundation for the establishment of a regularly held Embodied Mathematical Imagination and Cognition (EMIC) Working Group for PME-NA.

We present a new technology-based paradigm to support embodied mathematics educational games, using wearable devices in the form of SmartPhones and SmartWatches for math learning, for full classes of students in formal in-school education settings. The Wearable Learning Games Engine is web based infrastructure that enables students to carry one mob...

Formal mathematical reasoning provides an illuminating test case for understanding how humans can think about things that they did not evolve to comprehend. People engage in algebraic reasoning by 1) creating new assemblies of perception and action routines that evolved originally for other purposes (reuse), 2) adapting those routines to better fit...

Description of Presentation The primary goal of this discussion session is to brainstorm potential ways of using a dynamic technology tool, Graspable Math, as a method to assess problem solving strategy and mathematical flexibility at scale. We will begin the presentation with a brief theoretical rationale guiding the development of GM and present...

Computational fluency is composed of three components: efficiency, mathematical flexibility, and conceptual understanding. Although research highlights the importance of all three of these components in mathematical understanding, a majority of assessments primarily focus on efficiency. In this paper, we propose a novel way of measuring and explori...

Presents preliminary findings from the Study of Deeper Learning data

The cover story featured in WPIs annual Research magaizine is about my research!

Learning algebra is difficult for many students, in part due to an emphasis on the memorization of abstract rules. Algebraic reasoners across expertise levels often rely on perceptual-motor strategies to make these rules meaningful and memorable. However, in many cases, rules are provided as patterns to be memorized verbally, with little overt perc...

Pen and paper remain the preferred tools for solving mathematical problems – despite the fact that paper derivations are very challenging to master and are limited by the static nature of paper. While traditional computer algebra systems are not geared towards the need of learners, dynamic algebra notation systems (DANS) that bring derivations into...

Embodied cognition is growing in theoretical importance and as a driving set of design principles for curriculum activities and technology innovations for mathematics education. The central aim of the EMIC (Embodied Mathematical Imagination and Cognition) Working Group is to attract engaged and inspired colleagues into a growing community of discou...

This study looks at how use of a Social and Emotional Learning Program, the Responsive Classroom (RC) approach, alters the relations between mathematics teaching practices and student mathematics achievement. The study found that teachers trained in RC who used more RC practices provided stronger mathematics instruction, which in turn, contributed...

How do people stretch their understanding of magnitude from the experiential range to the very large quantities and ranges important in science, geopolitics, and mathematics? This paper empirically evaluates how and whether people make use of numerical categories when estimating relative magnitudes of numbers across many orders of magnitude. We hyp...

This study investigates the effectiveness of the Responsive Classroom (RC) approach, a social and emotional learning intervention, on changing the relations between mathematics teacher and classroom inputs (mathematical knowledge for teaching [MKT] and standards-based mathematics teaching practices) and student mathematics achievement. Work was con...

The goal of this chapter is to describe a process of touch screen technology development,
beginning from basic cognitive research and resulting in an applied educational intervention for algebra.
To that end, we introduce Graspable Mathematics (GM), a novel approach to algebra instruction that
integrates strong theory and evidence from perceptual l...

The goal of this chapter is to describe a process of touch screen technology development, beginning from basic cognitive research and resulting in an applied educational intervention for algebra. To that end, we introduce Graspable Mathematics (GM), a novel approach to algebra instruction that integrates strong theory and evidence from perceptual l...

This study examines whether exposure to mathematics content differentially contributes to mathematics achievement
in fifth grade depending on the racial composition of the students in the classroom. The study found that as exposure
to more diverse content increases, the racial mathematics achievement gap in the classroom narrows, suggesting that
in...

This study examines the impact of the Responsive Classroom® (RC) Approach on the use of
standards-based mathematics teaching practices in third grade classrooms. Results show that
RC teachers showed higher use of these standards-based mathematics teaching practices
than non-RC teachers.

This poster presents findings comparing 2 versions of the FH2T intervention (manual and automatic) to a control condition.

This study examines the quality of teacher-child interactions and exposure to mathematics instruction as predictors of 5th grade student mathematics achievement. The sample was a subset of children in the NICHD-SECC longitudinal study (n = 657). Results indicate that even after controlling for student demographic characteristics, more exposure to m...

Psychometric properties of 24 items from the fifth grade Early Childhood Longitudinal Study-Kindergarten Cohort Mathematics Teacher Questionnaire were investigated in a sample of 5,181 participants. These items asked teachers to report how often they had their classroom students engage in different mathematics content, skills and instructional prac...

The purpose of this study is to introduce a measure of standards-based mathematics teaching practices, the Mathematics Scan (M-Scan), and to examine its validity and score reliability. First, we define standards-based mathematics teaching practices based on eight dimensions that have emerged in recent conceptualizations by researchers and in the co...

This study uses a large nationally representative data set (ECLS-K) of 5,181 students to examine the extent to which exposure to content and instructional practice contributes to mathematics achievement in fifth grade. Using hierarchical linear modeling, results suggest that more exposure to content beyond numbers and operations (i.e., geometry, al...

Abstract This study highlights the connections between two facets of teachers' skills—those supporting teachers' mathematical instructional interactions and those underlying social interactions within the classroom. The impact of the Responsive Classroom (RC) approach and use of RC practices on the use of standards-based mathematics teaching practi...

We describe an intervention being developed by our research team, Pushing Symbols (PS). This intervention is designed to encourage learners to treat symbol systems as physical objects that move and change over time according to dynamic principles. We provide students with the opportunities to explore algebraic structure by physically manipulating a...

Mathematics teachers confront dozens of daily decisions about how to instruct students. It is well established that high-quality instruction provides benefits for students with diverse learning and family backgrounds. However, it is often difficult for teachers to identify the critical aspects of a successful mathematics lesson as they strive to im...

Evaluate the quality of your instruction by using the eight dimensions of M-Scan, an observation tool that links math standards with day-to-day practice.