### Junior scholar POSTER SESSION

There will be 20+ posters, each presented by junior scholars. Presenters, you will each have a 48” x 48” cork board to place your poster on - so stay within those size limitations as you design your poster!

**Andrea Alt, University of Northern Colorado**

*Embodied Cognition as a Lens in Professional Development*

I started my journey as a doctoral student with the hope to help mathematics graduate students transition into their teaching roles and as a biproduct improve mathematics teaching at the collegiate level. My research goals have focused to specifically blending my passion for collegiate mathematics professional development with the notion of embodied cognition. Under the guidance of Dr. Hortensia Soto, I hope to investigate the incorporation of embodied cognition at a new collegiate professional development seminar. The Synthesis and Design Workshop on EMIC is an excellent opportunity for me to learn more about embodied cognition and how I can best adopt this lens for my own research. At the end of my presentation, I hope others to realize that notion of embodied cognition is growing and infiltrating campuses across the nation.

**Andrea Donovan, University of Wisconsin - Madison**

*Math Manipulatives: Object and Body Go Hand in Hand*

There is a wealth of research exploring the effects of manipulatives on student achievement. One area that may influence the effectiveness of manipulatives is the physical attributes of the manipulatives and the affordances for action they lend. We hypothesize that manipulatives will have greater benefits for the math learner when the structure of the manipulatives closely aligns with the structure of the concepts to be learned. In order for manipulatives to highlight structure for the learner, it is critical that the manipulatives replicate key elements of the structure of the mathematical concept. We also hypothesize that manipulatives that allow the body to move in ways that align with the structure of the concept will further facilitate learning. Manipulatives offer a unique opportunity to enact actions on objects and if aligned with the concept, can act as another modality to highlight structure for the learner over and above traditional methods.

**David DeLiema, University of California, Berkeley, Graduate School of Education**

*Envisioning a Blended Math-CS Exploration of Geometric Constructions and Definitions through Movement, Failure, and Play*

In 2015, Kobiela and Lehrer published a phenomenal paper about 6th grade students’ extended efforts to define geometric shapes in a classroom in which the teacher created “monsters,” or faithful but ungenerous readings of students’ early-draft definitions to catalyze student thinking and argumentation. Using their study as a generative point of departure, could we envision a blended mathematics and LOGO-like computer-programming curriculum in which increasingly complex programming concepts (sequence → loops → functions → multi-parameter functions) enrich students’ iterative efforts to define geometric shapes? The goal of this project would be to design and study a learning environment that takes into consideration heterogeneous interactions between viewpoint/spatial reasoning in movement, play and games to structure activities, the process of debugging code and definitions, and crucially, decisions about when students are ready and interested in refactoring their approach using new levels of abstraction in their code and definitions.

**David Havas, University of Wisconsin - Whitewater**

*Embodied Emotions Constrain Cognition*

Emotions support, and sometimes confound, cognition. Two laboratory experiments in adults demonstrate how emotions constrain conceptualization. First, we show high-level cognition is sensitive to social emotions. Participants automatically and unconsciously mimic others’ facial expressions. This mimicry then influences emotional language comprehension by slowing processing of emotionally congruent sentences. Thus, embodied emotional reactions can hinder mental simulation. Second, we show verbal estimations of emotional force are subject to the same sensorimotor bias documented in physical force estimation. When asked to match the force of emotional language, participants consistently underestimate the force of their own emotional language leading to force escalation. Again, this finding points to a limitation of embodied activity: simulation of embodied force is prone to sensorimotor bias. Although emotion evolved to support adaptive action, it constrains the conceptual system for better or worse.

**Ekta Shokeen, University at Albany, SUNY**

*Using Embodied Cognition to Unpack Video Game Based Discussions*

With the growing use of video games for mathematical learning, there is a need to understand how such video games impact the mathematical thinking of players. In this poster, I investigate how undergraduate students make use of actions and gestures to share their experiences of playing the algebra game DragonBox 12+ in order to ground the meaning of abstract mathematical representation during discussions. Central to this inquiry are the two principles from the theory of embodied cognition (Wilson 2002): cognition is situated; and we off-load cognitive work onto the environment.

**Elizabeth Dutton, University of California, Berkeley, & San Francisco Unified School District**

*Mathematics Learning as Perceptual Reconstruction: The Role of Semiotic Breakdown in Collaborative Problem Solving*

How do multiple participants coordinate their collaborative action to solve a novel mathematical problem? The “4-Views” problem provides participants with a 2-dimensional diagram of the North, East, South, and West views of an unknown construction and asks them to “reconstruct” it in 3-dimensions. Analysis of 3 different groups of 4 participants solve the “4-Views” problem shows the discursive function of semiotic breakdown, when one participant invites other group members to recognize a designed impasse between the different 2-dimensional views. The breakdown pushes participants to negotiate their embodied perceptions of the construction, thus reconstructing the collaborative meaning of the provided diagram (i.e., the 2-dimensional views). Participants then see the views not as 2-dimensional facades of a construction but as projections of a 3-dimensional construction that has depth. Pedagogical implications include both designing impasses into collaborative group work and supporting students who are working collaboratively within the epistemic state of uncertainty.

**Fangli Xia, University of Wisconsin - Madison**

*Which mathematics materials matter? Exploring the effects of providing definitions and diagrams on geometric reasoning*

We investigate the influence of definitions and or diagrams on students’ mathematical reasoning for geometric intuition (snap judgement), insight (gist), and proof. Undergraduate students, mathematics experts and non-experts, were asked to generate proofs for four geometric conjectures. Conjectures varied by levels of scaffolding, offering either (1) no definition or diagram, (2) definition only, or (3) definition and diagram. Contrary to predictions, study 1 analysis demonstrated that clicking on definitions with diagrams was negatively associated with performance on insight (β = -0.74, p < .05) and proof of the 2D conjectures. As a follow-up, study 2 indicated a positive correlation for proof of the 3D conjecture with a definition only but a negative correlation for proof of the other 3D conjecture with a definition and a diagram, and negative correlation for insight regardless of the type of scaffolding.

**Hannah Smith, Worcester Polytechnic Institute**

*Quantity and Quality of Gestures are Related to Performance on an Embodied Geometric Estimation Task*

We propose that both quantity and quality of gestures may be associated with language during a geometric estimation task . We examine whether the type (dynamic or static) and the number of gestures are differentially associated with accuracy and precision of language used in a problem solving explanation. Participants completed estimation tasks where they measured different dimensions of shapes using either an unmarked 6- or 12-inch dowel. Afterwards, participants explained how they arrived at their answer for each task. Sessions were videotaped and later coded for the frequency and type of gestures and the correctness and precision of language used in the verbal explanation. Differences were found among participants who used correct vs. incorrect reasoning and precise vs. imprecise language. We also conducted this study with elementary students and are currently analyzing the data. Additional findings exploring the association between gesture and speech in elementary students, and developmental differences will be presented.

**Jenny Yun-Chen Chan, Worcester Polytechnic Institute**

*Aspects of Student Behavior in a Dynamic Algebra Notation System as Indicators of Their Algebraic Thinking*

Graspable Math (GM) is a web-based tool that allows users to dynamically transform algebraic expressions (e.g., from 2x+3+5x to 7x+3). Here, we examine the relations between aspects of behavior in GM and their associations with algebraic thinking. Thirty-seven ninth-graders completed an algebra assessment, then transformed expressions in GM. For each GM problem, we measured total time spent, proportion of time to first action (i.e., time to first action / total time), number of actions taken, and number of errors attempted (i.e., invalid transformation); and the values were averaged across problems within respective measures for individual students. We found that students with higher algebra knowledge were faster at completing GM problems. Students who spent more time to complete a GM problem took more actions and attempted more errors. Students who spent more time pausing before acting took fewer steps to complete a GM problem. Implications of the findings will be discussed.

**John D. McGinty, University of Wisconsin - Madison**

*A Proposed Theoretical Overlap of Conceptual Metaphors and Perceptual Symbol Systems*

Overlooking well-established cognitive development theory (Piaget & Inhelder, 1956; Bruner, 1966) and learning theory (Bransford, Brown, & Cocking, 2000; Koedinger, 2002), educational practice is overwhelmingly thought of, and implemented through, a Formalisms First approach, which prescribes that “learning and conceptual development proceeds first from knowledge and mastery of discipline-specific formalisms before learners can exhibit competency applying that knowledge to practical and clinical matters” (Nathan, 2012, p. 1). Innovative learning interventions based on the theory of embodied cognition are inspiring alternatives to a Formalisms First approach. However, a crucial next step needed for scaling embodied interventions seems to be establishing a theoretically based evaluation-and-explanation tool, so that teachers and researchers are able to identify student products that emulate embodied thinking, in situ, and also are able to articulate how that evidence is connected to embodied cognitive processes.

This proposal is for an interactive poster presentation intending to elicit thoughts from conference participants. The goal of the presentation is: 1) to identify what constitutes criteria for embodied thinking in students’ written and verbal responses to math problems; and 2) to identify how and why we think that evidence maps onto specific cognitive mechanisms. In order to initiate this dialogue, the poster will present a proposed theoretical overlap between Lakoff and Nunez’s book, Where Mathematics Comes From (2000), and Barsalou’s article, Perceptual Symbol Systems (1999). The poster will present a diagrammatic concept map illustrating the way perceptual symbols function within an embodied cognitive architecture, and will provide small cards depicting examples of relevant conceptual metaphors illustrating embodied thinking. Utilizing Velcro strips, participants will be able to affix the cards to the diagram, reflect on previous scholars’ mapping of conceptual metaphors onto the perceptual symbols system, and rearrange where necessary. Photos will be taken after each conceptual arrangement to record participants’ thought products.

**Jonathan Troup, University of Oklahoma**

*Developing Students’ Reasoning about the Derivative of Complex-Valued Functions with the Aid of Geometer’s Sketchpad (GSP)*

In this paper, I share results of a case study describing the development of two undergraduate students’ geometric reasoning about the derivative of a complex-valued function with the aid of Geometer’s Sketchpad (GSP). My participants initially had difficulty reasoning about the derivative as a rotation and dilation. Without the aid of GSP, they could describe the rotation and dilation aspect of the zing that the derivative is a local property.

**Kelsey Schenck, University of Wisconsin - Madison**

*Connecting to Geometric Proof Concepts using Gestures*

This paper uses grounded and embodied cognition (GEC) as a framework to investigate geometric reasoning about mathematical proof and related forms of reasoning, including mathematical insight and intuition. Although correlational, the findings (n=90) offer empirical support for claims, using mixed effects logistic regression, that geometry proof production is an embodied activity, as exhibited by gesture production, even when controlling for geometry knowledge, ELL status and spatial ability. Dynamic gestures are especially implicated because they allow participants to physically experience generalized properties through enactment. Geometry knowledge may be embodied, and best accessed and revealed through actions and gestures. These findings have implications for instruction, formative assessment, and the design of technology for promoting mathematical reasoning by promoting and tracking gesture production.

**Leah Rosenbaum, University of California, Berkeley**

*Participatory Facilitation in a Collaborative Embodied Geometry Game*

Geometris is a body-scale multi-party embodied learning environment (Malinverni & Pares, 2014), focused on geometry (e.g., Ma, 2017; Price & Duffy, 2018). As shapes appear on-screen, players collaboratively recreate each shape by positioning their bodies on a large-scale tangible user interface. Analysis of gameplay suggests that in some cases, more expert players seem to systematically position their body so as to facilitate their novice partners’ learning. This facilitation often reduces task complexity, for example activating two vertices of a target triangle, leaving the novice to find the last one. Expert players rapidly adapted, cast off, or took up these supports, seemingly in accordance with their impression of the novice’s skill and their comfort in the game (e.g. taking up in more challenging levels). I present cases of this participatory facilitation as a proposed means by which embodied learning environments enable movement to be leveraged as a flexible and responsive pedagogical support.

**Michael Swart, University of Wisconsin - Madison**

*¿What parts the whole story? InterActions learning frActions!*

Digital-tablets distribute cognition through visual, auditory and haptic interactivity. We designed a tutor-game that explored how narratives ((S)trong/(W)eak) and gestures ((I)conic/(D)eictic) could be combined to situate embodied learning. Students played seven levels of a fractions game designed to teach them how to create and compare fractions. One hundred thirty-one students (N=131, age x̄=8.78 yrs, 52.6% Female) were randomly assigned to one of four groups (SI, SD, WI, WD) in a 2x2 factorial experiment. Students completed pre/post direct and transfer assessments and tutor-game log data was mined to explore characteristics of students learning. Results revealed a significant interaction between narrative and gesture moderated by student proficiency. In effect, students new to fractions performed better in an abstract environment using deictic (pointing) gestures. However, as students' proficiencies improved, they learned better using iconically enactive gestures in strong narrative with setting, characters and a plot. This has important implications for designing adaptive learning platforms and curricula for teaching fractions.

**Michael Tscholl, Northern Illinois University**

*Bodily Production of Mathematical Notations*

The research explores the learning affordances of high school students’ production of notations of complex mathematical ideas through body actions. Prior work on the production of phenomena of physics (force and motion) has shown that seeding learner’s activities in an environment requires taking into account the constraints of the body, and has highlighted several issues related to interpretation and analysis of bodily movements. The presentation will discuss common design issues related to embodied production of concepts, and illustrate them with examples of a physics implementation. It will then present a draft design for embodied production of complex mathematical ideas, based on the assumption that body movements as well as body experiences both contribute to embodied learning. The questions raised by presented work as well as the proposed design will contribute to the theory of embodied cognition, especially the relative effect of embodied movements and embodied experiences on learning.

**Paul Reimer, AIMS Center for Math and Science Education & Michigan State University**

*Investigating the Role of Physical Interactions in Developing Meaning in Children’s Mathematical Play*

Play-based pedagogies are often seen in tension with increasing accountability for young children’s academic readiness, even though scholars have suggested that play is a critical disposition in STEM learning. Our research group is engaged in a multiyear partnership with two Head Start preschool centers to explore opportunities for informal mathematics learning in various seeded interest areas that encourage mathematical play (Wager, 2013). In this poster, I investigate how preschool children at these two centers interacted with materials in sessions of self-directed play. In particular, I examine how their artifact-mediated activity (Abrahamson & Lindgren, 2014) arose from the designed objects or ideas they developed while interacting with the objects. Findings suggest that children’s bodily engagement with materials and their own gesturing supported children’s mathematical problem posing and enhanced construction play.

**Taylyn Hulse, Worcester Polytechnic Institute**

*Measuring Math Proficiency within Graspable Math, a Dynamic Algebra Learning Technology*

Within the learning sciences field, we need to utilize learning technologies to design more formative measures that help students succeed by measuring the entire learning process in real time. We explore algebraic problem solving within Graspable Math (GM), a dynamic mathematics learning technology that digitizes algebra notation for students to physically move and play with equations. Utilizing clickstream data, this work aims to tease apart components of proficiency in mathematics, as defined by the five strands of mathematical proficiency (NRC, 2001). A conceptual framework is presented that hypothetically maps GM-based measures onto all five strands. These mappings are then explored using both a bottom-up and top-down approach across elementary, high school, and college populations. This kind of rich research presents an opportunity to tease apart the components of mathematical proficiency across different populations in a method that is more efficient and at a deeper level than traditional summative assessment.

**Virginia Flood, University of California, Berkeley**