This study presents a sequence of embodied learning designed to help students understand the concepts of rate of change and slope. The sequence with an embodied exploration of proportion using the Mathematics Imagery Trainer. Building on this experience, two other learning systems were developed These generate graphs when learners walk in proportions. Through the second task learners are expected to get a sense of rate of change, by blending the walking experience with the graphs. In the third task, learners generate movements corresponding to given graphs. This sequence of embodied experiences is designed to help learners integrate and qualitative understandings of rate of change with the formal notion of slope, through the process of conceptual blending.

We report the design and pilot testing of a digital application to help middle school children learn integers, Touchy-Pinchy Integers (TPI). The design rationale for this touchscreen-based learning system was based on a neutralization model of integers. To design this embodied mathematics learning system, we associated commonly used touchscreen interaction gestures with mathematical meaning related to integers. Users could manipulate two collinear towers of stacked positive and negative blocks, which together represent an integer expression. The learner could add either type of block, by tapping on the appropriate part of the screen. They could also subtract a desired number of either type of block, by slicing across the blocks. They could also neutralize a pair of positive and negative blocks, by pinching in. The pinch-out actions generated a new pair of positive and negative blocks. A flipping gesture reversed the polarity of the integer expression, which corresponded to a multiplication by -1. Results from a pilot study with grade 7s students indicated that the application helped students resolve deep conceptual issues related to negative numbers, through embodied learning. We present some of our observations from the study and interpret these episodes using embodied learning theory.

We present Active Pathways, an active tangible and tabletop system that aims to support collaborative discovery and learning in biochemical modeling. Our work extends ideas from embodied cognition that suggest that interactive systems that support model building by coupling actions made with the motor system to the dynamic properties of external and internal models can enhance the potential for insight and discoveries. We describe the motivation for our work and the design and development of our system. We also present the results of a user study with pairs of novice modelers, which suggest that our system is not only easy to use and learn but also successful at facilitating an understanding of complex systems and supporting collaboration.

We report on an ethnographic study of the work practice and discovery process in a systems biology lab, and outline a tabletop visualization that was developed based on this study, in collaboration with the researchers. The feedback from the researchers on the current prototype is presented, and ongoing revisions are outlined. We conclude with some of the challenges involved in developing such tangible visualizations for discovery.

We have developed an embodied puppet interface that translates a player's body movements to a virtual character, thus enabling the player to have a fine grained and personalized control of the avatar. To test the efficacy and short-term effects of this control interface, we developed a two-part experiment, where the performance of users controlling an avatar using the puppet interface was compared with users controlling the avatar using two other interfaces (Xbox controller, keyboard). Part 1 examined aiming movement accuracy in a virtual contact game. Part 2 examined changes of mental rotation abilities in users after playing the virtual contact game. Results from Part 1 revealed that the puppet interface group performed significantly better in aiming accuracy and response time, compared to the Xbox and keyboard groups. Data from Part 2 revealed that the puppet group tended to have greater improvement in mental rotation accuracy as well. Overall, these results suggest that the embodied mapping between a player and avatar, provided by the puppet interface, leads to important performance advantages.