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# Author Archives: Tobin White

## Wave Builder

The Waves application provides a platform for participants to collectively construct a traveling wave simulation. A primary goal of this tool is to help students make sense of the relationship between the sinusoidal oscillations, in time, of each point along a wave, and the sinusoidal oscillation across the entire collection of points, in space. To this end we animate a wave as a series of independently oscillating points; each individual point along the wave can be selected, and its oscillation represented as a point rotating around a unit circle in time (Figure 1). This is intended to provide a visual representation of the concept of phase or phase angle, which is commonly used in formal, mathematical descriptions of oscillatory motion. Because control over the oscillators’ motions is distributed across the students, successfully building a wave requires the students to coordinate with one another to set the motions of their individual oscillators. In sequences of tasks of building waves with different wavelengths and direction of travel, students investigate the relations between the motions of individual oscillators (and phases, as represented on the unit circle), the relative motions of neighboring oscillators, and the collective wave motion.

**Note:** If you would like access to the Wave Builder demonstration site, please contact us.

##### Figure 1. Screenshot from one student’s view of the *Wave Builder* app.

## Collaborative Learning with Classroom Networks: Integrating Technological and Pedagogical Innovations

*National Science Foundation Early Career Award, $649,312, 2008-2014.*

In order to maintain a dual focus on novel forms of learning and teaching in the context of collaborative designs for networked classroom devices, this research blends two approaches. The first involves a series of design experiments in which new technology designs provide a context for exploring student learning through collaborative problem-solving activities and investigations. The second involves alternating between two different settings for conducting four successive year-long cycles of those design experiments: a set of high school Algebra classrooms taught by teachers who serve as collaborative partners in the design and implementation of new activity designs, and another high school Algebra classroom in which the principal investigator spends portions of two different school years as a researcher-teacher.

Designs: Graphing in Groups, Terms & Operations, Two Sides, NetGeo, Code Breaker 3.0

Journal Articles:

- Lai, K. & White, T. (2014). How groups cooperate in a networked geometry learning environment.
*Instructional Science*,*42*(4): 615-637. - White, T. & Martin, L. (2014). Math and Mobile Learning.
*TechTrends**58*(1): 64-70. - Lai, K. & White, T. (2012). Exploring quadrilaterals in a small group computing environment.
*Computers & Education, 59*(3): 963-973. - White, T., Booker, A., Carter Ching, C. & Martin, L. (2012). Integrating digital and mathematical practices across contexts: A manifesto for mobile learning.
*International Journal of Learning and Media, 3*(3), 7-13. - White, T., Wallace, M., & Lai, K. (2012). Graphing in groups: Learning about lines in a collaborative classroom network environment.
*Mathematical Thinking and Learning, 14*(2), 149-172. - White, T. & Pea, R. (2011). Distributed by design: On the promises and pitfalls of collaborative learning with multiple representations.
*Journal of the Learning Sciences, 20*(3), 489-547.

Book Chapters:

- Brady, C., White, T., Davis, S. and Hegedus, S. (2013). SimCalc and the Networked Classroom. In S. Hegedus & J. Roschelle (Eds.),
*Democratizing Access to Important Mathematics through Dynamic Representations: Contributions and Visions from the SimCalc Research Program*(pp. 99-121). Advances in Mathematics Education Series, Springer. - White, T. (2013). Networked technologies for fostering novel forms of student interactions in high school mathematics classrooms. In C. Mouza & N. Lavigne (Eds.),
*Emerging Technologies for the Classroom: A Learning Sciences Perspective*. Springer.

Refereed Proceedings:

- Sutherland, S. & White, T. (2011). Differentiating algebraic equivalences in classroom networks. In T. Lamberg (Ed.),
*Proceedings of the 33rd Annual Meeting of the North-American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA 33)*, Reno, October 20-23, 2011. - White, T., Sutherland, S. & Lai, K. (2010). Constructing collective algebraic objects in a classroom network. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.),
*Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education,*pp. 1523-1530. Columbus, OH: The Ohio State University. - Lai, K. & White, T. (2010). Developing students’ geometric reasoning in a networked computer environment. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.),
*Proceedings of the 32nd annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education,*pp. - White, T. & Brady, C. (2010). Space and time in classroom networks: Mapping conceptual domains in mathematics through collective activity structures. In K. Gomez, L. Lyons & J. Radinsky (Eds.),
*Learning in the Disciplines: Proceedings of the International Conference of the Learning Sciences*. University of Illinois at Chicago: Chicago, IL. - White, T., Lai, K. & Kenehan, G. (2007). Designing collaborative mathematics activities for classroom device networks. In C. Chinn, G. Erkens, & S. Puntambekar (Eds.),
*Proceedings of the Biennial Conference on Computer Supported Collaborative Learning*. NJ: Rutgers University.

## Collaborative Mathematics Learning with Robots

*National Science Foundation, $300,000, 2012-2015*

In this exploratory project we are investigating how modular robotics technology and handheld computers can be used to engage students in collaborative learning mathematics concepts. In partnership with the UC Davis C-STEM center, we are working to develop technology and design principles for infusing middle school computing and mathematics courses with hands-on collaborative robotics tools and activities. We aim to use these novel designs to investigate aspects of collaborative learning processes that may be uniquely afforded by robotics materials and problem-solving challenges. The project also studies how to effectively integrate modular robots programs into the teaching and learning of introductory Algebra.

Publications from this project:

- Huang, W., White, T., Sutherland, S. & Cheng, H. (2015). Mathematical meaning-making through robot motion. In T. Bartell & K. Bieda (Eds.),
*Proceedings of the 37th Conference of the North-American Chapter of the International Group for the Psychology of Mathematics Education (PME-NA)*. East Lansing, MI: PME-NA. - Sutherland, S., White, T., Huang, J., & Cheng, H. (2014). Making mathematical meaning through robot enactment of mathematical constructs.
*Proceedings of the International Conference of the Learning Sciences (ICLS) 2014*, pp. 1609-1610. Boulder, CO.

## PHoTOnICs: Physics with Tablets Outside and Inside Classrooms

*National Science Foundation, $558,925, 2013-2017*

The aim of the PHoTOnICs project is two-fold: 1) to design technology-based learning activities that seize on emerging digital devices, particularly tablet and mobile PCs of the kind that are quickly becoming widespread on college campuses and in many k-12 school settings, as resources for extending best practices in physics instruction emerging from research-based course reform efforts, and 2) to conduct research into the nature of student learning and collaborative interaction supported by those designs. The project builds on close partnerships with two innovative instructional sites: an introductory series of physics courses at UC Davis, and a diverse, urban middle/high school that has a focus on bridging formal and informal learning experiences through student-driven inquiry. Our project will work synergistically with both sites by equipping students with tablet-based tools and learning activity designs intended to support their collaborative inquiry practice and their understanding of physics concepts.

Designs: Waves, E-Fields, CathMag

Publications from this project:

- Hardy, L. & White, T. (2016). Making sense of making waves: Co-constructing knowledge and group understanding without conceptual convergence. In C.-K. Looi, J. Polman, U. Cress, & P. Reimann (Eds.),
*“Transforming learning, empowering learners,” Proceedings of the International Conference of the Learning Sciences (ICLS) 2016*. Singapore: National Institute of Education. - Hardy, L. & White, T. (2015). Meaning-making in collaborative activity: Effort toward coherent, but not shared, interpretations of the problem. In T. Koschmann, P. Häkkinen, & P. Tchounikine (Eds.), “Exploring the material conditions of learning: opportunities and challenges for CSCL,” the
*Proceedings of the Computer Supported Collaborative Learning (CSCL) Conference*Gothenburg, Sweden: ISLS.