Research

• While mathematics educators develop their new theories, a robust, connected, extended community of unschoolers is living new ways of learning. It is time professional educators learned a thing or two from the top specialists on education practice in the world: parents.

• What toddler activities prepare future understanding of multiplication? How tables, pictures, fractals and other representations influence the ways multiplicative reasoning grows? What if kids studied counting and addition through multiplication? These and other questions are addressed in a series of studies.

• Pre-service teachers have to re-examine their understanding of mathematics from the new point of view: helping others learn. What tools can they use to increase their pedagogical understanding? What can teacher educators do to help pre-service teachers learn?

• Children learn mathematics using a "natural language" such as English. What happens if they learn a topic in one language, and then approach it in another language? Preliminary results show that problem solving strategies and ways of reasoning depend on the language the child is uses at the moment.

• Mathematics is a study of patterns. These mathematical patterns arise from any human endeavor, such as music or drawing. Learners who have extensive knowledge of any area can use that knowledge to study mathematics, if…

Publications and presentations

Berenson, S., Droujkova, M., Slaten, K., & Tombes, S. (In review). Learning the language of mathematics teaching: Situating the educative experiences of prospective teachers in the domain of diverse learners.

Droujkov, D., & Droujkova, M. (In review). Software for the development of multiplicative reasoning.

Droujkova, M. (In review). "Is this my mathematics?" Metaphor and early algebraic reasoning.

Droujkova, M. (In review). Tables and young children's algebraic and multiplicative reasoning.

Droujkova, M., Berenson, S., Slaten, K., & Tombes, S. (In review). A conceptual framework for studying teacher preparation: The Pirie-Kieren model, collective understanding, and metaphor.

Droujkova, M., & Droujkov, D. (In review). Software for the youngest mathematicians: Connecting qualitative, additive and multiplicative worlds with metaphors.

Slaten, K., Berenson, S., Droujkova, M., & Tombes, S. (In review). Assessing beginning pre-service teacher knowledge: An early intervention strategy.

Slaten, K., Berenson, S., Droujkova, M., & Tombes, S. (In review). Characterizing links among pre-service teachers' collections of proportional reasoning representations.

Slaten, K., Droujkova, M., Berenson, S., Williams, L., & Layman, L. (In review). Undergraduate student perceptions of pair programming and agile software methodologies: Verifying a model of social interaction.

Tombes, S., Berenson, S., Droujkova, M., & Slaten, K. (In review). Exploring styles of preservice teaching as seen through the Towers framework.

Droujkova, M. A. (2004). The spirit of four: Metaphors and models of number construction. Proceedings of the 26th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. Toronto, Ontario, Canada DOWNLOAD paper, slides

Berenson, S. B., Droujkova, M. A., & Slaten, K. (2004). Pre-service teachers' proportional reasoning. Paper presented at Robert Davis International Invitational Conference, Emerald Isle, NC

Droujkova, M. A. (2004). Roles of metaphor in the growth of understanding. Paper presented at Beyond IQ Conference, Manchester, NH

Droujkova, M. A. (2004). Roles of metaphor in the growth of mathematical understanding. Paper presented at the 3rd Annual Peter H. Martorella Colloquium, Raleigh, NC: North Carolina State University

Droujkova, M. (2004). Roles of metaphor in the growth of mathematical understanding. Unpublished Doctoral Dissertation, North Carolina State University, Raleigh. DOWNLOAD

Droujkova, M. A. (2003). The role of metaphors in the development of multiplicative reasoning of a young child. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th Annual Meeting of the International Group for the Psychology of Mathematics Education, p. 213. Honolulu, HI: University of Hawaii DOWNLOAD

Droujkova, M. A., & Berenson, S. B. (2003). Software design as a method of accessing students' understanding. In N. Pateman, B. Dougherty, & J. Zilliox (Eds.), Proceedings of the 27th Annual Meeting of the International Group for the Psychology of Mathematics Education, p. 283. Honolulu, HI: University of Hawaii DOWNLOAD

Droujkova, M. A. (2003). The role of metaphors in the development of multiplicative reasoning. Paper presented at the North Carolina Association for Research in Education Annual Meeting, Holly

Springs, NC

Droujkova, M. A., & Droujkov, D. A. (2003). Using XP with children for learning mathematics. Paper presented at the 4th International Conference on eXtreme Programming, Genova, Italy DOWNLOAD

Droujkova, M.A. (2001) Mathematical scaffolding: Changing math with and for students. Paper presented at the North Carolina Association for Research in Education Annual Meeting, Charlotte, NC

Berenson, S. B., Droujkova, M. A., Cavey, L.O., Smith, N.H., & Barnes, T.M. (2000). Girls on track with information technology. Meridian: A Middle School Computer Technologies Journal, 3(1). DOWNLOAD

Droujkova, M. A. (1998). Natural Math. Humanistic Mathematics Network Journal, 18, 1-10 DOWNLOAD