# Aaron Brakoniecki

Lecturer

Dr. Aaron Brakoniecki is a Lecturer in Mathematics Education at Boston University. He currently teaches mathematics education courses to prospective and practicing middle and high school mathematics teachers. Prior to coming to BU, Dr. Brakoniecki studied at Michigan State University, first receiving his B.S. in mathematics, and later receiving his Ph. D. in mathematics education. While at Michigan State University, Dr. Brakoniecki worked with their elementary and secondary teacher preparation programs, serving as a Field Instructor, Course Teaching Assistant, and Course Instructor. His research focuses on preservice teachers’ mathematics knowledge for teaching and the ways in which technology impacts that knowledge.

Dr. Brakoniecki’s dissertation, “Preservice Teachers’ Uses of the Internet to Support Their Learning of Mathematics: The Case of the Pythagorean Theorem”, explored the information seeking strategies employed by preservice teachers as they searched online for information about understanding a proof of the Pythagorean Theorem and its converse, the form and quality of the mathematical connections they were able to make while searching, and the ways in which their searching strategies related to the connections they made. Other areas of professional interest include supporting teachers’ uses of technology in their classrooms, the use of concept maps as a formative assessment tool, preservice teachers’ understanding of trigonometry, and the reading of geometric diagrams in mathematics texts.

### Education

Ph.D. in Mathematics Education, Michigan State University

B.S. in Mathematics, Michigan State University

### Courses

SED ME 559: Mathematics for Teaching: Geometry

SED ME 560: Mathematics for Teaching: Algebra

SED ME 563 - Problem Solving in Mathematics

### Research

Dr. Brakoniecki's research focuses on the development of teacher knowledge, both mathematical knowledge for teaching and technological pedagogical content knowledge. His work looks at the preparation of secondary mathematics teachers and how they develop this knowledge through their experiences in their teacher preparation programs.

Dr. Brakoniecki's work in mathematics education has looked at teacher preparation programs and how preservice and beginning teachers develop their mathematical knowledge for teaching through their programs. His own research interests have centered on the use of technological tools in the teaching and learning of mathematics, both how these tools can be used to further develop teachers' mathematical knowledge for teaching, and how they use these tools in their classrooms with students. Specifically, Dr. Brakoniecki's dissertation, “Preservice Teachers’ Uses of the Internet to Support Their Learning of Mathematics: The Case of the Pythagorean Theorem”, explored the information seeking strategies employed by preservice teachers as they searched online for information about understanding a proof of the Pythagorean Theorem and its converse, the form and quality of the mathematical connections they were able to make while searching, and the ways in which their searching strategies related to the connections they made. Most recently, he has explored how technological tools have impacted beginning teachers' conceptual understanding of trigonometric relationships. Dr. Brakoniecki has explored how these tools have impacted teachers' development of co-variational reasoning of trigonometric functions, and how this has been incorporated into their technological pedagogical content knowledge for teaching of trigonometric relationships. Additionally, he has continued the methodological work of his dissertation to explore the ways in which concept mapping can help assess the ways in which beginning teachers understand mathematics content and what connections between ideas they are making.

Recently, Dr. Brakoniecki was a researcher on the Enhancing the Potential of Intended Curriculum (EPIC) project (Dr. Leslie Dietiker, PI). The project examines the differences and similarities in the ways that expert teachers enact the same curriculum materials in their own classrooms. This work explores the impact that curriculum materials play in mathematical lessons. Additionally, Dr. Brakoniecki and Dr. Dietiker are also developing a framework to better help mathematics teachers, teacher educators, and researchers understand the complex ways that geometric diagrams can be read in mathematics text, and how those readings might affect mathematical reasoning.

Aaron Brakoniecki's Faculty Profile### Selected Publications

Brakoniecki, A., Glassmeyer, D., & Amador, J. (2016). Examining preservice teacher thinking about technology-based trigonometric explorations through a Replacing, Amplifying, and Transforming Framework. In *Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education*. Tucson, AZ: University of Arizona.

Brakoniecki, A. (2015). *Preservice teachers’ learning mathematics from the Internet.* In T. G. Bartell, K. N. Bieda, R. T. Putnam, K. Bradfield, & H. Dominguez (Eds.), Proceedings of the 37th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (pp. 1226–1229). East Lansing, MI: Michigan State University.

Dietiker, L., & Brakoniecki, A. (2014). Reading geometrically: The negotiation of the expected meaning of diagrams in geometry textbooks. In K. Jones, C. Bokhove, G. Howson, & L. Fan (Eds.), Proceedings of the International Conference on Mathematics Textbook Research and Development (ICMT-2014) (pp. 191–196). Southampton Education School, University of Southampton.

Brakoniecki, A. (2014). Preservice Teachers’ Uses of the Internet to Investigate the Proof of the Pythagorean Theorem and its Converse. In T. Fukawa-Connolly, G. Karakok, K. Keene, & M. Zandieh (Eds.), *Proceedings of the 17th Annual Conference on Research in Undergraduate Mathematics Education* (pp. 407–411). Denver, CO.

Brakoniecki, A., & Dietiker, L. (2010). When is seeing not believing: A look at diagrams in mathematics education. In P. Brosnan, D. B. Erchick, & L. Flevares (Eds.), *Proceedings of the Thirty Second Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education* (pp. 644–648). Columbus, OH: The Ohio State University.

Brakoniecki, A. (2009). Mathematical knowledge for teaching exhibited by preservice teachers responding to mathematical and pedagogical contexts. In S. L. Swars, D. W. Stinson, & S. Lemons-Smith (Eds.), *Proceedings of the Thirty-First Annual Meeting of the North America Chapter of the International Group for the Psychology of Mathematics Education *(pp. 1360–1369). Atlanta, GA: Georgia State University.

Brakoniecki, A. (2009). Taxicab geometry: Explorations in three dimensions. *Online Journal of School Mathematics*, 7(1). Retrieved from https://web.archive.org/web/20110726055314/http://nctm.org/eresources/tocgraphic.asp?journal_id=6

### Selected Presentations

Glassmeyer, D., Brakoniecki, A., & Amador, J. (2016). Angle and slope connections: Challenging teacher assumptions in trigonometry. Presented at the 2016 National Council of Teachers of Mathematics Research Conference, San Francisco, CA.

Brakoniecki, A. (2016). Preservice Mathematics Teachers’ Multiple Foci of Learning: Engaging Multiple Aspects of TPACK Through Isolation. Presentation at the 2016 Annual Conference of the Association of Mathematics Teacher Educators, Irvine CA.

Brakoniecki, A. (2016). The Development of Beginning Teachers' Understanding of Pythagorean Theorem from Two Internet-Based Activities. Presentation at the 2016 Joint Mathematics Meetings, Seattle, WA.

Brakoniecki, A. (2016). Concept Maps as a Way to Assess Form and Quality of Student Understanding of Algebra Concepts. Presentation at the 2016 Joint Mathematics Meetings, Seattle, WA.

Brakoniecki, A. (2015). Uses of the Internet to Support Pre-Service Teacher Learning of Mathematics. Presentation at the 2015 Annual Conference of the Association of Mathematics Teacher Educators, Orlando, FL.