Date of Award:


Document Type:


Degree Name:

Doctor of Philosophy (PhD)


School of Teacher Education and Leadership

Committee Chair(s)

Jessica F. Shumway


Jessica F. Shumway


Tye Campbell


Brynja Kohler


Kaitlin Bundock


Katherine Vela


Utilizing mathematical representations makes mathematical processes and thinking visible for the observer as well as the individual doing the mathematics. Mathematical representations have multifaceted meaning and is a critical area of research in mathematics education because of its role in conceptual understanding. Specifically, the Coordination of Multiple Mathematical Representations (CMMR) incorporates the mathematical practices and reasoning and communication skills. This study used content analysis to investigate CMMR for the study of algebraic functions in secondary mathematics textbooks during five eras of mathematics education in the U.S. from 1896 through 2016: Pre-New Math, New Math, Back-to-Basics, Standards Based Math/No Child Left Behind, and Common Core State Standards. Illustrating mathematical concepts using multiple representations is at the heart of conceptual understanding and mathematical communication. The findings of this analysis provide insight into the extent to which the analyzed textbooks utilize CMMR and to the quality of their included representations' aesthetics conducive to connection-making and appeal. All the textbooks analyzed displayed mathematical representations specific to the study of functions, the majority of which were used to develop procedural fluency. The use of multiple mathematical representations to promote and encourage conceptual understanding was observed 29 times more for the Common Core State Standards era than for all other eras combined. Disappointingly, only a very small proportion (2.46%) of all mathematical representations were deemed CMMR (one observation from the first four eras and 37 from the last era). Expansion of this work is essential.



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Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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