## Using a Technology-Supported Approach to Preservice Teachers’ Multirepresentational Fluency: Unifying Mathematical Concepts and Their Representations

**Source:** *Contemporary Issues in Technology and Teacher Education, 15(4), *2015.

(Reviewed by the Portal Team)

This article describes a project used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers.

The authors defined fluency as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to pass seamlessly among verbal, geometric, symbolic, and numerical representations of the same mathematical object.

The authors were interested to look at whether, and possibly how, such an intervention impacts preservice teachers.

**Methods **

The participants were six preservice teachers, who held bachelor’s degrees from a Puerto Rican college or university in a STEM field. All participants had completed at least one semester of a supervised teaching practicum in a secondary school in Puerto Rico.

The participants attended a seminar where they were introduced to the underlying concepts and the pedagogical advantages of multirepresentational fluency. For select topics, this idea was reinforced with interactive GeoGebra applets that allowed preservice teachers to alter a parameter and simultaneously view how it changes all four associated representations simultaneously.

Data were collected through observations of the participants during the orientation session, as well as pre- and post-intervention interviews with the participants.

**Discussion and Conclusions**

The findings show an improvement from the pre-intervention interview to the post-intervention interview in the preservice teachers’ abilities to respond to all questions related to exponential functions. Additionally, all the participating preservice teachers changed the way they solved some problems, even when their pre-intervention strategies were successful.

The authors found that the intervention produced two changes in the preservice teachers that were indicative of an improved awareness of the various registers associated with the same mathematical concept. The first change was a considerably improved ability to perform unfamiliar conversions between known registers of representation. The second change was a newfound practice of introducing intermediary representations when convenient to do so.

The data also reveal preservice teachers’ abilities to perform conversions between registers of representations of exponential functions. Pre-intervention, the preservice teachers struggled with less common conversions.

Furthermore, the second indication that the intervention helped produce simultaneous awareness of registers associated with the same mathematical concept was the participants’ introduction of additional representations as intermediary representations.

Hence, these findings indicate that students were evolving toward a fluency approach to problems involving conversions between registers. The manner in which this approach changed the way students made sense of problems was evidenced by all conversions to the symbolic register.

The authors found that during the post-intervention, preservice teachers were successful with all such conversions, and all used the same strategy.

In addition, one strong indication that the intervention had impacted the participants’ perspectives on what it meant to understand a concept emerged from the discussion during the orientation session. Before this orientation, the group agreed that a concept should be introduced using a single representation, and then its associated representations would follow.

Finally, the authors conclude that these findings suggested that the impact of this intervention were quite promising. The authors argue that the simultaneous access to all registers of representation seemed to move preservice teachers’ perspectives significantly away from a strictly procedural focus and to a more concept-driven approach to thinking about and doing mathematics.