Abstract

Several function families, including radical and those with negative integer exponents, play an important role in biological contexts where dynamics are modeled, ranging from allometric scaling to multi- species trophic interactions. These functions are important in various models of biological dynamics, from the study of allometric scaling to the study of multi- species trophic interactions, where they are observed simultaneously across several representations. However, the teaching of functions in secondary education remains largely on the algebraic register. This study investigates inter- register coordination and any changes that occur when an interactive visualization tool, GeoGebra, is used to study these two little- explored function families. A single- group pre- experimental pretest–posttest design was implemented with 16 first- grade secondary students at a private school in Ecuador, using a quantitative approach. In four workshops of five classes each, four registers (verbal, algebraic, tabular, graphical) were explained, and conversion tasks were set between the registers, while intra- register treatment tasks were facilitated with the aid of GeoGebra. Instruments included a pre- and post- intervention 24- item questionnaire, an observation sheet arranged by semiotic operation, and a rubric developed from 5 criteria, all of which were expert- judged. None of the respondents met the lower limit at the pretest. The Wilcoxon signed- rank test revealed a statistically significant difference (Z = 3. 516, p <. .001) with a large effect size (r =. .62), and all 16 students improved after the intervention. The unevenness of the relationship between the registers was examined as follows: The algebraic- to- tabular was the easiest to do, while the intra- register was the most difficult. The results indicate that interactive visualization is useful for making the conversions necessary to read a model of a biological phenomenon, whereas symbolic treatment, including explicit instruction, cannot. These results should be interpreted as evidence of association rather than causation because there was no control group.