Use of dynamic geometry as a support to paper and pencil activities for comprehension of ratio and proportion topics

Introduction. The present paper shows the importance of a joint use of pencil and paper activities and of technology so that students may develop a complete understanding of ratio and proportion. A previous experience with strategy use when solving ratio and proportion problems provided background. Prompted by a recognition of the cognitive components in students, we decided to offer support through the observation and manipulation of representations made using dynamic geometry software. Method. Application of three activities to be solved by a group of 29 sixth-grade pupils public, primary education in Mexico City. The activities were solved with paper and pencil and using dynamic geometry. Results. Students built figures proportional to others they were were given, using comparison by superimposing one figure over another, by dragging them, and by enlarging or reducing a figure by click-and-drag on one of its vertices. They also established numerically equivalent ratios by obtaining measurements for the figures given and making the comparison as a quotient. They also were able to recover data from the problems given and represent them using drawings, then they made use of these drawings to help them solve the assigned activity. Discussion and Conclusion. Most of the students could establish figures that were proportional to the ones given by using registers of representation, such as using drawings with the data that they were able to extract from the story problems, using a table which they filled in with both external and internal ratios, as well as equivalence relationships between the ratios and the operations used to get the numeric values. They also showed development in their qualitative proportional thinking as a support to quantitative proportional thinking.