Pre-service elementary mathematics teachers' methods when solving integral-volume problems and the rationale behind their selections

This study investigated the methods that pre-service teachers employed while finding volume using integration and the reasons why they utilized these methods (problems); the accuracy of their solutions was also analyzed in this study. Case study design, a qualitative research method, was used for this study. 45 sophomore pre-service teachers studying for the Middle School Mathematics Education degree programme at an Education Faculty in Anatolia. It is used to mean 45-second class preservice teachers studying for the Middle School Mathematics Education degree programme at an Education Faculty in Anatolia. Pre-service teachers were provided with a training programme that made use of GeoGebra software for four weeks as part of their mathematical analysis course. Pre-service teachers were provided with a written form containing five open-ended questions and given time to answer them. Data from the study was analyzed using the content analysis method. Results from these analyses showed that half of the pre-service teachers chose problems that requires the shell method to calculate volume and that the main determining factor was the ease of mathematical calculation provided by the shell method. Also, it was found out that the mistakes made by pre-service teachers originated from issues such as the inability to fully comprehend the subject at hand, errors in formulization and/or graphing, and problems taking the integral.