Assessing how pre-service teachers understand balance through clinical interviews and a virtual tool

Our study was enacted in mathematics education classes with pre-service teachers (PSTs). This research focused on videotaped PSTs’ interview responses used to assess their understanding of balance when challenged with tasks involving virtual manipulatives. PSTs relied on visual cues to implement procedures that were often inappropriate for the task at hand. When confronted with missing-value balance tasks, 47% of the PSTs attempted an incorrect procedure using direct proportions while others employed an incorrect fractional method. Only one PST systematically solved the tasks, where he invented an inverse proportions model. Most interviewees relied on intuition and qualitative guess and check reasoning.