Recording and Representing Student Mathematical Thinking: A Comparison of Preservice Teachers in the U.S. and Korea

The practice of recording and representing mathematical thinking of students is critical for enriching their understanding of mathematical concepts and procedures. However, teacher education often overlooks this competency, leaving it to be learned through experimentation in the field. This study aims to examine how mathematics preservice teachers (PSTs) perform in recording and representing mathematical ideas of students, offering insights to teacher educators to support PSTs' development of these skills. We compared PSTs in the U.S. and Korea in these teaching skills to reveal the intricate process involved. Ninety PSTs, 45 from each country, participated in representing and recording four different student mathematical strategies for two-digit addition problems. To examine PSTs' work in recording and representing student thinking, this study utilized an analytical framework consisting of five categories: authenticity, accuracy, organization, support for understanding, and specification. The findings indicate that both groups demonstrate higher performance in authentic translation of student work and accurate use of mathematical notation and values. However, both groups of PSTs show little evidence in their performance of representing mathematical thinking of students using a variety of visual models. We also found discrepancies between these two groups of PSTs. PSTs in Korea are more likely to record mathematical thinking as they are, while PSTs in the U.S. describe the student thinking pathways in more detail. This study has implications for mathematics teacher educators in both countries, highlighting specific elements they need to focus on to nurture PSTs' recording and representing of mathematical thinking of students.