Preservice Teachers' Understanding of Decimals using Standard Algorithm and Alternative Strategies


  • Eunmi Joung
  • Cheng-Yao Lin
  • YoungRae Kim


The purpose of this study is to explore preservice teachers’ (PTs’) ability to implement multiple strategies using standard algorithms and alternative strategies and to investigate their conceptual knowledge of decimal operations. There were 37 PTs who participated in this study, all of whom attended a mathematics course in the K-8 Teacher Education Program at a mid-western university. These participants were asked to solve the Decimal Knowledge Test (DKT) in multiple ways. A qualitative approach was used to analyze PTs’ responses to the problems on the DKT. The results indicated that using standard algorithms, PTs demonstrated higher ability in solving decimal addition, subtraction, and multiplication involving a whole number. Alternative strategies posed difficulties in solving decimal multiplication problems involving two decimals, and division problems. Similarly, when examining operations, showing smooth or difficult translations between the representations, PTs found it difficult to translate representational modes in operations with multiplication involving two decimals, two division problems. The same results were seen when examining PTs’ conceptual understanding based on the Lesh Translation Model. The results provide teacher education programs with opportunities to create various instructional approaches involving translations among multiple representations in mathematics methods and content courses.