Investigating prospective mathematics teachers’ use of concrete materials in place value concept in different bases: addition and subtraction with whole numbers

The aim of this study is to examine how prospective mathematics teachers (PMTs) conceptualize the place value concept in different number bases and how they utilize concrete materials in this process. To achieve this aim, a case study design was utilized. The participants of this study consist of 24 PMTs from a public university in Turkey. The participants of this study were asked to answer activity questions that required them to perform addition and subtraction operations on numbers written in base ten, base six and base three using at least two concrete materials. Participants completed this activity as a group, with four weeks to provide written responses and the freedom to use any type of concrete material. The findings revealed that PMTs employed not only proportional and non-proportional models, as stated in related literature, but also a mixed model approach. The use of the mixed model emerged as an effective strategy, allowing PMTs to leverage the strengths of both proportional and non-proportional models. Another finding indicated that PMTs were limited in generating solutions using a second concrete material. This limitation highlights the difficulties PMTs face in maintaining material diversity when working with different base systems, which in turn affects their ability to construct mathematical meaning.