Helping Preservice Teachers Make Sense of Whole Number Concepts and Operations: Working in Base 8

Document Type


Publication Date



How to improve teacher education programs to allow preservice teachers (PSTs) make sense of mathematics for depth, is a topic debated among educational researchers, especially in mathematics education. PSTs and inservice teachers (ISTs) need to be prepared to teach concepts and to understand how and why students come up with different strategies and whether those strategies will work all the time. Teaching whole number concepts and operations (WNCO) in a base other than 10 can challenge PSTs and ISTs to think about mathematics in ways similar to an elementary student. Previous studies have reported PSTs and ISTs struggle when using base systems other than base 10 in an education class or a professional development workshop just like their elementary students might struggle with base 10 (Andreasen, 2006; McClain, 2003; Yackel, Underwood, & Elias, 2007; Zazkis & Zazkis, 2011).

At one university, PSTs work in base 8 for an entire 4 week unit to gain a deeper understanding of WNCO. While learning in base 8, PSTs have to make sense of mathematics strategies in a deeper level than if they were learning about them in base 10. For example, if students are asked to add 7+6 in base 10, they will say 13. When asked “how do you know?” their most likely response is that they just know. By asking the same question in base 8, PSTs make sense of regrouping in a way that is similar to how beginning learners make sense of regrouping in base 10. This can address an important barrier in supporting PSTs and ISTs to understand WNCO in ways that are important for teaching.

The purpose of this research was to use qualitative data from interviews and observations to attempt to answer the question: In what ways do PSTs perceive learning WNCO in base 8? Interviews were conducted to ascertain how PSTs may or may not have changed their views on learning in base 8. Data from interviews of four PSTs indicated they initially struggled with learning WNCO using base 8 during the four week unit. In the beginning, PSTs were frustrated with learning in base 8 and did not understand why they needed to learn this way. However, as the unit continued, researchers found that PSTs were more accepting and realized the importance of learning in base 8. Most understood that although they will not be teaching their elementary students in base 8, learning in this base system had benefits they did not initially realize, for example understanding WNCO in depth.


North American Chapter of the International Group for the Psychology of Mathematics Education Annual Meeting (PMENA)


Tucson, AZ