Date of Award

Summer 8-11-2015

Degree Type


Degree Name

Doctor of Philosophy (PhD)


Early Childhood Education

First Advisor

Lynn Hart, Ph.D.

Second Advisor

Christine Thomas, Ph.D.

Third Advisor

Susan Swars, Ph.D.

Fourth Advisor

Julie Dangel, Ph.D.


This study explores the pedagogical approaches used by fifth grade teachers to introduce division with decimals and the resultant understandings of students in their classrooms. The study is important because of the need for students to gain conceptually-based understandings in mathematics and the limited research on instruction and related learning of the very difficult and complex concept of division with decimals. In particular, there is limited research on strategies teachers use to develop students’ conceptual understanding of division with decimals. Therefore, the research questions are as follows.

  • What strategies do teachers use to introduce division with decimals?
  • When first learning to divide decimal numbers, how do fifth-grade students explain the strategies they use?

The study is grounded in social constructivist learning theory and uses a collective case study methodology. Following the study design, three fifth-grade teachers from three schools were interviewed before and after an introductory lesson to division with decimals. They also were observed teaching the study lesson. Following the lesson, one to three students from each class (six in all) were interviewed on their understandings of division with decimals using their classwork from the lesson as a point of entry. The design includes three sources of data: transcriptions from semi-structured interviews of teachers and students, field notes from classroom observations, and artifacts from lessons. Results suggest that instruction of division with decimals varies such that the differences can be captured along a continuum of traditional to reform practices. The placement of the decimal point in the quotient is the focus of the discussion regardless of where the instruction lies on the continuum. Interestingly, as instruction moves towards the traditional end of the continuum, student engagement was a result of interaction with the teacher, whereas closer to the reform end of the spectrum students were engaged with the mathematics.