Text

theses

Recent data from a cross-national assessment, the Programme for International Student Assessment (PISA), place the United States performance in mathematics at 38 out of 71 countries (OECD, 2016) – one clear indication of the ongoing need for the improvement of mathematics education. This improvement relies, in part, on improving undergraduate mathematics education for prospective teachers of mathematics who should learn mathematics in a manner that encourages active engagement with mathematical ideas (National Research Council, 1989).  

Despite the importance of teacher rational number knowledge, the ways in which they successfully acquire that complex body of knowledge are not well understood (e.g. Depaepe et al., 2015; Krauss, Baumert, & Blum, 2008; Newton, 2008; Senk, 2012; Son & Crespo, 2009; Tirosh, 2000). Teachers’ capability of building and using different representations of math ideas, including rational number concepts, are considered important areas of mathematical knowledge that must be developed in order to provide meaningful learning experiences for students (National Governors Association for Best Practices & Council of Chief State School Officers, 2010; National Research Council, 2003). Studies on preservice teachers’ thinking about fractions have shown that while they bring some knowledge of fractions to their undergraduate mathematics classes (Mack 1990; Tirosh, 2000; Park, Güçler & McCrory, 2012), their misunderstandings are still similar to those reflected in children’s fractions learning (e.g. Ball, 1988; Osana & Royea, 2011; Zhou et al., 2006) . Studies have also reported that prospective teachers often enter teacher preparation programs with beliefs inconsistent with the conceptual teaching of mathematics (Ball, Lubienski & Mewborn, 2001; Strohlmann et al., 2015). If improvement in the teaching and learning of mathematics is to be realized, understanding how prospective teachers build and justify their solutions to rational numbers problems will be of importance.

This research, a component of a design study grant funded by the National Science Foundation, investigates how prospective teachers extend knowledge of rational number ideas, how they justify solutions and how their beliefs about teaching and learning mathematics evolve. The study also explores the instructor’s role and interventions employed within the classroom environment. The students worked on mathematically rich fractions tasks using Cuisenaire rods as they developed representations to understand the concept of unit fraction, to compare fractions, and to build ideas of fraction equivalence. The study is guided by the following research questions:
1.What role does the instructor play in the prospective teachers’ building and justification of ideas?
2.What types of interventions does she employ?
3.What changes, if any, in prospective teachers’ beliefs about doing, teaching and learning mathematics can be identified over the course of the intervention?

The videotaped data of six female subjects in a mathematics class at a liberal arts college were captured with two cameras for two 60-minute class sessions. During the sessions, students explored fractions ideas while working with partners in small groups, discussed solutions, and built models to justify solutions. Two sessions of videotaped data, transcripts, student work, beliefs assessments and observation notes were analyzed using the analytical model described by Powell, Francisco, and Maher (2003).

This study contributes to an under-researched body of literature by examining instructor’s pedagogical and question moves as prospective teachers build representations of rational number concepts and justifications for solutions to problems within an undergraduate mathematics course. Its findings may be of value to colleges of education as they redesign curricula intended to improve prospective teachers’ understanding of and capability for representing rational number ideas.

ETD_9381

Ed.D.

Includes bibliographical references

by Deidre C. Richardson

doi:10.7282/t3-c7qy-7m59

ETD doctoral

The author owns the copyright to this work.