As part of their mathematical knowledge for teaching (Ball et al., 2008), teachers must have a well-connected understanding of the subject matter they teach and must know this content in deeper and different ways than other adults. This is essential for quality teaching and learning, as teachers’ knowledge and understanding impact the nature and effectiveness of instruction (e.g., Hill et al., 2005). Since decimal concepts are part of elementary curriculum (National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010), and can be difficult for children and adults (e.g., Jacobson et al., 2020; Kastberg & Morton, 2014; Steinle & Stacey, 1998), mathematics teacher educators must consider how we can strengthen support for prospective teachers of elementary school (PTs), to deepen their mathematical knowledge for teaching decimals. This is of particular importance as existing research provides few rich characterizations of PTs’ decimal understanding and is limited in explorations into connections and mechanisms that may improve that understanding. In this dissertation, I attend to the research question, following engagement with rich conceptually focused decimal instruction, how may PTs’ conceptualizations of decimal place value and magnitude, and factors which have influenced this understanding, be characterized? I address some gaps in current literature by considering how robust decimal understanding for PTs may be connected to and grounded in their broader knowledge of the base-ten place value system, and to the decimal models which they use.
Following an introduction to the problem in Chapter One, and a review of relevant literature in Chapter Two, Chapter Three reports on a study in which I examined how PTs characterized the base-ten place value system, distinguishing between responses crafted by PTs who had demonstrated different levels of decimal understanding. This allowed me to identify elements of base-ten place value understanding which likely supported PTs’ thinking about decimal place value and magnitude. In the study in Chapter Four, I explored the nature of PTs’ decimal understanding and its relationships with decimal square or number line models that they used, finding that certain model features facilitated PTs’ ability to think about decimal place value and magnitude in ways that are more likely to be productive and appropriate for teaching. These two empirical studies are both qualitative content analyses (Hsieh & Shannon, 2005) carried out in the context of the Elementary Mathematics Project (Chapin et al., 2021). Though implications for teachers and teacher educators are incorporated in Chapters Three and Four, Chapter Five is a practitioner article in which I focus more directly on these implications, making recommendations about important model features and areas of emphasis for decimal instruction. Chapter Six looks across the dissertation, discussing overarching themes and directions for future research.
Results of this research may be used to support mathematics teacher educators in carrying out effective decimal instruction with their PT students, since better understanding of PTs’ thinking can help mathematics teacher educators to make informed curricular and pedagogical decisions to foster PT development. This is of high importance, since as PTs increase and enrich their decimal understanding, their students’ opportunities to learn will also expand. / 2027-04-30T00:00:00Z
| Identifer | oai:union.ndltd.org:bu.edu/oai:open.bu.edu:2144/44267 |
| Date | 20 April 2022 |
| Creators | Starks, Rachel N. |
| Contributors | Dietiker, Leslie |
| Source Sets | Boston University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
| Rights | Attribution-NonCommercial-ShareAlike 4.0 International, http://creativecommons.org/licenses/by-nc-sa/4.0/ |
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