This study used units coordination as a theoretical lens to investigate how whole number and fraction reasoning may be related for preservice teachers at the conclusion of a math methods class. The study contributes quantitative evidence that units coordination provides a common foundation for both mathematical knowledge for teaching whole number…

This dissertation case study examines how teachers' levels of units coordination afford their ability to reason multiplicatively and fractionally, as well as use their mathematics knowledge for teaching to analyze student multiplicative and fractional reasoning, when a two-year intervention is put into place to evoke new mathematical reasoning.…

Using multiple representations and changing between them is at the heart of the mathematics classroom; unconnected changes can, however, be obstructive for students' learning. In order to support students' learning with multiple representations, teachers have to link observed situation aspects with relevant professional knowledge, a competence we…

Prospective teachers (PTs) need opportunities to develop fraction number sense, yet little research has explicated how this development occurs. Our research team collaboratively designed a task targeted at helping PTs develop fraction number sense through an exploration of fraction comparison strategies. This paper focuses on developing one…

In order to provide a transforming way of knowing for teachers' professional learning, this paper uses narrative to present the knowledge emerging from teachers as participants in a concept study derived from complexity science. There are three components in the narrative: what knowledge emerged from concept study; what has been changed for the…

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

Supporting students to build robust fraction schemes and operations is an enduring challenge in mathematics education. Recent research has explored a developmental trajectory of fractions schemes and operations constructed by upper-elementary and middle school students in an effort to support student learning. This study broadened the existing…

We present a reconceptualized framework for opportunity to learn (OTL) in school mathematics that builds on previous conceptualizations of OTL and includes features related to both quantity (i.e., time) and quality. Our framework draws on existing literature and on our own observational research of mathematics teaching practices. Through the…

This study examined pre-service elementary teachers' change in their understanding of fraction operations while taking a mathematics methods course. Specifically, their explanations and justifications for common algorithms for multiplication and division of fractions were coded using an existing framework (SOLO; Biggs, 1999) for the assessment of…

The purpose of this study was to examine and elaborate upon elementary prospective teachers' (PSTs) conceptions of partitive division with fractions. We examined the degree to which PSTs' conceptions were connected (i.e., capable of translating between representations correctly; aware that partitive division generates a unit rate for its quotient)…

The Alabama State Department of Education (ALSDE) was grappling with several issues including: (1) A respectable rate of growth in student achievement for both fourth- and eighth-grade math in the state of Alabama, as measured by the National Assessment of Educational Progress (NAEP), but below the national average; and (2) A growing concern about…

The purpose of this study was to characterize and compare novice and experienced elementary teachers' pedagogical knowledge and pedagogical content knowledge of three major topics in mathematics: whole number operation, fractions, and geometry. The study participants were 26 preservice elementary teachers and 28 experienced kindergarten through…