With the changes in Common Core State Standards, it was essential to explore how elementary pre-service teachers' sense of fractions is developing and their thoughts about how to teach fractions. A gap in practice exists because it is unknown how pre-service elementary teachers, after student-teaching, perceive their level of in-practice knowledge…

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.…

Microcredentials are a promising means for expanding teacher access to high quality professional development. This study examined the effectiveness of online, self-paced microcredential courses designed for teachers working in underserved rural communities. The content of these competency-based microcredentials centered on recommended…

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…

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…

The interpretive cross-case study focused on the examination of connections between teacher and student topic-specific knowledge of lower secondary mathematics. Two teachers were selected for the study using non-probability purposive sampling technique. Teachers completed the Teacher Content Knowledge Survey before teaching a topic on division of…

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…

With the recent emergence of online professional development (PD), such opportunities are increasingly available to educators. It is important, then, to assess whether and how such options can be valuable and effective for them. The goal of this study was to assess whether and how a Massive Open Online Course for Educators (MOOC-Ed) can serve as…

This study investigates the problems posed by Turkish pre-service primary teachers and explores the issues they encountered while posing problems related to fractions. A free problem-posing task was administered to 98 pre-service primary teachers who are in sixth academic term, and task-based interviews were conducted with eight volunteered…

This study, part of a larger study focusing on studying a human tutor to design a computer simulation of expert tutoring (i.e., a self-improving intelligent tutoring system), conducted a detailed analysis of one expert tutor's (Nancy Mack) tutorial actions as she attempted to help students learn fractions with understanding. As Mack tutored…

Investigates preservice elementary school teachers' content knowledge and pedagogical content knowledge of decimal numeration. Indicates that most preservice teachers were aware of longer-is-larger misconceptions in students but had little awareness of shorter-is-larger misconceptions. Emphasizes content knowledge that integrates different aspects…

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…