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…

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…

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…

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…