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…

In this study, the middle school mathematics teachers' knowledge of division of fractions was investigated through the strategies that they proposed and the problems that they posed for division of fractions. The data was collected from 22 middle school mathematics teachers through the task and semi-structured interviews. The data of this case…

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 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…

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…

The third volume of this proceedings contains more of the research reports begun in Volume 2. Papers include: (1) "A Semiotic Model for Analyzing the Relationships between Thought, Language and Context in Mathematics Education" (Juan D. Godino and Angel M. Recio); (2) "Conceptions as Articulated in Different Microworlds Exploring…

The first volume of this proceedings contains an introduction and the plenary, research forum, working group, and discussion group papers. Papers include: (1) "Resources as a Verb: Recontextualizing Resources in and for School Mathematics" (Jill Adler); (2) "Markets and Standards: The Politics of Education in a Conservative Age" (Michael Apple);…

The second volume of this proceedings contains the first portion of the research reports. Papers include: (1) "Learning Algebraic Strategies Using a Computerized Balance Model" (James Aczel); (2) "Children's Perception of Multiplicative Structure in Diagrams" (Bjornar Alseth); (3) "A Discussion of Different Approaches to Arithmetic Teaching"…

The fourth volume of this proceedings contains 29 full research reports continuing on from Volume 3, 84 short oral communications (abstracts only) and 34 poster presentations (abstracts only). The full papers include: (1) "Beliefs, Teacher Education and the History of Mathematics" (George N. Philippou and Constantinos Christou); (2)…