In this introduction to the Special Issue on Capstone Courses we describe a range of models for the capstone course, common goals for these different courses, popular teaching methods, the use of capstone courses in program assessment, and issues related to course maintenance and faculty development.

In this study, we used problem posing as a measure of the effect of middle-school curriculum on students' learning in high school. Students who had used a standards-based curriculum in middle school performed equally well or better in high school than students who had used more traditional curricula. The findings from this study not only show…

The aim of this paper is to explore further an under-developed area--how drivers of curriculum, pedagogy and assessment conceptions and practices shape the creation and uses of technologically based resources to support mathematics learning across informal, non-formal and formal learning environments. The paper considers: the importance of…

A group of teacher educators and practitioners in mathematics education and early childhood education generalized a set of inquiry-based mathematics models for Taiwanese young children of ages 3-6 and designed a series of inquiry-based mathematics curriculum tasks in cultivate the children's diverse mathematical concepts and mathematical power. In…

This study examines primary grades teachers' instructional decisions in their mathematics classroom during their participation in a year-long professional development program on formative assessment. Teachers participated in 40 h of face-to-face workshops followed by 40 h of classroom-embedded activities that were facilitated in an asynchronous…

Community colleges are facing increased pressure to accelerate students through their developmental mathematics sequence. However, many individuals feel that some state legislatures and college leaders are frequently bypassing developmental math faculty expertise when implementing acceleration and compression initiatives. This qualitative study…

We discuss the pedagogical redesign of a liberal arts mathematics course that enrolls roughly 3000 students per year. Flipping the classroom is a prominent feature of the new pedagogical approach. We describe the nature of this redesign, course resources, and how students are assessed for both preparation and understanding. We also indicate how…

As an alternative to looking solely at linear functions, a three-lesson learning progression developed for Year 6 students that incorporates triangular numbers to develop children's algebraic thinking is described and evaluated.

Statistics is taught in mathematics courses in all school levels. We suggest that using rich tasks in statistics can develop statistical reasoning and create both intra and interdisciplinary links in students. In this paper, we present three case studies where middle school mathematics teachers used different tasks in lessons on pie charts. We…

This study examined the mathematical discourse of elementary school teachers and their students while participating in a year-long professional development project focused on implementing reform-based mathematics curriculum. The teacher participants included 12 teachers, two from each grade level from Kindergarten through Grade 5. Field notes were…

This article interrogates the extent to which the Organization for Economic Cooperation and Development (OECD) through its Programme for International Student Assessment (PISA) influenced the development of Project Maths, a new second-level mathematics education policy in Ireland. It argues that the Irish government, in its revision of mathematics…

Recommendations for reforming high school mathematics curricula emphasize the importance of engaging students in mathematical investigations of societal issues (CCSSI [Common Core State Standards Initiative] 2010; NCTM [National Council of Teachers of Mathematics] 2000). Proponents argue that these investigations can positively influence students'…

The authors of this article collaborated with fourth-grade teachers from two schools to support implementation of a research-based fraction and decimal curriculum (Rational Number Project: Fraction Operations and Initial Decimal Ideas). Through this study, they identified five indicators of rich conceptual understanding of decimals, which are…

We explore early childhood teachers' lived experiences learning and teaching mathematics with young children, adding finer-grained context and detail to broader research descriptions. We interviewed ten early childhood teachers in a university laboratory school about their mathematics training, classroom mathematics curriculum, who controls their…

This paper describes findings from a blocked randomized design (BRD) field study conducted to examine the "Next Generation Preschool Math" (NGPM) program's implementation in preschool classrooms and promise in improving young children's mathematic learning. NGPM integrates traditional preschool activities with developmentally appropriate…