Statistics has been a content domain in the mathematics curriculum for decades. However, statistics is a distinct discipline from mathematics and there are important differences in how one should teach the two disciplines. In this article, the authors consider how these differences can inform an adaptation to the 5 Practices for Orchestrating…

This study focused on the effects of an early math online professional learning course offered to preschool teachers. The course was designed to inform participants' knowledge of developmental progressions and promote daily mathematics instruction that encouraged students to view their world through a mathematical lens. A survey of preschool…

We report on a series of task-based interviews in which nine mathematicians were asked to evaluate a series of six mathematical arguments, purportedly produced either by fellow mathematicians or undergraduate students. In this paper, we attend to the role of context in mathematicians' responses, leading to four themes in expectations when…

Although research and policy documents provide recommendations to inform secondary mathematics teacher preparation, no single study has addressed the "big ideas" of courses in multiple programs and how those big ideas may be interpreted through the lens of recent research and policy documents. To answer this need, we focused on big ideas…

One desired outcome of introductory physics instruction is that students will develop facility with reasoning quantitatively about physical phenomena. Little research has been done regarding how students develop the algebraic concepts and skills involved in reasoning productively about physics quantities, which is different from either…

Professional organizations have provided recommendations for mathematics teaching and learning; however, few studies have investigated the practical integration of those recommendations into mathematics teacher education programs. In this study, we examine how the reported--"big ideas" of courses in secondary mathematics teacher…

This study examines how a models-and-modeling perspective affected teachers' attention to quantitative reasoning in task design. A Model-Eliciting Activity (MEA) was implemented with 21 teachers over four weeks, challenging teachers to design a quantitative reasoning task for their students. Teachers' initial quantitative reasoning tasks did not…

The purposes of calculus courses are often the acquisition of knowledge itself, the development of skills and the understanding of important concepts, such as functions, derivatives, the chain rule, integrals and the fundamental theorem of calculus. However, full conceptual understanding is frequently not achieved. In this article, we examine the…

This paper is written to provide ideas and guide faculty who want to design a mathematical modeling course for undergraduate mathematics majors and minors. We discuss course goals, assignments, and projects that can be used to help students gain experience relevant for careers and mathematical modeling opportunities. The authors designed this…

This article explores secondary teachers' opportunities to learn from an innovative real analysis course, as reflected in their actual classroom teaching. The course used cases of teaching as a site for applying mathematics and developing pedagogical mathematical practices. This article explores particular teaching moments in (N = 6) secondary…

Massive open online course "for educators" (MOOC-Ed) provide opportunities for using research-based learning and teaching practices, along with new technological tools and facilitation approaches for delivering quality online professional development. The "Teaching Statistics Through Data Investigations" MOOC-Ed course was…

Curriculum standards provide classroom teachers with frameworks to guide instruction during the academic year and throughout a student's schooling. Unfortunately, standards are misconstrued as all-encompassing--as a compendium of all mathematics content that can and should be taught to students. Such a view is unfortunate. Mathematics teachers…

Have your students ever wondered what NASA scientists do? Have they asked you what their science and mathematics lessons have to do with the real world? This unit about Earth's atmosphere can help to answer both of those questions. The unit described here showcases "content specific integration" of science and mathematics in that the lessons meet…

After-school programs specifically designed to improve students' mathematics achievement in collaboration with classroom teachers' planning and in class daily instruction have been found to be successful in improving student learning (Hock, Pulvers, Deshler, & Schumaker, 2001). The purpose of this article is to describe the results of an…

These instructional objectives, written by Harvey Reynolds, have been selected from materials used at Golden West College (California). These objectives are offered simply as samples that may be used where they correspond to the skills, abilities, and attitudes instructors want their students to acquire. These objectives may also serve as models…