PEMDAS is a mnemonic device to memorize the order in which to calculate an expression that contains more than one operation. However, students frequently make calculation errors with expressions, which have either multiplication and division or addition and subtraction next to each other. This article explores the mathematical reasoning of the…

The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…

What would be one of the most sensible ways for a country to invest to achieve maximal economic growth? A recent study (Chetty, Friedman, & Rockoff, 2011) by economists at Harvard and Columbia Universities shows that better teacher quality results in significantly higher students' lifetime earnings. And investing in public school teachers…

This article makes two simple observations about high-stakes assessments. The first is that, because mathematics is a very technical subject, an assessment item can be mathematically flawed regardless of how elementary it is. For this reason, every assessment project needs the active participation of high level mathematicians. A second point is…

We address issues related to gender and cultural equity in a history of mathematics course. We first look at the preponderance of male European mathematicians represented in textbooks of mathematics and history or mathematics. Then we discuss ways to highlight the presence of female and non-European mathematicians in the history of mathematics.…

Dr. Uri Treisman, professor of mathematics and public affairs at The University of Texas at Austin and the director of the Charles A. Dana Center, has deep and active roots in mathematics and mathematics education. Dr. Treisman is well known for his early work at the University of California at Berkeley, where he developed the Calculus Workshop…

The purpose of this article is to present the findings of a qualitative metasynthesis focused on Black learners negotiating their mathematics experiences in multiple settings (in school and out-of-school) and reflecting on experiences that contributed towards their mathematics identities over time. Five findings emerged from this qualitative…

During the last few decades, equity concerns have become a priority for some researchers and mathematics (education) organizations. Scholars have begun to address issues of equity through a critical lens (e.g., Boaler, 2007; Darling-Hammond, 2005; Martin, 2003) in their work and scholarship. In this article, the author seeks to add to the equity…

This study drew on data from a large, randomized trial of Cognitive Tutor Algebra (CTA) in high-poverty settings to investigate how mathematics curricula and classroom achievement related to teacher reports of time spent on inquiry-based and lecture-based mathematics activities. We found that teachers using the CTA curriculum reported more time on…

The Finnish National Board of Education has been publishing guidelines for the evaluation of student learning in the comprehensive school since the 1970s. This evaluation is two-fold: 1) during school it guides and supports students along their academic paths and 2) at the conclusion of the comprehensive school it expresses each student's level of…

Hostetler (2005) describes "good" education research as that which attends to the well-being of students, teachers, and communities. In this essay, the author proposes measuring equity-based research in mathematics education against Hostetler's standard. She argues that current equity-based research has not adequately addressed the…

In conjunction with the adoption and subsequent implementation of the "Common Core State Standards for Mathematics" (CCSSM), state-led consortia are developing next-generation assessments aligned to the CCSSM. This paper discusses the progress and plans of two main coalitions of states--the Partnership for Assessment of Readiness for…

The "Common Core State Standards for Mathematics" presents challenges and opportunities to contribute to a common understanding of the mathematical proficiencies expected of our students. This paper discusses the movement to establish multi-state assessment consortia in the United States based in the standards movement set in motion by…

We propose the development of a "population" of high-quality assessment tasks that cover the performance goals set out in the "Common Core State Standards for Mathematics." The population will be published. Tests are drawn from this population as a structured random sample guided by a "balancing algorithm."

Place matters in moderating variable relationships between algebra performance and educational variables because there are differences on the socioeconomic (SES) poverty-affluence continuum that shape local contexts. This article examines relationships between variables for school district demographic composition, teaching and financial contexts,…