An increasing number of students are "hyper-accelerating" their study of formal Algebra I to Grade 7 or earlier to maintain a competitive edge in the race to calculus. However, there is a lack of evidence that these students construct the conceptual foundations necessary for persistence in advanced mathematics. This paper maps the drive…

"Algebra-as-gatekeeper" is a powerful paradigm that structures students' experiences within mathematics class, as well as their future educational trajectories. In this paper, I show how modeling--when conceived as a culturally relevant practice--can support students to make sense of the key ideas of algebra as well as develop positive…

In this paper, we discuss the utilization of an innovative learning tool, the Sphero BOLT robot, in a 10-day algebra-based mathematics education course for graduate students. Students created routes for their BOLTs to travel and determined ways to measure the distance, rate, and time of their robots' movements. The student prompt, sample student…

Maryam Mirzakhani is the first and the only female winner of the Fields Medal since its establishment in 1936. She is arguably one of the greatest mathematicians of our generation. This biographical paper outlines her life and work. Her mathematical theorems and noteworthy accomplishments are just as impressive as her determination, imagination,…

Low passing rates in developmental mathematics have been a serious concern for community colleges for many years. A course in Quantitative Literacy (QL) offers non-STEM students an alternative option to introductory algebra as a path to a degree. This paper describes the implementation and evolution of QL at the Borough of Manhattan Community…

High school students often ask questions about the nature of infinity. When contemplating what the "largest number" is, or discussing the speed of light, students bring their own ideas about infinity and asymptotes into the conversation. These are popular ideas, but formal ideas about the nature of mathematical sets, or "set…

The purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK). As part of a larger study, nine current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT)--Mathematics assessment and the Cognitively Activating Instruction in Mathematics…

Mathematics teachers frequently provide concrete manipulatives to students during instruction; however, the rationale for using certain manipulatives in conjunction with concepts may not be explored. This article focuses on area models that are currently used in classrooms to provide concrete examples of integer and binomial multiplication. The…

This paper explores the viability and development of the first edition of the researcher's mathematical card game, Groups, as a learning tool for elementary group theory, a topic in abstract algebra. "Groups" was play-tested by six undergraduate students in late 2016 who provided feedback on "Groups" from both utility-centric…

This article compares the views of teachers and professors about the transition from secondary mathematics to tertiary calculus. Quantitative analysis revealed five categories where teachers and professors differed significantly in the relative frequency of addressing them. Using the rite of passage theory, the separation and incorporation phases…

The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

In this paper I describe how I have used the classic buried treasure problem with prospective and practicing mathematics teachers to enhance their problem solving abilities and disposition to integrate interactive geometry software (IGS) into the learning environment. I illustrate how IGS may be used as a strategic tool to gain insight into the…

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…

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…