Authors:Steve Deihl, Mara P. Markinson Pages: 1 - 7 Abstract: 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 theory,” are generally unknown to high school students. The authors propose a method for introducing basic ideas in set theory to high school trigonometry students by connecting prior knowledge of the tangent function and the unit circle to Georg Cantor’s ideas about infinity. By doing so, high school teachers have an opportunity to inspire their students with rich mathematics. PubDate: 2019-12-14 DOI: 10.7916/jmetc.v10i2.4190 Issue No:Vol. 10, No. 2 (2019)

Authors:Indira Gil, Laura Zamudio-Orozco, Barbara King Pages: 9 - 20 Abstract: When teaching through problem solving, effective mathematics teachers need to lead discussions that assist students in making connections between different solution strategies. However, while teaching a methods course for preservice teachers (PSTs), we noticed that after solving a problem and presenting various solution strategies, many PSTs seemed lost on how to proceed with the mathematics lesson. To address this issue, we designed an action research study where we implemented Smith and Stein’s (2011) five practices for orchestrating productive classroom discussions, and focused our attention on the fifth practice, making connections. Specifically, we designed an instructional intervention to examine the type of connections made by PSTs and how these connections changed as the course progressed to aid PSTs’ connection making skills. We identified three types of connections made by PSTs: superficial knowledge connections, procedural knowledge connections, and conceptual knowledge connections. Additionally, we observed a decrease in the amount of superficial knowledge connections and an increase in the amounts of procedural knowledge connections and conceptual knowledge connections made by PSTs throughout the course. PubDate: 2019-12-14 DOI: 10.7916/jmetc.v10i2.4191 Issue No:Vol. 10, No. 2 (2019)

Authors:Robert Reys, Barbara Reys, Jeffrey C. Shih Pages: 21 - 27 Abstract: Doctoral programs in mathematics education were established more than a century ago in the United States. From 2010-2014 over 120 different institutions graduated at least one doctorate in mathematics education. There has been limited research reported on the nature of doctoral programs in mathematics education and/or their doctoral graduates. This paper provides a synthesis of research findings related to doctoral preparation in mathematics education that is accompanied by a reflection on the findings and suggestions for future research. The intent of our paper is to provide a rallying call for more widespread and coordinated research on doctoral programs in mathematics education in order to strengthen the quality of doctoral preparation for the next generation of mathematics educators. PubDate: 2019-12-14 DOI: 10.7916/jmetc.v10i2.4192 Issue No:Vol. 10, No. 2 (2019)

Authors:Michael George, Yevgeniy Milman Pages: 29 - 35 Abstract: 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 College. Students enrolled in the 17 sections of QL were compared to a matched sample of students from Elementary Algebra. The students enrolled in QL in the Spring of 2013 were 175% more likely to have passed a credit-bearing mathematics course one year later, indicating that QL represents a valuable alternative for non-STEM college students placed into algebra level remediation. Further, the implementation and preliminary results of a corequisite course combining QL with college level Quantitative Reasoning (QR) are presented. PubDate: 2019-12-14 DOI: 10.7916/jmetc.v10i2.4193 Issue No:Vol. 10, No. 2 (2019)

Authors:Angie Hodge, Janice Rech, Michael Matthews, Kelly Gomez Johnson, Paula Jakopovic Pages: 37 - 43 Abstract: Mentoring is an important aspect of mathematics teacher education, and in particular, pre-service teacher education. Faculty at a large Midwestern university developed and refined a mentoring program designed to help pre-service secondary mathematics teachers, called Scholars, become future leaders in mathematics education. This paper describes how faculty mentors leveraged challenges in the mentoring program’s early stages based on their reflections and initial mentee outcomes to create a more effective mentoring program. Recommendations based on research and practice are provided for other university programs interested in mentoring future mathematics teachers. PubDate: 2019-12-14 DOI: 10.7916/jmetc.v10i2.4194 Issue No:Vol. 10, No. 2 (2019)