Proceedings for the 43rd Annual Meeting of the Research Council on Mathematics Learning Shining a Light on Mathematics Learning February 25 – 27, 2016 Orlando, Florida PRESIDENT, 2015-2017 INVESTIGATIONS EDITOR CONFERENCE COMMITTEE Juliana Utley (Appointed) Travis Olson (2013-2016) Oklahoma State University Drew Polly University of Nevada, Las Vegas Stillwater, OK University of North Carolina, Las Vegas, NV [email protected] Greensboro [email protected] Greensboro, NC PAST PRESIDENT, [email protected] Kansas Conrady (2013-2016) 2015-2016 University of Oklahoma Mary Swarthout INTERSECTIONS EDITOR Norman, OK Sam Houston State University (Appointed) [email protected] Huntsville, Texas 77341 Jonathan Bostic [email protected] Bowling Green State University Jonathan Bostic (2014-2017) Bowling Green, OH Bowling Green State University VICE PRESIDENT FOR [email protected] Bowling Green, OH CONFERENCES, 2014-2016 [email protected] Eileen Faulkenberry Tarleton State University MEMBERSHIP CHAIR Sean Yee (2014-2017) Stephenville, TX (Appointed) University of South Carolina [email protected] Sarah Pratt Columbia, SC University of North Texas [email protected] VICE PRESIDENT FOR Dallas, TX PUBLICATIONS [email protected] Bill McGalliard (2015-2018) Sheryl A. Maxwell University of Central Missouri University of Memphis (Retired) WEBMASTER Warrensburg, MO Memphis, TN (Appointed) [email protected] [email protected] Ryan Speer Perrysburg, Ohio Hope Marchionda (2015-2018) TREASURER, 2014-2016 [email protected] Western Kentucky University Kerri Richardson Bowling Green, KY University of North Carolina - [email protected] Greensboro PROCEEDINGS EDITOR Greensboro, NC (Appointed) CONFERENCE CHAIR [email protected] Keith Adophson Nancy Cerezo, Eastern Washington University Saint Leo University SECRETARY, 2015-2017 Cheney, WA St Leo, FL Sarah Pratt [email protected] [email protected] University of North Texas Denton, TX PROCEEDINGS CO-EDITOR PROGRAM CHAIR [email protected] (Appointed) Gabriel Matney Travis Olson Bowling Green State University ARCHIVIST University of Nevada, Las Vegas Bowling Green, OH William R. Speer Las Vegas, NV [email protected] University of Nevada, Las Vegas [email protected] Las Vegas, NV [email protected] THANK YOU TO OUR REVIEWERS Amy Adkins Timothy Folger Lance Kruse Melanie Autin Lucas Foster Ruby Lynch-Arroyo Summer Bateiha Ryan Fox Hope Marchionda Jonathan Bostic Kris Green Melfried Olson Justin Boyle Steven Greenstein Lindsay Prugh Kelley Buchheister Leigh Haltiwanger Matt Roscoe Kenneth Butler Mary Harper Anu Sharma Joanne Caniglia Elizabeth Howell Janet Shiver Nancy Cerezo Sarah Ives Amber Simpson Lynn Columba Christa Jackson Tracy Thompson Kansas Conrady William Jasper Mehmet Türegün Danya Corkin Elisabeth Johnston Juliana Utley Lina DeVaul Ed Keppelmann Linda Venenciano Bob Drake Dennis Kombe Brittany Webre Adem Ekmekci Karl Kosko Cong-Cong Xing Brian Evans Angela Krebs Fay Zenigami Citation: Authors. (2016). Article title. In Adolphson, K. V. and Olson, T. A. (Eds.). Proceedings of the 43rd Annual Meeting of the Research Council on Mathematics Learning. Orlando, FL. Graduate Student Editorial Assistant: Nicholas Kaleolani Wong, University of Nevada, Las Vegas Publication Acceptance Rate: Accepted 20 manuscripts out of 49 submissions. Acceptance Rate of 40.8% Please Note: Articles published in the proceedings are copyrighted by the authors. Permission to reproduce portions from an article must be obtained from the authors. RCML History The Research Council on Mathematics Learning, formerly The Research Council for Diagnostic and Prescriptive Mathematics, grew from a seed planted at a 1974 national conference held at Kent State University. A need for an informational sharing structure in diagnostic, prescriptive, and remedial mathematics was identified by James W. Heddens. A group of invited professional educators convened to explore, discuss, and exchange ideas especially in regard to pupils having difficulty in learning mathematics. It was noted that there was considerable fragmentation and repetition of effort in research on learning deficiencies at all levels of student mathematical development. The discussions centered on how individuals could pool their talents, resources, and research efforts to help develop a body of knowledge. The intent was for teams of researchers to work together in collaborative research focused on solving student difficulties encountered in learning mathematics. Specific areas identified were: 1. Synthesize innovative approaches. 2. Create insightful diagnostic instruments. 3. Create diagnostic techniques. 4. Develop new and interesting materials. 5. Examine research reporting strategies. As a professional organization, the Research Council on Mathematics Learning (RCML) may be thought of as a vehicle to be used by its membership to accomplish specific goals. There is opportunity for everyone to actively participate in RCML. Indeed, such participation is mandatory if RCML is to continue to provide a forum for exploration, examination, and professional growth for mathematics educators at all levels. The Founding Members of the Council are those individuals that presented papers at one of the first three National Remedial Mathematics Conferences held at Kent State University in 1974, 1975, and 1976. Table of Contents Illuminating Problems of Teaching A Student’s Conception of Negative Integers Karen Zwanch 1-8 Exploring Validity and Reliability for the Revised SMPs Look-for Protocol Jonathan Bostic, Gabriel Matney, and Toni Sondergeld 9-17 Colligation and Unit Coordination in Mathematical Argumentative Writing Karl W. Kosko and Rashmi Singh 18-25 Facilitating Mathematical Conversations in Diverse Classrooms: A Case Study Mercedes Sotillo Turner and Tashana Howse 26-33 Academic Rigor in Single-Sex and Coeducational Middle-Grades Math Classes Dennis Kombe, Traci L. Carter, and S. Megan Che 34-41 Limelight on Learning to be Teachers Learning about Elementary Preservice Teachers from Their Observations of Struggling Learners Meagan Burton 43-49 Draw Yourself Doing Mathematics: Assessing a Mathematics and Dance Class Rachel Bachman, Karlee Berezay, and Lance Tripp 50-57 Pre-Service Teachers’ Acceptance of Number Concepts Instruction in Base 8 Katie Harshman and Heidi Eisenreich 58-66 Beliefs about Social Justice among Elementary Mathematics Teachers Brian R. Evans 67-74 The Nature of Mathematical Conversations among Prospective Middle School Teachers in a Mathematics Content Course Kadian M. Callahan 75-82 Exploring Mental Models of “Doing Math” Through Drawings Ben Wescoatt 83-91 Elucidating Teachers’ Opportunities to Learn Factors that Influence Teachers’ Geometry Learning for Teaching Barbara Allen-Lyall 92-100 Teachers’ Self-Efficacy and Knowledge for the Integration of Technology in Mathematics Instruction at Urban Schools Danya Corkin, Adem Ekmekci, Carolyn White, and Alice Fisher 101-108 Deepening Statistical Content Knowledge for the Common Core Jacqueline Wroughton and Brooke Buckley 109-115 Mathematics Knowledge for Parenting (MKP): Workshops to Help Parents Make Sense of Mathematics Heidi Eisenreich 116-123 Kindling Diverse Thinking about Mathematics Learning An Alternative Route to Bypass Developmental Mathematics Linda Venenciano, Stephanie Capen, and Fay Zenigami 124-131 Math Dance: A Study of Effectiveness Rachel Bachman, Erik Stern, Julian Chan, Karlee Berezay, and Lance Tripp 132-139 The Role of Support Structures in the Success of Developmental Mathematics Programs Elizabeth Howell and Candace Walkington 140-148 Increasing Student Engagement in Math with Online Games and Elements of Game Theory Diana Perdue 149-157 Using Technology to Engage Students in Introductory Statistics Hope Marchionda and Melanie Autin 158-165 A STUDENT’S CONCEPTION OF NEGATIVE INTEGERS Karen Zwanch Virginia Tech [email protected] The purpose of this case study was to construct a model of one third grade student’s conception of negative integers, and was situated within the theoretical framework of Central Conceptual Structure of Numbers (CCSN). Constructs within this framework were utilized to understand the student’s mental model, and it was ultimately determined that the student had constructed a formal mental model with regard to the order and value of integers. This formal mental model implies a coordination between the negative and positive integers within his mental number line schema. Introduction Historically, negative numbers have been stigmatized as difficult; noted mathematicians such as Diophantus and Pascal have erroneously declared it impossible to subtract a larger number from a smaller, due to their inability to conceptualize negative integers (Bishop, Lamb, Philipp, Schappelle, & Whitacre, 2011). Within the frame of modern mathematics, a negative difference is no longer problematic; however, its history is interesting because developmentally immature students today may harbor the same misconception as did Diophantus and Pascal (Bishop, Lamb, Philipp, Schappelle, & Whitacre, 2011). Despite the advances of modern mathematics, students’ misconceptions regarding negative integers persist beyond the onset of instruction (Murray, 1985). Bofferding (2010) suggests that while the whole number system can be built by students through interaction with appropriate manipulatives, no such manipulatives exist for negative integers, therefore making the extension of the integer system to include negatives markedly more