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2- A Classroom Intervention: Strengthening Prospective Elementary Teachers’ Knowledge of Divisibility

Tuesday, April 12, 2016: 8:30 AM-9:00 AM
3007 (San Francisco Convention Center)

 

Lead Speaker:
Matt B. Roscoe

Full Conference Paper
  • RoscoeFeldman2016.pdf (566.3 kB)

  • Description of Presentation:

    This brief report presents a study investigating the impact of a sequence of instructional tasks on prospective elementary teachers’ (PSTs’) knowledge of divisibility. Analysis of written assessments revealed significant improvements in PSTs’ use of prime factorization to identify a variety of factor types, signaling a diminished dependence on more traditional and error-prone methods.

    Session Type: Brief Research Report




    3- A Practical and Powerful Screener of Middle School Mathematics Difficulties

    Tuesday, April 12, 2016: 8:30 AM-9:00 AM
    3008 (San Francisco Convention Center)

     

    Lead Speaker:
    Jessica Carrique
    Co-speakers:
    Nicole Hansen , Ilyse Resnick , Nancy I. Dyson , Ai Ye and Nancy C. Jordan

    Full Conference Paper
  • Carrique_NCTM 2016.pdf (455.0 kB)

  • Description of Presentation:

    This study identifies a fraction screener administered in elementary school as a strong diagnostic tool for the prediction of later middle school mathematics difficulties. Practitioners can utilize the screener to identify students who need supplemental support in order to attain desired mathematics benchmarks.

    Session Type: Brief Research Report




    4- Activity and Impact of Elementary Mathematics Specialists in Rural Schools

    Tuesday, April 12, 2016: 8:30 AM-9:00 AM
    3010 (San Francisco Convention Center)

     

    Lead Speaker:
    Patricia F. Campbell
    Co-Speaker:
    Matt Griffin

    Full Conference Paper
  • NCTM 2016 Research Final.pdf (359.0 kB)

  • Description of Presentation:

    This session will present the findings of a two-year randomized control-treatment study that investigated the impact of elementary mathematics specialists on student achievement in rural schools, characterized the amount and type of specialists’ professional activity, and, in treatment schools only, evalutated the relationship between the focus of specialists’ activities and student achievement.

    Session Type: Brief Research Report




    5- An Analysis of U.S. Expert Teachers’ Lessons on Inverse Relations

    Tuesday, April 12, 2016: 8:30 AM-9:00 AM
    3011 (San Francisco Convention Center)

     

    Lead Speaker:
    Meixia Ding
    Co-speakers:
    Ryan Hassler , Xiaobao Li and Wei Chen

    Full Conference Paper
  • AKT full paper_NCTM Resubmit.pdf (4.3 MB)
  • CoverPg_2016RC_Papers_MD.pdf (62.2 kB)

  • Description of Presentation:

    This study explores eight U.S. expert teachers’ algebraic knowledge for teaching (AKT) through analyzing 32 videotaped lessons on inverse relations (grades 1–4). Based on three IES recommendations, we explore common features of teachers’ effective use of worked examples, representations, and deep questions in existing classrooms. Challenges in these instructional components are identified.

    Session Type: Brief Research Report




    7- Approaches to Constructing General Mathematical Statements

    Tuesday, April 12, 2016: 8:30 AM-9:00 AM
    3020 (San Francisco Convention Center)

     

    Lead Speaker:
    Duane Graysay

    Full Conference Paper
  • Graysay_NCTM Research Conference 2016.pdf (498.3 kB)

  • Description of Presentation:

    I will share results from a study of university students’ construction of general mathematical statements. From analysis of data from ten students in math-focused majors, I describe approaches to constructing domains of applicability for given property statements. The approaches have implications for designing activities to increase students’ proficiency at conjecturing generalities in mathematics.

    Session Type: Brief Research Report




    8- Are Adolescents’ Views of Mathematics Changing?

    Tuesday, April 12, 2016: 8:30 AM-9:00 AM
    3022 (San Francisco Convention Center)

     

    Lead Speaker:
    Amber Simpson

    Full Conference Paper
  • Final_NCTM2016_Simpson.pdf (333.1 kB)

  • Description of Presentation:

    This study examines how adolescents’ view of mathematics as a gendered domain varies based on one’s gender and class type (i.e., single-sex or coeducational). One significant finding from the study is that participants typically associated mathematics as a neutral domain (i.e., for both females and males).

    Session Type: Brief Research Report




    10- Attending to Precision in Statistics

    Tuesday, April 12, 2016: 8:30 AM-9:00 AM
    3004 (San Francisco Convention Center)

     

    Lead Speaker:
    Christina Eubanks-Turner
    Co-Speaker:
    Anna E. Bargagliotti

    Full Conference Paper
  • Precision paper NCTM research.pdf (1.0 MB)

  • Description of Presentation:

    The Common Core Standards for Mathematical Practice are processes and proficiencies that mathematics educators would like to develop in their students. In this session, we present a case study of three teachers, which looks at the prevalence of Mathematical Practice 6, Attending to Precision, in a professional development statistics course for in-service teachers largely focused on open-ended activities. We also illustrate how the elicited Attending to Precision may differ in the context of statistics compared to mathematics.

    Session Type: Brief Research Report




    11- It Won't Work Every Time: The Refutations of Preservice Teachers

    Tuesday, April 12, 2016: 8:30 AM-9:00 AM
    3002 (San Francisco Convention Center)

     

    Lead Speaker:
    Michael Jarry-Shore

    Full Conference Paper
  • Session_41304_manuscript_174_0.pdf (284.7 kB)

  • Description of Presentation:

    Reforms to the teaching of mathematics encourage teachers to support students both in making conjectures and refuting those that are false using counterexamples. This study reports on the counterexamples provided by 17 preservice elementary teachers when asked to refute students' false conjectures about fractions. The analysis drew upon existing frameworks to distinguish the pedagogical power and accessibility of counterexamples. Findings indicate that preservice elementary teachers’ counterexamples lacked pedagogical power. Additionally, counterexamples that lacked pedagogical power also varied in terms of: (a) their mathematical complexity and (b) their ability to mirror the reasoning used by the student who authored the false conjecture being refuted. Future work may examine how counterexamples displaying a range of mathematical complexity and mirroring ability support students in abandoning their false conjectures.

    Session Type: Brief Research Report




    13- The Influence of Consecutive Flipped Courses on Students’ Math Anxieties

    Tuesday, April 12, 2016: 8:30 AM-9:00 AM
    3024 (San Francisco Convention Center)

     

    Lead Speaker:
    Anthony Michael Dove

    Full Conference Paper
  • NCTM 2016 Research AMDOVE.pdf (232.9 kB)

  • Description of Presentation:

    This session will examine how taking consecutive mathematics courses for elementary preservice teachers influenced their anxieties and perceptions of teaching and learning mathematics. Participants will examine preliminary data and discuss how this may impact those interested in trying to integrate flipped learning into their teaching practices.

    Session Type: Brief Research Report




    14- Understanding How to Differentiate Instruction for Middle School Students

    Tuesday, April 12, 2016: 8:30 AM-9:00 AM
    3016 (San Francisco Convention Center)

     

    Lead Speaker:
    Amy J. Hackenberg
    Co-speakers:
    Mark A. Creager , Mi Yeon Lee and Ayfer Eker

    Full Conference Paper
  • DI_SubmittedNCTM.pdf (4.6 MB)

  • Description of Presentation:

    Today’s middle school mathematics classrooms are marked by increasing cognitive diversity. Traditional responses to cognitive diversity are tracked classes that contribute to opportunity gaps and can result in achievement gaps. Differentiating instruction (DI) is a novel but untested response to cognitive diversity, in which teachers proactively plan to adapt pedagogical activities to address individual students’ needs in an effort to maximize learning for all students. This paper reports on this question: How did pedagogical activities facilitate and impede differentiating mathematics instruction for middle school students in an after school design experiment? The data comes from an 18-episode experiment with nine cognitively diverse seventh- and eighth-grade students, focusing on four episodes in which students worked on representing multiplicative relationships among quantitative unknowns. Analysis revealed two pedagogical activities that facilitated DI and three that both facilitated and impeded it.

    Session Type: Brief Research Report




    15- Beyond the Demonstration of Procedures in YouTube-Style Math Videos

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3004 (San Francisco Convention Center)

     

    Lead Speaker:
    Joanne Lobato
    Co-speakers:
    C. David Walters and Carren Walker

    Full Conference Paper
  • NCTM 2016_Lobato_Walters_Walker.pdf (514.6 kB)

  • Description of Presentation:

    Despite the tremendous growth in online mathematics videos for K–12 students, there is surprising uniformity in the expository mode of presentation and the procedural nature of the content. The purpose of this study was to locate, analyze, and categorize the approach of conceptually and/or dialogically oriented online math videos.

    Session Type: Brief Research Report




    16- Conferring in the Elementary Mathematics Classroom

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3007 (San Francisco Convention Center)

     

    Lead Speaker:
    Jen Munson

    Full Conference Paper
  • NCTM 2016 BR-Munson-Conferring in the Elementary Math Classroom.pdf (217.3 kB)

  • Description of Presentation:

    Math conferences, an interactional structure adapted from literacy instruction, can be used to provide responsive instruction in the moment to collaborating students. This qualitative study characterizes the math conference, identifies its defining feature—the nudge—and describes six types of nudges teacher use to push student thinking forward.

    Session Type: Brief Research Report




    17- Connections among Mathematics Vocabulary, General Vocabulary, and Computation

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3008 (San Francisco Convention Center)

     

    Lead Speaker:
    Sarah Rannells Powell
    Co-Speaker:
    Gena Nelson

    Full Conference Paper
  • NCTM upload 3-2-16.pdf (208.6 kB)

  • Description of Presentation:

    Understanding mathematics is more than working with numerals and symbols. In many instances, students must interpret vocabulary terms (e.g., prime number, improper fraction) to understand mathematics concepts and procedures. We conducted an analysis of the mathematics vocabulary knowledge of students at grades 1, 3, and 5. We present the longitudinal mathematics vocabulary knowledge of students as well as how general vocabulary and computation knowledge predict mathematics vocabulary understanding.

    Session Type: Brief Research Report




    18- Constructing and Critiquing Arguments: Effect of an Instructional Sequence

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3009 (San Francisco Convention Center)

     

    Lead Speaker:
    Sean P. Yee
    Co-speakers:
    Yi-Yin Ko , Sarah K. Bleiler and Justin D. Boyle

    Full Conference Paper
  • REVISED NCTM 2016 Research Conference Paper.pdf (766.6 kB)

  • Description of Presentation:

    We present the design and implementation of our before-during-after instructional sequence aimed at developing students’ capabilities in constructing viable arguments and critiquing the reasoning of others. The results show that our instructional sequence had a significant effect in students’ work shifting from empirical to deductive arguments.

    Session Type: Brief Research Report




    19- Constructions of Coordinate Systems: Four Ninth-Grade Students

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3010 (San Francisco Convention Center)

     

    Lead Speaker:
    Hwa Young Lee

    Full Conference Paper
  • NCTM.2016.BRR.CoordinateSystems.Lee.pdf (1.2 MB)

  • Description of Presentation:

    This paper presents data from a two-year teaching experiment with four ninth-grade students investigating their constructions of coordinate systems in organizing space. We will discuss the difference in perspectives the students were able to take in relation to the levels of units they were able to coordinate.

    Session Type: Brief Research Report




    20- Designing Professional Development to Support Teachers in Learning Trajectory-Based Instruction

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3011 (San Francisco Convention Center)

     

    Lead Speaker:
    Jennifer L. Kobrin
    Co-Speaker:
    Nicole Panorkou

    Full Conference Paper
  • Kobrin&Panorkou; NCTM 2016.pdf (268.0 kB)

  • Description of Presentation:

    The aim of this project was to examine the design and implementation of a professional development that was part of an integrated learning system developed to align performance assessments, classroom activities, and reporting with a learning trajectory on geometric measurement of area.

    Session Type: Brief Research Report




    21- Developing Ambitious Practice: A Cross-Case Analysis of Novice Mathematics Teachers

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3018 (San Francisco Convention Center)

     

    Lead Speaker:
    Dawn M. Woods

    Full Conference Paper
  • Woods_DevelopingAmbitiousPractice.pdf (217.1 kB)

  • Description of Presentation:

    In this study, I investigated how novice mathematics teachers work toward promoting access and equity within their classrooms through the implementation of high-leverage practices. I found that the high-leverage practice of building classroom culture emerged from the data as central to the work of novice mathematics teachers.

    Session Type: Brief Research Report




    22- Developing Facilitation Practices in a Secondary Math Teacher Learning Community

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3020 (San Francisco Convention Center)

     

    Lead Speaker:
    Terry Wan Jung Lin
    Co-speakers:
    Kara Jackson , Marta Kobiela and Zachary Parker

    Full Conference Paper
  • Developing Facilitation Practices in a Secondary Math Teacher Community_FINAL.pdf (141.8 kB)

  • Description of Presentation:

    Research has shown that teacher learning communities have potential in supporting teacher learning of more ambitious practices. In this paper, we contribute to an emerging body of work on development of facilitator practices. We provide a provisional trajectory based on an analysis of a facilitator’s practices in leading a secondary mathematics teacher learning community, and we describe how facilitation practices developed to increasingly provide opportunities for teacher learning. This expanding image of development will help to design supports for math leaders as they continue their work with teacher learning communities.

    Session Type: Brief Research Report




    24- Does Experiential Learning Influence the Way Students Learn Mathematics?

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3024 (San Francisco Convention Center)

     

    Lead Speaker:
    Manon LeBlanc
    Co-speakers:
    Mylène Savoie , Michel T. Léger , Mathieu Lang and Nicole T. Lirette-Pitre

    Full Conference Paper
  • ExperientialLearningMath_LeBlancEtAl(paper).v2.pdf (269.0 kB)

  • Description of Presentation:

    This experimental study aims to determine if teaching mathematics while respecting the four stages of the experiential learning cycle of Kolb (1984) has an effect on grade 7 students’ learning of probabilities. During the session, the study will be presented and participants will be invited to discuss how experiential learning can be integrated into the classroom. A discussion will also aim to develop a better understanding of the results.

    Session Type: Brief Research Report




    26- Underrepresented Students Pursuing Mathematics Degrees: Changes after Transitioning to College

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3006 (San Francisco Convention Center)

     

    Lead Speaker:
    Alison S. Marzocchi

    Full Conference Paper
  • Marzocchi Paper.pdf (432.5 kB)

  • Description of Presentation:

    This longitudinal qualitative study followed a cohort of mathematics-intending underrepresented high school students into their freshman year of college to identify changes on their path to mathematics-intensive degree attainment. Results indicated that four of the seven participants persisted on their degree path while the remaining three switched to less-mathematics-intensive programs. The greatest positively contributing factor for the participants who persisted was participation in collaborative learning with their peers in mathematics. The participants who did not persist reported that they experienced a decrease in their sense of competence in mathematics when they transitioned from high school to college. All participants, whether they persisted or not, reported that they felt underprepared for college-level mathematics. These results highlight the continued need for increased collaboration between stakeholders at the secondary and postsecondary levels.

    Session Type: Brief Research Report




    27- Using Video to Prepare Preservice Teachers to Pose Purposeful Questions

    Tuesday, April 12, 2016: 9:15 AM-9:45 AM
    3016 (San Francisco Convention Center)

     

    Lead Speaker:
    Christina Eubanks-Turner
    Co-Speaker:
    Anita Kreide

    Full Conference Paper
  • problemposing031416.pdf (656.4 kB)

  • Description of Presentation:

    This study documents the effects of exemplar video observation on the development of deep questioning skills of pre­service teachers (PSTs) with (experimental) and without (control) direct depth of knowledge instruction in a mathematical content course for K–8 pre­service teachers. In particular, we examine the questioning strategies used by preservice teachers in written responses related to Common Core–aligned videotaped math lessons. Data was analyzed to develop multi­tiered general categories and levels of questions used by the PSTs. Through an examination of the trending categories and question levels relational to the videos we offer suggestions for pre­service teacher education courses.

    Session Type: Brief Research Report




    42- Elementary Preservice Teachers’ Self-Efficacy for Teaching Mathematics and Content Knowledge

    Tuesday, April 12, 2016: 11:30 AM-12:00 PM
    3006 (San Francisco Convention Center)

     

    Lead Speaker:
    Rebecca M. Giles
    Co-speakers:
    Kelly O. Byrd and Angelia Bendolph

    Full Conference Paper
  • Giles NCTM Paper 2016.pdf (306.9 kB)

  • Description of Presentation:

    The possible relation between preservice teachers’ mathematics content knowledge and their self-efficacy for teaching mathematics is of particular importance to teacher educators. This experimental, one-group posttest-only study found no statistical significance for relationship between personal efficacy beliefs or mathematics teaching outcome expectancy and mathematics content knowledge.

    Session Type: Brief Research Report




    43- Elementary Students Articulation and Application of Theory of Measure

    Tuesday, April 12, 2016: 11:30 AM-12:00 PM
    3007 (San Francisco Convention Center)

     

    Lead Speaker:
    Alicia C. Gonzales
    Co-Speaker:
    Darrell Earnest

    Full Conference Paper
  • NCTMPaper.pdf (403.4 kB)
  • NCTMPaper.pdf (403.3 kB)

  • Description of Presentation:

    This project aimed to identify the different measurement principles elementary students articulate when solving clock problems. It was found that students articulate their theory of measure in different ways.

    Session Type: Brief Research Report




    44- Elicited Models of Resampling and Bootstrapping

    Tuesday, April 12, 2016: 11:30 AM-12:00 PM
    3008 (San Francisco Convention Center)

     

    Lead Speaker:
    Jeffrey Allen McLean
    Co-Speaker:
    Helen M. Doerr

    Full Conference Paper
  • NCTM 2016 Proposal (1).pdf (12.5 MB)

  • Description of Presentation:

    This study examines the models of resampling and bootstrapping constructed and developed by secondary and tertiary introductory statistics students while participating in a model-eliciting activity.

    Session Type: Brief Research Report




    45- Eliciting Student Understanding of Mathematical Aspects of the Multiplication Principle

    Tuesday, April 12, 2016: 11:30 AM-12:00 PM
    3009 (San Francisco Convention Center)

     

    Lead Speaker:
    Elise Lockwood

    Full Conference Paper
  • NCTM 2016 Proposal MP Long Paper.pdf (1.4 MB)

  • Description of Presentation:

    In this paper, we report on a subtle mathematical issue that is entailed in the multiplication principle (MP)—the independence of stages in a counting process—and we report on a particular task that helped students address this issue as they reinvented a statement of the MP. Doing so sheds light on students’ reasoning about the MP.

    Session Type: Brief Research Report




    46- Eliminating Counterexamples: A Conception of Contrapositive Proving for Adolescents

    Tuesday, April 12, 2016: 11:30 AM-12:00 PM
    3010 (San Francisco Convention Center)

     

    Lead Speaker:
    David A. Yopp

    Full Conference Paper
  • NCTM eliminate CEs paper.3.10.16.uploaded.pdf (4.8 MB)

  • Description of Presentation:

    This brief research report addresses implementing activities that promote reasoning and proving. An adolescent’s indirect reasoning is used to develop a conception of indirect argumentation that improves her understanding of contrapositive proving.

    Session Type: Brief Research Report




    47- Evaluating the Effectiveness of Symmetry Software for Early Elementary Children

    Tuesday, April 12, 2016: 11:30 AM-12:00 PM
    3016 (San Francisco Convention Center)

     

    Lead Speaker:
    Nicole Fletcher

    Full Conference Paper
  • Nicole Fletcher-NCTM Brief Research Report 2016.pdf (258.9 kB)

  • Description of Presentation:

    Children develop the ability to perceive symmetry very early in life; symmetry is abundant in the world around us, and it is a naturally occurring theme in children’s play and creative endeavors. This study sought to develop and evaluate a computer program that expands young children’s understanding of symmetry and its subtypes—reflection, translation, and rotation. Results showed that children assigned to the experimental condition were better able to identify and explain symmetry subtypes than the control group. Children who used the symmetry software also showed improvement compared to their peers in the control group in completing translation tasks and in overall posttest scores, controlling for pre-existing ability.

    Session Type: Brief Research Report




    49- Exploring the Narratively Constructed Mathematical Identities of Latina Bilingual Students

    Tuesday, April 12, 2016: 11:30 AM-12:00 PM
    3002 (San Francisco Convention Center)

     

    Lead Speaker:
    Suzanne E. Kaplan

    Full Conference Paper
  • Narratively Constructed Mathematical Identities NCTM 2016.pdf (393.5 kB)

  • Description of Presentation:

    This study involved exploring the mathematics stories of three seventh-grade Latina students who attended an urban middle school. The mathematics stories of one primary caregiver for each student and the students’ mathematics teacher were also explored. The goal was to understand the factors that attributed to the formation of the young girls’ mathematics identities and how these identities informed their decisions to engage with mathematical activity. The findings illuminated important classroom experiences, how the students made sense of these experiences, and how they took up and rejected opportunities to engage with mathematics because of those experiences.

    Session Type: Brief Research Report




    51- Simultaneous Measurement of Preservice Teachers’ Professional Noticing and MKT

    Tuesday, April 12, 2016: 11:30 AM-12:00 PM
    3000 (San Francisco Convention Center)

     

    Lead Speaker:
    Lara Dick, Ph.D.

    Full Conference Paper
  • LDick_NCTM2016_Final.pdf (470.0 kB)

  • Description of Presentation:

    The purpose of this session is to present the results of a research study focused on simultaneously measuring both professional noticing of children’s mathematical thinking and mathematical knowledge for teaching of elementary student teachers’ through an intervention focused on analysis of their students’ multi-digit addition and subtraction work.

    Session Type: Brief Research Report




    52- Using Content Maps to Represent Qualities of Teachers’ Mathematical Instruction

    Tuesday, April 12, 2016: 11:30 AM-12:00 PM
    3018 (San Francisco Convention Center)

     

    Lead Speaker:
    Steven Greenstein

    Full Conference Paper
  • NCTM 2016 Content maps_final.pdf (1.3 MB)

  • Description of Presentation:

    A scaling-up study of the SimCalc approach revealed significant learning gains that were robust across demographic and regional variation in teachers and students. In order to determine what might have contributed to these gains, we theorized that students’ opportunities to engage with content would be a significant source of information about what and how students learned. We developed a representational tool we call Content Maps that we used to analyze the content of classroom discourse around mathematical tasks. Maps that were generated from three teachers’ enactments of three lessons reveal the various ways in which these teachers drew on their mathematical knowledge in whole-class discussion. These maps may therefore prove to be a more useful assessment of their mathematical knowledge as a learning resource than quantitative measures of their mathematical knowledge for teaching.

    Session Type: Brief Research Report




    53- Utility of the TMSSR Framework for Investigating Instructional Practices

    Tuesday, April 12, 2016: 11:30 AM-12:00 PM
    3011 (San Francisco Convention Center)

     

    Lead Speaker:
    Lindsay Reiten
    Co-speakers:
    Zekiye Ozgur and Amy Ellis

    Full Conference Paper
  • Conference Submission_final.pdf (445.0 kB)

  • Description of Presentation:

    To illustrate the affordances of the Teacher Moves for Supporting Student Reasoning (TMSSR) Framework for investigating (a) the different ways teachers provide instructional support for students, and (b) how those differences may support students’ reasoning, we will present the analysis of two classroom implementations of a research-based unit via the TMSSR framework. We will also discuss the utility of the TMSSR framework as a tool for studying instructional practices.

    Session Type: Brief Research Report




    67- Who’s In Charge? Teachers' Talk Cultivates Students’ Mathematical Authority

    Tuesday, April 12, 2016: 1:15 PM-2:30 PM
    3004 (San Francisco Convention Center)

     

    Lead Speaker:
    Teresa K. Dunleavy
    Co-Speaker:
    Maria R. Zavala

    Handouts NCTM_2016_Class_Transcripts.pdf Teacher Talk Dunleavy Zavala_NCTM 2016.pdf

    Description of Presentation:

    Mathematics educators agree that students’ having mathematical authority is beneficial, but which teacher moves delegate authority to students? This research paper examines how two teachers in two diverse, urban, Algebra 1 schools used teacher talk to delegate mathematical authority to students. Implications for teacher education, in the era of the Common Core State Standards mathematical practices, are discussed. Participants will engage in transcript analysis.

    Session Type: Discussion Session




    68- Exploring Effects of Content Organization on Specific Algebraic Concepts

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3002 (San Francisco Convention Center)

     

    Lead Speaker:
    Derrick Saddler

    Full Conference Paper
  • Saddler_NCTM Research Conference 2016.pdf (331.6 kB)

  • Description of Presentation:

    In this study, a pretest-posttest study design was used to statistically compare algebraic performance of high school students who learn from a subject-specific course pathway and integrated course pathway. Data from a large-scale observational study was used. The results revealed no statistical differences exist in the outcomes between students from the two groups.

    Session Type: Brief Research Report




    70- Exploring the Use of Mathematics Coaches and Specialists

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3006 (San Francisco Convention Center)

     

    Lead Speaker:
    Kristin E. Harbour
    Co-speakers:
    Karen S. Karp and Jill L. Adelson

    Full Conference Paper
  • Harbour, Karp, & Adelson_MCSs_NCTM Research 2016-2.pdf (251.4 kB)

  • Description of Presentation:

    Using restricted-use data from the 2011 NAEP Mathematics Assessment and advanced statistical analyses, the current study examined the relationship between mathematics coaches and specialists (MCSs) and the mathematics achievement of more than 190,000 fourth-grade students in more than 7,400 schools nationwide. Additionally, the study examined whether that relationship differed for students with and without disabilities, a vital concern with the continued focus of equity in mathematics education. Lastly, the study examined the relationships between principal-reported time spent on the different NAEP-defined roles and responsibilities of MCSs and fourth-grade students’ mathematics achievement. Findings, implications, and future research will be shared and discussed.

    Session Type: Brief Research Report




    72- Ferris Wheels and Filling Bottles: Investigating a Student's Transfer

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3008 (San Francisco Convention Center)

     

    Lead Speaker:
    Heather Lynn Johnson
    Co-speakers:
    Evan McClintock and Peter Hornbein

    Full Conference Paper
  • JohnsonMcClintockHornben_FerrisWheelFillingBottleTransfer_NCTM2016_160327.pdf (6.3 MB)

  • Description of Presentation:

    We share results of a design experiment study in which we used an actor-oriented perspective on transfer to investigate the research question: What similarities might a student construe between Ferris wheel and filling bottle tasks, and how might that influence a student’s reasoning across tasks? We discuss implications for research and teaching.

    Session Type: Brief Research Report




    74- Generic Use of Examples for Proving

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3010 (San Francisco Convention Center)

     

    Lead Speaker:
    Orit Zaslavsky
    Co-Speaker:
    Inbar Aricha-Metzer

    Full Conference Paper
  • NCTM 2016_Generic Use of Examples for Proving.pdf (231.5 kB)

  • Description of Presentation:

    The study examines how students use examples in order to justify the truth value of mathematical statements. We focus on provided generic examples that have the potential of leading to a generic proof. The findings show how students build on these examples productively and gain insights to underlying proof ideas.

    Session Type: Brief Research Report




    75- How Novice Teachers Connect Tasks to the CCSSM Math Practices

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3011 (San Francisco Convention Center)

     

    Lead Speaker:
    Keely Machmer-Wessels

    Full Conference Paper
  • Machmer-WesselsCCSSMTasksNCTM2016.pdf (2.3 MB)

  • Description of Presentation:

    In order to engage students in the CCSSM math practices, teachers must select appropriate tasks for their students to work on. This study examines how first- and second-year teachers abstractly talked about tasks that addressed the math practices compared to specific tasks the teachers selected to engage their students in the practices.

    Session Type: Brief Research Report




    76- How Secondary Students Determine the Validity of Mathematical Arguments

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3016 (San Francisco Convention Center)

     

    Lead Speaker:
    Yating Liu

    Full Conference Paper
  • Uploaded paper.pdf (337.6 kB)

  • Description of Presentation:

    The study investigated the factors students considered when evaluating the validity of mathematical arguments. Analysis of 8 eighth graders' interview transcripts indicated that when determining the validity of mathematical arguments, the source of conviction seemed to have the largest impact, followed by the presentation of the argument, while the link to conclusion (or mode of reasoning) seemed to have the least impact.

    Session Type: Brief Research Report




    77- How Teachers’ Evaluate Breaches of Norms in High School Geometry

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3018 (San Francisco Convention Center)

     

    Lead Speaker:
    Nicolas Boileau
    Co-Speaker:
    Patricio G. Herbst

    Full Conference Paper
  • NCTM2016_BoileauHerbst.pdf (176.8 kB)
  • CoverPg_2016RC_Papers.pdf (60.0 kB)

  • Description of Presentation:

    This paper reports on a study of two norms of an instructional situation in high school geometry—Geometric Calculation in Algebra—that consisted of confronting practitioners with representations of practice as a way to stimulate them to relay their knowledge of practice. The purpose of the study was to determine whether participants recognize two hypothesized norms and how those participants evaluate actions that breach them. The focus of this paper is on our use of the Appraisal system (Martin and White 2005) in Systemic Functional Linguistics to detect evidence of participants’ evaluation of the breaches of one of those norms.

    Session Type: Brief Research Report




    78- Hypothesizing Fragmented Growth of Mathematical Proficiency for Teaching

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3020 (San Francisco Convention Center)

     

    Lead Speaker:
    Erik Daniel Jacobson
    Co-speakers:
    Fetiye Aydeniz , Mark A. Creager , Michael Daiga and Erol Uzan

    Full Conference Paper
  • Jacobson et al NCTM-RC-2016 fragmented growth.pdf (421.8 kB)

  • Description of Presentation:

    We compare two accounts of change in preservice teachers’ (PSTs') knowledge and motivation for teaching multi-digit addition and subtraction that were a result of taking a mathematics methods class. Using scales with strong psychometric properties, we found knowledge increased but found no evidence of change in motivation. However, by comparing pre-and posttest responses item by item we found compelling patterns of linked change.

    Session Type: Brief Research Report




    79- Impact of Early Algebra Instruction across Populations of Diverse Learners

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3022 (San Francisco Convention Center)

     

    Lead Speaker:
    Michael Eiland

    Full Conference Paper
  • Eiland_etal_Brief_Report_2016.pdf (170.2 kB)

  • Description of Presentation:

    Algebraic thinking and reasoning have been identified as an important and emerging curricular strand in K–8 education. Recognizing that historical paths to algebra have been largely unsuccessful, scholars now advocate that students have long-term algebra experiences, beginning in the elementary grades. Our purpose in this paper is to determine how students with low standardized test scores after receiving an algebra curriculum treatment perform relative to control students of all standardized performance levels.

    Session Type: Brief Research Report




    80- Initial Understanding of Fractions: Children with Learning Disabilities and Difficulties

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3024 (San Francisco Convention Center)

     

    Lead Speaker:
    Jessica Hunt
    Co-speakers:
    Juanita Silva and Jasmine Welch-Ptak

    Full Conference Paper
  • 2016 NCTM Research session Hunt et al.pdf (500.2 kB)

  • Description of Presentation:

    Little to no information exists explaining the nature of initial conceptions of fractions held by students with learning disabilities. This study extends existing literature by presenting key indicators of understandings of fractional quantity of 44 children with learning disabilities and difficulties as evidenced through their problem-solving strategy, observable operations, and language across six tasks based in the measure and partitive interpretations. Constant comparison analysis of the children's work across the tasks documents indicators reflective of a framework. Pending future research, the framework may be a useful tool to practitioners wishing to document students' initial conceptions of unit fractions.

    Session Type: Brief Research Report




    81- Student Internalization of Representations

    Tuesday, April 12, 2016: 2:45 PM-3:15 PM
    3000 (San Francisco Convention Center)

     

    Lead Speaker:
    Laban J. Cross
    Co-Speaker:
    David Barker

    Full Conference Paper
  • NCTM 2016 Paper Final (Cross, Barker).pdf (440.1 kB)

  • Description of Presentation:

    In this session we present the results of a study that investigated how students made use of their internal representations while generalizing algebraic tasks. A framework of internalization will be introduced and common pathways from this framework that students used to generalize each task will be discussed.

    Session Type: Brief Research Report




    114- Examining Teachers' Learning as They Use Learning Maps to Study Mathematics

    Tuesday, April 12, 2016: 5:00 PM-6:00 PM
    Third Level Prefunction (San Francisco Convention Center)

     

    Lead Speaker:
    Angela Broaddus

    Handouts 42861_Broaddus_Teacher Learning with Learning Maps_Paper.pdf 42861_Broaddus_TeacherLearning_Poster.pdf

    Description of Presentation:

    The present study examined teachers’ reflections of their professional learning in response to using learning maps to unpack mathematics content standards. Journal entries were analyzed to identify and describe teachers’ perceptions of their mathematical knowledge in terms of content knowledge, pedagogical knowledge, and instructional practices.

    Session Type: Poster Session




    144- Analyzing Classroom Interactions by Coordinating Status and Positioning Theories

    Wednesday, April 13, 2016: 8:30 AM-9:45 AM
    3011 (San Francisco Convention Center)

     

    Lead Speaker:
    Teresa K. Dunleavy

    Handouts Status Positioning Handout NCTM 2016.pdf NCTM 2016 Status Positioning.pdf

    Description of Presentation:

    This paper seeks to investigate classroom interactions through the coordination of Status and Positioning Theories. I show that coordinating these theories in a mathematics classroom relates students’ moment-to-moment discursive acts to their resulting classroom positions. I first describe how, on its own, Status Theory offers a way of understanding how valued status characteristics lead to generalized expectations for competence and an individual’s status. I then describe how Positioning Theory offers an in-depth look at the relationship between moment-to-moment discursive acts and an individual’s resulting position. I argue that by coordinating these two theories, discursive positioning moves mediate the development of expectations for individuals’ competence, over time. Participants will engage in transcript analysis.

    Session Type: Discussion Session




    160- Instruction, Self-Efficacy, and Achievement in Grades 4–8 Mathematics

    Wednesday, April 13, 2016: 12:30 PM-1:00 PM
    3002 (San Francisco Convention Center)

     

    Lead Speaker:
    Joe Champion
    Co-Speaker:
    Kimberly Moore

    Full Conference Paper
  • ProceedingsPaper-NCTM2016-ChampionandMoore.pdf (839.5 kB)

  • Description of Presentation:

    We will present preliminary results from a longitudinal investigation of N = 2,000 middle levels students’ self-efficacy, perceptions of instruction, and subsequent performance in state mathematics assessments. Findings include estimated direct and indirect effects of mathematics self-efficacy and active learning practices on future mathematics achievement.

    Session Type: Brief Research Report




    161- Investigating a Student’s Reasoning with Ratios: The Case of Gabriel

    Wednesday, April 13, 2016: 12:30 PM-1:00 PM
    3009 (San Francisco Convention Center)

     

    Lead Speaker:
    Fetiye Aydeniz

    Full Conference Paper
  • Aydeniz_NCTM_Submitted.pdf (197.7 kB)

  • Description of Presentation:

    The purpose of this session is to communicate about the role that distributive reasoning plays in the construction of ratio reasoning. The presenter will share findings from data with a middle school student and will seek participants’ input about their efforts to talk about the difficulties in this specific area.

    Session Type: Brief Research Report




    162- Investigating Fifth-Grade Students’ Conceptions of Fractions on the Number Line

    Wednesday, April 13, 2016: 12:30 PM-1:00 PM
    3010 (San Francisco Convention Center)

     

    Lead Speaker:
    Rukiye Didem Taylan, Dr.
    Co-speakers:
    Zelha Tunc-Pekkan , Utkun Aydin , Bengi Birgili and Mustafa Ozcan

    Full Conference Paper
  • Taylanetal_NCTM_2016.pdf (3.1 MB)

  • Description of Presentation:

    In this study, clinical interviews focusing on students’ understanding of fractions as numbers on the number line were conducted with six fifth-grade students both before and after an intervention designed by teacher-researchers. Although in general students demonstrated improved understanding of fraction concepts even in situations requiring reversible thinking, difficulties in finding benchmarks on the number line and a limited awareness of density of fractions on the number line persisted among students.

    Session Type: Brief Research Report




    164- Investigating Secondary Preservice Teachers’ Noticing of Student Thinking

    Wednesday, April 13, 2016: 12:30 PM-1:00 PM
    3008 (San Francisco Convention Center)

     

    Lead Speaker:
    Erin Krupa
    Co-speakers:
    Maryann Elizabeth Huey , Kristin Lesseig , Stephanie Casey and Debra Monson

    Full Conference Paper
  • 00. NCTM Research Session Paper_final.pdf (158.1 kB)

  • Description of Presentation:

    There is a need for research that examines how to support secondary teachers’ abilities to notice student thinking. We describe the impact of a curricular module, centered around a task-based interview, on secondary preservice teachers’ ability to attend to, interpret, and respond to student thinking.

    Session Type: Brief Research Report




    165- Linking Teacher Concerns and Professional Development with the CCSSM Implementation

    Wednesday, April 13, 2016: 12:30 PM-1:00 PM
    3016 (San Francisco Convention Center)

     

    Lead Speaker:
    Suzanne T. Jennings

    Full Conference Paper
  • Jennings_Herron Linking Teacher Concerns NCTM 2016.pdf (259.8 kB)

  • Description of Presentation:

    The purpose of this mixed methods study was to investigate and understand the concerns of secondary mathematics teachers during the initial stages of implementing the Common Core State Standards of Mathematics and to determine if a relationship existed between the concerns and professional development during the initial stages. The research was grounded in the theoretical framework of the Concerns Based Adoption Model focusing on the Stages of Concern. Data analysis methods encompassed quantitative, qualitative, and profile interpretation. Data gathered from this study is relevant as it could be used to project levels of use in subsequent stages of the curriculum implementation. These projections can be used by education leaders to design interventions and effective professional development aiding teachers in the continued implementation of CCSSM and to guide change facilitators to understand the relationship between teacher concerns and professional development.  

    Session Type: Brief Research Report




    166- Maintaining High Levels of Cognitive Demand through Student Silence

    Wednesday, April 13, 2016: 12:30 PM-1:00 PM
    3018 (San Francisco Convention Center)

     

    Lead Speaker:
    Jessica Lynn Jensen
    Co-speakers:
    Anna Kye , Marina Sherry and Kyong Mi Choi

    Full Conference Paper
  • NCTM2016.pdf (142.2 kB)

  • Description of Presentation:

    Student engagement in high-level cognitive demand instruction is pivotal for student learning. However, many teachers are unable to maintain such instruction, especially in instances of non-responsive students. This case study of three middle school teachers explores prompts that aim to move classroom discussions past student silence. Prompt sequences were categorized into progressing, focusing, and redirecting actions, and then analyzed for maintenance of cognitive demand. Results indicate that prompts that raise cognitive demand typically start out as procedural or concrete and progress to include students’ thoughts or ideas about mathematical concepts. This presentation aims to discuss implications on how teachers can use prompting techniques to effectively maintain high levels of cognitive demand during student silence.

    Session Type: Brief Research Report




    168- Principals and Implementation on Common Core State Standards for Mathematics

    Wednesday, April 13, 2016: 12:30 PM-1:00 PM
    3020 (San Francisco Convention Center)

     

    Lead Speaker:
    Adrian Larbi-Cherif

    Full Conference Paper
  • NCTM_Principals And CCSSM_AdrianLC.pdf (456.5 kB)

  • Description of Presentation:

    As noted in Principles to Actions, principals’ practices can influence successful implementation of CCSSM. In this literature review, twenty-nine studies are analyzed and synthesized to understand how principal instructional leadership influenced teachers’ classroom instruction with a particular focus on CCSSM. Overall, researchers have found that principals can influence instruction primarily through indirect practices, such as working with teachers to define an instructional vision. Additionally, the degree of principal involvement with instruction was most effective when it served to understand how to support teachers through professional development rather than direct feedback. Overall, the studies reviewed provide evidence on how principals influence instruction, yet more needs to be understood particularly in relation to CCSSM and how local contextual factors influence instructional leadership.

    Session Type: Brief Research Report




    169- Studying Mathematics Beginning Teaching Using MQI, CLASS, and FFT

    Wednesday, April 13, 2016: 12:30 PM-1:00 PM
    3000 (San Francisco Convention Center)

     

    Lead Speaker:
    L. Joy Johnson
    Co-speakers:
    Delena Harrison and Kolby J. Gadd

    Full Conference Paper
  • NCTM_2016_Paper_FINAL.pdf (156.0 kB)

  • Description of Presentation:

    Studies of student achievement suggest that beginning teachers are less effective than their more experienced peers. These findings lead us to investigate the features of early-career teaching. Using hierarchical measurement and logistics regression models, we analyze teacher observation data from 653 teachers in six districts to learn more about beginning mathematics teaching.

    Session Type: Brief Research Report




    170- The Algebraic Thinking of Teachers in China and the U.S.

    Wednesday, April 13, 2016: 12:30 PM-1:00 PM
    3011 (San Francisco Convention Center)

     

    Lead Speaker:
    Qintong Hu
    Co-speakers:
    Ji-Won Son and Lynn L. Hodge

    Full Conference Paper
  • Hu_2016NCTMpaper.pdf (409.4 kB)

  • Description of Presentation:

    The study investigated 20 Chinese and 20 U.S. high school teachers’ interpretation and response to a student’s errors in solving a quadratic equation. Analysis results show that the Chinese teachers provided more negative evaluations toward students’ errors and identified more students’ errors than the U.S. teachers did. Responding to students’ errors, the two groups of teachers highlighted conceptual explanations targeting students’ mistakes. The U.S. teachers were more likely to provide general knowledge guidance while the Chinese teachers tended to go back to basic knowledge.

    Session Type: Brief Research Report




    171- Third Graders’ Development of Quantitative Reasoning about Angle Measure

    Wednesday, April 13, 2016: 12:30 PM-1:00 PM
    3006 (San Francisco Convention Center)

     

    Lead Speaker:
    Amanda L. Miller
    Co-Speaker:
    Craig J. Cullen

    Full Conference Paper
  • NCTM 2016 angle Final.pdf (2.8 MB)

  • Description of Presentation:

    The purpose of this session is to report on the findings of a study investigating the effects of two instructional interventions designed to provide third graders with opportunities to work with dynamic and static models of angles in a dynamic geometry environment. We discuss the effects of the instructional interventions on the children’s development of quantitative reasoning about angle measure.

    Session Type: Brief Research Report




    177- MET Grants Support Classroom Research

    Wednesday, April 13, 2016: 1:15 PM-2:30 PM
    3009 (San Francisco Convention Center)

     

    Lead Speaker:
    Richard T Seitz
    Co-speakers:
    Haiping Hao , Mary Margaret Capraro , Kisha Lee , Maggie L. McHugh , Jennifer Kosiak , Beth Bos, EdD and Ryan Gertenbach

    Handouts MET-Summary-2016 (1).pdf

    Description of Presentation:

    Action and classroom research grants available through the MET will be described as possible funding sources for mathematics education research. Brief reports from three classroom research projects funded by the MET will be presented: Fostering Number Sense of Diverse Young Learners; Navigating Ratios and Proportions in a Project-Based Learning Environment; Student Built Widgets in a Pre-Calculus Class.

    Session Type: Invited




    186- Mathematical Discourse in a Kindergarten Classroom: A Case Study

    Wednesday, April 13, 2016: 2:45 PM-3:15 PM
    3002 (San Francisco Convention Center)

     

    Lead Speaker:
    Sarah Lord
    Co-speakers:
    Aimee H. Cardon and Hala Ghousseini

    Full Conference Paper
  • Math discourse in Kindergarten Classroom.pdf (126.0 kB)

  • Description of Presentation:

    Classroom discourse is integral to mathematics instruction at all levels. This work is challenging at all levels but especially for very young learners who are just beginning to learn the language of school. In this talk, we explore the following questions: How can kindergarten teachers support students in engaging in mathematical discourse? How do kindergartners engage in mathematical discourse? We use a case study of one kindergarten teacher’s classroom to look for the answers to this question, and we conclude that kindergartners are capable of authentic mathematical discourse using multiple modalities including formal and informal language, acting on manipulatives, drawings, gestures, and formal symbols. The teacher played a crucial role in supporting students in this work through laying groundwork for productive discourse, intentionally facilitating students’ sharing of ideas about mathematics, and refining students’ discourse toward more precise and sophisticated communication.

    Session Type: Brief Research Report




    188- Mathematical Play and Neuroplasticity in Children with Cancer

    Wednesday, April 13, 2016: 2:45 PM-3:15 PM
    3006 (San Francisco Convention Center)

     

    Lead Speaker:
    Megan L. Nickels

    Full Conference Paper
  • Session_42323_manuscript_120_0.pdf (167.2 kB)

  • Description of Presentation:

    In a 24-week study, we investigated an intervention for children with cancer using the Lego Mindstorms EV3 robotics kits. The intervention is designed to address issues of children’s mathematical thinking and learning and functional and structural changes to the brain following chemotherapy and/or radiation.

    Session Type: Brief Research Report




    189- Mathematics and the African American Males' Graduation Sucess

    Wednesday, April 13, 2016: 2:45 PM-3:15 PM
    3010 (San Francisco Convention Center)

     

    Lead Speaker:
    Claude N. Stuart
    Co-speakers:
    Stephanie L. Tatum and Elsa-Sofia Morote

    Full Conference Paper
  • NCTM Artcle.pdf (441.8 kB)

  • Description of Presentation:

    The purpose of the study is to examine the relationships among graduation of African American males from predominantly White institutions and historically Black colleges and universities and their mathematics self-efficacy, mathematics anxiety, mathematics attitude, deep learning, peer relationships, faculty relationship, major of study, social capital, and life satisfaction after graduation and critical race identity. Mathematics is the most important predictor of academic success at postsecondary institutions. The types of math courses students take in college affect their college graduation and their earning capacity in the job market. Students who take more advanced math classes will learn skills that might be directly applicable to certain jobs, and those learned skills are more strongly correlated with labor market success than other measures of student achievement. Critical race theory is the theoretical framework of this study.

    Session Type: Brief Research Report




    190- Measuring Primary Grade Teachers’ Mathematical Knowledge for Teaching

    Wednesday, April 13, 2016: 2:45 PM-3:15 PM
    3007 (San Francisco Convention Center)

     

    Lead Speaker:
    Wendy Bray
    Co-Speaker:
    Robert Schoen

    Full Conference Paper
  • Bray_Schoen_NCTMResearch2016_MeasuringPrimaryGradesTeachersMKT.pdf (5.0 MB)

  • Description of Presentation:

    We will share information about an instrument designed to measure Mathematical Knowledge for Teaching (MKT) of teachers of early elementary mathematics. We will discuss how we specified various facets of MKT and report scale reliability and other results from two field studies involving U.S. primary grades teachers in 2014 (n=413) and 2015 (n=636).

    Session Type: Brief Research Report




    191- Measuring Teachers' Beliefs in Relation to Standards for Mathematical Practice

    Wednesday, April 13, 2016: 2:45 PM-3:15 PM
    3008 (San Francisco Convention Center)

     

    Lead Speaker:
    Iris M. Riggs
    Co-speakers:
    Davida Fischman , Matt L. Riggs , Madeleine Jetter and Joseph Jesunathadas

    Full Conference Paper
  • NCTM_Research_2016.pdf (99.4 kB)

  • Description of Presentation:

    An instrument that measures the self-efficacy and outcome expectancy beliefs of teachers in regards to the Standards for Mathematical Practice will be presented.

    Session Type: Brief Research Report




    192- Navigating the Tension between Direct and Dialogic Mathematics Teaching Practices

    Wednesday, April 13, 2016: 2:45 PM-3:15 PM
    3009 (San Francisco Convention Center)

     

    Lead Speaker:
    Monica Smith Karunakaran

    Full Conference Paper
  • Karunakaran_NCTM_2016.pdf (116.5 kB)

  • Description of Presentation:

    This session reports on research findings describing a tension between direct and dialogic mathematics teaching practices in an upper elementary setting. Implications from findings of the study include recommendations for how to use Principals to Actions to create useful professional development in addressing the tension.

    Session Type: Brief Research Report




    195- Preservice Elementary Mathematics Lesson Study: Visions and Learning to Teach

    Wednesday, April 13, 2016: 2:45 PM-3:15 PM
    3020 (San Francisco Convention Center)

     

    Lead Speaker:
    Aki Murata
    Co-speakers:
    Anna McGee , Tia Madkins , Dennis Gillingham , Judith Fabrega , Hee-jeong Kim and Becca Shareff

    Full Conference Paper
  • Murata.vision.LS.pdf (539.0 kB)

  • Description of Presentation:

    This study investigated the learning process of presservice elementary teachers (PSTs) through lesson study in a mathematics teaching methods course. Lesson study meeting data of kindergarten PSTs were analyzed to examine the shifting focus on (1) student collaboration in classroom (vision), (2) teaching practices (making content accessible), and (3) understanding of student thinking of mathematics, in teachers’ talks. The four learning phases were identified in which the PSTs’ vision guided sense-making process, where lesson study provided the structure for the process. Visions can support or distract PSTs’ learning, and learning experiences should guide PSTs to understand how to enact their visions in relationship to classroom practices.

    Session Type: Brief Research Report




    196- Preservice Secondary Teachers' Learning of Purposeful Questioning

    Wednesday, April 13, 2016: 2:45 PM-3:15 PM
    3024 (San Francisco Convention Center)

     

    Lead Speaker:
    Ben Freeburn

    Full Conference Paper
  • Freeburn_NCTM 2016 .pdf (163.8 kB)

  • Description of Presentation:

    A number of mathematics teacher educators have begun to focus curricula of methods courses on mathematics teaching practices and designing coursework around pedagogies of practice. However, the field is just beginning to address preservice secondary teachers’ learning in such methods courses. This session shares results from a study examining preservice secondary teachers’ learning of a mathematics teaching practice (purposeful questioning) as they were enrolled in a methods course designed around pedagogies of practice.

    Session Type: Brief Research Report




    197- Teachers as Problem Solvers: Insights from Professional Development

    Wednesday, April 13, 2016: 2:45 PM-3:15 PM
    3000 (San Francisco Convention Center)

     

    Lead Speaker:
    Cinthia Rodriguez
    Co-speakers:
    Priya V. Prasad and Emily P. Bonner

    Full Conference Paper
  • Rodriguez-Prasad-Rodriguez (2016)TeachersAsProblemSolvers.pdf (286.3 kB)

  • Description of Presentation:

    This exploratory phenomenological study centers on secondary educators’ problem-solving experiences with the use of open-ended tasks. An analysis of a three-week professional development program focused on supporting middle school teachers’ conceptual and procedural knowledge through a first-hand involvement in problem solving processes. Data from journal reflections, mathematical work samples, and video segments are presented to explore educators’ personal experiences as learners and teachers of problem solving. The participants of this session will gain further understanding regarding the use of problem-solving tasks to support teacher content and pedagogical knowledge, consider a diverse set of teacher perspectives, and discuss implications for instructional practice.

    Session Type: Brief Research Report




    199- Reasoning Paths from Exploration to Argument

    Wednesday, April 13, 2016: 3:30 PM-4:00 PM
    3009 (San Francisco Convention Center)

     

    Lead Speaker:
    Anne E. Adams
    Co-speakers:
    David A. Yopp and Robert Ely

    Full Conference Paper
  • Reasoning Paths From Exploration to Argument Final.pdf (2.7 MB)

  • Description of Presentation:

    We present a framework for types of reasoning that can be used when generating and arguing for a general mathematical claim. The framework was used to analyze reasoning elicited in task-based interviews with eighth-grade students. We illustrate with examples of student reasoning and arguments for the audience to analyze.

    Session Type: Brief Research Report




    200- Refinement of the Conceptual Models for Integer Addition and Subtraction

    Wednesday, April 13, 2016: 3:30 PM-4:00 PM
    3010 (San Francisco Convention Center)

     

    Lead Speaker:
    Nicole M. Wessman-Enzinger

    Full Conference Paper
  • NCTMRB2016.pdf (845.8 kB)

  • Description of Presentation:

    The Conceptual Models for Integer Addition and Subtraction (CMIAS) were initially developed from the stories that students posed for integer addition and subtraction open number sentences. Three grade 5 students participated in a 12-week teaching experiment where they solved open number sentences for integer addition and subtraction open number sentences in four Individual Sessions. The students’ responses (verbal and drawings) as they solved these open number sentences were analyzed. This data supported the refinement of the CMIAS. The refinement of the CMIAS, which includes the changes that were made to initial descriptors and the data that supported these refinements, will be highlighted.

    Session Type: Brief Research Report




    202- Rethinking Elementary Preservice Teachers’ Addition Strategies

    Wednesday, April 13, 2016: 3:30 PM-4:00 PM
    3018 (San Francisco Convention Center)

     

    Lead Speaker:
    Carey Walls
    Co-speakers:
    Crystal Kalinec-Craig , Priya V. Prasad and Raquel Vallines-Mira

    Full Conference Paper
  • NCTM Rethinking Elementary Preservice Teachers Addition Strategies.pdf (184.5 kB)

  • Description of Presentation:

    This presentation will focus on an exploratory study of how elementary preservice teachers (PSTs) communicated their mathematical thinking while solving carefully selected, multi-digit, addition problems. The numbers were purposefully chosen for the problems to elicit both procedural and conceptual knowledge. This presentation seeks to demonstrate that although many PSTs used the standard algorithm, some simultaneously used unprompted conceptual strategies based on their own prior mathematical knowledge and experiences. This presentation will discuss the implications of this study for mathematics teacher educators as they leverage the nuanced ways that PSTs’ communicate their mathematical thinking while developing PSTs’ pedagogical content knowledge.

    Session Type: Brief Research Report




    203- Sustaining Lesson Study: Mathematics Teachers’ Conceptions of Lesson Study

    Wednesday, April 13, 2016: 3:30 PM-4:00 PM
    3024 (San Francisco Convention Center)

     

    Lead Speaker:
    Bridget Druken

    Full Conference Paper
  • NCTMpaper031116_PDF.pdf (178.7 kB)

  • Description of Presentation:

    This study on mathematics teacher professional development and sustaining lesson study examines practicing U.S. teachers’ conceptions of mathematics lesson study and demonstrates how some conceptions supported teachers’ ability to sustain lesson study while other conceptions constrained them.

    Session Type: Brief Research Report




    206- The Connections between Number and Notation: Elementary PSTs’ Understanding

    Wednesday, April 13, 2016: 3:30 PM-4:00 PM
    3007 (San Francisco Convention Center)

     

    Lead Speaker:
    Christy Pettis

    Full Conference Paper
  • NCTM 2016 upload paper final draft.pdf (3.2 MB)

  • Description of Presentation:

    This study reports on the ways that 32 elementary preservice teachers understood whole and rational numbers and notation and the connections between them at the start of their mathematics education coursework and after participation in a number and numeration unit designed to develop their understanding of the connections. Results indicate that PSTs typically did not begin their education coursework with a strong understanding of rational numbers, fractions, and decimals but were able to develop a stronger understanding during the unit. Activities that supported non-symbolic representations of both fractions and rational decimals (especially repeating decimals) were particularly supportive.

    Session Type: Brief Research Report