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Introductory Texts, Georgia Association Of Mathematics Teacher Educators

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Coverpage

GAMTE Information

Letter from the President

Table of Contents

Paper 1: Engaging In Lesson Study At Georgia College, Angel R. Abney, Brandon Samples, Doris Santarone

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

A lesson study cycle is a professional development process that integrates research and reflection through collaboration. The cycle allows a group to refine a lesson based on these collaboration efforts such as interaction with students and the post-lesson discussion. Secondary pre-service teachers in a mathematics methods course engaged in a lesson study cycle through collaboration between in-service teachers, Georgia College professors, and students in a local high school classroom. We systematically investigated this process to determine that through preparing, enacting and reflecting on their practice, Pre-service Teachers (PST) developed insight, reasoning, and understanding of the mathematics that they taught.

Paper 2: Using Ti-Nspire To Engage Preservice Mathematics Teachers In An Exploratory Geometry Module, Alesia D. Mickle, Pier A. Junor Clarke

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

In the mathematics classroom, most preservice mathematics teachers possess basic skills to use technology as an instructional strategy in communicating content standards. However, today’s demands for preservice teachers to engage in a variety of “best teaching practices” in their preservice teaching and edTPA requirements can oftentimes place the acquisition of technical skills and integration of new technology in content curriculum far from the forefront of their minds. Ertmer, Conklin, Lewandowski, Osika, Selo, and Wignall (2003) acknowledged preservice teachers’ desires to gain the adequate technical skills necessary to use technology in teachers’ daily tasks of facilitating and managing their classrooms. They …

Paper 1: A Proposed Pedagogical Approach For Preparing Teacher Candidates To Incorporate (Academic) Language, Woong Lim, Lynn Stallings

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

The edTPA is a performance-based assessment that aims to measure teacher candidates’ readiness for teaching. Beginning in the fall of 2015, this assessment will be a mandatory requirement for those seeking certification in Georgia. General agreement exists in the field of education about the basic knowledge and skills essential for beginning teachers to demonstrate in classroom teaching. Does edTPA measure the knowledge and skills essential for beginning mathematics teachers in particular? Assuming that edTPA can successfully measure that knowledge and skills for beginning teachers, the use of the assessment could be valuable.

One of the critical components of edTPA is …

Paper 2: Design Considerations For Visually-Aided Discussion Prompts: Emphasizing Mathematical Reasoning In Teacher Education, Anne Marie S. Marshall, Kadian M. Callahan

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

The availability and familiarity of online discussion tools create new instructional options that teacher educators can use to foster prospective teachers’ understanding of mathematics. In particular, online discussion blogs provide an avenue through which teacher educators can press prospective teachers to explore mathematical concepts and share their mathematical reasoning with peers. Furthermore, by incorporating visual stimulations as a design component of these discussion blogs, prospective teachers can make sense of and respond to others’ ideas about mathematical concepts with greater clarity. This paper shares preliminary findings of a research study that examined the extent to which the design of a …

Paper 5: Caep, Nctm, And Secondary Mathematics Program Revisions, Dianna J. Spence

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Eight assessments were developed for CAEP (formerly NCATE) and NCTM recognition of our secondary mathematics program. These assessments include internship work samples, field evaluations, and candidate portfolios addressing content knowledge, pedagogical methods, and mathematics technology. Based on data collected from these assessments, alongside ongoing evaluation of the program, several curriculum and program revisions were implemented, including: 1) development of mathematics content-specific courses in classroom management, assessment, and secondary curriculum; 2) restructuring of a senior seminar course in mathematics education; and 3) an increased content focus in probability and statistics. The adoption of new NCTM standards in the CAEP review process …

Paper 6: A Mathematics Teacher’S Journey Of Identity Construction And Change, Anthony B. Stinson

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Despite some gains, improving mathematics instruction remains an area of concern in the United States. The implementation of the Common Core Standards and the challenge of teaching the 21st Century student require mathematics teachers to examine their pedagogy to determine if they need to change or improve their practices. This paper provides a personal account of my journey when determining my identity as a mathematics teacher and how constructing my identity helped in changing and improving my practices as a mathematics teacher. The study was done using autoethnography, a burgeoning research method, and identity theory. This study has the goals …

Paper 3: Differences In Beliefs Across A Series Of Four Mathematics Content Courses, Susanna Molitoris Miller, Caitlin Walkey

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

College students often ask questions such as, “Why do I have to take this class? Is there a point to it?” For Early Childhood Education (ECE) majors these questions may often take on a slightly different form, wondering, “How can I incorporate this information into my classroom?” or “Do I understand this well enough to teach this to my students?” It is especially important for pre- service teachers to feel confident working with the mathematical content that they are learning and for them to believe that they can successfully teach that same information to a group of students. Swackhamer, Koellner, …

Introductory Texts, Georgia Association Of Mathematics Teacher Educators

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Coverpage

GAMTE Information

Letter from the President

Table of Contents

Paper 4: Do You See What I See? Deepening Teachers’ Understanding Of Linear Equations Through Student Interviews, Tamara Pearson, Kelli Nipper, Catherine Matos

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Many teachers have trouble transitioning their students between natural recursive thinking about the data and algebraic notation for representing linear functions (Zazkis & Liljedahl, 2002).

In this study, we interviewed eighteen middle school students to see how they used prior instruction to think about a geometric pattern and construct its corresponding linear equation. All students

were given the same task to complete and were questioned about their thinking during the interview.

We found that the recording of pattern recognition plays a substantial part in helping students recognize and write explicit patterns. By having students decompose the total perimeter into how …

Paper 2: The Mathematics Teacher Educator's Reflection On Edtpa: The Basics And The Complexity Of Georgia's Implementation, Woong Lim, Lynn Stallings

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Beginning in fall 2015, Georgia will require that all teacher candidates pass the edTPA, a performance-based assessment, as a requirement for initial certification. With the potential to impact teacher preparation programs in a profound way, the questions and issues related to the implementation of edTPA merit some critical reflection. In this article, we introduce the brief history of the instrument and review the basics of edTPA with a particular interest in middle grades mathematics. Furthermore, drawing upon our experience with edTPA during a pilot program and the extensive knowledge base of edTPA rubrics and scoring process, we present issues related …

Introductory Texts, Georgia Association Of Mathematics Teacher Educators

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Coverpage

GAMTE Information

Letter from the President

Table of Contents

Paper 3: Extending K-8 Mathematics Concepts In Alternate Bases, Dianna J. Spence

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

When learning to represent mathematics with manipulatives, many pre-service K-8 teachers rely on memorized rote procedures to perform the associated mathematical tasks; then they arrange the manipulatives to match their result, often with minimal understanding of underlying mathematical connections. In a Number and Operations course for K-8 pre-service teachers, a portion of the class was conducted in alternate bases: Base 6 and Base 8 Blocks were used to model operations with integers to facilitate deeper understanding of the number systems and arithmetic processes being represented. Fractions and decimals were later covered only in Base 10. On midterm and final exams, …

Paper 5: Embracing The Vision: Our Work With Teachers Implementing Gps, Sarah Ledford, Wendy B. Sanchez, Marian Fox

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

In 2005, three Kennesaw State University mathematics education faculty members began a series of workshops titled “Implementing the Georgia Performance Standards [GPS]: Embracing the Vision.” This workshop series has been underwritten by Georgia’s Teacher Quality Higher Education Program. The first series of workshops began with 6th grade teachers the first year the GPS was implemented and the project has been funded each subsequent year since its inception. Currently, we are working with Math III teachers as they implement the course for the first time. The initial focus for the project was on conceptual understanding versus procedural understanding, writing tasks that …

Paper 1: Investigating Mathematical Literacy Through Teacher Language, Alyson Lischka

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Communication about mathematical concepts using appropriate terminology is a standard established by the National Council of Teachers of Mathematics. However, international test results show that United States’ students are lagging in mathematical literacy. This case study analyzes the ways in which instructors use language to help students move toward conceptual understanding of mathematical vocabulary. Three mathematics education professors at a mid-size four year institution were observed teaching math classes to students enrolled in elementary or secondary certification programs. Collected data included: audio-recorded observations and field notes, lesson artifacts such as quizzes and handouts, and audio-recorded interviews with each participant. Findings …

Introductory Texts, Georgia Association Of Mathematics Teacher Educators

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Cover Page

GAMTE Information

Table of Contents

Paper 2: Collaborating To Meet The Standards: Implications For Professional Development, Erik D. Jacobson, Laura M. Singletary

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Researchers from the University of Georgia interviewed 27 Mathematics 1 teachers about their experiences during the first year of the high school implementation of the Georgia Performance Standards (GPS). We report our findings about teachers’ experiences with Mathematics 1 professional development and describe features of professional development that teachers identified as most beneficial. Some teachers offered suggestions for professional development that differed from the professional development they had experienced. In addition, we found that many teachers used collaborative strategies to meet the demands of the new curriculum and the perceived inadequacies of resources and training. We discuss the various models …

Paper 4: Basic Skills Testing In Math 2008, Susie M. Lanier, Sharon Taylor, Donna B. Saye

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Math 2008 is an Area F course for early childhood majors in the University System of Georgia. The course covers basic skills that pre-service teachers will most likely be teaching in their career. At Georgia Southern University, many students in the course do not possess or have forgotten these basic skills. In Fall 2009, a basic skills test was implemented for Math 2008. Students must earn a score of 90 or higher on the test in order to pass the course. The test not only serves to let students know their areas of weakness, but also informs the instructor’s teaching. …

Paper 2: Content Knowledge And Pedagogical Content Knowledge Of Algebra Teachers And Changes In Both Types Of Knowledge As A Result Of Professional Development, Joy W. Black

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

In seeking to improve the mathematics education of all students, it is important to understand the connection between the content knowledge and pedagogical content knowledge of mathematics and how professionals can influence growth in both of these types of knowledge. We do not have an answer about the interplay of content knowledge and pedagogical content knowledge in successful instructional practices in the mathematics classroom. This study involves assessing the content knowledge and pedagogical content knowledge of secondary teachers of Algebra I. In addition, how are these types of knowledge expressed in instructional practices? Last, how do content knowledge, pedagogical content …

Paper 3: Authentic Discovery Projects In Statistics, Dianna Spence, Robb Sinn

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

We report the activities and findings of a 3-year project, ―Authentic, Career-Specific, Discovery Learning Projects in Introductory Statistics,‖ funded by the National Science Foundation. The project scope includes: 1) development of teaching materials for using discovery learning projects to teach statistics; 2) training secondary teachers to use the materials developed; 3) evaluation of student outcomes, in both content knowledge and attitudes toward statistics; and 4) extending and refining teacher training.

With input from an interdisciplinary team of instructors, materials were developed to assist the teacher in facilitating collaborative discovery projects using linear regression techniques and comparison techniques with appropriate t-tests. …

Paper 1: Analysis Of Achievement For Understanding Geometry, Linda Nash, Annita Hunt, Denise Huddlestun, Kelli Nipper

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

The purpose of this study was to investigate the effectiveness of a mathematics professional development course. More specifically, in this study we examine whether geometric experiences have an impact on level of performance in mathematics. The van Hiele (Fuys, D., Geddes, D., & Tischler, R., 1988) model of geometric understanding provided a research framework from which to view geometric understanding. This model suggests five levels of understanding that should be taken into consideration when examining levels of geometric thinking: Visual, Descriptive/Analytic, Abstract/Relational, Formal Deduction/Proof, and Rigor.

The sample under study was three cohorts of practicing elementary teachers and mathematics coaches …

Introductory Texts, Georgia Association For Mathematics Teacher Educators

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Cover page

GAMTE Information

Table of Contents

Paper 2: Virtual Vs. Concrete Manipulatives In Mathematics Teacher Education: A Call For Research, Annita W. Hunt

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Are virtual manipulatives as effective as concrete (hands-on) manipulatives to build conceptual understanding of number concepts and relationships in pre-service middle grades teachers? In the past, the use of concrete manipulatives in mathematics courses for Clayton State University’s preservice middle grades teachers has proven to be a very effective way to build conceptual understanding of a variety of mathematical topics. This paper presents an argument for the need for research into the usefulness of virtual manipulatives for enhancing mathematics teacher education and their potential to supplement (or replace?) concrete manipulatives.

Introductory Texts, Georgia Association Of Mathematics Teacher Educators

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Cover page

GAMTE Information

Letter from the President

Table of Contents

Paper 4: The Paaps Strategy For Teaching Mathematics Content, Gregory K. Harrell

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

In the fall of 2005, I started teaching the mathematics content course Algebra and Geometry for Teachers. The majority of students in the course are pre-service middle school teachers. Instead of teaching the course by demonstrating rigorous proofs, I wanted to use teaching strategies that would build the students’ content knowledge and connect to their roles as future mathematics teachers. I chose to make problem solving a focal process standard by having students problem- solve for a majority of classroom time. In addition, the students complete a major project entitled “Provide, Attempt, and Assess Problem Solving” or PAAPS. For PAAPS, …

Paper 5: Preservice Teachers’ Disposition Self-Appraisals: Is There A Connection To Mathematics Instructional Practices?, Shonda Lemons-Smith

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

This paper explores preservice teachers’ dispositions and the connection to mathematics instructional practices. The Theory of Culturally Relevant Pedagogy served as the theoretical grounding for the study. Hence, its three broad propositions: conceptions of self and others, social relations, and conceptions of knowledge structure the argument presented. The participants in the study are elementary preservice teachers enrolled in a post-baccalaureate alternative certification program. The full-time, accelerated program focuses on and is specifically designed for individuals committed to teaching in urban, high-poverty schools. A dispositions survey, open-ended narratives, and teaching observation rubric served as data sources for the qualitative study. Findings …

Paper 3: Actively Engaging Pre-Service Teachers In Geometry And Measurement, Kadian M. Callahan

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Current work in mathematics education suggests that the learning experiences in which teachers engage during undergraduate study influences their knowledge of and beliefs about mathematics and the ways in which they will teach (Allen, et. al., 2008; CBMS, 2001; Hill, Rowan, & Ball, 2005; National Research Council, 2001). However, very little is known about pre-service teachers’ learning experiences and how those experiences influence their thinking about mathematics teaching and learning. The classroom excerpt described here attempts to illuminate how pre-service, elementary teachers’ active engagement in the learning of geometry and measurement influences their mathematical power: a positive disposition toward mathematics, …

Paper 1: Becoming Critical Mathematics Pedagogues: A Journey, David W. Stinson, Carla R. Bidwell, Ginny C. Powell, Mary M. Thurman

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

This session will report the findings of a study that explored the beginning transformations in the pedagogical philosophies and practices of three mathematics teachers (middle, high school, and 2-year college) who completed a graduate-level mathematics education course that focused on critical theory and teaching for social justice, and how these transformations are compatible (or not) with reform mathematics education as suggested by the National Council of Teachers of Mathematics (NCTM), and in turn, the new Georgia Performance Standards (GPS). The study employed Freirian participatory research methodology; in fact, the participants were not only co- researchers, but also co-authors of the …

Introductory Texts, Georgia Association Of Mathematics Teacher Educators

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

Cover page

GAMTE Information

Table of Contents

List of Abstracts

Paper 2: The Mathematical Preparation Of Secondary School Teachers, Kelly W. Edenfield

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference

In the summer of 2007, a group of doctoral students at the University of Georgia gathered to discuss the mathematical preparation of secondary teachers. The group used Mathematics for High School Teachers: An Advanced Perspective by Usiskin, Peressini, Marchisotto, and Stanley (2003) as the catalyst for the discussion. Participants agreed that future teachers need opportunities to examine high school and college mathematics differently from the way they had as students, with specific emphasis on connections, representations, and history. Features of this text that were highlighted in the discussions were the attention topics with commonly held misconceptions, the historical rationales and …