Science and Mathematics Education Commons^™

Addressing Impulsive Disposition: Using Non-Proportional Problems To Overcome Overgeneralization Of Proportionality, Kien Lim, Osvaldo Morera

Departmental Papers (Math)

Impulsive disposition is an undesirable way of thinking where one spontaneously applies the first idea that comes to mind without checking its relevance. In this research, we explore (a) the possibility of helping pre-service teachers improve their disposition, from being impulsive to being analytic, in one semester, and (b) the effect of using non-proportional situations. This study involves two sections of a mathematics course for pre-service teachers for Grades 4-8. The lessons were designed whenever possible to elicit students’ impulsive disposition so that they could become cognizant of it and make conscious attempts to overcome it. Some test items were …

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 (2007-2019)

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

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference (2007-2019)

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, …

Selecting Effective Mathematics Interventions In The Rti Process Via Brief Experimental Analyses, Carmen Daniela Reisener

Dissertations

The treatment utility of brief experimental analyses (BEAs) for identifying effective treatments for individual students experiencing mathematics difficulties is a novel area of research; especially in a Response-to-intervention (Rtl) framework. One fourth and three sixth grade students served as participants in the current study. The effects of a variety of evidence-based mathematics computation fluency interventions were examined in a BEA format. Effective treatments identified from the BEA for each participant were alternated during an extended analysis. The results of the current investigation indicated variability within and across participants in response to a variety of evidence-based interventions. Visual analysis of the …

Teaching Mathematics For Social Justice: Reflections On A Community Of Practice For Urban High School Mathematics Teacher, Lidia Gonzalez

Publications and Research

In this article, the author reports on a study that explored, in part, the developing identities of seven New York City public high school mathematics teachers as teachers of mathematics and agents of change. Meeting regularly as a community of practice, the teachers and author/researcher discussed issues of teaching mathematics for social justice; explored activities and lessons around social justice; and created a unit of study that attempted to meet high school level mathematics standards, while addressing a social justice issue affecting the lives of urban students. The author reports on the mathematics teachers, growing awareness of and concerns about …

Review Of Calculation Vs. Context: Quantitative Literacy And Its Implications For Teacher Education By Bernard L. Madison And Lynn Arthur Steen (Editors), Maura B. Mast

Numeracy

Madison, Bernard L. and Steen, Lynn Arthur (Eds.). Calculation vs. Context: Quantitative Literacy and Its Implications for Teacher Education. (Washington, DC: Mathematical Association of America, 2009). 197 pp. Softcover. ISBN 978-0-88385-908-7. Available free on the MAA website at http://www.maa.org/ql/calcvscontext.html

The papers in Calculation vs. Context discuss the role of quantitative literacy in the K-12 curriculum and in teacher education. The papers present a varied set of perspectives and address three themes: the changing environment of education in American society; the challenges, and the necessity, of preparing teachers to teach quantitative literacy and of including quantitative literacy in the K-12 education; …

The Influence Of Risk Taking On Student Creation Of Mathematical Meaning: Contextual Risk Theory, Erin Nicole Houghtaling

Theses and Dissertations

The primary concerns of mathematics educators are learning and teaching mathematics. It is, therefore, natural to ask "what implications and benefits might there be if learning were perceived as a risk-taking event?" (Atkinson, 1957, p. 266). The underlying motivation of this study is to analyze the risks students take in the mathematics classroom and how risk influences student creation of meaning and development of understanding. I define risk in the mathematics classroom to be any observable act that entails uncertain outcome. The research presented here focuses on a table of four students: Andrew, Carina, Kam, and Mark as they grapple …

Uncovering Transformative Experiences: A Case Study Of The Transformations Made By One Teacher In A Mathematics Professional Development Program, Rachelle Myler Orsak

Theses and Dissertations

Effective professional development is vital for improving mathematics teaching (National Council of Teachers of Mathematics [NCTM], 2007), so studying effective professional development programs is important to the field of mathematics education. This case study presents findings on one teacher, Rebecca, and her experiences in a five-semester mathematics professional development for elementary teachers. The participants in this professional development engaged in collaborative problem solving of challenging mathematical tasks over extended periods of time. I used qualitative research methods based on grounded theory methodology (Charmaz, 2006) to analyze Rebecca's entrance and exit surveys, video data of Rebecca's individual interviews, and video data …

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 (2007-2019)

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 …

Mathematics Student Teaching In Japan: A Multi-Case Study, Allison Turley Shwalb

Theses and Dissertations

Nearly all research that seeks to assist in reforming mathematics student teaching in the United States has been limited in that it (1) does not consider student teaching models in non-Western cultures, and (2) has not sufficiently studied the unique context of mathematics in student teacher-cooperating teacher interactions. This multi-case study addresses these issues by analyzing the interactions between three cooperating teachers and two student teachers in the mathematics student teaching setting in Japan. Four conclusions are presented to generate a coherent picture of the principles of teaching and learning to teach that are emphasized during this Japanese student teaching …

Similar But Different: The Complexities Of Students' Mathematical Identities, Diane Skillicorn Hill

Theses and Dissertations

We, as a culture, tend to lump students into broad categories to describe their relationships with mathematics, such as ‘good at math’ or ‘hates math.’ This study focuses on five students each of whom could be considered ‘good at math,’ and shows how the beliefs that make up their mathematical identities are actually significantly different. The study examined eight beliefs that affect a student's motivation to do mathematics: confidence, anxiety, enjoyment of mathematics, skill level, usefulness of mathematics, what mathematics is, what it means to be good at mathematics, and how one learns mathematics. These five students' identities, which seemed …

How Eighth-Grade Students Estimate With Fractions, Audrey Linford Hanks

Theses and Dissertations

This study looked at what components are in student solutions to computational estimation problems involving fractions. Past computational estimation research has focused on strategies used for estimating with whole numbers and decimals while neglecting those used for fractions. An extensive literature review revealed one study specifically directed toward estimating with fractions (Hanson & Hogan, 2000) that researched adult estimation strategies and not children's strategies. Given the lack of research on estimation strategies that children use to estimate with fractions, this study used qualitative research methods to find which estimation components were in 10 eighth-grade students' solutions to estimation problems involving …

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 (2007-2019)

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.

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

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference (2007-2019)

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, …

The Main Challenges That A Teacher-In-Transition Faces When Teaching A High School Geometry Class, Greg Brough Henry

Theses and Dissertations

During a semester-long action research study, the author attempted to implement a standards-based approach to teaching mathematics in a high school geometry class. Having previously taught according to a more traditional manner, there were many challenges involved as he made this transition. Some of the challenges were related to Geometry and others were related to the standards-based approach in general. The main challenges that the author encountered are identified and discussed. A plan of action for possible solutions to these challenges is then described.

What Are Some Of The Common Traits In The Thought Processes Of Undergraduate Students Capable Of Creating Proof?, Karen Malina Duff

Theses and Dissertations

Mathematical proof is an important topic in mathematics education research. Many researchers have addressed various aspects of proof. One aspect that has not been addressed is what common traits are shared by those who are successful at creating proof. This research investigates the common traits in the thought processes of undergraduate students who are considered successful by their professors at creating mathematical proof. A successful proof is defined as a proof that successfully accomplishes at least one of DeVilliers (2003) six roles of proof and demonstrates adequate mathematical content, knowledge, deduction and logical reasoning abilities. This will typically be present …

Paper 3: Using Technology To Design Teaching Modules In Mathematics And Science, Ollie Irons Manley

Georgia Association of Mathematics Teacher Educators (GAMTE) Annual Conference (2007-2019)

Technology is changing the way in which mathematics and science are taught, and this radical transformation in teaching is causing teachers to take a closer look at how lessons are designed. In an effort to demonstrate how to design instructional modules using technology, this paper will include the following: 1)A review of the National Educational Technology Standards for teachers to establish a framework for the development of the teaching modules; 2)instructional designs and techniques with special emphasis on multiple intelligence and critical thinking skills; 3) strategies and techniques for infusing technology into a standard based curriculum; and 4) an analysis …

Gaining Options: A Mathematics Program For Potentially Talented At-Risk Adolescent Girls, Pamela Trotman Reid, Sally K. Roberts

Teacher Education Faculty Publications

In response to indicators that a decline in interest in mathematics occurs among girls—particularly those from low-income and minority groups—during middle school, the GO-GIRL (Gaining Options: Girls Investigate Real Life) program was designed to help potentially talented at-risk girls. The program aimed to build mathematical confidence, skills, and conceptual understanding by integrating mathematics and social science research in a single-sex, technology-rich environment supported by university student mentors. The program targeted seventh-grade urban girls from public and private schools. Participants met over the course of ten Saturdays to learn research methods, computer skills, mathematics, and descriptive statistics. Quantitative data from the …

An Examination Of The Role Of Writing In Mathematics Instruction, Amy Jeppsen

Theses and Dissertations

This study uses qualitative methods to investigate the use of writing in a content course for elementary education majors in which writing was considered an important part of mathematical learning. The study differs from previous studies by investigating the role of writing in the everyday instructional activities, rather than investigating writing as a separate mathematical activity. An analysis of the instruction and class discussions that took place in this class reveals that components of writing that were addressed implicitly and explicitly in classroom instruction were developed simultaneously with conceptual understanding, suggesting a much stronger and more integral relationship between writing …

The Influence Of Teacher Preparation Programs On Student Achievement And Nctm Standards In Algebra I Classrooms, Belinda Gimbert, Linda Bol, Denelle Wallace, Dean S. Cristol

STEMPS Faculty Publications

The impact of traditional and alternative teacher preparation programs on student achievement and the instructional delivery methods used in secondary school Algebra classrooms was explored through a mixed method comparative design. The research site was a high-need urban, majority-minority school system in partnership with a local university, a school-university partnership that offered a Transition To Teaching program. The data analyses revealed that alternative teacher preparation program is a viable avenue for meeting the needs of public schools for qualified and highly effective teachers in mathematics classrooms at the middle school and high school levels. Disaggregated data from the standardized state …

Mathematics Placement Test: Helping Students Succeed, Norma Rueda, Carole Sokolowski

Mathematics Faculty Publications

A study was conducted at Merrimack College in Massachusetts to compare the grades of students who took the recommended course as determined by their mathematics placement exam score and those who did not follow this recommendation. The goal was to decide whether the mathematics placement exam used at Merrimack College was effective in placing students in the appropriate mathematics class. During five years, first-year students who took a mathematics course in the fall semester were categorized into four groups: those who took the recommended course, those who took an easier course than recommended, those who took a course more difficult …

Changes In Mathematics Achievement Over Time In Australia And Ethiopia, Tilahun Mengesha Afrassa

Shannon Research Press

This study has five major purposes: to develop a general theoretical model which considers the multivariate structure of the available data; to examine the changes of the mathematics achievement level of Australian lower secondary school students over time; to develop a common mathematics scale to enable investigation of mathematics achievement over time and across countries; to develop a theoretical model of student level factors influencing the mathematics achievements of lower secondary students in Australia and Ethiopia and to examine these hypothesised interrelationships between variables; and to investigate the views and attitudes of Australian and Ethiopian students towards mathematics and schooling …

How Elementary School Teachers Learn To Teach Mathematics, Phyllis Schneider Kirschner

Educational Studies Dissertations

This study examines how elementary school teachers learned to teach mathematics during their pre-service education and during their first few years of teaching. The study identifies those experiences teachers found to be most significant in their development as mathematics teachers. All seven teachers in this study had been taught using procedural methods and each had to find a way to integrate conceptual mathematics education into their own understanding. The study examines the teachers' motivations for pursuing this understanding and the circumstances that provided opportunities to do so.

Reforming Math And Science In Rural Schools, Hobart Harmon, Stephen A. Henderson, Wimberly C. Royster

Mathematics Faculty Publications

What happens when you devote $10 million and five years to improving math and science programs in rural schools in districts in which 30% or more of the students live in poverty? As participants of the ARSI project discovered, it is a long and evolving journey.

The Appalachian Rural Systemic Initiative: Improving Science And Mathematics Student Achievement In Economically Disadvantaged Rural Counties In Central Appalachia Through A School-Based, Teacher Partner Approach, Stephen A. Henderson, Wimberly C. Royster

Mathematics Faculty Publications

This article was written in response to "Top-Down, Routinized Reform in Low-income, Rural Schools: NSF's Appalachian Rural Systemic Initiative, by Robert Bickel, Terry Tomaskek, and Teresa Hardman Eagle which was published in the Education Policy Analysis Archives as Number 12 of Volume 8 on February 21, 2000.

Integrating Writing To Enhance Mathematical Skills At The Elementary Level, Kendra J. Kupp

All Graduate Projects

The recommendations of the National Council of Teachers of Mathematics and the Washington State Commission on Student Learning Essential Academic Requirements are addressed. The benefits of integrating mathematics and writing are studied. Integrated activities and materials for a first and second grade mathematics curriculum are developed. Recommendations for implementing the project are given.

Real World Mathematics Skills Within The Elementary Resource Classroom, Stacy Schilperoort

All Graduate Projects

A project, including activities, to assist elementary special education teachers in incorporating real world mathematics skills within their own resource classrooms was developed. A literature review of current research on the topic of real world math skills in schools around the country is also included as part of this project. The literature indicates that students with learning disabilities might benefit and become better prepared for the future as adult citizens by receiving an education that includes math activities that relate to the real world outside the classroom walls.

A Study Of Calculator Usage On The Mathematics Achievement Of Seventh- And Eighth-Grade Students And On Attitudes Of Students And Teachers, Tracie Bidwell Ellerman

Doctoral Dissertations

The purpose of this study was to examine the effects of calculator usage on the mathematics achievement of seventh and eighth grade students as measured by the Mathematics Concepts and Applications sections of the California Achievement Test. The study also investigated the attitudes of students and teachers toward calculator usage. Student attitudes were measured through responses to the Student Calculator Survey. Teacher attitudes were measured through responses to the Attitude Instrument for Mathematics and Applied Technology-Version II.

Intact classes from two north central Louisiana school systems were assigned randomly to treatment and control groups. The sample consisted of 1070 students …

The Implementation Of Radical Constructivism Within The Urban Mathematics Classroom, Randy Lattimore

Trotter Review

One of the most serious problems in mathematics education continues to be the dismal statewide mathematics proficiency test performance of African-American students in urban schools. It has been argued that one of the best ways to improve performance is by connecting the pedagogy of mathematics to the lives and experiences of these students. Although many theories have been implemented in the urban mathematics classroom to assist African-American students in developing and increasing conceptual understanding, members of the urban mathematics education community should take a closer, more serious look at the implementation of radical constructivism within urban mathematics classrooms.

A number …

Project Mime: Reshaping Mathematics Education In Secondary Schools, Joseph A. Meyinsse

Trotter Review

For a number of years the movement to reform the content and processes of mathematics education has gained momentum. At this time the consensus of professional thought based on student performance is that the old methods of teaching based on performance objectives have failed. As a result, these must be replaced from kindergarten through college by methods which emphasize hands-on activities and thereby actively involve the learner in the educational process and which promote the development of higher order cognitive skills. It is also the consensus that this process will develop students who are mathematically and scientifically literate and who …