Mathematics Commons^™

Curriculum Connectivity In Montclair State University’S Undergraduate Mathematics Program, Ana G. Da Silva Jesus

Theses, Dissertations and Culminating Projects

According to Piaget’s cognitive development theory and the constructivism learning theory of education, real learning occurs when students establish long term connections between disciplines by either adapting or redefining previously acquired knowledge. These ideologies have important teaching and learning implications that directly influence curriculum development and the design of a course of study. This thesis explores the interconnectedness of the subjects required for the successful completion of an undergraduate math program at Montclair State University. More specifically, it models students’ unique connections through a learning network and investigates the correlation between the interconnectivity of subjects and students’ overall performance. Results …

Investigating Elementary School Students’ Reasoning About Dynamic Angles, Erell Germia

Theses, Dissertations and Culminating Projects

Angle measurement is a significant topic in almost all areas of mathematics learning and also in many disciplines outside mathematics education, such as engineering and architecture. According to the literature, there are three common conceptions of angles – as union of rays, rotations, and wedges. Researchers argued that students must consider these three angle concepts together to construct a meaningful understanding of angles. However, the curriculum standards for mathematics often present these angle conceptions separately to students, probably resulting in a fragmented understanding of the angle concept. In addition to this problem, the research literature documents multiple alternative conceptions that …

Using Teacher Noticing And Video-Mediated Professional Learning To Develop Preservice Teachers’ Knowledge For Teaching The Derivative, Alfred M. Limbere

Theses, Dissertations and Culminating Projects

This study investigated how problem-solving videos can be used in video-mediated professional learning to support secondary preservice mathematics teachers (PMTs) in developing teacher knowledge for noticing student thinking in the context of the derivative concept in calculus. A model of the trajectory of PMTs’ noticing was constructed as six PMTs viewed and analyzed videos of students’ problem solving. At the same time, the nature of video-mediated interactions that were found to be productive in supporting this knowledge development was examined. A design experiment was used as the research methodology. Data was collected from video recordings of eight semi-structured teaching episodes …

Secondary Teachers’ Noticing Of Students’ Mathematical Thinking As They Participate In A Professional Development Program Centered On Task-Based Student Interviews, Gurkan Kose

Theses, Dissertations and Culminating Projects

Teacher’s noticing of students’ mathematical thinking has been an important focus of research in the past two decades (e.g., Jacobs et al., 2010; Sherin et al., 2011). Noticing matters, but it is not an end in itself (Schoenfeld, 2011). It is operationalized within the context of teachers’ dispositions and knowledge which shape decisions teachers make while responding to student thinking and planning the next instructional steps. In order for teachers to adapt productive beliefs about how children learn and shift to student-centered instruction, they need to acknowledge the importance of understanding students' existing conceptions of mathematical ideas (Carpenter & Lehrer, …

Fostering Mathematical Creativity Among Middle School Mathematics Teachers, Ceire H. Monahan

Theses, Dissertations and Culminating Projects

The purpose of this research was to understand in-service teachers’ experiences with and ideas about mathematical creativity after participating in a targeted professional development program. The professional development program encouraged participants to think creatively and foster students’ creativity. In this study I present the results from the main unit of analysis, 12 participants in a professional development program, along with a deep analysis of three exemplar teachers from each of the identified groups, adherence to traditional teaching practices (traditional), appreciation for teaching for creativity (creative but hesitant), and teaching for creativity (creative). The findings of this study highlight the combination …

Transitioning Secondary Mathematics Pedagogy Towards Reform-Oriented Practice Through Coteaching, Jessica Tybursky Nuzzi

Theses, Dissertations and Culminating Projects

Reform standards in mathematics education have called for classrooms that are student-centered and that incorporate problem solving and reasoning for meaningful learning. After decades of reform efforts involving multiple stakeholders, research indicates that most classrooms remain teacher-centered and procedurally focused, due to the complexity of concerns and competing intentions that teachers face in their work. Coteaching, a commitment between two teachers to coplan, coenact, and coreflect on lessons, can serve as an ongoing, sustained, focused, integrated, reflective professional development structure that supports teachers towards growth. The theoretical constructs used to describe possible growth towards reform orientations in teaching secondary mathematics …

The Role Of Covariational Reasoning In Pre-Service Teachers’ Meanings For Quadratic And Exponential Relationships, Madhavi Vishnubhotla

Theses, Dissertations and Culminating Projects

Researchers have indicated that students have difficulties recognizing quadratic and exponential change and do not maintain productive meanings for these relationships. Other researchers have documented that students are capable of developing productive meanings for mathematical ideas via covariational reasoning. This dissertation reports the results of an investigation into ways in which preservice teachers can leverage covariational reasoning to develop meanings for quadratic and exponential relationships. I collected data by engaging two preservice teachers in semi-structured clinical interviews and a semester long teaching experiment. My analyses reveal that whereas in the pre-interviews, the participants did not have meanings that supported differentiating …

A Community Of Learning In An Elementary School Mathematics Classroom, Megan Louise Roeder

Theses, Dissertations and Culminating Projects

The goal of this study was to investigate opportunities for cultivating a community of learning in an elementary school mathematics classroom using four guiding principles for productive disciplinary engagement. A community of learning involves teachers and students participating equally in negotiating, sharing, and producing knowledge as co-learners, coteachers, and co-collaborators in the classroom. Characteristics of a community of learning align with effective teaching and learning practices described by national governing bodies and researchers in the field of mathematics education. The essence of a community of learning is beneficial in an elementary mathematics classroom because it invokes deep learning about disciplinary …

Video Case Materials And The Development Of Collective Professional Knowledge, Victoria D. Bonaccorso

Theses, Dissertations and Culminating Projects

The dynamic nature of teaching means that teachers are making in-the-moment decisions on a daily basis. Video case study professional development can be used as a way to provide teachers an opportunity to analyze real teaching scenarios to prepare to make these decisions in practice. While work has been done to reveal the effectiveness of using case studies as a teaching tool, there has not been research conducted to determine if video case studies can be used to foster the development of collective professional knowledge. This study utilizes a particular professional development model using video case studies grounded in the …

Examining Students’ Covariational Reasoning Through Mathematical Modeling Activities Embedded In The Context Of The Greenhouse Effect, Debasmita Basu

Theses, Dissertations and Culminating Projects

The greenhouse effect is one of the most pressing environmental as well as social issues of the present age. In news media and weather reports, most of the essential information about the phenomenon is expressed in forms of graphs and pictures. However, the interpretation of such graphs is challenging for students; they often focus on the shape of the graphs, overlooking the covariational relationships between the concerned quantities. Building on the framework of critical mathematics literacy and social justice mathematics, in this study I aimed to explore the power of dynamic mathematical modeling activities for engaging students in covariational reasoning …

One Teacher's Transformation Of Practice Through The Development Of Covariational Thinking And Reasoning In Algebra : A Self-Study, Jacqueline Dauplaise

Theses, Dissertations and Culminating Projects

CCSSM (2010) describes quantitative reasoning as expertise that mathematics educators should seek to develop in their students. Researchers must then understand how to develop covariational reasoning. The problem is that researchers draw from students’ dialogue as the data for understanding quantitative relationships. As a result, the researcher can only conceive the students’ reasoning. The objective of using the self-study research methodology is to examine and improve existing teaching practices. To improve my practice, I reflected upon the implementation of my algebra curriculum through a hermeneutics cycle of my personal history and living educational theory. The critical friend provoked through dialogues …

Assimilating Mathematical Thinking To The Learning Of Shadows, Taheeda Shwana Street-Conaway

Theses, Dissertations and Culminating Projects

This study focuses on a teaching experiment with 33 six-graders in a Kearny public school in Hudson County, New Jersey, during the 2017-2018 academic year. More specifically, this study explored a) the types of tasks and tools that can be used to develop students’ covariational and correspondence reasoning in learning about shadows and b) the nature of students’ reasoning about covariation and correspondence relationships as students engage in the use of tools and tasks. The results showed that the simulation and the tasks I designed had the students engaged in the learning process. Students were able to reason about the …

Characterizing The "Realistic-Ness" Of Word Problems In Secondary Mathematics Textbooks, Mary L. Dalton

Theses, Dissertations and Culminating Projects

Word problems are an integral part of any secondary mathematics curriculum and one purpose has been to prepare students for the real-world – for everyday events as well as workplace problem-solving. Prior literature suggests that word problems have not met this objective, in part, because the textbook problems do not mirror the kinds of problems commonly found in real life situations.

In this dissertation, I investigate a sample of word problems from two contemporary non-traditional textbooks to uncover the aspects that may influence if and how the problems might be used in the classroom. I utilize a qualitative content analysis …

Adult Learners, Learning Disabilities, And Mathematics : A Case Study, Marguerite Sheehan Flood

Theses, Dissertations and Culminating Projects

The purpose of this research was to understand how mathematics is taught at a small, liberal arts college that self-advertised as accommodating diverse learners. A qualitative case study was conducted on the mathematics program at Waterview College. Waterview College is unique in that almost half of their students self-identify with a disability, including learning disabilities (LD). The number of students with learning disabilities that attend college is increasing; therefore it is important for mathematics instructors to understand and accommodate diverse learners. The data for this research were collected using one-on-one instructor interviews, classroom observations, and student focus group interviews. The …

How Do Manipulatives Help Students Communicate Their Understanding Of Double-Digit Subtraction?, Rabab Abi-Hanna

Theses, Dissertations and Culminating Projects

Multi-digit subtraction is difficult for students to learn. The purpose of this study is to explore how second-grade students communicate their understanding of double-digit subtraction through the use of manipulatives/tools. This qualitative study reports on six case studies of second-grade students where clinical interviews were the main source of data. Findings suggest that manipulatives/tools helped reveal cognitive constructs and difficulties that the handwritten algorithms were not conveying. For example, students who exhibited an understanding of the subtraction process had not yet developed an understanding of ten and 10 ones interchangeability. These results highlight the potential role of manipulatives/tools as communication …

Quantitative Literacy And High School Mathematics : The Evolution Of A Collaboratively Constructed Course And Its Impact On Students' Attitudes And Numeracy, Mark Francis Russo

Theses, Dissertations and Culminating Projects

This study describes a practitioner action research project in which I co-constructed a high school mathematics elective course with my students. The focus of the course was on developing students’ quantitative literacy. I examined the impact of the coconstruction process on the evolution of the course, analyzed how the course influenced students’ quantitative literacy and attitudes about mathematics, and reflected on some of the lessons I learned about making mathematics more relevant for my students. This study fills a gap in the literature by describing the impact of a quantitative literacy course at the high school level and by documenting …

The Study Of Middle School Mathematics And Science Teachers' Practices, Perceptions, And Attitudes Related To Mathematics And Science Integration, Eliza Leszczynski

Theses, Dissertations and Culminating Projects

The purpose of this qualitative study was to investigate the nature of mathematics and science connections made by sixth and seventh grade mathematics and science teachers in their classrooms. This study also examined the extent to which these connections represented mathematics and science integration and described the teachers’ perceptions of and attitudes about mathematics and science integration. The primary data sources included classroom observations and teacher interviews.

Findings suggested that teacher practices in making mathematics and science connections in the classroom incorporated many of the characteristics of integrated instruction presented in the literature. Teacher attitudes toward integration were found to …

Teaching Social Justice Mathematics In A Privileged Setting, Rick Mcnamee

Theses, Dissertations and Culminating Projects

This practitioner action research using qualitative techniques of gathering data looks at the experiences of students in a mostly white, upper-middle class suburb who enrolled in a class that integrated mathematics with social justice issues. The researcher designed the curriculum and co-taught the one semester course. The data were collected from pre-interviews, beginning and end of class questionnaires, quick writes, field notes, and end of class focus group interviews with all the students. The author chose a practitioner action research design because he wanted to be an integral part of the study. The cyclical nature of action research allowed him …

Serving Two Masters : A Study Of Quantitative Literacy At Small Colleges And Universities, Jodie Ann Miller

Theses, Dissertations and Culminating Projects

The past twenty years have seen a growing interest in promoting quantitative literacy (QL) courses at the college level. At small institutions, financial realities impose limitations on faculty size and therefore the variety of courses that may be offered. This study examined course offerings below calculus at four hundred twenty-eight small colleges to gain a thorough understanding of the approaches to developing QL among the general population of undergraduate students. Using a three-phase model of examining progressively narrower subsets of QL programs at small institutions, document-based data from college catalogs and communication with mathematics program chairs were studied to summarize …

American Mathematical Association Of Two Year Colleges Reform Policies In Practice : Implementing Standards In Classroom Instruction For Basic Skills Mathematics At One Four-Year College In New Jersey, Patricia J. Garruto

Theses, Dissertations and Culminating Projects

High school graduates continue to enter post-secondary education lacking in basic mathematical skills and thus not academically prepared to enroll in college-level mathematics courses (ACT, 2010). Although it can be argued that those mathematical concepts should have been mastered in grades K-12, educating those students in basic skills mathematics has become the responsibility of universities and colleges. Two publications of the American Mathematical Association of Two Year Colleges (AMATYC), Crossroads (1995) and Beyond Crossroads (2006) set forth standards for mathematics programs and courses offered to students during their first two years of postsecondary education, which includes basic skills programs. Those …

From College Prep High School Courses To College Remedial Courses : Bridging The Gap, Tracy K. Abar

Theses, Dissertations and Culminating Projects

This study investigated students’ use of, and access to, the calculator in high school mathematics courses and compared it to the accessibility of a calculator during college placement tests. In spring 1999, at the request of the College Board, the Educational Testing Service (ETS) conducted a survey on calculator use in the nation’s schools. Ninety-nine point nine percent of the schools surveyed indicated they either required or allowed calculators for part of their college preparatory mathematics sequence. Accompanying the increased role of calculators in mathematics learning and the use of technology in the classroom, significant changes were introduced into many …

Use Of Logic Game To Improve High School Students' Logical Reasoning Skills : Results Of A Teaching Experiment, Frank Forte

Theses, Dissertations and Culminating Projects

High school students often struggle with the concept of logical reasoning. A study conducted with 37 ninth grade geometry students involved a teaching experiment. This study documented whether instruction on a logic game called the Color of the Board Game helped students’ logical reasoning skills, and if those skills could be reflected in a “‘pencil and paper” test. Each student in a control and treatment group received a pre-test with 25 multiple-choice logic questions and an open-ended question. Multiple-choice questions were based on geometry and contextual logic. The treatment group received the Color of the Board Instructional Unit between the …

The Effects Of Using The Geometer’S Sketchpad On Student Learning Of Transformations In The Coordinate Plane, Leeann Elizabeth Gennett

Theses, Dissertations and Culminating Projects

The primary purpose of this study was to investigate how grade nine honors geometry students and grade ten regular geometry students learn and retain information about three basic rigid geometric transformations with the support of the software package The Geometer’s Sketchpad in comparison to the traditional, non-software supported method of instruction.

The study was conducted in a high school with two tenth grade regular geometry classes and two ninth grade honors geometry classes. The researcher and another teacher each conducted a one-week instructional unit on the three basic, isometric transformations. Thirty-four students agreed to participate in the study. Nineteen students …