Education Commons^™

Developing Understanding Of Fraction And Decimal Magnitude: A Teaching Experiment, Elizabeth Cutter-Lin

Theses and Dissertations

ABSTRACT

DEVELOPING UNDERSTANDING OF FRACTION AND DECIMAL MAGNITUDE: A TEACHING EXPERIMENT

by

Elizabeth Cutter-Lin

The University of Wisconsin-Milwaukee, 2023Under the Supervision of Professor DeAnn Huinker

This study investigated how three fifth-grade students’ understanding of fraction and decimal magnitude evolved over the course of a five-week teaching experiment. Students participated in teaching and learning sessions focused on developing concepts of fraction and decimal magnitude. The following questions guided this study: (1) How do fifth grade students reason about the magnitude of fractions and decimals? (2) What are the shifts in mathematical thinking that occur with students’ evolving understanding as they progress …

Recognizing And Reducing Ambiguity In Mathematics Curriculum And Relations Of Θ-Functions In Genus One And Two: A Geometric Perspective, Shantel Spatig

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Anxiety and mathematics come hand in hand for many individuals. This is due, in
part, to the fact that the only experience they have with mathematics is what some
mathematics educators refer to as "schoolmath," which uses a somewhat different
language than real mathematics. The language of schoolmath can cause individu-
als to have confusion and develop misconceptions related to several mathematical
concepts. One such concept is a fraction. In chapter one of this report, one possible
reason for this is discussed and a possible solution is purposed.
In chapter three of this report, genus-two curves admitting an elliptic involution …

Exploring The Use Of Concrete Materials In Teaching And Learning Of Fractions In Grade Three: A Case Study Of A Public Primary School In Homa-Bay County, Kenya, Ouma Patrick Okoth

Theses & Dissertations

Learners who struggle with mathematics may have difficulties in comprehending the core ideas in mathematics. The concrete-representational-abstract (CRA) instructional sequence of teaching allows teachers to assist pupils in making sense of numbers and the mathematical concepts they represent. The use of concrete materials is critical in the teaching of mathematics to young children; they are the major instruments that early childhood teachers use to train young learners in their mathematics classes today. To encourage the use of concrete materials in mathematics instruction, this research investigates how mathematics teachers use concrete materials in the teaching and learning of mathematics, as well …

The Effect Of Using Virtual Manipulatives On Students’ Ability To Mentally Compare Proper Fractions, William Wilson Mcneary Iii

Dissertations

This study proposes a method to analyze the effects of the use of virtual fraction models (circle/bar/number line) on students’ ability to mentally compare proper fractions. Since developing a sense of magnitude with both whole numbers and rational numbers is highly correlated with improved performance on standardized assessments and improved performance in later algebra classes, special attention is directed to the bar and number line as they are linear representations.

The study used an experimental pretest/posttest group design by randomly assigning subjects within class sections to a control group (physical fraction circles) and treatment groups with seven different methods of …

Mathematical Literacy: The Effects Of Mathematics Journals On Student Understanding Of Fractions In A Montessori Classroom, Eileen Bechler

Masters of Arts in Education Action Research Papers

It is a typical Monday morning. As students enter the classroom wearing brightly colored polo shirts embroidered with the school logo, their smiles are equally bright. This Title I public school in the heart of the city where 96% of the students qualify for free or reduced lunch has recently opened a Montessori option. Walking into the classroom, one 5th grade student eagerly asks, “Who’s on the bread committee this week?” Baking bread is a weekly occurrence in the upper elementary (4th – 6th grade) Montessori classroom. During the first week of school, this same student vehemently threw materials to …

The Impact Of Small Group Intervention Focusing On Operations With Rational Numbers On Students’ Performance In The Florida Algebra I End-Of-Course Examination, Evelyn Dopico

Theses and Dissertations

In Florida, passing the Algebra I end-of-course examination (EOCE) is a graduation requirement. The test measures knowledge of basic algebra. In spring 2015, the Department of Education introduced a different version of the test. For the first two administrations of the new test, the failure rate for 9th-grade students in the state was almost 50%. In contrast, the failure rate for students in the school where this study was implemented exceeded 70%. The purpose of this study was to determine the outcome of small group intervention focusing on operations with rational numbers of high school students’ performance on the Algebra …

Examining The Influence Of Number Line Fraction Task Characteristics On Student Work, Sharlee Hatch

Boise State University Theses and Dissertations

Research supports the claim that classrooms with teachers who respond to student thinking in the mathematics classroom will see greater student gains and student success (Lamon, 1996; Sleep & Boerst, 2012). The topic of fractions is both difficult to teach and learn, but has important implications on future success in mathematics and in life. This study set out to explore the ways in which student work is influenced by characteristics of number line fraction tasks. By examining task type, number line structure, and number choice this study shares the way these task characteristics influenced student strategies. The relationship between task …

Investigating Math Students' Ability To Conceptualize Fractions As Two Numerals Having A Single Value, William Carroll Fanning

Open Access Theses & Dissertations

It is no secret that math students of all ages have misconceptions about fractions. Multiple studies have shown that math students invariably see fractions as two separate and unrelated numbers, the numerator and the denominator, rather than a single number with specific value. This study is designed to investigate studentsâ?? interpretations of a fraction in terms of having a single value in relation to its two numbers, the numerator and the denominator.

For the purpose of this study, the investigator developed and pilot-tested seven items that have the potential to uncover whether students attend to the value of a fraction …

The Impact Of An Interactive Technology Application On Elementary Student Achievement In Fractions., Shannon M. Stone

Electronic Theses and Dissertations

Data reported locally and nationally show that students struggle to understand fractional concepts. The purpose of this study was to examine the effects of an interactive tablet application on student achievement in fractions. Students in grades three through five at the treatment school worked with an interactive tablet application designed to facilitate student construction of fractions knowledge. The interactive tablet application is an open-platform that allowed teachers the autonomy to work with the researcher to load their desired content activities on the topic of fractions to develop instructional sessions for students. Students worked independently during the math workshop to complete …

The Importance Of A Strong Mathematical Foundation, Jasmine M. Wriston

Williams Honors College, Honors Research Projects

The mathematical skills students learn from kindergarten through eighth grade are the foundational skills upon which all higher level mathematics courses build. It is highly beneficial that students master previous mathematics concepts, applications, and skills, prior to learning algebra and other higher level mathematical courses. Mastering elementary and middle level mathematics before learning algebra increases students’ chances for success when taking an algebra course. This study tested 39 ninth and tenth graders, from the college preparatory program Upward Bound, on the mathematical domains of fractions and ratios/proportions. Participants took one of two tests, each composed of three questions increasing in …

Evaluating The Use Of The Math Reasoning Inventory For Improvement In Fraction Instruction, Kathy Huffman Boyer

Dissertations

In an attempt to close the mathematic achievement gap between students from the United States and students from other countries, a new national set of standards, the Common Core State Standards for Mathematics, was developed and adopted by the state of Michigan in 2010. These standards emphasize mathematical reasoning and application, rather than the previous emphasis on performing calculations. Unfortunately, teachers generally have had little training in how to assess students’ mathematical reasoning, how to teach mathematical reasoning, or how to provide remediation to those students who show need. The purpose of this study was to see if use of …

Supporting Middle School Students With Emotional Or Behavioral Disorders In Blended Learning: A Fraction Intervention Using Virtual Manipulatives, Barbara Serianni

Electronic Theses and Dissertations

Students with emotional or behavioral disorders (EBD) are more likely than other students with disabilities to drop out of school (Blackorby & Wagner, 1996) and suffer societal consequences that include higher probabilities and rates of incarceration, poverty, drug abuse, homelessness, low wages, and unemployment (Bradley, Doolittle, & Bartolotta, 2008; Wagner, 1995). High school graduation is a critical factor to improve post-secondary outcomes for students with EBD; yet it is often mathematics, specifically algebra, that stands in the way of graduation (Blackorby & Wagner). Students with EBD often enter middle school lacking foundational mathematics skills, such as fractions, which sets them …

Integrating Math And Language Arts In The Classroom, Emilee Blake

Honors Projects

This is a unit outline with detailed lesson plans and a reflection. It is a unit teaching about adding and subtracting fractions with like denominators for fourth grade students. The unit focuses on incorporating language arts in the math classroom focusing on reading, writing, and speaking.

Effectiveness Of Teacher Professional Learning : Enhancing The Teaching Of Fractions In Primary Schools, Derek Hurrell

Theses: Doctorates and Masters

This study was motivated by the need to develop professional learning for primary school teachers that would support them to more effectively teach the mathematics topic of fractions. What seemed evident, was that previous professional learning attended by teachers had not adequately met their needs.

The aim of this study was to investigate whether professional learning, with a focus on subject content knowledge, pedagogical knowledge and reflective practice could enhance primary school teachers’ PCK for teaching fractions and make them more confident teachers of fractions. Demonstrating this to be the case would have wide implications for the development of professional …

A Learning Progression For Identifying And Placing Fractions On A Number Line, Corinne Dorothy Marshall

Theses Digitization Project

This project provides a learning progression for identifying and placing fractions on a number line that teachers can consider when introducing fractions on number lines. The number line is one of the most useful ways to represent all real numbers in relation to each other. It allows students to experience the density of the number system since all real numbers, natural numbers, whole numbers, integers, rational numbers and irrational numbers have an exact and unique location on the number line.

The Effects Of Concrete-Representational-Abstract Sequenced Instruction On Struggling Learners Acquisition, Retention, And Self-Efficacy Of Fractions, Elizabeth Hughes

All Dissertations

A growing body of research supports instructional strategies, such as concrete-representational-abstract (CRA) sequence, to teach mathematics to students at risk of failure, including those with disabilities. This study extends the current body of CRA research by analyzing the effects of CRA sequence of instruction on student achievement, and retention, and self-efficacy of performance on computations of fractions. Thirty-five students participated in this study. A series of repeated measures ANOVAs were performed to assess main effects and interaction effects for performance and self-efficacy of students in a control group who received traditional fractions instruction and a treatment group who received CRA …

Influence Of Using Context Supportive Of The Area Model On Sixth Grade Students' Performance When Writing Word Problems For Fraction Subtraction And Multiplication, Monica L. Friske

Electronic Theses and Dissertations

The purpose of this action research study was to evaluate my own practice of teaching writing word problems with fraction subtraction and fraction multiplication using appropriate context. I wanted to see how focusing my instruction on the use of the area model and manipulatives could develop students’ understanding of fractions when writing word problems. I chose this topic because Florida has adopted the Common Core State Standards and will be implementing them in the coming years. These standards encourage the development of deeper understanding of mathematics, including fractions. I hoped this research would give my students the opportunity to make …

The Effects Of A Ratio-Based Teaching Sequence On Performance In Fraction Equivalency For Students With Mathematics Disabilities, Jessica H. Hunt

Electronic Theses and Dissertations

This study examined the effects of a ratio-based supplemental teaching sequence on third grade students‘ equivalent fraction performance as measured by a curriculum-based measure and a standardized test. Participants included students identified as being learning disabled in mathematics (MLD), struggling (SS), or typically achieving (TA). Nineteen students were assigned to the experimental group and 19 additional students formed the control group. The difference between the two groups was that the experimental group received the ratio-based teaching sequence. Both groups continued to receive textbook based instruction in fraction equivalency concepts in their regular mathematics classroom. Qualitative interviews were employed to further …

The Relationship Between Special Education Teachers' Mathematical Knowledge, Instructional Choices, And Beliefs About Teaching And Learning Mathematics, Virginia Rich Lee

Legacy Theses & Dissertations (2009 - 2024)

Thirty-four certified special education teachers completed four instruments in addition to viewing video recordings of students engaging in mathematical tasks. The mathematical beliefs of special education teachers were investigated through the use of the Mathematics Beliefs Scales (Capraro, 2005). Special education teachers' mathematical knowledge was measured using the Fraction Knowledge Assessment, which included a range of fraction tasks drawn from state and national elementary level mathematics standards. The proposed instruction of the special education teachers was examined through participants' written responses to video recordings of students solving fraction problems. Demographic information was obtained through the use of a questionnaire. Results …

Fostering Teacher's Conceptual Understanding Of Ordering, Adding, And Subtracting Fractions Through School-Based Professional Development, Jessica Maguhn

Electronic Theses and Dissertations

In an attempt to examine my practice of providing conceptually-based professional development on fractions to fifth grade teachers, I conducted a series of four one hour professional development workshops. I focused on the conceptual understanding of ordering, adding, and subtracting fractions. I examined the solution process that teachers used to solve fraction problems and their abilities to explain and justify their solutions in an attempt to interpret their understanding. My data showed the effects of this workshop series. The study helped determine the effects of conceptually-based professional development on fractions as demonstrated in the teachers' discussions, participation, and written explanations.

Preservice Elementary Teachers' Diverlopment Of Rational Number Understanding Through The Social Perspective And The Relationship Among Social And Individual Environments, Jennifer Tobias

Electronic Theses and Dissertations

A classroom teaching experiment was conducted in a semester-long undergraduate mathematics content course for elementary education majors. Preservice elementary teachers' development of rational number understanding was documented through the social and psychological perspectives. In addition, social and sociomathematical norms were documented as part of the classroom structure. A hypothetical learning trajectory and instructional sequence were created from a combination of previous research with children and adults. Transcripts from each class session were analyzed to determine the social and sociomathematical norms as well as the classroom mathematical practices. The social norms established included a) explaining and justifying solutions and solution processes, …

Using Communication Techniques In The Low-Performing Mathematics Classroom: A Study Of Fractions,Decimals,Performance And Attitu, Pamela Guyton

Electronic Theses and Dissertations

Within a low-performing seventh grade mathematics classroom, communication techniques including discourse, collaborative groups, listening, reading, and writing were implemented during a six week period. This study shows how the use of these techniques led to the twenty four students' conceptual understanding of fraction and decimal concepts. This research study provides insight to the deep-seeded beliefs of low-performing students. It provides a record of how the teacher used communication techniques in the classroom and had a strong positive impact on the attitudes and performance of these struggling students.

Examining Sociomathematical Norms Within The Context Of Decimals And Fractions In A Sixth Grade Classroom, Marino Nardelli

Electronic Theses and Dissertations

Social norms are patterns of behavior expected within a particular society in a given situation. Social norms can be shared belief of what is normal and acceptable shapes and enforces the actions of people in a society. In the educational classroom, they are characteristics that constitute the classroom participation structure. Sociomathematical norms are fine-grained aspects of general social norms specifically related to mathematical practices. These can include, but are not limited to, a student-centered classroom that includes the expectation that the students should present their solution methods by describing actions on mathematical objects rather than simply accounting for calculational manipulations. …

Preservice Teachers' Procedural And Conceptual Understanding Of Fractions And The Effects Of Inquiry-Based Learning On This Understanding, Hope Marchionda

All Dissertations

ABSTRACT Non-negative rational numbers play a major role in the K-8 curriculum and continue to permeate mathematics content through high school and college in all strands of mathematics. The difficulty that both students and teachers encounter with these concepts is well documented in the literature. This study looked at preservice teacher knowledge and how an alternative means of instruction might improve their conceptual understanding of fractions. To accomplish this task, the study took place in two stages over the course of two semesters. During the first stage, preservice teachers' conceptual and procedural knowledge of fractions and their associated algorithms were …

Fraction Multiplication And Division Image Change In Pre-Service Elementary Teachers, Jennifer J. Cluff

Theses and Dissertations

This study investigated three pre-service elementary teachers' understanding of fractions and fraction multiplication and division. The motivation for this study was lack of conceptual understanding of fractions and fraction multiplication and division. Pre-service elementary teachers were chosen because teachers are the conduit of information for their students. The subjects were followed through the fractions unit in a mathematics methods course for pre-service elementary teachers at Brigham Young University. Each subject volunteered to participate and were interviewed and videotaped throughout the study, and they also provided copies of all work done in the fractions unit in the course. The data is …

Fractions, Decimals, And Percents : A Fifth Grade Curriculum Unit, Jeffrey Li

Graduate Student Independent Studies

This independent study outlines a fifth grade curriculum unit for fractions, decimals, and percents. The unit utilizes a problem-solving approach to lead to deep understanding of fractions and their relations to decimals and percents. The study is influenced by writings by Hiebert, Dewey, Piaget, \/ygotsky, and Fosnot, and uses a lesson planning format created by Hal Melnick. Four explorations drive the unit:

Exploration 1: What is a fraction?

Exploration 2: Going Deeper with Fractions

Exploration 3: Connecting Fractions to Decimals and Percents

Exploration 4: Comparing Fractional Amounts

Fraction Models That Promote Understanding For Elementary Students, Lynette Hull

Electronic Theses and Dissertations

This study examined the use of the set, area, and linear models of fraction representation to enhance elementary students' conceptual understanding of fractions. Students' preferences regarding the set, area, and linear models of fractions during independent work was also investigated. This study took place in a 5th grade class consisting of 21 students in a suburban public elementary school. Students participated in classroom activities which required them to use manipulatives to represent fractions using the set, area, and linear models. Students also had experiences using the models to investigate equivalent fractions, compare fractions, and perform operations. Students maintained journals throughout …

Integrating Internet Technology To Support Fraction Instruction In The Elementary Classroon, Melonie Ann Jacksin

Theses Digitization Project

No abstract provided.

The Effects Of A Direct Instruction Program In Fractions On Academic And Mathematics Self-Concept, William H. Lowry

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The study investigated the effect of a videodisc-based, teacher-controlled, direct instruction-based program in fractions content, on self-concept. Self-concept was operationally defined as scores on a slightly modified version of Marsh's Self-Description Questionnaire (Marsh, 1988). A quasi-experimental, nonequivalent control group design was used to compare the self-report self-concept of two groups of upper elementary students (N = 337). The treatment group (n = 171) received instruction in fractions via the teacher-directed, videodisc-based, Mastering Fractions program (Systems Impact, 1986a). The control group (n = 166) received their normal grade four or grade five mathematics program, but did not include common fractions.

Differences …