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 …

Multiplying And Dividing Fractions And Mixed Numbers Using Multiple Models, Pavithra Sridhar

Inclusive Strategies for Teaching Secondary Mathematics and Science

This lesson is based on the study of Multiplying and Dividing Fractions using multiple representations, and the subsequent application of these concepts to real-life situations. In this lesson, we demonstrate/model multiplication and division of fractions (proper or improper) and mixed numbers using multiple models. We solve single-step and multistep practical problems involving addition, subtraction, multiplication, and division with and without models. The sum, difference, product, and quotient of fraction and mixed number problems are determined. We also determine the sum and difference of fraction, mixed number, and fraction, division, and product of mixed numbers. This lesson focuses on the use …

Elementary Preservice Mathematics Teachers Fraction Knowledge: An Integrative Review Of Research, Cody J. Perry

Educational Considerations

Elementary preservice teachers struggle with fractions and explaining them despite taking numerous mathematics courses. Therefore, they may have issues when they teach fractions and related concepts. Since fractions underlie many concepts like algebra, improving teachers’ fraction knowledge is imperative. This integrative review of research synthesized findings about teachers’ fractions knowledge to provide potential strategies educator preparation programs (EPPs) can use to improve fraction mastery. The literature shows teachers lacked conceptual knowledge, used incorrect strategies and too few representations, and misunderstood magnitude and manipulatives. However, number lines and teaching conceptually helped improve mastery of fractions. Resolving issues with fraction mastery may …

Cache Code Math: Mathematics Lesson Plans: Fractions, Kimberly Beck, Jessica F. Shumway, Aubrey Rogowski, Umar Shehzad, Jody Clarke-Midura, Mimi Recker

Instructional resources

This document entails three 5^th grade mathematics lesson plans. The lessons are intended to be implemented in conjunction with the computer lab activities found in "Cache Code Math: Fractions, Functions, & For-Loops." The mathematics focus of these lessons is multiplying fractions, which is paired with the computer coding concepts of functions and for-loops.

The Effects Of Computer-Assisted Instruction On Student Learning Of Fractions In Middle School Mathematics, Rebecca Love Palculict

Doctoral Dissertations and Projects

In today’s increasingly technologically-driven classroom, exploring whether computer-assisted instruction ensures students gain critical mathematic skills is an important area of study. The purpose of this study was to explore the effect of computer-assisted instruction in learning manipulation of fractions. This study used archival data collected in August 2021 (pre-test) and January 2022 (post-test). Sixty-nine fifth-grade students in a middle school in rural Mississippi were participants in the study. This quantitative quasi-experimental pre-test/post-test control group design analyzed data from the i-Ready diagnostic using an Analysis of Covariance. Results indicated a significant difference between the post-test scores of students who received interventions …

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 …

Math Basics Afterschool Club, Lexi Soukup, Meg Williams

Honors Expanded Learning Clubs

This is a compilation of Lexi Soukup and Meg Williams’ work as Club Leaders in an Afterschool Club run through the University of Nebraska- Lincoln and YMCA Afterschool Programs titled Math Basics. Our club is an interactive, hands-on math exploration where students are challenged to change their perspective of math, and it is meant to occur once weekly. During this club, we try to challenge their current views of math and expand their knowledge on math concepts they learn in class through activities and games. This is meant to make math FUN! Our compilation of lesson plans are sure to …

Using Gamification To Teach Foundational Fractions In The Third Grade: Year One, Makeba Mccray

Kean Quest

Schools face an instructional dilemma with how to create a motivational environment where fractions are fun, interactive, and induce problem-solving skills through real-time application. The concept of gamification has been utilized in business for marketing, employee training, customer retention, health, and fitness with much success. How can primary educational institutions harness the potential of gamification to close academic gaps or prevent stopgaps? This situation is particularly challenging at this level because there has to be a balance between interaction, gamification, and content delivery; while also providing effective instructional learning objectives for knowledge mastery without overloading students with information and digital …

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 …

Learning To Transform, Transforming To Learn: Children’S Creative Thinking With Fractions, Higinio Dominguez, Sandra Crespo, Tamara Del Valle, Melissa Adams, Megan Coupe, Gustavo Gonzalez, Yordhan Ormazabal

Journal of Humanistic Mathematics

In this paper we contribute an alternative conceptualization of creativity by highlighting movement as creating spatial and temporal dimensions that are important to make sense of creativity in children mathematical thinking. Using data from an international collaboration between two teaching-research teams from the United States and Chile, we trace how children mobilized their social bodies, materials, tools, images, metaphors, languages, and improvisations in order to make sense of the concept of fractions. Based on these findings we offer a number of discussion points that highlight the importance of creating these kinds of learning spaces, the role of tasks in promoting …

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 …

Preservice Teachers’ Strategies For Interpreting Fractions Represented In Discrete And Continuous Models, Victoria Webster

Transformations: Research Papers

Teaching and learning fractions have been a focus of research in mathematics education for decades. Current practices of teaching fractions emphasize the partitioning perspective, or part-whole, to conceptualize fractions. Another approach to teaching fractions is measurement. The part-whole approach limits students’ conceptualization of fractions and impedes learning improper fractions, whereas the measurement approach has the potential to overcome these difficulties and supports learning improper fractions. In this study, 55 preservice teachers engaged in an intervention to reexamine fractions using a measurement perspective. Before and after the intervention, the preservice teachers were asked to interpret proper and improper fractions using discrete …

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

Derek Hurrell

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 …

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 …

Math Technology: Assessing The Educational Value Of A Supplemental Practice Program, Shannon Tesch

Master's Theses & Capstone Projects

The purpose of this action research project was to determine if the use of a supplemental computerized math practice program increases student achievement in the fractions domain for fifth graders. Two fifth grade math classes received the same classroom instruction. However, one class also utilized a computerized program three times per week for 20-30 minutes over a six-week period. Data was collected through quantitative pre- and post-assessments, quantitative survey questions, and qualitative student responses. Analysis of the data collected suggests that using the supplemental computerized math program, Front Row Education, in addition to regular classroom instruction, increases student achievement in …

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 …

The Importance Of Fractions In Being A Successful Mathematics Student, Derek Hurrell, Lorraine Day

Derek Hurrell

Research and experience tells us that fractions are not easy to teach and learn and that a solid conceptual understanding of fractions has far reaching ramifications in the secondary mathematics classroom. A failure to acknowledge and remediate 'inherited' challenges to this understanding may result in the further success of students being severely impeded.

The Importance Of Fractions In Being A Successful Mathematics Student, Derek Hurrell, Lorraine Day

Lorraine Day

Research and experience tells us that fractions are not easy to teach and learn and that a solid conceptual understanding of fractions has far reaching ramifications in the secondary mathematics classroom. A failure to acknowledge and remediate 'inherited' challenges to this understanding may result in the further success of students being severely impeded.

Five Key Ideas To Teach Fractions And Decimals With Understanding, Sam Strother, Jonathan L. Brendefur, Keith Thiede, Sarah Appleton

Curriculum, Instruction, and Foundational Studies Faculty Publications and Presentations

The teaching of fractions and decimals is a significant challenge for many teachers due to the inherent difficulty of the topic for students as well as the lack of high-quality, modernized curricular materials. This article examines the key ideas of teaching fractions and decimals for understanding that are evident in the current research literature and the curricular materials and teaching strategies from high-achieving nations.

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 Impact Of Pictorial Representations In Teaching Math Word Problems To A Child With Autism, Hossein Shirvani

Teaching and Learning Faculty Publications and Presentations

The study used a single subject A-B-A research design because it used one subject, an 18-year old boy participant who was diagnosed with having higher spectrum Autism (Asperger). The investigator examined the effect of pictorial representations of math word problems on the participant’s performance in solving one step, two steps, and three steps math word problems. The investigator found that the use pictorial representations improved the participant’s math achievement in solving math word problems. The investigator also found that the participant had difficulty understanding words with mathematical connotations.

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 …

The Importance Of Fractions In Being A Successful Mathematics Student, Derek Hurrell, Lorraine Day

Education Conference Papers

Research and experience tells us that fractions are not easy to teach and learn and that a solid conceptual understanding of fractions has far reaching ramifications in the secondary mathematics classroom. A failure to acknowledge and remediate 'inherited' challenges to this understanding may result in the further success of students being severely impeded.

Generating Procedural And Conceptual Knowledge Of Fractions By Pre-Service Teachers, Mohan Chinnappan, Patricia Forrester

Faculty of Social Sciences - Papers (Archive)

Knowledge that teachers bring to the teaching context is of interest to key stakeholders in improving levels of numeracy attained by learners. In this regard, the centrality of, and the need to investigate, the quality of teachers' mathematical knowledge for teaching mathematics has been gaining momentum in recent years. There is a general consensus that teachers need a robust body of content and pedagogical knowledge related to mathematics and that one impacts on the other. However, in current debates about this interconnection between content knowledge and pedagogical content knowledge, there is limited analysis about the procedural-conceptual nature of content knowledge …

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.

Honors Research Symposium Program [Spring 2013], University Honors Program Students And Staff

University Honors Research Symposium Programs

No abstract provided.