Academic literature on the topic 'Fractions, Decimals'

Thesis (M.S.)--Central Connecticut State University, 1999.<br>Thesis advisor: Dr. Philip Halloran. " ... in partial fulfillment of the requirements for the degree of Master of Science [in Mathematics]." Includes bibliographical references (leaves 74-75).

The purpose of this thesis is to seek evidence of commonalities in the mental representations of fractions and decimals between zero and one. The focus is on the mental representations of non-familiar fractions and decimals in adults. In addition, individual differences in the extent of common fraction and decimal mental representations are explored and their links to mathematical understanding of numbers between zero and one. For whole numbers, number comparison tasks have found evidence of an ordered, magnitude mental representation known as the mental number line through which the magnitude of a whole number is automatically processed. This evidence consists of phenomena such as the distance effect and SNARC effect. Here, indications of a similar magnitude representation common to both fractions and decimals are sought through a task in which a fraction is compared with a decimal. Substantial evidence of a distance effect is presented but not a SNARC effect, indicating that fractions and decimals can have mental representations containing or accessing a common magnitude but that this magnitude is not automatically processed. In addition, two emergent phenomena are reported. The first is an effect of location which is contrasted with the size effect in whole numbers and a previously reported anchor-point effect. The second is a larger-stimulus effect which is an indication of differences in the mental representations of fractions and decimals. These effects are explored in two additional, simple magnitude and location tasks. Furthermore, success but not speed within the comparison task is linked to strength of the distance effect for individuals. Therefore the number comparison task is repeated in series with a test designed to uncover common misconceptions of fractions and decimals. Patterns with the individual differences in responses to the test and comparison task are explored. By making links between the features and commonalities of individuals’ mental representations of fractions and decimals and quality of their understanding, this research hopes to be of value to mathematical educators.

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. For this action research study, my goal was to determine if the role of the teacher would influence the social and sociomathematical norms in a mathematics classroom and in what ways are sociomathematical norms reflected in students' written work. I focused specifically on students' mathematics journal writing and taped conversations. I discovered that students tended to not justify their work. Also, I discovered that my idea of justification was not really justification. I learned from this and was able to change my idea of justification. By encouraging the students to socialize in mathematics class, I found that the quality of their dialogue improved. Students readily discussed mathematical concepts within small groups and whole class discussions.<br>M.Ed.<br>Department of Teaching and Learning Principles<br>Education<br>K-8 Math and Science MEd

Thesis (Ph. D.)--Illinois State University, 2006.<br>Title from title page screen, viewed on June 8, 2007. Dissertation Committee: Norma C. Presmeg (chair), Cynthia W. Langrall, Beverly S. Rich, Janet Warfield. Includes bibliographical references (leaves 177-187) and abstract. Also available in print.

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.<br>M.Ed.<br>Department of Teaching and Learning Principles<br>Education<br>K-8 Math and Science MEd

Over the past decade, technology has become a prominent feature in our lives. Technology has not only been integrated into our lives, but into the classroom as well. Teachers have been provided with a tremendous amount of technology related tools to educate their students. However, many of these technologically enhanced tools have little to no research supporting their claims to enhance learning. This study focuses on one aspect of technology, the iBook, to complete homework relating to fractions, decimals, and percents in a sixth grade classroom. An iBook is a digital textbook that allows the user to interact with the book through various features. Some of these features include galleries, videos, review quizzes, and links to websites. These interactive features have the potential to enhance comprehension through interactivity and increased motivation. Prior to this study, two pilot iterations were conducted. During each pilot study, students in two sixth grade classrooms used the iBook to supplement learning of fractions, decimals, and percents. A comparison group was not included during either iteration, as the goal was to fine-tune the study prior to implementation. The current study was the third iteration, which included a comparison and treatment group. During this study, three research questions were considered: 1) When learning fractions, decimals, and percents, in what ways, if any, do students achieve differently on a unit test when using an interactive iBook for homework as compared to students who have access to the same homework questions in an online static PDF format? 2) What are students' perceptions of completing homework regarding fractions, decimals, and percents with an interactive iBook compared to students who complete homework in an online static PDF format? 3) In what ways does students' achievement on homework differ when completing homework related to fractions, decimals, and percents from an interactive iBook and a static PDF online assignment? Thirty students from a small charter school in southeast Florida participated in the third iteration of this study. Fifteen students were in the comparison group and fifteen were in the treatment group. Students in both groups received comparable classroom instruction, which was determined through audio recordings and similar lesson plans. Treatment group students were provided with a copy of the iBook for homework. Comparison group students were provided with a set of questions identical to the iBook questions in a static digital PDF format. The comparison group students also had access to the textbook, but not the iBook nor the additional resources available within the iBook. The study took place over three weeks. At the commencement of the study, all students were given a pretest to determine their prior knowledge of fractions, decimals, and percents. Students were also asked to respond to questions regarding typical homework duration, level of difficulty, overall experience, and additional resources used for support. During the study, both classes received comparable instruction, which included mini lessons, manipulative based activities, mini quizzes, and group activities. Nightly homework was assigned to each group. At the conclusion of the study, both groups were given a posttest, which was identical to the pretest. Students were asked identical questions about their homework perceptions as prior to the study, but were asked to respond in regards to the study alone. All participating students completed a questionnaire to describe their perceptions of completing homework regarding fractions, decimals, and percents with an iBook as opposed to static digital PDF homework. Lastly, six students from the comparison group participated in a focus group and six students from the treatment group participated in a separate focus group. Data were collected from the pretest and posttest, pre and post homework responses, collected homework, mini quizzes, audio recordings, teacher journal, questionnaires, and the focus group. No difference in achievement was found between the two groups. However, both groups improved significantly from the pretest to posttest. Based on the questionnaires and focus groups, both groups of students felt they learned fractions, decimals, and percents effectively. However, the questionnaire data showed the treatment group found the iBook more convenient than the comparison group did the textbook. Data from this study provide a baseline for future studies regarding iBooks in middle school mathematics. Although the data show no difference in achievement between the two groups, further studies should be conducted in regards to the iBook. Questionnaire and focus group data suggest, with modifications, students may be more inclined to use the resources within the iBook, which may enhance achievement with fractions, decimals, and percents.

Understanding the relationship between fractions and decimals is an important step in developing an overall understanding of rational numbers. Research has demonstrated the feasibility of technology in the form of virtual manipulatives for facilitating students’ meaningful understanding of rational number concepts. This exploratory dissertation study was conducted for the two closely related purposes: first, to investigate a sample of fifth-grade students’ reasoning regarding the relationship between fractions and decimals for fractions with terminating decimal representations while using virtual manipulative incorporating parallel number lines; second, to investigate the affordances of the virtual manipulatives for supporting the students’ reasoning about the decimal-fraction relationship. The study employed qualitative methods in which the researcher collected and analyzed data from fifth-grade students’ verbal explanations, hand gestures, and mouse cursor motions. During the course of the study, four fifth-grade students participated in an initial clinical interview, five task-based clinical interviews while using the number line-based virtual manipulatives, and a final clinical interview. The researcher coded the data into categories that indicated the students’ synthetic models, their strategies for converting between fractions and decimals, and evidence of students’ accessing the affordances of the virtual manipulatives (e.g., students’ hand gestures, mouse cursor motions, and verbal explanations). The study yielded results regarding the students’ conceptions of the decimal-fraction relationship. The students’ synthetic models primarily showed their recognition of the relationship between the unit fraction 1/8 and its decimal 0.125. Additionally, the students used a diversity of strategies for converting between fractions and decimals. Moreover, results indicate that the pattern of strategies students used for conversions of decimals to fractions was different from the pattern of strategies students used for conversions of fractions to decimals. The study also yielded results for the affordances of the virtual manipulatives for supporting the students’ reasoning regarding the decimal-fraction relationship. The analysis of students’ hand gestures, mouse cursor motions, and verbal explanations revealed the affordances of alignment and partition of the virtual manipulatives for supporting the students’ reasoning about the decimal-fraction relationship. Additionally, the results indicate that the students drew on the affordances of alignment and partition more frequently during decimal to fraction conversions than during fraction to decimal conversions.

The aim of this study is to investigate how the connection between fractions, decimals and percent are taught in grade 4-6 with more focuson the fractions. The empirical data was obtained by qualitative methods comprising interviews with four mathematic elementary school teachers, in addition to two observations with two classrooms in grade 6. The data presented is from one school. The theoretical framework is based on Liping Ma profound understanding of fundamental mathematics and theories of subject didactic concepts of Kilborn, Löwing, Karlsson &amp; Kilborn and MacIntosh. The results of the interviews and observations show that the connection between fractions, decimals and percent is being taught without illuminating how the mentioned are connected. The aspect of fractions, which has been taught to show the relation between fractions and decimals, was division as metaphor. While there was no aspect of fractions has been taught to show the relation between it and percent except that a percent is a hundredth. Such as 40% is equal with 40/100. In addition, fractions has been taught by using visual aids, but never taught by using number line. In conclusion the connection between fractions, decimals and percent has not been related clearly with basic concept fractions.