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This study compared two representations for teaching fraction equivalence. It traced the implications of both representations on the student’s comprehension of fractions as well as their ability to perform operations with fractions. The participants in the study included 65 sixth grade students in three extant classrooms. Two classes were instructed using the textbook representation while the third class received instruction using a representation presented by Van de Walle and recommended by the National Council for Teaching Mathematics. Data were collected from pre-tests, post-tests, student work samples, field notes and a semi-structured interview. Qualitative analyses were used to analyze the data. Items were coded for procedural and conceptual understanding and categorized into levels of proficiency. Additionally, items involving operations with fractions were coded for error patterns. Conclusions were drawn about how the different representations affected student comprehension and faculty with fractions.

This research study is an investigation that describes how intermediate mathematics teachers use laptop technology in their classrooms and the influence of this technology on mathematics teaching and learning using the framework of the Ten Dimensions of Mathematics Education (McDougall, 2004). This study was a qualitative analysis of the experiences of six teachers, as well as the classroom environments they created with the use of technology. Data were gathered using a variety of methods including observation, field notes, interviews, and surveys. Previous research suggests that mathematics teachers have not used laptops frequently, and when they are used, they are used in traditional ways. This study shows that there is potential for mathematics teachers to be effective implementers of laptop technology. The role of the teacher in the studied one-to-one laptop classrooms became one of a facilitator. These teachers were able to be more student-centred in their delivery of the mathematics curriculum. These teachers were also more creative and they were able to use multiple resources to demonstrate mathematical concepts. Because of the wide variety of resources available, these laptop classrooms were more exploratory in nature. These teachers faced barriers such as students being distracted and the extra time it took to plan lessons. The participants indicated that these barriers could be overcome by being patient with their students and by collaborating with their colleagues. Using the framework of the Ten Dimensions of Mathematics Education, it was found that the presence of a one-to-one laptop environment in these classrooms influenced mathematics teaching and learning in a few key areas. The teachers in this study perceived that meeting individual needs, increased use of manipulatives and technology, and appropriate use of assessment techniques were the aspects that changed the most when laptops were present in the classroom. One-to-one laptop technology can change the teaching and learning that takes place in schools. The researched classrooms became more student-centred, exploratory, and engaging for students. Thus, this study shows that the presence of laptop technology has the potential to move mathematics classrooms towards a more reform vision of teaching and learning.

This research study is an investigation that describes how intermediate mathematics teachers use laptop technology in their classrooms and the influence of this technology on mathematics teaching and learning using the framework of the Ten Dimensions of Mathematics Education (McDougall, 2004). This study was a qualitative analysis of the experiences of six teachers, as well as the classroom environments they created with the use of technology. Data were gathered using a variety of methods including observation, field notes, interviews, and surveys. Previous research suggests that mathematics teachers have not used laptops frequently, and when they are used, they are used in traditional ways. This study shows that there is potential for mathematics teachers to be effective implementers of laptop technology. The role of the teacher in the studied one-to-one laptop classrooms became one of a facilitator. These teachers were able to be more student-centred in their delivery of the mathematics curriculum. These teachers were also more creative and they were able to use multiple resources to demonstrate mathematical concepts. Because of the wide variety of resources available, these laptop classrooms were more exploratory in nature. These teachers faced barriers such as students being distracted and the extra time it took to plan lessons. The participants indicated that these barriers could be overcome by being patient with their students and by collaborating with their colleagues. Using the framework of the Ten Dimensions of Mathematics Education, it was found that the presence of a one-to-one laptop environment in these classrooms influenced mathematics teaching and learning in a few key areas. The teachers in this study perceived that meeting individual needs, increased use of manipulatives and technology, and appropriate use of assessment techniques were the aspects that changed the most when laptops were present in the classroom. One-to-one laptop technology can change the teaching and learning that takes place in schools. The researched classrooms became more student-centred, exploratory, and engaging for students. Thus, this study shows that the presence of laptop technology has the potential to move mathematics classrooms towards a more reform vision of teaching and learning.

Research paper (M.A.) -- Cardinal Stritch College -- Milwaukee, 1980. / A research paper submitted in partial fulfillment of the requirements for the degree of Master of Arts in Education (Special Education). Includes bibliographical references (p.40-43).

While exploring unfamiliar concepts and striving to grasp higher level mathematics, secondary and postsecondary mathematics students often ask, “When will we ever use this?” Although this question typically stems from students’ frustration, skepticism, and confusion, the question has great potential for teachable moments. Mathematics has countless applications in people’s daily lives, but the common person often fails to recognize this; those who realize the worldly importance of applicable mathematics often cannot provide specific examples nor understand the rigorous mathematics involved. It is important for mathematics teachers to have a conceptual understanding of the subject, and to be able to provide specific examples of applicable mathematics to students. Although the limit of applicable mathematics examples is infinite, a few cases are explored in this report. / text

Thesis (M. Ed(Curriculum studies)--University of Pretoria, 2004. / Includes bibliographical references.

Thesis (M. Ed.)--University of Hong Kong, 1980. / Includes bibliographical references (leaf 143-144).

Thesis (M.Ed.)--University of Hong Kong, 1980. / Includes bibliographical references (leaf 143-144). Also available in print.

This exploratory descriptive case study aimed to identify key issues in the transformation of mathematics teaching in elementary schools. This study told the story of what happened to sixteen elementary teachers who embarked on a quest to improve their mathematics teaching by participating in at least two in-depth professional development experiences over an interval of three years. It traced their ideas about how and why to improve instruction, identified their challenges with prevailing school organizational conditions, and reported perceived changes that were made in their teaching. The research data, comprised of quotations from teachers' writing while they were engaged in professional development experiences at SummerMath for Teachers of Mt. Holyoke College and the researcher's notes from interviews, formed the data for analysis to answer four interrelated research questions: (1) What changes in instruction do selected elementary teachers of mathematics report that they made as a result of participating in professional development for improving the teaching of mathematics? (2) What do selected elementary teachers of mathematics report are the reasons for the changes they made in instruction? (3) What changes in instruction do selected elementary teachers of mathematics report that they regard as most effective for improving student learning? (4) What organizational conditions in their local elementary schools do selected elementary teachers of mathematics report helped or hindered their changes in instruction? The major findings based on the collected data were summarized and presented according to the four research questions that guided this study. The major findings related to changes in instruction fell under five prominent categories: increased emphasis on student thinking and understanding, increase in student-centered activities, changes in classroom discourse, increase in conceptually-based mathematics content, and a shift in the teacher's role from an authoritarian model of instruction to one that is student-centered. Findings from this study suggested some recommendations for educational practice for institutions preparing elementary teachers of mathematics, for in-service teacher professional development programs, and for school policies and organizational structures. One primary recommendation involved engaging pre- and in-service teachers in revisiting the mathematics content that they currently teach or will teach within an inquiry-based teaching and learning environment so that they might draw their own conclusions as to the implications for teaching mathematics.