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FOSTERING TEACHER'S CONCEPTUAL UNDERSTANDING OF ORDERING, ADDING, AND SUBTRACTING FRACTIONS THROUGH SCHOOL-BASED PROFESSIONAL DEVELOPMENT
Title
FOSTERING TEACHER'S CONCEPTUAL UNDERSTANDING OF ORDERING, ADDING, AND SUBTRACTING FRACTIONS THROUGH SCHOOL-BASED PROFESSIONAL DEVELOPMENT.
Creator
Maguhn , Jessica, Dixon , Juli, University of Central Florida
Abstract / Description
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...
Show moreIn 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.
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Date Issued
2009
Identifier
CFE0002608, ucf:48259
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0002608
EFFECTS OF DISCUSSION AND WRITING ON STUDENT UNDERSTANDING OF MATHEMATICS CONCEPTS
Title
EFFECTS OF DISCUSSION AND WRITING ON STUDENT UNDERSTANDING OF MATHEMATICS CONCEPTS.
Creator
Roicki, Joseph, Ortiz, Enrique, University of Central Florida
Abstract / Description
For this action research project, I wanted to examine my practice of teaching mathematics. Specifically, I encouraged students to improve their communication skills during my math class through daily discussion and writing tasks. After establishing a class set of sociomathematical norms, the students solved problems provided by the Every Day Counts: Calendar Math program and used verbal and written formats to describe their problem solving methods and reasons. My study showed the effects of...
Show moreFor this action research project, I wanted to examine my practice of teaching mathematics. Specifically, I encouraged students to improve their communication skills during my math class through daily discussion and writing tasks. After establishing a class set of sociomathematical norms, the students solved problems provided by the Every Day Counts: Calendar Math program and used verbal and written formats to describe their problem solving methods and reasons. My study showed the effects of using discussion and writing to help students develop their conceptual understanding of mathematical ideas. Focus was placed on the quality of daily discussions and written tasks both at the beginning of the study and continually as the study progressed. Through daily discussions, monthly written assessments, and student interviews, the study helped to determine the importance of developing students' mathematical communication skills and building conceptual understanding of mathematical ideas.
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Date Issued
2008
Identifier
CFE0002026, ucf:47627
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0002026
Secondary and Postsecondary Calculus Instructors' Expectations of Student Knowledge of Functions: A Multiple-case Study
Title
Secondary and Postsecondary Calculus Instructors' Expectations of Student Knowledge of Functions: A Multiple-case Study.
Creator
Avila, Cheryl, Ortiz, Enrique, Dixon, Juli, Hynes, Michael, Andreasen, Janet, Mohapatra, Ram, University of Central Florida
Abstract / Description
This multiple-case study examines the explicit and implicit assumptions of six veteran calculus instructors from three types of educational institutions, comparing and contrasting their views on the iteration of conceptual understanding and procedural fluency of pre-calculus topics. There were three components to the research data recording process. The first component was a written survey, the second component was a (")think-aloud(") activity of the instructors analyzing the results of a...
Show moreThis multiple-case study examines the explicit and implicit assumptions of six veteran calculus instructors from three types of educational institutions, comparing and contrasting their views on the iteration of conceptual understanding and procedural fluency of pre-calculus topics. There were three components to the research data recording process. The first component was a written survey, the second component was a (")think-aloud(") activity of the instructors analyzing the results of a function diagnostic instrument administered to a calculus class, and for the third component, the instructors responded to two quotations. As a result of this activity, themes were found between and among instructors at the three types of educational institutions related to their expectations of their incoming students' prior knowledge of pre-calculus topics related to functions. Differences between instructors of the three types of educational institutions included two identifiable areas: (1) the teachers' expectations of their incoming students and (2) the methods for planning instruction. In spite of these differences, the veteran instructors were in agreement with other studies' findings that an iterative approach to conceptual understanding and procedural fluency are necessary for student understanding of pre-calculus concepts.
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Date Issued
2013
Identifier
CFE0004809, ucf:49758
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004809
AN ACTION RESEARCH STUDY INVOLVING FIFTH-GRADE STUDENTS LEARNING FRACTIONS THROUGH A SITUATIVE PERSPECTIVE WITH STORY PROBLEMS
Title
AN ACTION RESEARCH STUDY INVOLVING FIFTH-GRADE STUDENTS LEARNING FRACTIONS THROUGH A SITUATIVE PERSPECTIVE WITH STORY PROBLEMS.
Creator
Allen, Colleen, Dixon, Juli, University of Central Florida
Abstract / Description
ABSTRACT The purpose of this action research study was to investigate the affects of teaching through a situative perspective with story problems on students' understanding of fraction concepts and operations in my fifth-grade mathematics classroom. Students participated in twelve weeks of instruction. Data was collected in the form of pre and post tests, audiotaped and videotaped recordings of instructional sessions, and student work samples. Data analysis revealed that my students...
Show moreABSTRACT The purpose of this action research study was to investigate the affects of teaching through a situative perspective with story problems on students' understanding of fraction concepts and operations in my fifth-grade mathematics classroom. Students participated in twelve weeks of instruction. Data was collected in the form of pre and post tests, audiotaped and videotaped recordings of instructional sessions, and student work samples. Data analysis revealed that my students constructed their own knowledge about various fraction concepts and operations because students engaged in discussions, after solving story problems, that developed, extended and restructured their knowledge. One example of this occurred after students had solved an equal-sharing problem. Two students came up with different answers and another student explained why both answers were equivalent. Student work samples and post test results indicated that the one student's explanation was understood, adopted and extended by all the students in my class. The data also revealed that students' pictures typically represented the context and action of the story problems. For example, subtraction problems dealing with length were usually represented by number lines or horizontal rectangles with crossed-out markings to show the subtraction operation. Throughout this research study, I discovered that my students were capable of learning from each other and solving problems for which they have no preconceived algorithm. I also learned that analyzing students' work and listening to their discussions in ways that focused on their thinking, not their answers, provided me with information about what my students were grasping and not grasping.
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Date Issued
2005
Identifier
CFE0000538, ucf:46423
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0000538
The Impact of using a Computer Algebra System in High School Calculus on High Performing Students' Conceptual and Procedural Understanding
Title
The Impact of using a Computer Algebra System in High School Calculus on High Performing Students' Conceptual and Procedural Understanding.
Creator
Bawatneh, Zyad, Haciomeroglu, Erhan, Dixon, Juli, Ortiz, Enrique, Saleh, Suha, University of Central Florida
Abstract / Description
Recently, there has been an increasing interest in high school mathematics education, especially in the teaching and learning of calculus. For example, studies conducted by Bressoud (2010); Judson and Nishimori (2005); Koh and Divaharan (2011); and St. Jarre (2008) all looked at how to improve the understanding of calculus students and what roles the educator must take to ensure that their students are successful. The purpose of this study was to determine if there was a significant...
Show moreRecently, there has been an increasing interest in high school mathematics education, especially in the teaching and learning of calculus. For example, studies conducted by Bressoud (2010); Judson and Nishimori (2005); Koh and Divaharan (2011); and St. Jarre (2008) all looked at how to improve the understanding of calculus students and what roles the educator must take to ensure that their students are successful. The purpose of this study was to determine if there was a significant difference between instruction using computer algebra system (CAS) compared to instruction using the graphing calculator in high school calculus on students' conceptual and procedural understanding. This study explored and compared two different types of instruction based on the use of two different types of technology, CAS and graphing calculator. The total population for this study consisted of 333 students. There were 187 students classified as using the graphing calculator and 146 students classified as using CAS. The data for this study were collected from four Advanced Placement (AP) calculus AB courses from high schools in Florida. The study used observations and two sets of calculus tasks in order to gather data. The research questions for this study looked at comparing the grades of students categorized based on the type of instruction received during the learning of calculus. The statistical procedure that was used was a simple one-way analysis of variance (ANOVA). The results indicated that there was no significant difference between the two types of instruction on the students' procedural knowledge, however, there was statistical significance on the students' conceptual understanding in favor of the CAS students. The study introduces a framework on how to obtain information about the effects of different types of instruction on students' understanding of calculus. The results of this study contribute in assisting teachers and future researchers on how to analyze student work in order to obtain information about the students' conceptual and procedural understanding of first semester calculus.
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Date Issued
2012
Identifier
CFE0004514, ucf:49278
Format
Document (PDF)
PURL
http://purl.flvc.org/ucf/fd/CFE0004514