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Euclid, the van Hiele levels, and the Geometer's Sketchpad
Title
Euclid, the van Hiele levels, and the Geometer's Sketchpad.
Creator
Thompson, Elpida, Florida Atlantic University, Yiu, Paul Y.
Abstract/Description
As an educator, my greatest concern is to provide my students with instruction that will raise their level of understanding in mathematics. For geometry in particular, the van Hiele Theory is a way to measure a student's level of geometric understanding. Geometry instruction that raises a student's van Hiele level can be enhanced with two important resources, the ancient text of Euclid's Elements a contemporary dynamic geometry software program like the Geometer's Sketchpad. Euclid's Elements...
Show moreAs an educator, my greatest concern is to provide my students with instruction that will raise their level of understanding in mathematics. For geometry in particular, the van Hiele Theory is a way to measure a student's level of geometric understanding. Geometry instruction that raises a student's van Hiele level can be enhanced with two important resources, the ancient text of Euclid's Elements a contemporary dynamic geometry software program like the Geometer's Sketchpad. Euclid's Elements can be read as a book of geometric constructions rather than a list of theorems neatly arranged in logical order. The Geometer's Sketchpad is a convenient and efficient tool for geometric constructions. It is only natural to incorporate these two resources in geometry instruction. The logical structure of Euclid's Elements is intimidating to most learners, but teaching and learning need not be pursued logically linearly. This thesis is an attempt to incorporate some of the important constructions in Euclid's Elements with Geometer's Sketchpad, through the design of instruction modules in geometric constructions, to help students better understand geometry, and to improve their van Hiele level of understanding of geometry.
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Date Issued
2006
PURL
http://purl.flvc.org/fcla/dt/13366
Subject Headings
Geometry--Study and teaching (Secondary), Mathematics--Study and teaching--Technological innovations
Format
Document (PDF)
Teaching students with learning disabilities to solve word-problems: A comparison of a cognitive strategy and a traditional textbook method
Title
Teaching students with learning disabilities to solve word-problems: A comparison of a cognitive strategy and a traditional textbook method.
Creator
Lambert, Monica Ann., Florida Atlantic University, Taylor, Ronald L.
Abstract/Description
The current emphasis in mathematics curricula is placed on mathematical applications to real-life word-problem solving. Therefore, it is critical that all secondary students receive instruction in problem solving. Although many mathematics textbooks provide steps for students to follow when solving word-problems they do not meet the needs of all students, especially those with learning disabilities (LD). Students with LD lack knowledge in cognitive and metacognitive strategies, although they...
Show moreThe current emphasis in mathematics curricula is placed on mathematical applications to real-life word-problem solving. Therefore, it is critical that all secondary students receive instruction in problem solving. Although many mathematics textbooks provide steps for students to follow when solving word-problems they do not meet the needs of all students, especially those with learning disabilities (LD). Students with LD lack knowledge in cognitive and metacognitive strategies, although they are able to use these strategies when taught. The purpose of this study was to compare the effectiveness of a cognitive problem solving strategy and a traditional textbook method in solving three-step word-problems consisting of whole numbers, decimals, fractions, and percents. Four teachers who taught two Specific Learning Disabilities (SLD) math classes volunteered to participate in the study. Each teacher taught one of his/her math classes the cognitive strategy and the other class the textbook method. A total of 76 students from grades 9 through 12 who attended a part-time SLD math class were used as subjects. The two groups were taught through direct instruction with scripted lessons. The cognitive strategy group was taught an eight-step strategy that included self-talking and self-questioning. The textbook method group was taught a traditional textbook method which consisted of a four-step plan. Treatment for both groups included a pretest, describing and modeling the strategy or method, verbally rehearsing the cognitive strategy or textbook method, practice solving word-problems, and a posttest of the three-step word-problems. The results indicated that there were no significant differences between the cognitive strategy and textbook method. However, the observed power was not sufficient to determine if there was or was not a treatment effect. Informal error analyses indicated subjects did perform better after direct instruction in solving word-problems. Although subjects were attempting to solve more problems, however, other types of errors were being made, such as choosing and using the wrong operation. This indicates students may need to be taught a strategy on how to choose the correct operation to solve word-problems.
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Date Issued
1996
PURL
http://purl.flvc.org/fcla/dt/12470
Subject Headings
Learning disabled--Education--Mathematics, Learning disabilities, Mathematics--Study and teaching (Secondary), Cognition in children
Format
Document (PDF)
Some Construction Problems Related to the Incircle of a Triangle
Title
Some Construction Problems Related to the Incircle of a Triangle.
Creator
Bell, Amy B., Yiu, Paul Y., Florida Atlantic University
Abstract/Description
This thesis explores several construction problems related to the incircle of a triangle. Firstly, as a generalization of a theorem of D. W. Hansen, we find two quadruples of quantities related to a triangle which have equal sums and equal sums of squares. We also study the construction problems of triangles with centroid on the incircle, and those with a specified cevian - a median, an angle bisector, or an altitude- bisected by the incircle. Detailed analysis leads to designs of animation...
Show moreThis thesis explores several construction problems related to the incircle of a triangle. Firstly, as a generalization of a theorem of D. W. Hansen, we find two quadruples of quantities related to a triangle which have equal sums and equal sums of squares. We also study the construction problems of triangles with centroid on the incircle, and those with a specified cevian - a median, an angle bisector, or an altitude- bisected by the incircle. Detailed analysis leads to designs of animation pictures using the dynamic software Geometer's Sketchpad.
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Date Issued
2006
PURL
http://purl.flvc.org/fau/fd/FA00000725
Subject Headings
Geometry--Problems, exercises, etc, Geometry--Study and teaching (Secondary), Mathematics--Study and teaching--Technological innovations
Format
Document (PDF)
Understanding how national board certified secondary mathematics teachers integrate academic and social knowledge of students into their practice
Title
Understanding how national board certified secondary mathematics teachers integrate academic and social knowledge of students into their practice.
Creator
Cook, Karen, Burnaford, Gail, Florida Atlantic University, College of Education, Department of Curriculum, Culture, and Educational Inquiry
Abstract/Description
This qualitative case study investigated how six National Board Certified secondary mathematics teachers integrate knowledge of students into their practice to create socio- academic spaces for learning. Individual audiotaped interviews were utilized to generate data about what knowledge these teachers had of their students, how they gathered this knowledge, and how this knowledge of students influenced their decisions related to curriculum and instruction. The data were used to form an...
Show moreThis qualitative case study investigated how six National Board Certified secondary mathematics teachers integrate knowledge of students into their practice to create socio- academic spaces for learning. Individual audiotaped interviews were utilized to generate data about what knowledge these teachers had of their students, how they gathered this knowledge, and how this knowledge of students influenced their decisions related to curriculum and instruction. The data were used to form an understanding of the nature and function of the socio- academic spaces that teachers create in planning for and delivering instruction. The study revealed that as teachers interact independently with the curriculum, they create spaces for analysis and reflection. In addition, as they interact with their students around the curriculum, they create spaces for their students to practice, to make connections, to communicate, and to apply and experience math.
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Date Issued
2015
PURL
http://purl.flvc.org/fau/fd/FA00004357, http://purl.flvc.org/fau/fd/FA00004357
Subject Headings
Classroom environment, Curriculum planning, Education, Secondary, Educational psychology, Educational sociology, Mathematics -- Study and teaching (Secondary), National Board for Professional Teaching Standards (U.S.)
Format
Document (PDF)
Teacher collegiality and collaboration in exemplary high school math departments
Title
Teacher collegiality and collaboration in exemplary high school math departments.
Creator
Numeroff, Donna., Florida Atlantic University, Acker-Hocevar, Michele A.
Abstract/Description
Research maintains that teacher collegiality and collaboration are important for developing professional learning communities, and promoting leadership of teaching and learning. As we enter the 21st century, subject departments in secondary schools remain a common and important entity in the professional life of a teacher, yet scarce in educational research literature. Using qualitative methodology, three exemplary, collegial, yet demographically diverse high school math departments in the...
Show moreResearch maintains that teacher collegiality and collaboration are important for developing professional learning communities, and promoting leadership of teaching and learning. As we enter the 21st century, subject departments in secondary schools remain a common and important entity in the professional life of a teacher, yet scarce in educational research literature. Using qualitative methodology, three exemplary, collegial, yet demographically diverse high school math departments in the state of Florida were involved in this multi-site case study. The researcher collected data from interviews, observations, and documents. Sixty-one math teachers including department chairs were individually interviewed. These interviews were transcribed and coded for commonalities. Observations were recorded during teacher planning hours, department meetings, and teacher lunch times. Also, pertinent documents such as course syllabi, department mission statements, school mission statements, and school improvement plans were collected. All data were triangulated and analyzed, and findings support that collegial relationships impact teachers' work lives, which reduce uncertainty and stress; collegial departments are tightly structured democratic systems where distributed leadership increases instructional effectiveness and creates a familial environment; collaborative cultures affect student learning by emphasizing a fair and equitable education for all students improving parental involvement; and the department chair as instructional and managerial leader plays a major role as a change agent within the professional collegial community.
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Date Issued
2005
PURL
http://purl.flvc.org/fcla/dt/12128
Subject Headings
Teachers--Professional relationships, Educational leadership--Case studies, Classroom management--Florida--Case studies, Mathematics--Study and teaching (Secondary)
Format
Document (PDF)
The Effectiveness Of The National Board Certification As It Relates To The Advanced Placement Calculus AB Exam
Title
The Effectiveness Of The National Board Certification As It Relates To The Advanced Placement Calculus AB Exam.
Creator
Antunez, Fernando Oscar, Furner, Joseph M., Florida Atlantic University, College of Education, Department of Curriculum, Culture, and Educational Inquiry
Abstract/Description
This study compared data related to National Board Certification (NBC) of mathematics teachers in a South Florida school district. Data included 1,162 student scores on the 2014 AP Calculus AB exam, student gender, student grade level, and eligibility for free or reduced price lunch (FRL) status. Teachers completed the Standards' Beliefs Instrument (SBI) (Zollman & Mason, 1992) to determine alignment of their beliefs with the National Council of Teachers of Mathematics (NCTM) standards....
Show moreThis study compared data related to National Board Certification (NBC) of mathematics teachers in a South Florida school district. Data included 1,162 student scores on the 2014 AP Calculus AB exam, student gender, student grade level, and eligibility for free or reduced price lunch (FRL) status. Teachers completed the Standards' Beliefs Instrument (SBI) (Zollman & Mason, 1992) to determine alignment of their beliefs with the National Council of Teachers of Mathematics (NCTM) standards. Interviews were conducted with five NBC mathematics teachers to understand how they incorporate best mathematics teaching practices in their daily instruction. A t-test analysis revealed that students taught by NBC teachers scored significantly higher (M = 3.70) on the AP Calculus AB Exam than those taught by non-NBCTs (M = 2.74); Cohen's d (.6429) indicated a moderately large effect size. No causation is to be implied; various confounding factors may also contribute to the variance in student scores. Three factorial ANOVA tests were performed to test interaction effects. Two significant interaction effects were detected: (1) NBCT status and student grade level; and (2) NBCT status and student FRL (free and reduced price lunch) status. No significant interaction was found between NBCT status and student gender. With a reliability estimate using Cronbach's alpha, a second t-test was conducted. A statistically significant difference was found regarding the mean scores of NBCTs and non-NBCTs regarding their beliefs according to the vision of the NCTM. NBCTs generally have practices that align more with the NCTM mathematics teaching standards. Interviews with five NBC teachers of AP Calculus provided rich qualitative descriptions of their teaching philosophies, approaches, and best practices contributing to student success. The results of this study reinforce evidence from previous research that the process of obtaining the NBC contributes to a teacher's professional expertise and is related to student success; however, since there may be other confounding factors related to teachers, students, and their schools, the NBC cannot be considered the sole factor contributing to student success in AP coursework and exams.
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Date Issued
2015
PURL
http://purl.flvc.org/fau/fd/FA00004477, http://purl.flvc.org/fau/fd/FA00004477
Subject Headings
Achievement in education -- Florida, Advanced placement programs (Education), Calculus -- Examinations, questions, etc, Mathematics -- Study and teaching (Secondary), National Board for Professional Teaching Standards (U.S.), Teacher effectiveness -- Florida, Teachers -- Certification -- Florida
Format
Document (PDF)