This study examined the effects of using graphing calculators with a numerical approach designed by the researcher on students learning of limits and derivatives in an Applied Calculus course at a community college. The purposes of this study were to investigate the following: (1) students achievement in solving limit problems (Skills, Concepts, and Applications) with a numerical approach compared to that of students who solved limit problems with a traditional approach (primarily an algebraic approach); and (2) students achievement in solving derivative problems (Skills, Concepts, and Applications) with a numerical approach compared to that of students who solved derivative problems with a traditional approach (primarily an algebraic approach). Students (n = 93) in all four daytime sections of an Applied Calculus course in a community college participated in the study during the spring 2005 semester. One of two MWF sections and one of two TR sections served as the treatment groups; the other two sections served as the control groups. Two instructors other than the researcher participated in the study. Instructor A taught one treatment group (a TR section) and one control group (a MWF section); instructor B taught one treatment group (a MWF section) and one control group (a TR section). Dependent variables were achievement to solve skill, concept, and application limit problems and skill, concept, and application derivative problems, measured by two teacher-made tests. A pretest administered on the first day of class determined that no significant difference existed between the groups on prerequisite algebra skills. Separate ANCOVA tests were conducted on the skill, concept, and application portions of each of the limit and derivative exams. Data analyses revealed the following: (1) there was no significant difference found on the skill portion of the limit topic (unit 1 exam) due to instruction or to instructor; (2) there was a significant difference found on the concept portion of the limit topic due to instruction and to instructor; (3) there was a significant difference found on the application portion of the limit topic due to instruction but not due to instructor; (4) the interaction effects between instructor and instruction were not significant on the skill, concept, and application portions of the limit topic; (5) there was a significant difference found on the skill portion of the derivative topic (unit 2 exam) due to instruction but not due to instructor; (6) there was a significant difference found on the concept portion of the derivative topic due to instruction and to instructor; (7) there was a significant difference found on the application portion of the derivative topic due to instruction but not due to instructor; and (8) the interaction effects between instructor and instruction were not significant on the skill, concept, and application portions of the derivative topic. All significant differences were in favor of the treatment group.

Social, political, and technological events of the past two decades have had considerable bearing on science education. While sociological studies of scientists at work have seriously questioned traditional histories of science, national and state educational systemic reform initiatives have been enacted, stressing standards and accountability. Recently, powerful instructional technologies have become part of the landscape of the classroom. One example, graphing calculator-based technology, has found its way from commercial and domestic applications into the pedagogy of science and math education. The purpose of this study was to investigate the culture of an "alternative" science classroom and how it functions with graphing calculator-based technology. Using ethnographic methods, a case study of one secondary, team-taught, Environmental/Physical Science (EPS) classroom was conducted. Nearly half of the 23 students were identified as students with special education needs. Over a four-month period, field data was gathered from written observations, videotaped interactions, audio taped interviews, and document analyses to determine how technology was used and what meaning it had for the participants. Analysis indicated that the technology helped to keep students from getting frustrated with handling data and graphs. In a relatively short period of time, students were able to gather data, produce graphs, and to use inscriptions in meaningful classroom discussions. In addition, teachers used the technology as a means to involve and motivate students to want to learn science. By employing pedagogical skills and by utilizing a technology that might not otherwise be readily available to these students, an environment of appreciation, trust, and respect was fostered. Further, the use of technology by these teachers served to expand students' social capital--the benefits that come from an individual's social contacts, social skills, and social resources. / Ph. D.

Graphing calculator programs have been used on high-stakes tests and teacher-created assessments at the secondary and college level for many years. These programs- are even used on college-placement tests such as the ACT. Beginning with the 2011-2012 school year, the Mississippi Department of Education (MDE) made the decision to no longer allow the use of graphing calculator applications and/or programs on the Subject Area Testing Program (SATP2) for Algebra I. Currently, limited research exists to address the influence of graphing calculator program use on high-stakes assessments. The programming capabilities of graphing calculators should not be ignored. Because of the 2011-2012 graphing calculator policy change, a unique opportunity exists in Mississippi to provide valuable information about this issue. Gaining insight about how the use of graphing calculator programs has affected assessment results in the past will give policy makers needed information for creating equitable assessment policies in the future. This research used a causal-comparative research design to determine the influence of the MDE’s decision to no longer allow the use of graphing calculator programs on Mississippi’s Algebra I SATP2. The research questions consider the influence of the policy change with regards to three groups: students, schools in general, and Title I schools in particular. A chi-square test for association was used to examine the student-level data associated with research questions one and two. This analysis examined students’ ability to pass and their performance level on the Algebra I SATP2. The results for both of the chi-square analyses indicated significant results. For research question three, a two-way mixed ANOVA was used to examine the influence of the policy change on Title I schools. For this analysis, Title I schools represent disadvantaged populations. The results indicated no interaction between graphing calculator program use and type of school, but did reveal a main effect for the school type.

The purpose of this study was to advance knowledge about the relationship between graphing calculator use and classroom norm development. An interpretive case study design incorporating qualitative and quantitative research methods was used to explore the question: What happens when an exemplary teacher uses graphing calculators in a college algebra class? The purposively selected participants were the teacher and eleven students of a Texas community college algebra course. All 29 classes of the 14-week spring 2006 semester were observed in their entirety by the researcher. The theoretical frameworks guiding the study were the affective representation system and the Multiple Representations Model of Learning and Teaching with the use of the Mathematics and Science Classroom Observation System for data collection, analysis, and profiling of classroom lessons. Originally developed for grades K-12, the use of the instrument was extended to college algebra. Triangulation of data sources using constant comparative and content analysis methods were used to support the three major findings: (1) The instructor's proactive orchestration of specialized instruction, support materials, and designed activities contributed to the establishment of graphing calculator use as an essential part of classroom norms and promoted students' independent use of the tool; (2) The dynamic and interactive features of the TI-84 Plus graphing calculator facilitated the delivery of instruction at high cognitive levels during student interactive activities providing access to, exploration of, and use of multiple representations for some mathematical concepts and solutions not easily attainable using traditional methods; and (3) Although the majority of students had never used a graphing calculator before the course, all students used the tool at appropriate times during instructional activities, self-reporting that their use of the calculator was generally beneficial for enhancing their understanding of lessons and supporting class interactions. Additionally, all students independently chose to use the calculator during major assessments and reported knowledgeable use of the tool to facilitate improved test performance. Replication of the study is limited because the norms developed in this case are unique to the teacher and students who negotiated their establishment. Suggestions are given regarding educational policies, reform practices, and research extensions.

This diploma thesis discusses the work with the graphing calculator TI- 92 Plus, its advantages and disadvantages for use in mathematics education. The aim of the thesis is to determine whether this tool will facilitate the work of students in solving problems, and if its contribution is so minimal, that is not worthy including work with him, which of course requires some knowledge of students in the teaching of mathematics. For this apparent effort is the aim to find the type of tasks, which is working with the graphing calculator faster, easier and above all better understand. One of the aims is also to introduce the reader into the connection of the graphing calculator to the PC, by which the owner obtains a wealth of other functions associated with an interactive environment that this creates - such as the ability to capture screen of the calculator, install other applications into memory of the calculator, backup and restore data, etc.

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 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 oneway analysis of variance (ANOVA). The results indicated that there was no significant difference between the two types of instruction on the students’ procedural knowledge, iii 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.