Thesis (Ph. D.)--Harvard University, 1970. / Includes bibliographical references (p. 286-319).

Thesis (Ph.D.)--Baylor University, 2009. / Includes bibliographical references (p. 66-68).

The purpose of this descriptive study was to investigate the availability and distribution of calculators and computers for the mathematics classes in public high schools across the State of Virginia; examine professional development activities used by teachers to prepare for the use of calculators and computers in the classroom; explore factors that may guide and influence mathematics teachers in the use of calculators and computers; examine the familiarity and degree of influence assigned by teachers to documents advocating technology use in mathematics education; determine in which SOL courses - Algebra I, Geometry, Algebra II, Math Analysis, Calculus, Discrete Mathematics, Probability & Statistics, and Computer Mathematics - calculators and computers are being used, as well as the frequency and type of usage; and explore the ways in which teachers have incorporated the use of calculators and computers into mathematics courses, as well as the problems overcome and successes which have resulted. The study surveyed the mathematics department heads from 80 public high schools from school divisions located throughout the State of Virginia through the use of a self-administered mail questionnaire. From these questionnaires, the data gathered about calculator and computer availability, factors influencing teachers' professional development, and actual usage in SOL courses were analyzed to provide a picture of the current state of technology use in the high school mathematics programs of these high schools. Results from this study indicate that: (1) Through funding provided by the State of Virginia, adequate quantities of graphing calculators and computers exist for use by students in mathematics classes; (2) the widespread use of graphing calculators in the classroom is being driven by the Standards of Learning for Virginia Public Schools; computer use is more limited, despite the availability of computers in classroom and lab settings; and (3) teachers are reported as wanting more professional development activities designed for incorporating calculator and computer use into the classroom, but have taken only limited advantage of existing opportunities, preferring to use self-training and school or division in-service activities to satisfy their needs. / Ed. D.

The purpose of this study was to investigate the effectiveness of the graphing calculator on the achievement, attitude toward mathematics, and confidence in learning mathematics of Algebra II students.

Kwan Wing Hon. / Thesis (M.B.A.)--Chinese University of Hong Kong. / Bibliography: leaves 128-129.

The thesis investigates the role a calculator can play in the developing number knowledge of three girls and three boys as part of their mathematics program, during their first two years at primary school. Random sampling was used initially to select six girls and six boys from the twenty-four children entering a 1993 prep class. These twelve children were interviewed on entrance to school and based on the performance of the twelve children on the initial interview, a girl and a boy were chosen from the higher, middle and lower achievers to take part in the full study. The class teachers involved were previously participants in the ‘Calculators in Primary Mathematics’ research program and were committed to the use of calculators in their mathematics program. A case study approach using qualitative methods within the activity theory framework is used to collect relevant data and information, an analysis of five interviews with each child and observations of the children in forty-one classroom lessons provides comprehensive data on the children's developing number knowledge during the two years. The analysis questionnaires establishes each teacher's perceptions of the children's number learning at the beginning and end of each year, compares teacher expectations with children's actual performance for the year and compares curriculum expectations with children's actual performance. A teacher interview established reasons for changes in teaching style; teacher expectations; children's number learning; and was used to confirm my research findings. An activity theory framework provides an appropriate means of co-coordinating perspectives within this research to enable a description of the child's number learning within a social environment. This framework allows for highlighting the mediation offered by the calculator supporting the children's number learning in the classroom. Levels of children's developing number knowledge reached when working with a calculator and as a result of calculator use are mapped against the levels recommended in ‘Mathematics in the National Curriculum’ (National Curriculum Council, December 1988), and the Curriculum and Standards Framework: Mathematics (Board of Studies 2000). Findings from this comparison illustrate that the six children's performance in number was enhanced when using a calculator and indicate that on-going development and understanding of number concepts occurred at levels of performance at least two years in advance of curriculum recommendations for the first two years of school.

There has been widespread interest in the potential impact of the graphics calculator on system wide 'high stakes' end of secondary school mathematics examinations. This thesis has focused on one aspect, the way in which examiners have gone about writing examination questions in a graphics calculator assumed environment. Two aspects of this issue have been investigated. The first concerns the types of questions that can be asked in a graphics calculator assumed environment and their frequency of use. The second addresses the level of skills assessed and whether with the introduction of the graphics calculator has been associated with an increase in difficulty as has been frequently suggested. A descriptive case study methodology was used with three examination boards, the Danish Ministry of Education, Victorian Curriculum and Assessment Authority and the International Baccalaureate Organization. Four distinct categories of questions were identified which differed according to the potential for the graphics calculator to contribute to the solution of the question and the freedom the student was then given to make use of this potential. While all examination boards made use of the full range of questions, the tendency was to under use questions in which required the use of the calculator for their solution. In respect to the level of skills assessed, it was found that both prior to and after the introduction of the graphics calculator, all three examination boards used question types that primarily tested the use of lower level mathematical skills. With exceptions, where graphics calculator active questions have been used, the tendency has been to continue to ask routine mechanistic questions. In this regard, there is no evidence of the introduction of the graphics calculator being associated with either lowering or raising of the level of the mathematical skills assessed. For all cases studied, the graphics calculator was introduced with minimal change to the curriculum and examination policies. The role of the graphics calculator in the enacted curriculum was left implicit. The resulting examinations were consistent with the stated policies. However, the inexperience of some examiners and a general policy of containment or minimal change enabled examiners to minimise the impact of the introduction of the graphics calculators on assessment.

The purpose of the study was to investigate students' learning of the function concept and the role of the graphing calculator in a College Algebra course. Differences between students with high symbolic manipulation skills. and students with low symbolic manipulation skills were also examined. On the basis of an algebraic skills test administered by the instructor (high/low) and students' academic majors (math & science, business, and liberal arts), 25 students from one College Algebra class were placed into six categories. To gather data on students' understanding of functions, a pretest and posttest were administered. The Function Test consisted of four identification questions given in each of the representations, three questions asking for the definition, an example, and a nonexample of functions, and 15 questions consisting of three problem situations given in the numerical, graphical, and symbolic representations. To gather data on the role of the graphing calculator, daily classroom observations were conducted. To verify students' responses and classroom observations, formal interviews with students and informal interviews with the instructor were conducted. Students' personal definition progressed towards the formal definition of functions. Yet, students had difficulties with the univalence requirement in three areas: (a) order of domain and range, (b) preference for simple algorithms, and (c) the restriction that functions were one-to-one. Compared to students with low symbolic manipulation skills, students with high symbolic manipulation skills were more flexible working between representations of functions. Half of the interviewed students with low symbolic manipulation skills perceived a single function given in numerical, graphical, and symbolic representations as separate entities. The graphing calculator played a role in all phases of the solution process. During the initial phases, students used calculators to develop a symbolic approach. The prime motivation for using graphing calculators during the solution-execution phase was to avoid careless errors. The most common use of graphing calculators was to check answers during the solution-monitoring phase. However, graphing calculators created difficulties for students who accepted graphs at face value. Interpreting the truncated graph shown by the calculator, students determined that exponential functions possessed a bounded domain because they did not explore the graph. / Graduation date: 2001

This paper is divided into two parts. The first part traces (in details providing proofs and examples) the history of the solutions of polynomial equations(of the first, second, third, and fourth degree) by radicals from Babylonian times (2000 B.C.) through 20th century. Also it is shown that there is no solution by radicals for the quintic (fifth degree) and higher degree equations. The second part of this thesis illustrates both numerical and graphical solutions of the quintic and higher degree polynomial equations using modern technology such as graphics calculators (TI-85, and HP-48G) and software packages (Matlab, Mathematica, and Maple). / Graduation date: 1995

The purpose of this study was to evaluate the effectiveness of a mathematics enrichment activity used to improve the mathematics performance of students relative to participation in the State Agricultural Mechanics Career Development Event (CDE) and in mandated assessments. The treatment group (13 schools, 43 students) participated in a mathematics enrichment activity situated in an agricultural mechanics context. The control group (16 schools, 56 students) did not participate in the enrichment activity. Both groups, as part of the CDE, were tested with a 100-question word problem examination, completed a individual skill and team activity, and completed a demographic instrument regarding participation in agricultural mechanics CDEs, scholastic performance, use of graphing calculators, enrollment in STEM, agricultural science, and fine arts courses, and other information. After the survey was conducted, schools were asked to provide TAKS exit scores on participating students. These scores were compared between schools and against statewide TAKS scores. Results of the study showed a significant improvement in scores on the individual written examination and teams scores for the agricultural mechanics CDE and on the TAKS exit level mathematics assessment. Mean written examination scores for the treatment group were 69.53; non-cooperators were 57.16. Mean total team scores for cooperating teams were 420.39; non-cooperators had a mean score of 368.13. Mean TAKS exit level mathematics scores for cooperators were 2336.78; non-cooperators had a mean TAKS exit level score of 2331.77. Participation in the enrichment activity improved both CDE and mathematics achievement scores.