Thesis (M. Ed.), Memorial University of Newfoundland, 1998. / Restricted until November1999. Includes bibliographical references.

This paper describes a computer model for running individual retirement portfolios over different historical periods to see the actual retirement incomes they would have provided. Such an approach is much more sophisticated and insightful than simply applying an annuity formula to retirement assets and assuming a real arbitrary rate of return.

Arbetets syfte var att undersöka hur lärare använder miniräknaren i sin undervisning men även hur eleverna använder den och om det finns några skillnader i attityder och användning mellan elever och lärare. Undersökningen gick också ut på att se om användandet har ökat eller minskat i gymnasieskolan. Arbetet syftade också till att undersöka om det finns några skillnader mellan tjejer och killars attityder till miniräknaren och tjejer och killars användning av den. En lärarenkät och en elevenkät delades ut på fem olika skolor och dessa låg till grund för undersökningen. Resultatet pekar på en ökad användning, en mer positiv attityd till miniräknaren hos gymnasielärarna och att alla lärare, i någon form, tar hänsyn till miniräknaren vid prov. Arbetet visar även att lärare oftast ser miniräknaren som ett pedagogiskt verktyg medan eleverna ser den mer som ett redskap för att effektivisera framförallt huvudräkning och tabellhantering. Det visar också på att killar har en mer positiv attityd till miniräknaren än vad tjejer har, tjejer är mer oroliga för att deras huvudräkningsförmåga ska försämras om de använder miniräknaren för ofta, detta är också något som flera lärare är oroliga för. Samtidigt är det fler killar än tjejer som inte använder miniräknare. / The main purpose was to investigate how teachers use calculators in their education but also to investigate how students use them and if it exists any differences concerning attitudes and usage between students and teachers. Another purpose was to see if the usage of calculators have increased or decreased and to see if there are any differences in gender. Different surveys were used, one for teachers and one for students at five different schools. The results suggested an increased usage, a more positive attitude towards calculators among the teachers and that every teacher uses calculators in some form when the construct tests. Another results shows that teachers seem to use calculators as a pedagogic tool but the students use them to handle tables more afficient. The work also shows that boys has a more positive attitude towards calculators than girls, girls are more worried that they will loose their ability to count using their head. It shows that this is also something the teachers are concerned about. There is also a lot more boys than girls that dont own a calculator.

The objective of this thesis is to develop and implement a power systems analysis package for use on minicomputers and programmable calculators. Algorithms for four different load flow techniques are developed and tested on the HP9830A programmable calculator. The transient stability analysis problem is reviewed, with special attention being given to the solution of the system performance equations by either the bus impedance matrix approach or the bus admittance matrix approach. Also attention is focused on the solution of the machine swing equations by the state transition method and by the technique of fourth-order Runge-Kutta. Comparisons are made between the different load flow methods to possibly determine the 'best' method to be used in the analysis package. Comparisons are also made between the methods of solving the swing equations in order to select a preferred technique for use in the stability program. / Master of Science

Thesis (M. Ed.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 132-138).

Thesis (M.Ed.)--University of Hong Kong, 1996. / Includes bibliographical references (leaves 132-138). Also available in print.

This study analyzed the eighth grade mathematics portion of the spring 2004 Maine Educational Assessment (MEA) achievement test and the survey questions that were also administered. The analysis was on a school-wide level (n = 182). The two survey questions used were: “Which statement best describes the use of calculators in your mathematics classes?” and "Which statement best describes how you use your laptop in mathematics class: getting data from the Web, finding mathematics problems online, creating graphs?" Correlational analysis, partial correlation, and regression were used to determine if there was any association between calculator usage, laptop usage, and mathematics achievement for girls and for boys in the first state-wide group of students to have one-to-one laptops in Maine. Calculator usage was found to be positively associated with mathematics achievement for both girls (partial correlation coefficient of .189 (p = .011)) and for boys (partial correlation coefficient of .193 (p = .010)) even after controlling for school size and socio-economic status. Though no significant association between laptop usage and mathematics achievement for either girls or boys was found, this may be more a reflection on the survey question being a weak measure than the usage of laptops. In a post-hoc analysis of findings, schools were rank ordered based on the average mathematics achievement score regardless of gender; the top 25% (n = 45) and the lower 25% (n = 45) of the schools were evaluated. In the top 25%, there was no statistically significant difference between school-wide girls' and boys' mathematics achievement scores. However, in the lower 25% of the schools, there was a statistically significant difference (p = .01) between the school-wide average of girls' and boys' mathematics achievement scores, with the girls' score being 1.49 points higher (p = .01, d = .447) than the boys'. Recommendations for refinement of MEA survey questions as well as future studies are provided.

This mixed-method study investigated the impact of graphing calculator use on high school calculus students' reasoning skills through calculus problems when applying to concepts of the definite integral and its applications. The study provides an investigation of the effects on reasoning when graphing calculators are used, since it is proposed that, through reasoning, conceptual understanding can be achieved. Three research questions were used to guide the study: (1) Does the use of the graphing calculator improve high school calculus students' reasoning ability in calculus problems applying the definite integral? (2) In what specific areas of reasoning does use of the graphing calculator seem to be most and least effective? and (3) To what extent can students who have used the graphing calculator demonstrate ability to solve problems using pencil and paper methods? The study included a quantitative, quasi-experimental component and a qualitative component. Results of the quantitative and qualitative analysis indicate that (1) graphing calculators had a positive impact upon students' reasoning skills (2) graphing calculators were most effective in the areas of initiating a strategy and monitoring progress (3) students' reasoning skills were most improved when graphing calculators were used together with the analytic approach during both instruction and testing and (4) students who used the graphing calculator performed equally as well in all elements of reasoning as those who used pencil and paper to solve problems.

The concept of function is one of the essential topics in the teaching and learning of secondary mathematics because of the central and unifying role it plays within secondary and college level mathematics. Organizations, such as the National Council of Teachers of Mathematics, suggest students should be able to make connections across multiple representations of mathematical functions by the time they complete high school. Despite the prominent role functions play in secondary mathematics curriculum, students continue to struggle with the complex notion of functions and especially have difficulty using the different representations that are inherent to functions (algebraic, graphical and tabular). Technology is often considered an effective tool in raising student achievement, especially in learning functions where the different representations of a graphing calculator are analogous to the different representations of a function. Opportunity to learn is another important consideration when examining achievement and is generally considered one of, if not the most important, factor in student achievement. Opportunity to learn, or the measure of to what extent students have had an opportunity to learn or review a concept, is often measured with self-reports of content coverage. This study examined the relationship between opportunity to learn, students'; use of graphing calculators, and achievement within a curriculum that supports integrated use of technology and focuses on conceptual understanding of mathematical concepts. The research questions focused on what opportunities students had to learn functions from the enacted curriculum, what calculator strategies students used when solving function problems, how both opportunity to learn and calculator strategies influenced student achievement, and what relationships exist between opportunity to learn, use of calculator strategies, and student achievement. This study is an in-depth secondary analysis of a portion of data collected as part of the evaluation study of Precalculus and Discrete Mathematics (Third Edition, Field-Trial Version) developed by the University of Chicago School Mathematics Project. Participants in this study (n = 271) came from six schools, seven teachers, and 14 classes. Instruments in this study include two pretests (one with technology and one without) and three posttests (two with technology and one without) and a calculator usage survey for one posttest. In addition to five student assessments, teachers completed opportunity-to-learn surveys for the posttests and chapter evaluations forms on which they indicated the lessons taught and the homework problems assigned from the textbook. Some students (n = 151) had access to graphing calculators equipped with computer algebra systems (CAS) while others (n = 120) had access to graphing calculators. Students had multiple opportunities to learn functions as measured by lessons taught, homework assigned, and posttest items teachers reported as having taught or reviewed the content necessary for students to correctly answer the items. Overall, students showed a positive increase in achievement between the pretests and posttests. In general, achievement was positively correlated to OTL Lessons, negatively correlated to OTL Homework, and had no correlation to OTL Posttests when controlling for prior knowledge. Results indicate students appear to be, for the most part, making wise choices about when and how to use graphing calculators to solve function items. Students prefer the graphical representation and are rarely using CAS features or tables, even when they are the best choices for solving a problem. Results from hierarchical linear models (HLM) show use of strategies (beta = 0.96), access to CAS (beta = 5.12), and OTL lessons (beta = 0.75) all had significant and positive impacts on student achievement for one of the posttests, when controlling for prior knowledge. Results from path analyses also indicated use of strategies had a direct and positive effect (beta =0 .14) on student achievement but showed access to CAS had a negative indirect effect (beta = -0.64) on student achievement for the same posttest mitigated through OTL Lessons (beta = 0.30). The results of this study have implications for both researchers and mathematics educators who seek to understand ways in which teachers can increase students'; understanding of functions and student achievement. The relationship between the use of technology and student achievement in relation to opportunity to learn is complex, but use of calculator strategies appears to have a positive effect on students' opportunity to learn functions and student achievement when used in a curriculum that focuses on conceptual understanding and integrates technology.

The complete solution of real/life problems starts with the specification of the problem, its expression using mathematical concepts, solving it using a mathematical apparatus and interpreting its results using the terminology of the original problem area. In this four-stage process, graphic calculators can be efficiently used for speeding up its third (“purely mathematical”) stage. The application of ICT will free the teachers’ hands and allow them to concentrate on the pre-solution and post-solution relationships between the problem and its mathematical classification, representation, and meaning. During our 60-minute hands-on workshop, this principle will be demonstrated on examples from financial mathematics and other real-life problems using CASIO ClassPad. The workshop participants can play the role of learners. They are also invited to discuss and express their opinions on even more effective exploitation of this flexible tool. No previous experience with CASIO ClassPad is needed.