The introduction of graphing calculators into senior secondary schools and mandating of their use in high stakes assessment makes student expertise in finding a complete graph of a function essential. This thesis investigated the cognitive, metacognitive, mathematical, and technological processes senior secondary students used in seeking a complete graph of a difficult cubic function. A pretest of function knowledge was administered to two mixed ability classes in their final two years of secondary school. Five pairs of experienced users of TI-83 or 82 graphing calculators from these classes were audio and videotaped solving a problem task. Protocols were constructed and subjected to intensive qualitative macroanalysis and microanalysis using tools developed by the researcher from Schoenfeld’s work. / The findings were: (1)all students demonstrated understanding of the local and global nature of functions and the synthesis of these in determining a complete graph; (2) a range of mathematical and graphing calculator knowledge was applied in seeking a global view of the function with their combined application being more efficient and effective; (3) an understanding of automatic range scaling features facilitated efficient finding of a global view; (4) all pairs demonstrated having a clear mental image of the function sought and the possible positions of the calculator output relative to this; (5) students were able to resolve situations involving unexpected views of the graph to determine a global view; (6) students displayed understanding of local linearity of a function; (7) when working in the graphical representation, students used the algebraic but not the numerical representation to facilitate and support their solution; (8) scale marks were used to produce more elegant solutions and facilitate identification of key function features to produce a sketch but some students misunderstood the effect of altering these; (9) pairs differed in the proportion of cognitive and metacognitive behaviours demonstrated with question asking during evaluation supporting decision making; (10) correct selection of xxi an extensive range of graphing calculator features and use of dedicated features facilitated efficient and accurate identification of coordinates of key function features.

Doctor of Philosophy / Curriculum and Instruction Programs / Jennifer M. Bay-Williams / Graphing calculators have been used in education since 1986, but there is no consensus as to how, or if, they should be used. The National Council of Teachers of Mathematics and the National Research Council promote their use, and ample research supports the positive benefits of their use, but not all teachers share this view. Also, rural schools face obstacles that may hinder them from implementing technology. The purpose of this study is to determine how graphing calculators are used in mathematics instruction of high schools in western Kansas, a rural region of the state. In addition to exploring the introduction level of graphing calculators, the frequency of their use, and classes in which they are used, this study also investigated the beliefs of high school mathematics teachers as related to teaching mathematics and the use of graphing calculators. Data were collected through surveys, interviews, and observations of classroom teaching. Results indicate that graphing calculators are allowed or required in almost all of the high schools of this region, and almost all teachers have had some experience using them in their classrooms. Student access to graphing calculators depends more on the level of mathematics taken in high school than on the high school attended; graphing calculator calculators are allowed or required more often in higher-level classes than in lower-level classes. Teachers believe that graphing calculators enhance student learning because of the visual representation that the calculators provide, but their teaching styles have not changed much because of graphing calculators. Teachers use graphing calculators as an extension of their existing teaching style. In addition, nearly all of the teachers who were observed and classified as non-rule-based based on their survey utilized primarily rule-based teaching methods.

Made available in DSpace on 2014-06-11T19:24:52Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-02-20Bitstream added on 2014-06-13T20:13:17Z : No. of bitstreams: 1 scucuglia_r_me_rcla.pdf: 2169829 bytes, checksum: 4fcea48798ae4ad65d55b601401c6e23 (MD5) / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / A informática vem gerando discussões sobre fundamentos da Matemática e reorganizando dinâmicas em Educação Matemática. Baseado nessa idéia, e em meu engajamento como pesquisador participante do GPIMEM, estruturei uma pesquisa onde discuto como Estudantes-com-Calculadoras-Gráficas investigam o Teorema Fundamental do Cálculo (TFC). Apoiado na perspectiva epistemológica Seres-Humanos-com-Mídias, que evidencia o papel das tecnologias no processo de produção de conhecimento, realizei experimentos de ensino com duplas de estudantes do primeiro ano da graduação em matemática, UNESP, Rio Claro, SP. A partir da análise de vídeos da primeira sessão de Experimentos de Ensino notei que a utilização de programas e comandos da Calculadora Gráfica TI-83 condicionou o pensamento das estudantes na investigação dos conceitos de Soma de Riemann e Integração (conceitos intrinsecamente inerentes ao TFC). Na segunda sessão, explorando exemplos de funções polinomiais com o comando de integração definida da Calculadora Gráfica, os coletivos pensantes formados por Estudantes-com-Calculadoras- Gráficas-Lápis-e-Papel estabeleceram conjecturas sobre o TFC. No processo de demonstração deste Teorema, foram utilizadas noções intuitivas e notações simplificadas, antes que fosse usada a simbologia padronizada pela Matemática Acadêmica. Essa abordagem possibilitou o engajamento gradativo das estudantes em discussões matemáticas dedutivas a partir dos resultados obtidos experimentalmente com as atividades propostas na pesquisa. / Information technology has been generating discussion regarding the foundations of mathematics, and reorganizing dynamics in mathematics education. Based on this idea, and on my engagement as a researcher participating in GPIMEM, I designed a study in which I discuss how students-with-graphing-calculators investigate the Fundamental Theorem of Calculus (FTC). Based on the epistemological perspective of humans-with-media, which emphasizes the role of technology in the process of knowledge production, I conducted teaching experiments with pairs of students enrolled in the first year of the mathematics program at the State University of São Paulo (UNESP), Rio Claro campus. Based on analysis of video-tapes of the first teaching experiments session, I noted that the use of programs and commands of the TI-83 graphing calculator conditioned the students thinking in the inquiry into the concepts Riemann Sums and Integration (concepts intrinsically inherent to the FTC). In the second session, exploring examples of polynomial functions with the definite integration command by the graphing calculator, the thinking collectives composed of students-withgraphing- calculators-paper-and-pencil established conjectures regarding the FTC. In the process of demonstrating this theorem, intuitive notions and simplified notations were used before using the standardized symbology of academic mathematics. This approach made it possible for the students to become gradually engaged in deductive mathematical discussions based on the results obtained experimentally through the activities proposed in the study.

Orientador: Marcelo de Carvalho Borba / Banca: Mônica E. Villarreal / Banca: Telma de S. Gracias / Resumo: A informática vem gerando discussões sobre fundamentos da Matemática e reorganizando dinâmicas em Educação Matemática. Baseado nessa idéia, e em meu engajamento como pesquisador participante do GPIMEM, estruturei uma pesquisa onde discuto como Estudantes-com-Calculadoras-Gráficas investigam o Teorema Fundamental do Cálculo (TFC). Apoiado na perspectiva epistemológica Seres-Humanos-com-Mídias, que evidencia o papel das tecnologias no processo de produção de conhecimento, realizei experimentos de ensino com duplas de estudantes do primeiro ano da graduação em matemática, UNESP, Rio Claro, SP. A partir da análise de vídeos da primeira sessão de Experimentos de Ensino notei que a utilização de programas e comandos da Calculadora Gráfica TI-83 condicionou o pensamento das estudantes na investigação dos conceitos de Soma de Riemann e Integração (conceitos intrinsecamente inerentes ao TFC). Na segunda sessão, explorando exemplos de funções polinomiais com o comando de integração definida da Calculadora Gráfica, os coletivos pensantes formados por Estudantes-com-Calculadoras- Gráficas-Lápis-e-Papel estabeleceram conjecturas sobre o TFC. No processo de demonstração deste Teorema, foram utilizadas noções intuitivas e notações simplificadas, antes que fosse usada a simbologia padronizada pela Matemática Acadêmica. Essa abordagem possibilitou o engajamento gradativo das estudantes em “discussões matemáticas dedutivas” a partir dos resultados obtidos “experimentalmente” com as atividades propostas na pesquisa. / Abstract: Information technology has been generating discussion regarding the foundations of mathematics, and reorganizing dynamics in mathematics education. Based on this idea, and on my engagement as a researcher participating in GPIMEM, I designed a study in which I discuss how students-with-graphing-calculators investigate the Fundamental Theorem of Calculus (FTC). Based on the epistemological perspective of humans-with-media, which emphasizes the role of technology in the process of knowledge production, I conducted teaching experiments with pairs of students enrolled in the first year of the mathematics program at the State University of São Paulo (UNESP), Rio Claro campus. Based on analysis of video-tapes of the first teaching experiments session, I noted that the use of programs and commands of the TI-83 graphing calculator conditioned the students’ thinking in the inquiry into the concepts Riemann Sums and Integration (concepts intrinsically inherent to the FTC). In the second session, exploring examples of polynomial functions with the definite integration command by the graphing calculator, the thinking collectives composed of students-withgraphing- calculators-paper-and-pencil established conjectures regarding the FTC. In the process of demonstrating this theorem, intuitive notions and simplified notations were used before using the standardized symbology of academic mathematics. This approach made it possible for the students to become gradually engaged in “deductive mathematical discussions” based on the results obtained “experimentally” through the activities proposed in the study. / Mestre

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.

The purpose of this study was to determine the extent to which six cognitive and attitudinal variables predicted pre-service elementary teachers' performance on line graphing. Predictors included Illinois teacher education basic skills sub-component scores in reading comprehension and mathematics, logical thinking performance scores, as well as measures of attitudes toward science, mathematics and graphing. This study also determined the strength of the relationship between each prospective predictor variable and the line graphing performance variable, as well as the extent to which measures of attitude towards science, mathematics and graphing mediated relationships between scores on mathematics, reading, logical thinking and line graphing. Ninety-four pre-service elementary education teachers enrolled in two different elementary science methods courses during the spring 2009 semester at Southern Illinois University Carbondale participated in this study. Each subject completed five different instruments designed to assess science, mathematics and graphing attitudes as well as logical thinking and graphing ability. Sixty subjects provided copies of primary basic skills score reports that listed subset scores for both reading comprehension and mathematics. The remaining scores were supplied by a faculty member who had access to a database from which the scores were drawn. Seven subjects, whose scores could not be found, were eliminated from final data analysis. Confirmatory factor analysis (CFA) was conducted in order to establish validity and reliability of the Questionnaire of Attitude Toward Line Graphs in Science (QALGS) instrument. CFA tested the statistical hypothesis that the five main factor structures within the Questionnaire of Attitude Toward Statistical Graphs (QASG) would be maintained in the revised QALGS. Stepwise Regression Analysis with backward elimination was conducted in order to generate a parsimonious and precise predictive model. This procedure allowed the researcher to explore the relationships among the affective and cognitive variables that were included in the regression analysis. The results for CFA indicated that the revised QALGS measure was sound in its psychometric properties when tested against the QASG. Reliability statistics indicated that the overall reliability for the 32 items in the QALGS was .90. The learning preferences construct had the lowest reliability (.67), while enjoyment (.89), confidence (.86) and usefulness (.77) constructs had moderate to high reliabilities. The first four measurement models fit the data well as indicated by the appropriate descriptive and statistical indices. However, the fifth measurement model did not fit the data well statistically, and only fit well with two descriptive indices. The results addressing the research question indicated that mathematical and logical thinking ability were significant predictors of line graph performance among the remaining group of variables. These predictors accounted for 41% of the total variability on the line graph performance variable. Partial correlation coefficients indicated that mathematics ability accounted for 20.5% of the variance on the line graphing performance variable when removing the effect of logical thinking. The logical thinking variable accounted for 4.7% of the variance on the line graphing performance variable when removing the effect of mathematics ability.

This thesis reports on a research study based on data from experimental teaching. Students were invited, through real-world problem tasks that raised central conceptual issues, to invent major ideas of calculus. This research focuses on work and thinking of the students, as they sought to build key ideas, representations and compelling lines of reasoning. This focus on the students' and their agency as learners has brought about a new development of the psychological and logical perspectives, as well as, highlighted students' choices in academic and social roles. Such choices facilitated continued learning among these students.

This study examined how intermediate elementary students' mathematics and science background knowledge affected their interpretation of line graphs and how their interpretations were affected by graph question levels. A purposive sample of 14 6th-grade students engaged in think aloud interviews (Ericsson & Simon, 1993) while completing an excerpted Test of Graphing in Science (TOGS) (McKenzie & Padilla, 1986). Hand gestures were video recorded. Student performance on the TOGS was assessed using an assessment rubric created from previously cited factors affecting students' graphing ability. Factors were categorized using Bertin's (1983) three graph question levels. The assessment rubric was validated by Padilla and a veteran mathematics and science teacher. Observational notes were also collected. Data were analyzed using Roth and Bowen's semiotic process of reading graphs (2001). Key findings from this analysis included differences in the use of heuristics, self-generated questions, science knowledge, and self-motivation. Students with higher prior achievement used a greater number and variety of heuristics and more often chose appropriate heuristics. They also monitored their understanding of the question and the adequacy of their strategy and answer by asking themselves questions. Most used their science knowledge spontaneously to check their understanding of the question and the adequacy of their answers. Students with lower and moderate prior achievement favored one heuristic even when it was not useful for answering the question and rarely asked their own questions. In some cases, if students with lower prior achievement had thought about their answers in the context of their science knowledge, they would have been able to recognize their errors. One student with lower prior achievement motivated herself when she thought the questions were too difficult. In addition, students answered the TOGS in one of three ways: as if they were mathematics word problems, science data to be analyzed, or they were confused and had to guess. A second set of findings corroborated how science background knowledge affected graph interpretation: correct science knowledge supported students' reasoning, but it was not necessary to answer any question correctly; correct science knowledge could not compensate for incomplete mathematics knowledge; and incorrect science knowledge often distracted students when they tried to use it while answering a question. Finally, using Roth and Bowen's (2001) two-stage semiotic model of reading graphs, representative vignettes showed emerging patterns from the study. This study added to our understanding of the role of science content knowledge during line graph interpretation, highlighted the importance of heuristics and mathematics procedural knowledge, and documented the importance of perception attentions, motivation, and students' self-generated questions. Recommendations were made for future research in line graph interpretation in mathematics and science education and for improving instruction in this area.

No description available.

This study examined the effects of peer tutoring and self-monitoring interventions on the oral reading performance of students exhibiting symptoms of AttentionDeficit/Hyperactivity Disorder: Predominantly Inattentive Type. A multiple baseline across participants design was used to evaluate the effectiveness of the peer tutoring and self-monitoring interventions with four second grade students who were tutored by fourth grade students. Results indicated that the median number of words read correct per minute as measured by curriculum-based measurement reading probes increased from baseline to intervention phases for three of the four tutee participants. In addition, the median number of errors from baseline to intervention phases decreased for three of the four participants. However, data were highly variable for three of the four participants. In addition, the percentage of intervention data points that overlapped baseline data was higher than the percentage of non-overlapping data points. Consumer satisfaction was rated positively by tutee and teacher participants. All tutee participants rated peer tutoring as a fair intervention and agreed that this intervention would help them do better in school. In addition, teacher ratings indicated that peer tutoring was an acceptable and beneficial intervention for students. The teachers reported that they liked the procedures used in this intervention. Teacher ratings also indicated that these teachers would recommend this intervention to other teachers and would implement this intervention with other students. These teachers also strongly agreed that this intervention would be appropriate for a variety of students. Implications for future research and practice are discussed.